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Sample records for cancer equation calculating

  1. A simple algebraic cancer equation: calculating how cancers may arise with normal mutation rates

    Directory of Open Access Journals (Sweden)

    Shibata Darryl

    2010-01-01

    Full Text Available Abstract Background The purpose of this article is to present a relatively easy to understand cancer model where transformation occurs when the first cell, among many at risk within a colon, accumulates a set of driver mutations. The analysis of this model yields a simple algebraic equation, which takes as inputs the number of stem cells, mutation and division rates, and the number of driver mutations, and makes predictions about cancer epidemiology. Methods The equation [p = 1 - (1 - (1 - (1 - udkNm ] calculates the probability of cancer (p and contains five parameters: the number of divisions (d, the number of stem cells (N × m, the number of critical rate-limiting pathway driver mutations (k, and the mutation rate (u. In this model progression to cancer "starts" at conception and mutations accumulate with cell division. Transformation occurs when a critical number of rate-limiting pathway mutations first accumulates within a single stem cell. Results When applied to several colorectal cancer data sets, parameter values consistent with crypt stem cell biology and normal mutation rates were able to match the increase in cancer with aging, and the mutation frequencies found in cancer genomes. The equation can help explain how cancer risks may vary with age, height, germline mutations, and aspirin use. APC mutations may shorten pathways to cancer by effectively increasing the numbers of stem cells at risk. Conclusions The equation illustrates that age-related increases in cancer frequencies may result from relatively normal division and mutation rates. Although this equation does not encompass all of the known complexity of cancer, it may be useful, especially in a teaching setting, to help illustrate relationships between small and large cancer features.

  2. Difference equations in massive higher order calculations

    International Nuclear Information System (INIS)

    The calculation of massive 2-loop operator matrix elements, required for the higher order Wilson coefficients for heavy flavor production in deeply inelastic scattering, leads to new types of multiple infinite sums over harmonic sums and related functions, which depend on the Mellin parameter N. We report on the solution of these sums through higher order difference equations using the summation package Sigma. (orig.)

  3. The new pooled cohort equations risk calculator

    DEFF Research Database (Denmark)

    Preiss, David; Kristensen, Søren L

    2015-01-01

    total cardiovascular risk score. During development of joint guidelines released in 2013 by the American College of Cardiology (ACC) and American Heart Association (AHA), the decision was taken to develop a new risk score. This resulted in the ACC/AHA Pooled Cohort Equations Risk Calculator. This risk...... calculator, based on major National Heart, Lung, and Blood Institute-funded cohort studies, is designed to predict 10-year risk of 'hard' atherosclerotic cardiovascular disease (ASCVD) events, namely, nonfatal myocardial infarction, fatal coronary heart disease, nonfatal, or fatal stroke. Considerable...... disease and any measure of social deprivation. An early criticism of the Pooled Cohort Equations Risk Calculator has been its alleged overestimation of ASCVD risk which, if confirmed in the general population, is likely to result in statin therapy being prescribed to many individuals at lower risk than...

  4. Equation of State from Lattice QCD Calculations

    CERN Document Server

    Gupta, Rajan

    2011-01-01

    We provide a status report on the calculation of the Equation of State (EoS) of QCD at finite temperature using lattice QCD. Most of the discussion will focus on comparison of recent results obtained by the HotQCD and Wuppertal-Budapest (W-B) collaborations. We will show that very significant progress has been made towards obtaining high precision results over the temperature range of T=150-700 MeV. The various sources of systematic uncertainties will be discussed and the differences between the two calculations highlighted. Our final conclusion is that the lattice results of EoS are getting precise enough to justify being used in the phenomenological analysis of heavy ion experiments at RHIC and LHC.

  5. Equation of State from Lattice QCD Calculations

    Energy Technology Data Exchange (ETDEWEB)

    Gupta, Rajan [Theoretical Division, Los Alamos National Lab, Los Alamos, N.M. 87545 (United States)

    2011-07-15

    We provide a status report on the calculation of the Equation of State (EoS) of QCD at finite temperature using lattice QCD. Most of the discussion will focus on comparison of recent results obtained by the HotQCD and Wuppertal-Budapest (W-B) collaborations. We will show that very significant progress has been made towards obtaining high precision results over the temperature range of T=150-700 MeV. The various sources of systematic uncertainties will be discussed and the differences between the two calculations highlighted. Our final conclusion is that the lattice results of EoS are getting precise enough to justify being used in the phenomenological analysis of heavy ion experiments at RHIC and LHC.

  6. Calculation of evapotranspiration using the Penman-Monteith equation

    OpenAIRE

    Žugelj, Marko

    2016-01-01

    This thesis is presenting the most important facts in the process of evapotranspiration, with some definitions and Penman–Montetith equation, which is a standard equation for evapotranspiration calculation. In this work a calculation of reference evapotranspiration is presented, using Penman–Monteith equation, for Ljubljana-Bežigrad meteorological station. Several calculation procedures are presented, such as calculation using diffrent time steps of the data (hourly, daily, ten days, month...

  7. Calculation of transonic flows using an extended integral equation method

    Science.gov (United States)

    Nixon, D.

    1976-01-01

    An extended integral equation method for transonic flows is developed. In the extended integral equation method velocities in the flow field are calculated in addition to values on the aerofoil surface, in contrast with the less accurate 'standard' integral equation method in which only surface velocities are calculated. The results obtained for aerofoils in subcritical flow and in supercritical flow when shock waves are present compare satisfactorily with the results of recent finite difference methods.

  8. An integral equation solution for multistage turbomachinery design calculations

    Science.gov (United States)

    Mcfarland, Eric R.

    1993-01-01

    A method was developed to calculate flows in multistage turbomachinery. The method is an extension of quasi-three-dimensional blade-to-blade solution methods. Governing equations for steady compressible inviscid flow are linearized by introducing approximations. The linearized flow equations are solved using integral equation techniques. The flows through both stationary and rotating blade rows are determined in a single calculation. Multiple bodies can be modelled for each blade row, so that arbitrary blade counts can be analyzed. The method's benefits are its speed and versatility.

  9. Recursive integral equations with positive kernel for lattice calculations

    International Nuclear Information System (INIS)

    A Kirkwood-Salzburg integral equation, with positive defined kernel, for the states of lattice models of statistical mechanics and quantum field theory is derived. The equation is defined in the thermodynamic limit, and its iterative solution is convergent. Moreover, positivity leads to an exact a priori bound on the iteration. The equation's relevance as a reliable algorithm for lattice calculations is therefore suggested, and it is illustrated with a simple application. It should provide a viable alternative to Monte Carlo methods for models of statistical mechanics and lattice gauge theories. 10 refs

  10. Solar plasma: calculation of thermodynamic functions and equation of state

    International Nuclear Information System (INIS)

    Calculations of thermodynamic properties for the solar plasma are presented. Effects of Coulomb interaction, exchange and diffraction effects, free electron degeneracy, relativistic corrections and radiation pressure contributions are taken into account. Calculations of the equation of state of the solar plasma with different element compositions are carried out. The contribution of various plasma effects and chemical element abundance to thermodynamic functions and in particular Γ1 is discussed

  11. Equations-of-motion approach to shell-model calculations

    International Nuclear Information System (INIS)

    The authors present an approach to shell-model calculations which works with the equations of motion for pair operators. A central feature of this approach is that it provides the natural framework for a wide variety of approximations. This should allow one to address specific features of the physics of a many-body problem in a particularly economical and practical way

  12. An economical method to calculate eigenvalues of the Schroedinger equation

    International Nuclear Information System (INIS)

    A method is presented which is an extension to negative energies of a spectral integral equation method to solve the Schroedinger equation, developed previously for scattering applications. One important innovation is a re-scaling procedure in order to compensate for the exponential behaviour of the negative energy Green's function. Another is the need to find approximate energy eigenvalues, to serve as starting values for a subsequent iteration procedure. In order to illustrate the new method, the binding energy of the He-He dimer is calculated, using the He-He TTY potential. In view of the small value of the binding energy, the wavefunction has to be calculated to a distance of 3000 au. Two hundred and twenty mesh points were sufficient to obtain an accuracy of three significant figures for the binding energy, and with 320 mesh points the accuracy increased to six significant figures. An application to a potential with two wells, separated by a barrier, is also made

  13. Decomposition of Resonance Fixed Source Equation for MOC Calculation

    Energy Technology Data Exchange (ETDEWEB)

    Cho, Jin Young; Kim, Kyo Youn; Lee, Hyun Chul [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

    2010-05-15

    Resonance fixed source problem is a boundary condition problem. Therefore, if the incoming angular fluxes are given at the problem boundary, this problem can be solved by one ray sweeping in MOC calculation. Also Resonance fixed source problem can be efficiently solved by decomposing the original problem into homogeneous and heterogeneous problems. In this paper, these two concepts are introduced on the resonance fixed source equation for the MOC codes such as DeCART and KARMA

  14. Parametric equations for calculation of macroscopic cross sections

    Energy Technology Data Exchange (ETDEWEB)

    Botelho, Mario Hugo; Carvalho, Fernando, E-mail: mariobotelho@poli.ufrj.br [Coordenacao dos Programas de Pos-Graduacao em Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear

    2015-07-01

    Neutronic calculations of the core of a nuclear reactor is one thing necessary and important for the design and management of a nuclear reactor in order to prevent accidents and control the reactor efficiently as possible. To perform these calculations a library of nuclear data, including cross sections is required. Currently, to obtain a cross section computer codes are used, which require a large amount of processing time and computer memory. This paper proposes the calculation of macroscopic cross section through the development of parametric equations. The paper illustrates the proposal for the case of macroscopic cross sections of absorption (Σa), which was chosen due to its greater complexity among other cross sections. Parametric equations created enable, quick and dynamic way, the determination of absorption cross sections, enabling the use of them in calculations of reactors. The results show efficient when compared with the absorption cross sections obtained by the ALPHA 8.8.1 code. The differences between the cross sections are less than 2% for group 2 and less than 0.60% for group 1. (author)

  15. Deterministic Partial Differential Equation Model for Dose Calculation in Electron Radiotherapy

    CERN Document Server

    Duclous, Roland; Frank, Martin

    2009-01-01

    Treatment with high energy ionizing radiation is one of the main methods in modern cancer therapy that is in clinical use. During the last decades, two main approaches to dose calculation were used, Monte Carlo simulations and semi-empirical models based on Fermi-Eyges theory. A third way 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. Starting from these, 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 [BerCharDub], that exactly preserves key properties of the analytical solution on the discrete level. Several numerical results for test cases from the medical physics literature are presented.

  16. Master equation calculations of cluster formation in supersonic jets

    International Nuclear Information System (INIS)

    The kinetics of cluster formation in supersonic jets is examined by numerical integration of the master equation system. Some general characteristics of cluster kinetics could be formulated. Excellent agreement between experimental curves of p-cresol (H2O)0,1,2,3 formation as function of H2O pressure and the corresponding calculated curves were obtained assuming successive cluster formation. From the kinetic curves, and unambiguous assignment of cluster size was possible which agreed with mass-resolved REMPI measurements. The fit of the rate coefficients shows the formation of p-cresol (H2O)1 to be faster than p-cresol (H2O)2 and p-cresol (H2O)3. (orig.)

  17. Coupling algorithm for calculating sensitivities of Smoluchowski's coagulation equation

    CERN Document Server

    Man, Peter L W; Bailleul, Ismael F; Kraft, Markus

    2009-01-01

    In this paper, two new stochastic algorithms for calculating parametric derivatives of the solution to the Smoluchowski coagulation equation are presented. It is assumed that the coagulation kernel is dependent on these parameters. The new algorithms (called `Single' and `Double') work by coupling two Marcus-Lushnikov processes in such a way as to reduce the difference between their trajectories, thereby significantly reducing the variance of central difference estimators of the parametric derivatives. In the numerical results, the algorithms are shown have have a O(1/N) order of convergence as expected, where N is the initial number of particles. It was also found that the Single and Double algorithms provide much smaller variances. Furthermore, a method for establishing `efficiency' is considered, which takes into account the variances as well as CPU run times, and the `Double' is significantly more `efficient' compared to the `Independent' algorithm in most cases.

  18. Efficient implementation of core-excitation Bethe Salpeter equation calculations

    CERN Document Server

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

    2016-01-01

    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) [Phys. Rev. B 83, 115106 (2011)]. Here, we present additional efficiencies that enable us to evaluate spectra for systems ten times larger than previous...

  19. A Simple and Reasonable Calculation Equation of Balanced Fertilization

    Directory of Open Access Journals (Sweden)

    Shenwu Lv

    2015-05-01

    Full Text Available Reasonable fertilization is a primary concern for agronomy scientists and farmers. However, there is still no satisfying calculation formula to guide farmer’s fertilizing. Five kinds of indices were tested in more than 500 field plots successively, and more than 50 pieces of long-term and short-term fertilizer field test data acquired by others were analyzed. Quick-acting fertilizers should be applied for balanced fertilization if the soil-available nutrient content is within the normal range. Through rigorous derivation and validation by a multi-year continuous 15N tracer field test, it is obtained that, total soil exogenous N = total output N − total recovery N + soil profit or lost N; utilization efficiency of fertilizer N = (output N − exogenous N ÷ balanced application amount of N fertilizer. Optimal balanced utilization efficiency of fertilizer N, P, K = total recovery efficiency, and soil nutrient net amount = total amount after test − total amount before test. Equation application parameters were collected from more than 50 tests, which is more applicable than collecting from a single test. When soil-available nutrient content is excessively low or excessively high, adjusting this should be based on balanced fertilization to properly increase or reduce the fertilization rate.

  20. Calculation of unsteady transonic flows using the integral equation method

    Science.gov (United States)

    Nixon, D.

    1978-01-01

    The basic integral equations for a harmonically oscillating airfoil in a transonic flow with shock waves are derived; the reduced frequency is assumed to be small. The problems associated with shock wave motion are treated using a strained coordinate system. The integral equation is linear and consists of both line integrals and surface integrals over the flow field which are evaluated by quadrature. This leads to a set of linear algebraic equations that can be solved directly. The shock motion is obtained explicitly by enforcing the condition that the flow is continuous except at a shock wave. Results obtained for both lifting and nonlifting oscillatory flows agree satisfactorily with other accurate results.

  1. Prediction Equation for Calculating Fat Mass in Young Indian Adults

    OpenAIRE

    Sandhu; Gupta; Shenoy

    2010-01-01

    Purpose Accurate measurement or prediction of fat mass is useful in physiology, nutrition and clinical medicine. Most predictive equations currently used to assess percentage of body fat or fat mass, using simple anthropometric measurements were derived from people in western societies and they may not be appropriate for individuals with other genotypic and phenotypic characteristics. We developed equations to predict fat mass from anthropometric measurements in young Indian adul...

  2. Prediction Equation for Calculating Fat Mass in Young Indian Adults

    Directory of Open Access Journals (Sweden)

    Sandhu

    2010-06-01

    Full Text Available Purpose Accurate measurement or prediction of fat mass is useful in physiology, nutrition and clinical medicine. Most predictive equations currently used to assess percentage of body fat or fat mass, using simple anthropometric measurements were derived from people in western societies and they may not be appropriate for individuals with other genotypic and phenotypic characteristics. We developed equations to predict fat mass from anthropometric measurements in young Indian adults. Methods Fat mass was measured in 60 females and 58 males, aged 20 to 29 yrs by using hydrostatic weighing and by simultaneous measurement of residual lung volume. Anthropometric measure included weight (kg, height (m and 4 skinfold thickness [STs (mm]. Sex specific linear regression model was developed with fat mass as the dependent variable and all anthropometric measures as independent variables. Results The prediction equation obtained for fat mass (kg for males was 8.46+0.32 (weight − 15.16 (height + 9.54 (log of sum of 4 STs (R2= 0. 53, SEE=3.42 kg and − 20.22 + 0.33 (weight + 3.44 (height + 7.66 (log of sum of 4 STs (R2=0.72, SEE=3.01kg for females. Conclusion A new prediction equation for the measurement of fat mass was derived and internally validated in young Indian adults using simple anthropometric measurements.

  3. Solid body equations to calculate the trajectory of ramjet

    OpenAIRE

    Imai, Kenji

    1982-01-01

    Six-degree-of-freedom trajectory equations for a ranrjet propelled, gun launched projectile are formulated. An outline for FORTRAN computer program flow charts also appear in the report. Special emphasis is given to the effect of wind on trajectory errors.

  4. 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 th

  5. 43 CFR Appendix A to Part 418 - Calculation of Efficiency Equation

    Science.gov (United States)

    2010-10-01

    ... 43 Public Lands: Interior 1 2010-10-01 2010-10-01 false Calculation of Efficiency Equation A Appendix A to Part 418 Public Lands: Interior Regulations Relating to Public Lands BUREAU OF RECLAMATION.... 418, App. A Appendix A to Part 418—Calculation of Efficiency Equation ER18DE97.008 ER18DE97.009...

  6. Calculation of Effective Freezing Time in Lung Cancer Cryosurgery Based on Godunov Simulation

    OpenAIRE

    Т.G. Kotova; V.I. Kochenov; D.Y. Madai; А.V. Gurin; S.N. Tsybusov

    2016-01-01

    There have been presented the results of lung cancer cryosurgery simulation using numerical solutions of enthalpy equation according to Godunov method. For the cryodestruction improvement purposes we successfully calculated the effective freezing time taking into account the evolution of an ice ball covering the tumor area. Geometrical transformation parameters of an ice ball have been measured by calculating the temperature distribution and the interface position in biological tissu...

  7. Calculation of Effective Freezing Time in Lung Cancer Cryosurgery Based on Godunov Simulation

    OpenAIRE

    Т.G. Kotova; V.I. Kochenov; S.N. Tsybusov; D.Y. Madai; А.V. Gurin

    2016-01-01

    There have been presented the results of lung cancer cryosurgery simulation using numerical solutions of enthalpy equation according to Godunov method. For the cryodestruction improvement purposes we successfully calculated the effective freezing time taking into account the evolution of an ice ball covering the tumor area. Geometrical transformation parameters of an ice ball have been measured by calculating the temperature distribution and the interface position in biological tissue. Mathem...

  8. Numerical Calculation of the Flow Inside Pump Impellers Using 3D Euler Equations

    OpenAIRE

    SARIOĞLU, Kemal; Ayder, Erkan

    1999-01-01

    The flow pattern inside an impeller should be determined for maximum efficiency and performance. The effects of the design parameters on the pump performance can be determined using numerical calculations instead of empirical equations. Incompressible 3D time-dependent Euler equations, written in a conservative form, are used. An artificial pressure term is added to preserve the hyperbolic character of the equations. A finite-volume technique is used for space discretization. A fou...

  9. Calculated lung cancer mortality due to radon

    International Nuclear Information System (INIS)

    From studies of miners, it is clear that an exposure to high concentrations of radon daughters leads to an increased incidence of lung cancer. In this Chapter the authors discuss how the experience for miners is used to estimate the incidence of radon-induced lung cancer among the general population. Such estimates cannot be very precise, in part because the miners studies do not lead to a well-determined relationship between the rate of cancer induction and the exposure levels. In particular, there are disparities in the results of studies for different groups of miners. These disparities may arise from the difficulties in obtaining accurate crucial data, such as the year-by-year exposure history over the working lifetime of the individual miners. Other differences may arise from differences in the smoking patterns in different groups and in details of the handling of the data. In any event, there remain substantial uncertainties in the conclusions for the miners themselves, both as to the ''average'' rate of cancer induction per WLM and as to the variation of this rate with the magnitude of the total exposure. Further, there are problems in using results obtained for miners at relatively high radon exposure levels for the prediction of the effects of radon at the much lower levels encountered in the normal indoor environment. Here one faces the problem of extrapolating from large dose levels to small dose levels. The generally adopted solution is to assume linearity

  10. Calculation of B/A for n-alkane liquids using the Tait equation

    Science.gov (United States)

    Hartmann; Lee; Balizer

    2000-07-01

    The B/A parameter of acoustic nonlinearity was calculated for a series of n-alkane liquids using the Tait PVT equation of state supplemented with specific heat data. The calculations of sound speed, sound speed derivatives, the two components of B/A, and the value of B/A itself were compared with experimental data taken from the literature and with earlier calculations using a different equation of state. In addition, a comparison of the results with Ballou's rule (linear relation of B/A and reciprocal sound speed) was made. It is concluded that B/A can be calculated from the Tait equation of state with about the same accuracy as direct measurements of sound speed versus pressure and temperature, though the the temperature derivatives of the sound speed are calculated with much lower accuracy than pressure derivatives. The calculations made using the Tait equation are about the same accuracy as calculations made using our equation of state. Also, Ballou's rule does not hold for these liquids. PMID:10923871

  11. A simple approach for the direct calculation of electron density by passing the Schroedinger equation

    International Nuclear Information System (INIS)

    In the paper, recent work carried out dealing with a quadratic equation for the direct calculation of the electronic density and properties of atoms and ions is discussed. The equation incorporates a first-gradient kinetic energy correction, Dirac exchange and Wigner-type correlation contributions. Its results for various atomic and ionic systems are surprisingly good, considering the simplicity of the equation. The equation also yields a universal density criterion which unifies and correlates various empirical radii (covalent, ionic, Van der Waals and Wigner-Seitz radii) as well as other properties of atoms and ions. (author). 22 refs., 6 figs., 1 tab

  12. Multiple pass application of the Boltzmann transport equation to ion implantation calculation in multilayer targets

    International Nuclear Information System (INIS)

    An improved solution of the Boltzmann transport equation was developed for calculating the results of ion implantation into a multilayer target. A multiple pass scheme is used to integrate the coupled, linearized transport equations describing the momentum distributions of the implanted ion and the recoil particles. The multiple-pass approach correctly treats the case of ions scattered by more than 900, whereas in previous calculations these ions were assumed to be stopped at the scattering point. The accurate treatment of these ions is essential for calculations involving light ions and/or low ion energies, and also an essential prerequisite for two-dimensional calculations. The nuclear cross section used is improved over previous TE calculations by removing the small-angle approximation in the LSS formation of nuclear scattering. Implanted and recoil ion range and damage distributions can be calculated directly for multilayer targets, including stoichiometric disturbances in compounds and recoil yields between target layers

  13. On the use of the backward Fokker-Planck equation to calculate range profiles

    International Nuclear Information System (INIS)

    A new mathematical model for range calculations of implanted impurities - the backward Fokker-Planck equation - is derived from the backward Boltzmann transport equation using decomposition of the scattering integral for small energy transfers in nuclear collisions. The present model describes ion transport processes dominated by collisions with small energy transfer such as the diffusion-like motion of the angular direction. Furthermore, we extend the present model to take into account single collisions events in high-energy implantation

  14. Equation of state for technetium from X-ray diffraction and first-principle calculations

    Science.gov (United States)

    Mast, Daniel S.; Kim, Eunja; Siska, Emily M.; Poineau, Frederic; Czerwinski, Kenneth R.; Lavina, Barbara; Forster, Paul M.

    2016-08-01

    The ambient temperature equation of state (EoS) of technetium metal has been measured by X-ray diffraction. The metal was compressed using a diamond anvil cell and using a 4:1 methanol-ethanol pressure transmitting medium. The maximum pressure achieved, as determined from the gold pressureEquation of state for technetium from X-ray diffraction and first-principle calculations scale, was 67 GPa. The compression data shows that the HCP phase of technetium is stable up to 67 GPa. The compression curve of technetium was also calculated using first-principles total-energy calculations. Utilizing a number of fitting strategies to compare the experimental and theoretical data it is determined that the Vinet equation of state with an ambient isothermal bulk modulus of B0T=288 GPa and a first pressure derivative of B‧=5.9(2) best represent the compression behavior of technetium metal.

  15. First-Principles Molecular Dynamics Calculations of the Equation of State for Tantalum

    Directory of Open Access Journals (Sweden)

    Shigeaki Ono

    2009-10-01

    Full Text Available The equation of state of tantalum (Ta has been investigated to 100 GPa and 3,000 K using the first-principles molecular dynamics method. A large volume dependence of the thermal pressure of Ta was revealed from the analysis of our data. A significant temperature dependence of the calculated effective Grüneisen parameters was confirmed at high pressures. This indicates that the conventional approach to analyze thermal properties using the Mie-Grüneisen approximation is likely to have a significant uncertainty in determining the equation of state for Ta, and that an intrinsic anharmonicity should be considered to analyze the equation of state.

  16. Calculation of background lifetime risk of cancer mortality in Japan

    International Nuclear Information System (INIS)

    This study was designed to calculate the background lifetime risk of cancer mortality in Japan. The mortality and population data obtained from national surveys for the vital statistics and population census in 2010 are stratified at 5-year age intervals of 0-4, 5-9, ..., 80-84, with a final open interval of 85+ for use in a life table. It was found that the gender-averaged background lifetime risk of cancer mortality ranges from 23.7% to 28.3% among 47 prefectures, and the arithmetic mean was calculated to be 25.4%. It is important to consider the incremental risk of cancer mortality posed by exposure to ionizing radiation (e.g., an additive lifetime risk of 0.5% at the effective dose of 100 mSv) in the context of the level of the background lifetime risk of cancer mortality of the exposed population. (author)

  17. Influence of the equation of state on boiling point. Calculations for crude oils

    Energy Technology Data Exchange (ETDEWEB)

    Rocha, Paulo S.M.V. [PETROBRAS S.A., Salvador, BA (Brazil). Unidade de Negocios da Bahia]. E-mail: psrocha@petrobras.com.br; Sacramento, Vinicio S.; Costa, Gloria M.N. [Universidade Salvador (UNIFACS), Salvador, BA (Brazil). Centro de Estudos em Petroleo e Gas Natural (CEPGN)]. E-mail: gloria.costa@unifacs.br

    2004-07-01

    Cubic equations of state are used to calculate volumetric and phase behavior of oils. Numerous equations of state have been published in literature and promising new equations continue appearing. A few number of comparative studies, which are limited to predictions of volumetric and vapour-liquid equilibrium properties of oils, have shown that certain equations exhibit a higher overall accuracy. But the reliability of these results is sustained for few experimental data. The saturation pressure is, probably, the most important property of a reservoir fluid for phase behavior studies. Furthermore, it needs a high weighting factor in order to calibrate or tune an equation of state model with experimental data. This paper evaluates the reliability of three equations of state: Soave-Redlich-Kwong, Peng-Robinson and Adachi-Lu-Sugie for predicting the saturation pressure. To explore their strengths and weaknesses and to reexamine the predictive capability of these equations, a total of 120 reservoir fluids obtained from 38 different references were employed. The comparison shows that Soave- Redlich- Kwong and Adachi-Lu- Sugie equations give the best prediction results, but far from the 5% deviation exhibited in literature. (author)

  18. Empirical rate equation model and rate calculations of hydrogen generation for Hanford tank waste; FINAL

    International Nuclear Information System (INIS)

    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 with in a factor of two to three

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

    International Nuclear Information System (INIS)

    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

  20. Nonlinear Oscillator Hamiltonian from Nonlinear Differential Equation and Calculation of Accurate Energy Levels

    OpenAIRE

    Rath, Biswanath; Mallick, P.

    2014-01-01

    A new method for generating analytical expression of quantum Hamiltonian from non-linear differential equation with stationary energy level has been formulated.Further calculation of energy levels have been carried out analytically using and numerically using matrix diagonalisation method.

  1. A boundary integral equation method for the calculation of the effective permittivity of periodic composites

    OpenAIRE

    Sareni, Bruno; Krähenbühl, Laurent; Beroual, Abderrahmane; Nicolas, Alain; Brosseau, C.

    1997-01-01

    We present a numerical method based upon the resolution of boundary integral equations for the calculation of the effective permittivity of a lossless composite structure consisting of a two component mixture, each with its own dielectric anti shape characteristics. The topological arrangements considered are periodic lattices inhomogeneities. Our numerical simulations are compared to the effective medium approach and with results of previous works.

  2. Calculation of Spin Observables for Proton-Neutron Elastic Scattering in the Bethe-Salpeter Equation

    CERN Document Server

    Kinpara, Susumu

    2016-01-01

    Bethe-Salpeter equation is applied to $p$-$n$ elastic scattering. The spin observables are calculated by the M matrix similar to $p$-$p$ case. The parameters of the meson-exchange model are used with the cut-off for the pion exchange interaction. Change of the M matrix indicates breaking of the charge independence in the nucleon-nucleon system.

  3. Calculation of electronic transport coefficients by a variational method for the linearized Boltzmann equation

    International Nuclear Information System (INIS)

    A variational procedure is applied to a linearized Boltzmann equation to calculate electric conductivity, thermal conductivity and Seebeck coefficient. Interaction of electrons with vacancies and impurities as well as with magnetic ions and phonons are taken into consideration. As an example these three transport coefficients are evaluated for GdAl2 in the temperature range 0-300 0K. (G.Q.)

  4. Mean-field potential calculations of high-pressure equation of state for BeO

    Institute of Scientific and Technical Information of China (English)

    Zhang Qi-Li; Zhang Ping; Song Hai-Feng; Liu Hai-Feng

    2008-01-01

    A systematic study of the Hugoniot equation of state, phase transition, and the other thermodynamic properties including the Hugoniot temperature, the electronic and ionic heat capacities, and the Griineisen parameter for shockcompressed BeO, has been carried out by calculating the total free energy. The method of calculations combines first-principles treatment for 0 K and finite-T electronic contribution and the mean-field-potential approach for the vibrational contribution of the lattice ion to the total energy. Our calculated Hugoniot is in good agreement with the experimental data.

  5. Precise integration method without inverse matrix calculation for structural dynamic equations

    Institute of Scientific and Technical Information of China (English)

    Wang Mengfu; F. T. K. Au

    2007-01-01

    The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.

  6. 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.

  7. Calculation of Effective Freezing Time in Lung Cancer Cryosurgery Based on Godunov Simulation

    Directory of Open Access Journals (Sweden)

    Т.G. Kotova

    2016-03-01

    Full Text Available There have been presented the results of lung cancer cryosurgery simulation using numerical solutions of enthalpy equation according to Godunov method. For the cryodestruction improvement purposes we successfully calculated the effective freezing time taking into account the evolution of an ice ball covering the tumor area. Geometrical transformation parameters of an ice ball have been measured by calculating the temperature distribution and the interface position in biological tissue. Mathematical cryosurgical procedures are described by heat transfer equations in solid and liquid phases. Numerical results for one-dimensional case were verified by comparing with exact solutions. In twodimensional modeling an effective cryotherapy time, which corresponds to freezing time of all tumor parts, was calculated as the area of forming ice balls covering all tumor region. The findings enable to set the effective time of a cryosurgical procedure in lung cancer. The knowledge of temperature distribution and interface position in biological tissue offers an opportunity to a cryosurgeon to finish the procedure within a certain time period to minimize the healthy tissue damage and destroy tumor cells to the maximum. Simulation application enables to schedule cryotherapy in lung cancer more effectively and to a good quality.

  8. Solution of thermal neutron diffusion equation for the two-component system by perturbation calculation

    International Nuclear Information System (INIS)

    A method of solving the diffusion equation for the th ermal neutron flux in a heterogeneous medium is presented. Perturbation calculation is successfully applied for the cylindrical concentric system after testing this method for the spherical concentric geometry analytically solved by Czubek (1981). The method permits to calculate the t hermal neutron decay constant and the space distribution of the thermal neutron flux in a heterogeneous geom etry. The condition of the constant value of the neutron flux in the inner part of the system has to be m et. This method has an application in the measurement of the thermal neutron absorption cross section, presented by Czubek (1981). (author)

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

    DEFF Research Database (Denmark)

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

    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....... 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...

  10. Range profile calculations by direct numerical solution of linearized Boltzmann transport equations

    International Nuclear Information System (INIS)

    A new method to determine the depth distributions of implanted ions and recoil target atoms in amorphous targets is developed. Our procedure is based on the direct numerical solution of one-dimensional linearized Boltzmann transport equations for the scalar fluxes of the ions and the recoils. We consider characteristic examples of ion implantation into homogeneous and layered targets. The profiles calculated by the new method are compared with range distributions obtained from TRIM Monte Carlo simulations. Our program BOTE is up to two orders of magnitude faster than the TRIM calculations. (author)

  11. Analytical calculation of nonadiabatic transition probabilities from the monodromy of differential equations

    International Nuclear Information System (INIS)

    The nonadiabatic transition probabilities in the two-level systems are calculated analytically by using the monodromy matrix determining the global feature of the underlying differential equation. We study the time-dependent 2 x 2 Hamiltonian with the tanh-type plus sech-type energy difference and with constant off-diagonal elements as an example to show the efficiency of the monodromy approach. We also discuss the application of this method to multi-level systems

  12. Calculation of the reflexive and transmitive matrices by iteration of the transport equations

    International Nuclear Information System (INIS)

    In this paper are proposed some new ways for the calculation of the reflective and transmitted matrix, that is reflected and transmitted flux, by iteration of the transport equations. For the sake of better understanding of the methodology we will restrict the treatment on the transport of monoenergetic neutrons in plain geometry. The main purpose of the new approach is developed of a method for other geometries as well as for two dimensional problem. (author)

  13. Fast near-field calculation for volume integral equations for layered media

    OpenAIRE

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

    2005-01-01

    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. 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 nea...

  14. Exact Dirac equation calculation of ionization induced by ultrarelativistic heavy ions

    OpenAIRE

    Baltz, Anthony J.

    1999-01-01

    The time-dependent Dirac equation can be solved exactly for ionization induced by ultrarelativistic heavy ion collisions. Ionization calculations are carried out in such a framework for a number of representative ion-ion pairs. For each ion-ion pair, the computed cross section consists of two terms, a constant energy independent term and a term whose coefficient is ln(gamma). Scaled values of both terms are found to decrease with increasing Z of the nucleus that is ionized.

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

    International Nuclear Information System (INIS)

    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)

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

    International Nuclear Information System (INIS)

    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

  17. Solution of dense systems of linear equations in electromagnetic scattering calculations

    Energy Technology Data Exchange (ETDEWEB)

    Rahola, J. [Center for Scientific Computing, Espoo (Finland)

    1994-12-31

    The discrete-dipole approximation (DDA) is a method for calculating the scattering of light by an irregular particle. The DDA has been used for example in calculations of optical properties of cosmic dust. In this method the particle is approximated by interacting electromagnetic dipoles. Computationally the DDA method includes the solution of large dense systems of linear equations where the coefficient matrix is complex symmetric. In the author`s work, the linear systems of equations are solved by various iterative methods such as the conjugate gradient method applied to the normal equations and QMR. The linear systems have rather low condition numbers due to which many iterative methods perform quite well even without any preconditioning. Some possible preconditioning strategies are discussed. Finally, some fast special methods for computing the matrix-vector product in the iterative methods are considered. In some cases, the matrix-vector product can be computed with the fast Fourier transform, which enables the author to solve dense linear systems of hundreds of thousands of unknowns.

  18. An analytical solution of the gyrokinetic equation for the calculation of neoclassical effects

    CERN Document Server

    Casolari, Andrea

    2016-01-01

    The purpose of this document is to find an analytical solution for the gyrokinetic equation under specific, simplificative hypotheses. The case I am considering is that of a collisional plasma in the presence of a chain of magnetic islands. The presence of the magnetic islands causes the onset of perturbative fields, in particular an electrostatic field, with a gradient length-scale comparable with the island's width. When the island's width w becomes comparable with the ion Larmor radius rho_i , the drift-kinetic equation is inadequate to treat the transport and the calculation of the neoclassical effects. Nevertheless, I'm going to solve the equation with the methods described by S. P. Hirshman and D. J. Sigmar in the review paper "Neoclassical transport of impurities in tokamak plasmas", which was developed to solve the drift-kinetic equation in different regimes of collisionality. I'm going to remind first the drift-kinetic theory, which was largely used to study classical and neoclassical transport in ma...

  19. A Nonlinear Programming Perspective on Sensitivity Calculations for Systems Governed by State Equations

    Science.gov (United States)

    Lewis, Robert Michael

    1997-01-01

    This paper discusses the calculation of sensitivities. or derivatives, for optimization problems involving systems governed by differential equations and other state relations. The subject is examined from the point of view of nonlinear programming, beginning with the analytical structure of the first and second derivatives associated with such problems and the relation of these derivatives to implicit differentiation and equality constrained optimization. We also outline an error analysis of the analytical formulae and compare the results with similar results for finite-difference estimates of derivatives. We then attend to an investigation of the nature of the adjoint method and the adjoint equations and their relation to directions of steepest descent. We illustrate the points discussed with an optimization problem in which the variables are the coefficients in a differential operator.

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

    Energy Technology Data Exchange (ETDEWEB)

    Wills, John M [Los Alamos National Laboratory; Mattsson, Ann E [Sandia National Laboratories

    2012-06-06

    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.

  1. Total Sensitivity Index Calculation of Tool Requirement Model via Error Propagation Equation

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    A new and convenient method is presented to calculate the total sensitivity indices defined by variance-based sensitivity analysis. By decomposing the output variance using error propagation equations, this method can transform the "double-loop" sampling procedure into "single-loop" one and obviously reduce the computation cost of analysis. In contrast with Sobol's and Fourier amplitude sensitivity test (FAST) method, which is limited in non-correlated variables, the new approach is suitable for correlated input variables. An application in semiconductor assembling and test manufacturing (ATM) factory indicates that this approach has a good performance in additive model and simple non-additive model.

  2. Second order particle motion equations and linear chromaticity calculation in accelerator rings

    International Nuclear Information System (INIS)

    The first part of this note presents a thorough study on the second order particle motion equations, both in continuous field and in hard edges, with emphasis put on the latter. Having quite general conditions and strict mathematical treatments, it provides a sound ground from which many problems can be solved without fear of being misled. Then the linear CHR calculation is inspected, the first step being a general analytical expression of the transverse oscillation phase increment due to a small disturbance. The expression for the CHR is then readily obtained since tune is the transverse oscillation number per turn and the CHR is the linear dependence of the tune on particle energy/momentum deviation. The last part gives the formulae for practical CHR calculation, which are general enough to include almost all the magnet types commonly used in various accelerator rings and are simpler than can be found elsewhere

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

    International Nuclear Information System (INIS)

    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

  4. A new approach to calculating powder diffraction patterns based on the Debye scattering equation.

    Science.gov (United States)

    Thomas, Noel William

    2010-01-01

    A new method is defined for the calculation of X-ray and neutron powder diffraction patterns from the Debye scattering equation (DSE). Pairwise atomic interactions are split into two contributions, the first from lattice-pair vectors and the second from cell-pair vectors. Since the frequencies of lattice-pair vectors can be directly related to crystallite size, application of the DSE is thereby extended to crystallites of lengths up to approximately 200 nm. The input data correspond to unit-cell parameters, atomic coordinates and displacement factors. The calculated diffraction patterns are characterized by full backgrounds as well as complete reflection profiles. Four illustrative systems are considered: sodium chloride (NaCl), alpha-quartz, monoclinic lead zirconate titanate (PZT) and kaolinite. The effects of varying crystallite size on diffraction patterns are calculated for NaCl, quartz and kaolinite, and a method of modelling static structural disorder is defined for kaolinite. The idea of partial diffraction patterns is introduced and a treatment of atomic displacement parameters is included. Although the method uses pair distribution functions as an intermediate stage, it is anticipated that further progress in reducing computational times will be made by proceeding directly from crystal structure to diffraction pattern. PMID:20029134

  5. Impact of Heterogeneity-Based Dose Calculation Using a Deterministic Grid-Based Boltzmann Equation Solver for Intracavitary Brachytherapy

    International Nuclear Information System (INIS)

    Purpose: To investigate the dosimetric impact of the heterogeneity dose calculation Acuros (Transpire Inc., Gig Harbor, WA), a grid-based Boltzmann equation solver (GBBS), for brachytherapy in a cohort of cervical cancer patients. Methods and Materials: The impact of heterogeneities was retrospectively assessed in treatment plans for 26 patients who had previously received 192Ir intracavitary brachytherapy for cervical cancer with computed tomography (CT)/magnetic resonance-compatible tandems and unshielded colpostats. The GBBS models sources, patient boundaries, applicators, and tissue heterogeneities. Multiple GBBS calculations were performed with and without solid model applicator, with and without overriding the patient contour to 1 g/cm3 muscle, and with and without overriding contrast materials to muscle or 2.25 g/cm3 bone. Impact of source and boundary modeling, applicator, tissue heterogeneities, and sensitivity of CT-to-material mapping of contrast were derived from the multiple calculations. American Association of Physicists in Medicine Task Group 43 (TG-43) guidelines and the GBBS were compared for the following clinical dosimetric parameters: Manchester points A and B, International Commission on Radiation Units and Measurements (ICRU) report 38 rectal and bladder points, three and nine o’clock, and D2cm3 to the bladder, rectum, and sigmoid. Results: Points A and B, D2 cm3 bladder, ICRU bladder, and three and nine o’clock were within 5% of TG-43 for all GBBS calculations. The source and boundary and applicator account for most of the differences between the GBBS and TG-43 guidelines. The D2cm3 rectum (n = 3), D2cm3 sigmoid (n = 1), and ICRU rectum (n = 6) had differences of >5% from TG-43 for the worst case incorrect mapping of contrast to bone. Clinical dosimetric parameters were within 5% of TG-43 when rectal and balloon contrast were mapped to bone and radiopaque packing was not overridden. Conclusions: The GBBS has minimal impact on clinical

  6. A mean field calculation of the equation of state of supernova matter

    International Nuclear Information System (INIS)

    The equation of state for hot dense matter occuring in stellar collapse is calculated using the Hartree-Fock approximation at finite temperature. The effective nucleon-nucleon interaction is a modified Skyrme force which gives a rather good value of the compression modulus in nuclear matter. Results are presented for the adiabat S=1 per baryon, with a fixed value of the electron fraction Ysub(e)=0.25, in the density range rho=0.02 to 0.07 baryons per fm3. We find that nuclei are still present in the medium. As a consequence the adiabatic index is slightly less than 4/3. We also discuss the presence of a transition, around half nuclear matter density, towards a phase made of bubbles

  7. Transonic flow calculations using a flux vector splitting method for the Euler equations

    Science.gov (United States)

    Seaford, C. M.; Hassan, H. A.

    1984-01-01

    A study of the flux vector splitting method of Steger and Warming for the solution of the time dependent Euler equations in strong conservation law form for arbitrary two-dimensional geometries is presented. The procedure employed here differs from that of Buning and Steger in that it uses a different algorithm and employs implicit boundary conditions. Moreover, the method, as implemented here, does not contain any explicit smoothing or any adjustable parameters. Calculations were carried out for an NACA 0012 airfoil at various Mach numbers and angles of attack, and cylinders. Steady symmetric solutions were obtained for the full cylinder at a freestream Mach number of .5 without imposing a symmetry condition. In general, good agreement with other methods was obtained.

  8. A unified approach for numerical calculation of space-dependent kinetic equation

    International Nuclear Information System (INIS)

    A unified numerical method based on the factorization approach is developed to solve the space-dependent neutron kinetic equation. Various numerical methods for solving the space-dependent kinetic equation have been developed so far. These methods can be classified into two categories, i.e., the direct and the factorization methods. The factorization method is known as an effective numerical method. In the present study, a new factorization method named the multigrid amplitude function (MAF) method is developed. Unlike the improved quasi-static (IQS) method, an independent amplitude function is assigned for each spatial region and energy group in the MAF method. The MAF method is a generalization of conventional methods, e.g., the frequency transform, IQS, and Theta methods. To evaluate the amplitude function in the MAF method, the time-dependent coarse-mesh finite difference (TCMFD) method is developed. The MAF method is implemented into a space-dependent kinetic code on the basis of the analytical polynomial nodal method. In order to verify the effectiveness of the MAF method, the TWIGL, Langenbuch, Maurer, and Werner (LMW), and Laboratorium fur Reaktorregelung and Anlagensicherung (LRA) benchmark problems are analyzed. The calculation results show the effectiveness of the present method. (author)

  9. Thermal Decomposition of NCN: Shock-Tube Study, Quantum Chemical Calculations, and Master-Equation Modeling.

    Science.gov (United States)

    Busch, Anna; González-García, Núria; Lendvay, György; Olzmann, Matthias

    2015-07-16

    The thermal decomposition of cyanonitrene, NCN, was studied behind reflected shock waves in the temperature range 1790-2960 K at pressures near 1 and 4 bar. Highly diluted mixtures of NCN3 in argon were shock-heated to produce NCN, and concentration-time profiles of C atoms as reaction product were monitored with atomic resonance absorption spectroscopy at 156.1 nm. Calibration was performed with methane pyrolysis experiments. Rate coefficients for the reaction (3)NCN + M → (3)C + N2 + M (R1) were determined from the initial slopes of the C atom concentration-time profiles. Reaction R1 was found to be in the low-pressure regime at the conditions of the experiments. The temperature dependence of the bimolecular rate coefficient can be expressed with the following Arrhenius equation: k1(bim) = (4.2 ± 2.1) × 10(14) exp[-242.3 kJ mol(-1)/(RT)] cm(3) mol(-1) s(-1). The rate coefficients were analyzed by using a master equation with specific rate coefficients from RRKM theory. The necessary molecular data and energies were calculated with quantum chemical methods up to the CCSD(T)/CBS//CCSD/cc-pVTZ level of theory. From the topography of the potential energy surface, it follows that reaction R1 proceeds via isomerization of NCN to CNN and subsequent C-N bond fission along a collinear reaction coordinate without a tight transition state. The calculations reproduce the magnitude and temperature dependence of the rate coefficient and confirm that reaction R1 is in the low-pressure regime under our experimental conditions. PMID:25853321

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

    International Nuclear Information System (INIS)

    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 III1) are presented. These treatment can be extended to the other velocity profiles by slight midifications. (author)

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

    Science.gov (United States)

    Gillingham, D. R.; Antonsen, T. M., Jr.

    2007-05-01

    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.

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

    International Nuclear Information System (INIS)

    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

  13. Gaussian-basis LDA and GGA calculations for alkali-metal equations of state

    International Nuclear Information System (INIS)

    Recently there has been renewed interest in implementations of density-functional theory for solids using various types of localized basis sets, including atom-centered Gaussian-type functions. While such methods are clearly well adapted to most insulating and semiconducting systems, one might expect them to give a less-than-optimal description of metals relative to plane-wave-type methods. Nevertheless, several successful applications of local-basis methods to metals have recently been reported. Here, we report an application of our Gaussian linear combination of atomic orbitals (LCAO) code to some extremely free-electron-like metals, namely, the alkali metals Li, Na, and K. In agreement with other calculations (both local and plane wave) we find that the local-density approximation (LDA) lattice constants are relatively poor (∼-3% from experiment for the alkali metals versus ±1% for many other solids) and that the LDA bulk moduli are ∼30% too high. We find that the Perdew-Burke-Enzerhof (PBE) version of the generalized-gradient approximation (GGA) corrects most of this error, in agreement with earlier calculations using similar GGA functionals. The Becke-Lee-Yang-Parr GGA functional gives similar results for the alkali-metal equations of state but is found to overcorrect the errors of the LDA for the cohesive energies, for which the PBE functional is in better agreement with experiment. Our results indicate that the Gaussian-LCAO method should be able to give accurate results for nearly any crystalline solid, since it succeeds even where it would be expected to have the most difficulty. copyright 1998 The American Physical Society

  14. First-principles calculation method for electron transport based on the grid Lippmann-Schwinger equation.

    Science.gov (United States)

    Egami, Yoshiyuki; Iwase, Shigeru; Tsukamoto, Shigeru; Ono, Tomoya; Hirose, Kikuji

    2015-09-01

    We develop a first-principles electron-transport simulator based on the Lippmann-Schwinger (LS) equation within the framework of the real-space finite-difference scheme. In our fully real-space-based LS (grid LS) method, the ratio expression technique for the scattering wave functions and the Green's function elements of the reference system is employed to avoid numerical collapse. Furthermore, we present analytical expressions and/or prominent calculation procedures for the retarded Green's function, which are utilized in the grid LS approach. In order to demonstrate the performance of the grid LS method, we simulate the electron-transport properties of the semiconductor-oxide interfaces sandwiched between semi-infinite jellium electrodes. The results confirm that the leakage current through the (001)Si-SiO_{2} model becomes much larger when the dangling-bond state is induced by a defect in the oxygen layer, while that through the (001)Ge-GeO_{2} model is insensitive to the dangling bond state. PMID:26465580

  15. An alternative scheme for calculating the unrestricted Hartree-Fock equation: Application to the boron and neon atoms

    Energy Technology Data Exchange (ETDEWEB)

    Miyasita, Mitiyasu, E-mail: miyasita.mitiyasu@gmail.com [Graduate School of Science and Engineering, Shinshu University, Ueda 386-8567 (Japan); Higuchi, Katsuhiko [Graduate School of Advanced Science of Matter, Hiroshima University, Higashi-Hiroshima 739-8527 (Japan); Higuchi, Masahiko [Department of Physics, Faculty of Science, Shinshu University, Matsumoto 390-8621 (Japan)

    2012-07-15

    We present an alternative scheme for calculating the unrestricted Hartree-Fock (HF) equation. The scheme is based on the variational method utilizing the sophisticated basis functions that include no adjustable parameters. The validity of the present scheme is confirmed by actual calculations of the boron and neon atoms. The total energy of the present scheme is lower than that of the conventional restrictive HF equation, but higher than that of the CI method. Also, the resultant wave function satisfies the electron-nucleus cusp condition.

  16. 3-D resistive MHD calculations for tokamak plasmas: beyond the simple reduced set of equations

    International Nuclear Information System (INIS)

    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)

  17. TH-E-BRE-02: A Forward Scattering Approximation to Dose Calculation Using the Linear Boltzmann Transport Equation

    International Nuclear Information System (INIS)

    Purpose: To investigate the use of the linear Boltzmann transport equation as a dose calculation tool which can account for interface effects, while still having faster computation times than Monte Carlo methods. In particular, we introduce a forward scattering approximation, in hopes of improving calculation time without a significant hindrance to accuracy. Methods: Two coupled Boltzmann transport equations were constructed, one representing the fluence of photons within the medium, and the other, the fluence of electrons. We neglect the scattering term within the electron transport equation, resulting in an extreme forward scattering approximation to reduce computational complexity. These equations were then solved using a numerical technique for solving partial differential equations, known as a finite difference scheme, where the fluence at each discrete point in space is calculated based on the fluence at the previous point in the particle's path. Using this scheme, it is possible to develop a solution to the Boltzmann transport equations by beginning with boundary conditions and iterating across the entire medium. The fluence of electrons can then be used to find the dose at any point within the medium. Results: Comparisons with Monte Carlo simulations indicate that even simplistic techniques for solving the linear Boltzmann transport equation yield expected interface effects, which many popular dose calculation algorithms are not capable of predicting. Implementation of a forward scattering approximation does not appear to drastically reduce the accuracy of this algorithm. Conclusion: Optimized implementations of this algorithm have been shown to be very accurate when compared with Monte Carlo simulations, even in build up regions where many models fail. Use of a forward scattering approximation could potentially give a reasonably accurate dose distribution in a shorter amount of time for situations where a completely accurate dose distribution is not

  18. Exact calculation of the time convolutionless master equation generator: Application to the nonequilibrium resonant level model

    International Nuclear Information System (INIS)

    The generalized quantum master equation provides a powerful tool to describe the dynamics in quantum impurity models driven away from equilibrium. Two complementary approaches, one based on Nakajima–Zwanzig–Mori time-convolution (TC) and the other on the Tokuyama–Mori time-convolutionless (TCL) formulations provide a starting point to describe the time-evolution of the reduced density matrix. A key in both approaches is to obtain the so called “memory kernel” or “generator,” going beyond second or fourth order perturbation techniques. While numerically converged techniques are available for the TC memory kernel, the canonical approach to obtain the TCL generator is based on inverting a super-operator in the full Hilbert space, which is difficult to perform and thus, nearly all applications of the TCL approach rely on a perturbative scheme of some sort. Here, the TCL generator is expressed using a reduced system propagator which can be obtained from system observables alone and requires the calculation of super-operators and their inverse in the reduced Hilbert space rather than the full one. This makes the formulation amenable to quantum impurity solvers or to diagrammatic techniques, such as the nonequilibrium Green’s function. We implement the TCL approach for the resonant level model driven away from equilibrium and compare the time scales for the decay of the generator with that of the memory kernel in the TC approach. Furthermore, the effects of temperature, source-drain bias, and gate potential on the TCL/TC generators are discussed

  19. Exact calculation of the time convolutionless master equation generator: Application to the nonequilibrium resonant level model

    Energy Technology Data Exchange (ETDEWEB)

    Kidon, Lyran [School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978 (Israel); The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978 (Israel); Wilner, Eli Y. [School of Physics and Astronomy, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978 (Israel); Rabani, Eran [The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978 (Israel); Department of Chemistry, University of California and Lawrence Berkeley National Laboratory, Berkeley California 94720-1460 (United States)

    2015-12-21

    The generalized quantum master equation provides a powerful tool to describe the dynamics in quantum impurity models driven away from equilibrium. Two complementary approaches, one based on Nakajima–Zwanzig–Mori time-convolution (TC) and the other on the Tokuyama–Mori time-convolutionless (TCL) formulations provide a starting point to describe the time-evolution of the reduced density matrix. A key in both approaches is to obtain the so called “memory kernel” or “generator,” going beyond second or fourth order perturbation techniques. While numerically converged techniques are available for the TC memory kernel, the canonical approach to obtain the TCL generator is based on inverting a super-operator in the full Hilbert space, which is difficult to perform and thus, nearly all applications of the TCL approach rely on a perturbative scheme of some sort. Here, the TCL generator is expressed using a reduced system propagator which can be obtained from system observables alone and requires the calculation of super-operators and their inverse in the reduced Hilbert space rather than the full one. This makes the formulation amenable to quantum impurity solvers or to diagrammatic techniques, such as the nonequilibrium Green’s function. We implement the TCL approach for the resonant level model driven away from equilibrium and compare the time scales for the decay of the generator with that of the memory kernel in the TC approach. Furthermore, the effects of temperature, source-drain bias, and gate potential on the TCL/TC generators are discussed.

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

    International Nuclear Information System (INIS)

    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

  1. Difference between CKD-EPI and MDRD equations in calculating glomerular filtration rate in patients with cirrhosis

    Institute of Scientific and Technical Information of China (English)

    Yu-Wei Chen; Han-Hsiang Chen; Tsang-En Wang; Ching-Wei Chang; Chen-Wang Chang; Chih-Jen Wu

    2011-01-01

    AIM: To evaluate the difference between the performance of the (CKD-EPI) and Modification of Diet in Renal Disease (MDRD) equations in cirrhotic patients. METHODS: From Jan 2004 to Oct 2008, 4127 cirrhotic patients were reviewed. Patients with incomplete data with respect to renal function were excluded; thus, a total of 3791 patients were included in the study. The glomerular filtration rate (GFR) was estimated by the 4-variable MDRD (MDRD-4), 6-variable MDRD (MDRD-6), and CKD-EPI equations. RESULTS: When serum creatinine was 0.7-6.8 mg/dL and 0.6-5.3 mg/dL in men and women, respectively, a significantly lower GFR was estimated by the MDRD-6 than by the CKD-EPI. Similar GFRs were calculated by both equations when creatinine was > 6.9 mg/dL and > 5.4 mg/dL in men and women, respectively. In predicting in-hospital mortality, estimated GFR obtained by the MDRD-6 showed better accuracy [81.72%; 95% confidence interval (CI), 0.94-0.95] than that obtained by the MDRD-4 (80.22%; 95%CI, 0.96-0.97), CKD-EPI (79.93%; 95%CI, 0.96-0.96), and creatinine (77.50%; 95%CI, 2.27-2.63). CONCLUSION: GFR calculated by the 6-variable MDRD equation may be closer to the true GFR than that calculated by the CKD-EPI equation.

  2. Hard-sphere fluids inside spherical, hard pores. Grand canonical ensemble Monte Carlo calculations and integral equation approximations

    DEFF Research Database (Denmark)

    Sloth, Peter

    1990-01-01

    Density profiles and partition coefficients are obtained for hard-sphere fluids inside hard, spherical pores of different sizes by grand canonical ensemble Monte Carlo calculations. The Monte Carlo results are compared to the results obtained by application of different kinds of integral equation...

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

    International Nuclear Information System (INIS)

    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

  4. Orbital-free extension to Kohn-Sham density functional theory equation of state calculations: application to silicon dioxide

    OpenAIRE

    Sjostrom, Travis; Crockett, Scott

    2015-01-01

    The liquid regime equation of state of silicon dioxide SiO$_2$ is calculated via quantum molecular dynamics in the density range 5 to 15 g/cc and with temperatures from 0.5 to 100 eV, including the $\\alpha$-quartz and stishovite phase Hugoniot curves. Below 8 eV calculations are based on Kohn-Sham density functional theory (DFT), above 8 eV a new orbital-free DFT formulation, presented here, based on matching Kohn-Sham DFT calculations is employed. Recent experimental shock data is found to b...

  5. Resolution of the multigroup scattering equation in a one-dimensional geometry and subsidiary calculations: the MUDE code

    International Nuclear Information System (INIS)

    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 (keff, 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)

  6. Bypass Transitional Flow Calculations Using a Navier-Stokes Solver and Two-Equation Models

    Science.gov (United States)

    Liuo, William W.; Shih, Tsan-Hsing; Povinelli, L. A. (Technical Monitor)

    2000-01-01

    Bypass transitional flows over a flat plate were simulated using a Navier-Stokes solver and two equation models. A new model for the bypass transition, which occurs in cases with high free stream turbulence intensity (TI), is described. The new transition model is developed by including an intermittency correction function to an existing two-equation turbulence model. The advantages of using Navier-Stokes equations, as opposed to boundary-layer equations, in bypass transition simulations are also illustrated. The results for two test flows over a flat plate with different levels of free stream turbulence intensity are reported. Comparisons with the experimental measurements show that the new model can capture very well both the onset and the length of bypass transition.

  7. A CORRELATION EQUATION FOR CALCULATING INCLINED JET PENETRATION LENGTH IN A GAS-SOLID FLUIDIZED BED

    Institute of Scientific and Technical Information of China (English)

    Ruoyu Hong; Haibing Li; Jianmin Ding; Hongzhong Li

    2005-01-01

    Numerical simulation of gas-solid flow in a two-dimensional fluidized bed with an inclined jet was performed. The numerical model is based on the two-fluid model of gas and solids phase in which the solids constitutive equations are based on the kinetic theory of granular flow. The improved ICE algorithm, which can be used for both low and high-velocity fluid flow, were used to solve the model equations. The mechanism of jet formation was analyzed using both numerical simulations and experiments. The emergence and movement of gas bubbles were captured numerically and experimentally. The influences of jet velocity, nozzle diameter, nozzle inclination and jet position on jet penetration length were obtained. A semi-empirical expression was derived and the parameters were correlated from experimental data. The correlation equation, which can be easily used to obtain the inclined jet penetration length, was compared with our experimental data and published correlation equations.

  8. 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)

    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)

  9. Calculation of Volume Properties for Saturated Vapour by Using the Modified Truncated Virial Equation

    Institute of Scientific and Technical Information of China (English)

    JingshanTong; GuanghuaGao

    1995-01-01

    In this paper,a molecular gaaregation function which represents the degree of molecular aggregation is derived based on statistical mechanic method.Then,a trucated virial equation is modified by the molecular aggregation theory.THe propsed extended equation of state gives good representation of the PVT properties of sturated vapors for some strong polar fluids including water,alcohols and carboxylic acid etc.

  10. Modified Eyring viscosity equation and calculation of activation energy based on the liquid quasi-lattice model

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    Viscosity is an important physical parameter of fluid,and the Eyring viscosity equation is a popular viscosity theory.Based on the Eyring reaction rate equation and Boltzmann statistical theory,and including the probabilities of creating a hole in liquid and the transition to the neighboring hole,a modified Eyring viscosity equation was proposed.According to the structural characteristics of short-range order,liquid is treated as a quasi-lattice structure in a small region.The activation energy,which is the minimum energy needed for the molecule to jump to its neighboring hole because of the restriction of other molecules around it,was analytically calculated from an intermolecular Lennard-Jones potential function and a Stockmayer potential function.The viscosity values of 37 kinds of typical liquids at 25°C and the dependence of viscosity of three kinds of liquids on temperatures were calculated with this modified viscosity equation,and the calculated results agree with the experimental values to some extent.This work not only enriches the understanding of the mechanism of liquid viscosity,but also could provide some theoretical guides for the relevant studies and applications.

  11. A linear integral-equation-based computer code for self-amplified spontaneous emission calculations of free-electron lasers

    International Nuclear Information System (INIS)

    The linear integral-equation-based computer code 'Roger Oleg Nikolai' (RON), which was recently developed at Argonne National Laboratory, was used to calculate the self-amplified spontaneous emission (SASE) performance of the free-electron laser (FEL) being built at Argonne. Signal growth calculations under different conditions were used to estimate tolerances of actual design parameters and to estimate optimal length of the break sections between undulator segments. Explicit calculation of the radiation field was added recently. The measured magnetic fields of five undulators were used to calculate the gain for the Argonne FEL. The result indicates that the real undulators for the Argonne FEL (the effect of magnetic field errors alone) will not significantly degrade the FEL performance. The capability to calculate the small-signal gain for an FEL-oscillator is also demonstrated

  12. Comparison of actual evaporation from water surface measured by GGI-3000 evaporimeter with values calculated by the Penman equation

    Science.gov (United States)

    Kohu, Mojmír; Rožnovský, Jaroslav; Knozová, Grazyna

    2014-09-01

    Information about water evaporation is essential for the calculation of water balance. Evaporation, however, is a very complex physical process and it is therefore difficult to quantify. Evaporation measurements from the weather station network of the Czech Hydrometeorological Institute between 1968 and 2011 were performed using the evaporimeter GGI-3000. Evaporation was calculated using modified standard method based on FAO. The aim of the article was to compare the measured values and calculations. It has been found that the evaporation values from water surface calculated using the empirical equation are usually higher than the measured values by on average 0.8 mm, in extreme cases even 6.9 mm. The measured data shows higher variability than the calculated values, which means that correlations between series are not strong, the correlation coefficient being 0.7. Nevertheless the findings can be used for homogenization of series measured by the GGI-3000 evaporimeter.

  13. 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

    BACKGROUND: The incidence rates of cervical cancer and the coverage in cervical cancer screening are usually reported by including in the denominator all women from the general population. However, after hysterectomy women are not at risk anymore of developing cervical cancer. Therefore, it makes...... 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......, 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...

  14. Two Approaches to the Calculation of Approximate Symmetry of Ostrovsky Equation with Small Parameter

    International Nuclear Information System (INIS)

    In this paper, two methods of approximate symmetries for partial differential equations with a small parameter are applied to a perturbed nonlinear Ostrovsky equation. To compute the first-order approximate symmetry, we have applied two methods which one of them was proposed by Baikov et al. in which the infinitesimal generator is expanded in a perturbation series; whereas the other method by Fushchich and Shtelen [3] is based on the expansion of the dependent variables in perturbation series. Especially, an optimal system of one dimensional subalgebras is constructed and some invariant solutions corresponding to the resulted symmetries are obtained

  15. Two Approaches to the Calculation of Approximate Symmetry of Ostrovsky Equation with Small Parameter

    Energy Technology Data Exchange (ETDEWEB)

    Mahdavi, Abolhassan, E-mail: ad.mahdavi@kiau.ac.ir [Karaj Branch Islamic University, Department of Mathematics (Iran, Islamic Republic of); Nadjafikhah, Mehdi, E-mail: mnadjafikhah@iust.ac.ir [Iran University of Science and Technology, School of Mathematics (Iran, Islamic Republic of); Toomanian, Megerdich, E-mail: megerdich.toomanian@kiau.ac.ir [Karaj Branch Islamic University, Department of Mathematics (Iran, Islamic Republic of)

    2015-12-15

    In this paper, two methods of approximate symmetries for partial differential equations with a small parameter are applied to a perturbed nonlinear Ostrovsky equation. To compute the first-order approximate symmetry, we have applied two methods which one of them was proposed by Baikov et al. in which the infinitesimal generator is expanded in a perturbation series; whereas the other method by Fushchich and Shtelen [3] is based on the expansion of the dependent variables in perturbation series. Especially, an optimal system of one dimensional subalgebras is constructed and some invariant solutions corresponding to the resulted symmetries are obtained.

  16. Calculations of scattering lengths in four-nucleon system on the basis of cluster reduction method for Yakubovsky equations

    CERN Document Server

    Yakovlev, S L

    1997-01-01

    The cluster reduction method for the Yakubovsky equations in configuration space is used for calculations of zero-energy scattering in four-nucleon system. The main idea of the method consists in making use of expansions for the Yakubovsky amplitudes onto the basis of the Faddeev components for the two-cluster sub-Hamiltonian eigenfunctions. The expantions reduce the original equations to ones for the functions depending on the relative coordinates between the clusters. On the basis of the resulting equations the N-(NNN) zero-energy scattering problems are solved numerically with the MT I-III model for N-N forces and neglegting the Coulomb interaction between protons.

  17. Cancer Patients’ Survival: Standard Calculation Methods And Some Considerations Regarding Their Interpretation

    Directory of Open Access Journals (Sweden)

    Zadnik Vesna

    2016-02-01

    Full Text Available Cancer patients’ survival is an extremely important but complex indicator for assessing regional or global inequalities in diagnosis practices and clinical management of cancer patients. The population-based cancer survival comparisons are available through international projects (i.e. CONCORD, EUROCARE, OECD Health Reports and online systems (SEER, NORDCAN, SLORA. In our research we aimed to show that noticeable differences in cancer patients’ survival may not always reflect the real inequalities in cancer care, but can also appear due to variations in the applied methodology for relative survival calculation.

  18. Application of Tate equation for calculation of thermal conductivity of solutions of sunflower oil and isomer hexane

    International Nuclear Information System (INIS)

    Present article is devoted to application of Tate equation for calculation of thermal conductivity of solutions of sunflower oil and isomer hexane. The dependence of thermal conductivity of sunflower oil solution and isomer hexane on temperature was considered. The thermal conductivity of sunflower oil depending on mass concentration of isomer hexane at temperature ranges 290-410 K and pressure ranges 0.101-49.1 Mpa was studied.

  19. A Steady-State Approximation to the Two-Dimensional Master Equation for Chemical Kinetics Calculations.

    Science.gov (United States)

    Nguyen, Thanh Lam; Stanton, John F

    2015-07-16

    In the field of chemical kinetics, the solution of a two-dimensional master equation that depends explicitly on both total internal energy (E) and total angular momentum (J) is a challenging problem. In this work, a weak-E/fixed-J collisional model (i.e., weak-collisional internal energy relaxation/free-collisional angular momentum relaxation) is used along with the steady-state approach to solve the resulting (simplified) two-dimensional (E,J)-grained master equation. The corresponding solutions give thermal rate constants and product branching ratios as functions of both temperature and pressure. We also have developed a program that can be used to predict and analyze experimental chemical kinetics results. This expedient technique, when combined with highly accurate potential energy surfaces, is cable of providing results that may be meaningfully compared to experiments. The reaction of singlet oxygen with methane proceeding through vibrationally excited methanol is used as an illustrative example. PMID:25815602

  20. 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...... provide new improved equations to predict the joint centre locations. The 'true' joint centres of the knee and ankle joint were obtained in vivo by MRI scans on 10 male subjects whereas the 'true' hip joint centre was obtained in 10 male and 10 female cadavers by CT scans. For the hip joint the errors...... ranged from 26.7 (8.9) to 29.6 (7.5) mm, for the knee joint 5.8 (3.1) to 22.6 (3.3) mm and for the ankle joint 14.4 (2.2) to 27.0 (4.6) mm. This differed significantly from the improved equations by which the error for the hip joint ranged from 8.2 (3.6) to 11.6 (5.6) mm, for the knee joint from 2.9 (2...

  1. Comparing Stochastic Differential Equations and Agent-Based Modelling and Simulation for Early-Stage Cancer

    OpenAIRE

    Figueredo, Grazziela P.; Peer-Olaf Siebers; Owen, Markus R.; Jenna Reps; Uwe Aickelin

    2014-01-01

    There is great potential to be explored regarding the use of agent-based modelling and simulation as an alternative paradigm to investigate early-stage cancer interactions with the immune system. It does not suffer from some limitations of ordinary differential equation models, such as the lack of stochasticity, representation of individual behaviours rather than aggregates and individual memory. In this paper we investigate the potential contribution of agent-based modelling and simulation w...

  2. A unified equation for calculating methane vapor pressures in the CH4-H2O system with measured Raman shifts

    Science.gov (United States)

    Lu, W.; Chou, I.-Ming; Burruss, R.C.; Song, Y.

    2007-01-01

    A unified equation has been derived by using all available data for calculating methane vapor pressures with measured Raman shifts of C-H symmetric stretching band (??1) in the vapor phase of sample fluids near room temperature. This equation eliminates discrepancies among the existing data sets and can be applied at any Raman laboratory. Raman shifts of C-H symmetric stretching band of methane in the vapor phase of CH4-H2O mixtures prepared in a high-pressure optical cell were also measured at temperatures between room temperature and 200 ??C, and pressures up to 37 MPa. The results show that the CH4 ??1 band position shifts to higher wavenumber as temperature increases. We also demonstrated that this Raman band shift is a simple function of methane vapor density, and, therefore, when combined with equation of state of methane, methane vapor pressures in the sample fluids at elevated temperatures can be calculated from measured Raman peak positions. This method can be applied to determine the pressure of CH4-bearing systems, such as methane-rich fluid inclusions from sedimentary basins or experimental fluids in hydrothermal diamond-anvil cell or other types of optical cell. ?? 2007 Elsevier Ltd. All rights reserved.

  3. Efficient solution of Poisson's equation in linear combination of atomic orbitals (LCAO) electronic structure calculations

    International Nuclear Information System (INIS)

    An accurate and efficient method is described for the evaluation of electrostatic contributions in LCAO electronic structure calculations. The charge density rho(r) is decomposed into rho/sup(1)(r), a component whose rapid variation near any nucleus reproduces that of rho(r) to a very good approximation, and a remainder density deltarho(r)equivalentrho(r)-rho/sup(1)(r), which is thereby guaranteed to be slowly varying in space. The power of the decomposition resides in the fact that rho/sup(1)(r) can be expressed exactly as a sum of one-center densities, without the use of any fit procedure. Because rho/sup(1)(r) is a sum of one-center multipolar densities, the Hartree potential is a function with a simple one-dimensional integral representation, and its matrix elements can be obtained by performing one-dimensional integrals over it. Since deltarho(r) is spatially slowly varying, the Hartree potential to which it corresponds and the matrix elements of this potential can accurately be evaluated on a relatively coarse coordinate space mesh, using fast Fourier transforms. The method is illustrated via molecular structure calculations for N2 and NH3. The calculations are accurate to a few percent when the required integrals over deltarho(r) and deltaV(r) are performed on a mesh of spacing 0.4 a.u. The N--N bond length and stretch frequency are found to equal 2.10 a.u. and 2.3 x 103 cm-1, respectively. The equilibrium N--H bond length and H--N--H angle are calculated to be 1.93 a.u. and 1050, respectively, while the NH3 inversion barrier turns out to equal 0.25 eV. These results are in good agreement with earlier calculations

  4. Calculation of second-order rough and temporal accuracy for diffusion equation on strongly distorted meshes

    International Nuclear Information System (INIS)

    Numerical solution of the diffusion equation plays a key role in the study of inertial confinement fusion (ICF). In this paper, based on the global support operator method, a flux-based scheme is proposed. The scheme has local stencil with second-order accuracy both in space and time. For strongly distorted meshes, a procedure of normal direction fix is adopted with proper methods for the computation of corner volume weights, which obtains accurate discretization of the face flux. Numerical experiments show that the scheme can obtain accurate solution for linear problems on non-convex meshes. The method has second-order spatial and temporal accuracy on non-smooth meshes. The method can also preserve the symmetry well and can be extended to the three dimensional unstructured meshes. (authors)

  5. Boundary integral equation method calculations of surface regression effects in flame spreading

    Science.gov (United States)

    Altenkirch, R. A.; Rezayat, M.; Eichhorn, R.; Rizzo, F. J.

    1982-01-01

    A solid-phase conduction problem that is a modified version of one that has been treated previously in the literature and is applicable to flame spreading over a pyrolyzing fuel is solved using a boundary integral equation (BIE) method. Results are compared to surface temperature measurements that can be found in the literature. In addition, the heat conducted through the solid forward of the flame, the heat transfer responsible for sustaining the flame, is also computed in terms of the Peclet number based on a heated layer depth using the BIE method and approximate methods based on asymptotic expansions. Agreement between computed and experimental results is quite good as is agreement between the BIE and the approximate results.

  6. Anisotropy scattering consideration when calculating constants of the neutron transfer multigroup equation

    International Nuclear Information System (INIS)

    The importance of accounting for resonance self-screening effects in multigroup cross sections when calculating fast reactors and neutron shields is considered. Formulae for averaging cross sections over resonance features with the account of anisotropy for scattering with large energy losses are derived. The model calculations of neutron fluxes have been performed for a U-H mixture (rhosub(H)/rhosub(U)=0.1), a U-Fe-H mixture and for the latter with rhosub(5)/rhosub(Fe)=0.01-0.5. It is concluded that in hydrogen-containing reactors the effect may be significant if the core contains iron in large quantities. The cross section averaging is considered for 3 systems: the KBR-2 critical assembly, spherical model of a large breeder, critical sphere of UO2 with 30% enrichment. The scattering anisotropy changes the multiplication factors of the first two systems by about 0.3%

  7. Calculated methods for table diagnosis of lung cancer metastases to regional lymph nodes

    International Nuclear Information System (INIS)

    The literary data and the author's material (132 patients with peripheral lung cancer and 112 patients with central lung cancer) are used to develop a technique for calculated table diagnosis of lung cancer metastases to regional lymph nodes. The results of table diagnostics are compared with therapeutic and computer diagnostics. The above technique improves the diagnostics of lung cancer metastases to regional lymph nodes by 20%. However, the results of table diagnostics of metastases are somewhat worse (2.8-4.4 %) than those of computer diagnosis. 5 refs.; 3 tabs

  8. 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.

  9. 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.

  10. Amplitude-phase calculations of Regge poles obtained from coupled radial Dirac equations

    Energy Technology Data Exchange (ETDEWEB)

    Thylwe, K-E [KTH-Mechanics, Royal lnstitute of Technology, S-100 44 Stockholm (Sweden); McCabe, P, E-mail: ket@mech.kth.se [CCDC, 12 Union Road, CB2 1EZ, Cambridge (United Kingdom)

    2011-07-08

    A recently developed amplitude-phase method for spinor-wave solutions is applied to the calculations of Regge pole positions and residues of Dirac particles. At a given energy the Dirac spin causes two sets of Regge poles that tend to coalesce in the non-relativistic limit. For the particular case of equal Lorentz-type vector and scalar potentials there is only one pole string, located very close to the non-relativistic pole string.

  11. A computer program incorporating Pitzer's equations for calculation of geochemical reactions in brines

    Science.gov (United States)

    Plummer, L.N.; Parkhurst, D.L.; Fleming, G.W.; Dunkle, S.A.

    1988-01-01

    The program named PHRQPITZ is a computer code capable of making geochemical calculations in brines and other electrolyte solutions to high concentrations using the Pitzer virial-coefficient approach for activity-coefficient corrections. Reaction-modeling capabilities include calculation of (1) aqueous speciation and mineral-saturation index, (2) mineral solubility, (3) mixing and titration of aqueous solutions, (4) irreversible reactions and mineral water mass transfer, and (5) reaction path. The computed results for each aqueous solution include the osmotic coefficient, water activity , mineral saturation indices, mean activity coefficients, total activity coefficients, and scale-dependent values of pH, individual-ion activities and individual-ion activity coeffients , and scale-dependent values of pH, individual-ion activities and individual-ion activity coefficients. A data base of Pitzer interaction parameters is provided at 25 C for the system: Na-K-Mg-Ca-H-Cl-SO4-OH-HCO3-CO3-CO2-H2O, and extended to include largely untested literature data for Fe(II), Mn(II), Sr, Ba, Li, and Br with provision for calculations at temperatures other than 25C. An extensive literature review of published Pitzer interaction parameters for many inorganic salts is given. Also described is an interactive input code for PHRQPITZ called PITZINPT. (USGS)

  12. Thermodynamic calculation and experimental determination of the equation of state of oxide fuels up to 5000 K

    International Nuclear Information System (INIS)

    The safety analysis of fast reactors requires the knowledge of the thermodynamic data of state of the nuclear fuel materials up to 5000 K. Based on the law of mass action, the saturation vapor pressure curves p(T) have been calculated for uranium dioxide and stoichiometric and hypostoichiometric (U,Pu) mixed oxide up to 5000 K. The functions used of the free energies of formation and of the oxygen potentials and the resulting partial vapor pressures are represented. The present scatter of the input data leads to a tolerable uncertainty of the calculated equations of state of +-50%. Vapor pressure measurements at very high temperatures require the application of dynamic measuring methods with pulse heating. The potential is discussed of the various experimental techniques: electrical resistive heating, electron beam heating, neutron pulse heating, and laser beam heating. A measuring method using a laser heating technique is described. Vapor pressure measurements with liquid UO2 up to 4200 K are reported. The resulting vapor pressure data fairly well agree with the calculated equation of state of UO2.00. For pyrometric measurements of liquid fuel the exact value of the spectral emissivity of the fuel surface is needed which depends on temperature. Measurements of the emissivity of liquid UO2 at 0.65 μm are shortly described. (orig.)

  13. Dielectric function and plasmons in graphene: A self-consistent-field calculation within a Markovian master equation formalism

    Science.gov (United States)

    Karimi, F.; Davoody, A. H.; Knezevic, I.

    2016-05-01

    We introduce a method for calculating the dielectric function of nanostructures with an arbitrary band dispersion and Bloch wave functions. The linear response of a dissipative electronic system to an external electromagnetic field is calculated by a self-consistent-field approach within a Markovian master-equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations. The SCF-MMEF accurately accounts for several concurrent scattering mechanisms. The method captures interband electron-hole-pair generation, as well as the interband and intraband electron scattering with phonons and impurities. We employ the SCF-MMEF to calculate the dielectric function, complex conductivity, and loss function for supported graphene. From the loss-function maximum, we obtain plasmon dispersion and propagation length for different substrate types [nonpolar diamondlike carbon (DLC) and polar SiO2 and hBN], impurity densities, carrier densities, and temperatures. Plasmons on the two polar substrates are suppressed below the highest surface phonon energy, while the spectrum is broad on the nonpolar DLC. Plasmon propagation lengths are comparable on polar and nonpolar substrates and are on the order of tens of nanometers, considerably shorter than previously reported. They improve with fewer impurities, at lower temperatures, and at higher carrier densities.

  14. 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)

    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.

  15. Calculation of correlated initial state in the hierarchical equations of motion method using an imaginary time path integral approach

    International Nuclear Information System (INIS)

    Based on recent findings in the hierarchical equations of motion (HEOM) for correlated initial state [Y. Tanimura, J. Chem. Phys. 141, 044114 (2014)], we propose a new stochastic method to obtain the initial conditions for the real time HEOM propagation, which can be used further to calculate the equilibrium correlation functions and symmetrized correlation functions. The new method is derived through stochastic unraveling of the imaginary time influence functional, where a set of stochastic imaginary time HEOM are obtained. The validity of the new method is demonstrated using numerical examples including the spin-Boson model, and the Holstein model with undamped harmonic oscillator modes

  16. Electron swarm transport coefficients in mixtures of H2O with He and Ar: Experiment and Boltzmann equation calculations

    Science.gov (United States)

    de Urquijo, Jaime; Basurto, E.; Juarez, A. M.; Ness, Kevin; Robson, Robert; Brunger, Michael; White, Ron

    2014-10-01

    The drift velocity of electrons in mixtures of gaseous water with helium and argon are measured over the range of reduced electric fields from 0--300 Td using a pulsed-Townsend technique. Small admixtures of water to both helium and argon are found to produce negative differential conductivity (NDC), despite NDC being absent from the pure gases. Comparison of the measured drift velocities with those calculated from a multi-term solution of Boltzmann's equation provides a further discriminative assessment on the accuracy and completeness of electron water vapour cross-sections. Funding acknowledgements: ARC, Mexican govt (PAPIIT IN 111014).

  17. Calculation of correlated initial state in the hierarchical equations of motion method using an imaginary time path integral approach

    Energy Technology Data Exchange (ETDEWEB)

    Song, Linze; Shi, Qiang, E-mail: qshi@iccas.ac.cn [Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190 (China)

    2015-11-21

    Based on recent findings in the hierarchical equations of motion (HEOM) for correlated initial state [Y. Tanimura, J. Chem. Phys. 141, 044114 (2014)], we propose a new stochastic method to obtain the initial conditions for the real time HEOM propagation, which can be used further to calculate the equilibrium correlation functions and symmetrized correlation functions. The new method is derived through stochastic unraveling of the imaginary time influence functional, where a set of stochastic imaginary time HEOM are obtained. The validity of the new method is demonstrated using numerical examples including the spin-Boson model, and the Holstein model with undamped harmonic oscillator modes.

  18. Calculation of correlated initial state in the hierarchical equations of motion method using an imaginary time path integral approach.

    Science.gov (United States)

    Song, Linze; Shi, Qiang

    2015-11-21

    Based on recent findings in the hierarchical equations of motion (HEOM) for correlated initial state [Y. Tanimura, J. Chem. Phys. 141, 044114 (2014)], we propose a new stochastic method to obtain the initial conditions for the real time HEOM propagation, which can be used further to calculate the equilibrium correlation functions and symmetrized correlation functions. The new method is derived through stochastic unraveling of the imaginary time influence functional, where a set of stochastic imaginary time HEOM are obtained. The validity of the new method is demonstrated using numerical examples including the spin-Boson model, and the Holstein model with undamped harmonic oscillator modes. PMID:26590526

  19. 3He(d,p)4He reaction calculation with three-body Faddeev equations

    International Nuclear Information System (INIS)

    In order to investigate the 3He-n-p system as a three-body problem, we have formulated 3He-n and 3H-p effective potentials using both a microscopic treatment and a phenomenological approach. In the microscopic treatment, potentials are generated by means of the resonating group method (RGM) based on the Minnesota nucleon-nucleon potential. These potentials are converted into separable form by means of the microscopic Pauli correct (MPC) method. The MPC potentials are properly formulated to avoid Pauli forbidden states. The phenomenological potentials are obtained by modifying parameters of the EST approximation to the Paris nucleon-nucleon potential, such that they fit the low-energy 3He-n, 3H-p, and 3He-p phase shifts. Therefore, they describe the 3He-n differential cross section, the polarization observables, and the energy levels of 4He. The 3He-n-p Faddeev equations are solved numerically. We reproduce correctly the ground state and the first excited state of 5Li. Furthermore, the Paris-type potential is used to investigate the 3He(d,p)4He reaction at a deuteron bombarding energy of 270 MeV, where the system is treated as a three-body problem. Results for the polarized and unpolarized differential cross sections demonstrate convergence of the Born series. (orig.)

  20. First-Principles Equation of State Calculations of Warm Dense Nitrogen

    CERN Document Server

    Driver, K P

    2016-01-01

    Using path integral Monte Carlo (PIMC) and density functional molecular dynamics (DFT-MD) simulation methods, we compute a coherent equation of state (EOS) of nitrogen that spans the liquid, warm dense matter (WDM), and plasma regimes. Simulations cover a wide range of density-temperature space, $1.5-13.9$~g$~$cm$^{-3}$ and $10^3-10^9$~K. In the molecular dissociation regime, we extend the pressure-temperature phase diagram beyond previous studies, providing dissociation and Hugoniot curves in good agreement with experiments and previous DFT-MD work. Analysis of pair-correlation functions and the electronic density of states in the WDM regime reveals an evolving plasma structure and ionization process that is driven by temperature and pressure. Our Hugoniot curves display a sharp change in slope in the dissociation regime and feature two compression maxima as the K and L shells are ionized in the WDM regime, which have some significant differences from the predictions of plasma models.

  1. Calculation and experimental estimation of the equation of state of irradiated fuel

    International Nuclear Information System (INIS)

    The gas pressure development in an irradiated mixed oxide fuel is mainly influenced by fission gases and volatile fission products in the temperature range below the melting point and by the fuel material itself and the less volatile fission products in the temperature region above 4000 K. Besides the temperature the important factors for the vapor pressure are the oxygen potential of the fuel and the concentration of fission products in the fuel. As demonstrated previously the oxygen potential influences strongly the pressure of vapor species above (U Pu)O2. The pressure of the species U, UO, UO2, Pu, PuO, PuO2 varies over a range of more than five orders of magnitude by variation of the oxygen potential at 2000 K. Similar effects were observed with oxides of the fission products. Fission products dissolved in mixed oxide fuel on the other hand can influence significantly the oxygen potential of the irradiated mixed oxide. In the first paragraph of the paper an attempt is made to calculate oxygen potentials of mixed oxides containing dissolved fission products. The model used is based on the equilibrium of oxygen defects in the mixed oxide. The chemical state and distribution of fission products is a further behavior that should be considered in calculation of the local and overall pressures and behavior of the fuel. Fission products were transported during the irradiation time and collect at different positions within the fuel pin. This process can produce high local concentrations of fission products, thus enabling elements with low overall concentrations to reach their saturation pressure. The distribution of fission products and their behavior in irradiated mixed oxide fuel is described in the second paragraph. The third paragraph deals with the calculation of vapor pressures that has been conducted using a model described for uranium-plutonium mixed oxides. This model is based on the law of mass action and provides vapor pressures as a function of temperature

  2. Tissue heterogeneity in IMRT dose calculation for lung cancer.

    Science.gov (United States)

    Pasciuti, Katia; Iaccarino, Giuseppe; Strigari, Lidia; Malatesta, Tiziana; Benassi, Marcello; Di Nallo, Anna Maria; Mirri, Alessandra; Pinzi, Valentina; Landoni, Valeria

    2011-01-01

    The aim of this study was to evaluate the differences in accuracy of dose calculation between 3 commonly used algorithms, the Pencil Beam algorithm (PB), the Anisotropic Analytical Algorithm (AAA), and the Collapsed Cone Convolution Superposition (CCCS) for intensity-modulated radiation therapy (IMRT). The 2D dose distributions obtained with the 3 algorithms were compared on each CT slice pixel by pixel, using the MATLAB code (The MathWorks, Natick, MA) and the agreement was assessed with the γ function. The effect of the differences on dose-volume histograms (DVHs), tumor control, and normal tissue complication probability (TCP and NTCP) were also evaluated, and its significance was quantified by using a nonparametric test. In general PB generates regions of over-dosage both in the lung and in the tumor area. These differences are not always in DVH of the lung, although the Wilcoxon test indicated significant differences in 2 of 4 patients. Disagreement in the lung region was also found when the Γ analysis was performed. The effect on TCP is less important than for NTCP because of the slope of the curve at the level of the dose of interest. The effect of dose calculation inaccuracy is patient-dependent and strongly related to beam geometry and to the localization of the tumor. When multiple intensity-modulated beams are used, the effect of the presence of the heterogeneity on dose distribution may not always be easily predictable. PMID:20970989

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

    International Nuclear Information System (INIS)

    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

  4. Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smoothed particle hydrodynamics

    International Nuclear Information System (INIS)

    The calculation of diffusion-controlled ligand binding rates is important for understanding enzyme mechanisms as well as designing enzyme inhibitors. We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) BC, is considered on the reactive boundaries. This new BC treatment allows for the analysis of enzymes with “imperfect” reaction rates. The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to a mouse acetylcholinesterase (mAChE) monomer. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature

  5. 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.

  6. 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.

  7. An exact solution of the linearized Boltzmann transport equation and its application to mobility calculations in graphene bilayers

    Science.gov (United States)

    Paussa, A.; Esseni, D.

    2013-03-01

    This paper revisits the problem of the linearized Boltzmann transport equation (BTE), or, equivalently, of the momentum relaxation time, momentum relaxation time (MRT), for the calculation of low field mobility, which in previous works has been almost universally solved in approximated forms. We propose an energy driven discretization method that allows an exact determination of the relaxation time by solving a linear, algebraic problem, where multiple scattering mechanisms are naturally accounted for by adding the corresponding scattering rates before the calculation of the MRT, and without resorting to the semi-empirical Matthiessen's rule for the relaxation times. The application of our rigorous solution of the linearized BTE to a graphene bilayer reveals that, for a non monotonic energy relation, the relaxation time can legitimately take negative values with no unphysical implications. We finally compare the mobility calculations provided by an exact solution of the MRT problem with the results obtained with some of the approximations most frequently employed in the literature and so discuss their accuracy.

  8. Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smooth particle hydrodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Pan, Wenxiao; Daily, Michael D.; Baker, Nathan A.

    2015-12-01

    We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to an acetylcholinesterase monomer. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) boundary condition, is considered on the reactive boundaries. This new boundary condition treatment allows for the analysis of enzymes with "imperfect" reaction rates. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.

  9. A numerical solution to the Boltzmann equation for use in calculating pumping rates in a CO2 discharge laser

    Science.gov (United States)

    Honey, David Alan

    1989-12-01

    The collisional Boltzmann equation was solved numerically to obtain excitation rates for use in a CO2 laser design program. The program was written in Microsoft QuickBasic for use on the IBM Personal Computer or equivalent. Program validation involved comparisons of computed transport coefficients with experimental data and previous theoretical work. Four different numerical algorithms were evaluated in terms of accuracy and efficiency. L-U decomposition was identified as the preferred approach. The calculated transport coefficients were found to agree with empirical data within one to five percent. The program was integrated into a CO2 laser design program. Studies were then performed to evaluate the effects on predicted laser output power and energy density as parameters affecting electron kinetics were changed. Plotting routines were written for both programs.

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

    International Nuclear Information System (INIS)

    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

  11. 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.

  12. Calculation of unsteady small disturbance transonic flow at arbitrary reduced frequency using an extended integral equation method.

    Science.gov (United States)

    Lamah, C. A.; Harris, W. L.

    1983-01-01

    A novel analytical-numerical method for calculating unsteady small disturbance transonic flow over airfoils has been developed. The method uses an extended integral equation technique, based on both the velocity potential and the acceleration potential, to predict unsteady aerodynamic loading on airfoils oscillating in subcritical transonic free stream conditions. The formulation is an extension of the work of Sivaneri and Harris (1980) for steady, non-lifting flows and utilizes the linear theory of Landahl (1961) for decoupling of steady and unsteady components. The analytical-numerical procedure involves several intnegrating schemes and applies to general frequencies of oscillations. The technique is illustrated by computing the transonic flow about parabolic arc airfoils. Specific unsteady results for reduced frequencies based on semi-chord of 0.01, 0.1, 0.3, 0.4 and 0.6 are given. Comparison of results with those obtained by an ADI finite difference scheme is made.

  13. Minimising the error in eigenvalue calculations involving the Boltzmann transport equation using goal-based adaptivity on unstructured meshes

    International Nuclear Information System (INIS)

    This article presents a method for goal-based anisotropic adaptive methods for the finite element method applied to the Boltzmann transport equation. The neutron multiplication factor, keff, is used as the goal of the adaptive procedure. The anisotropic adaptive algorithm requires error measures for keff with directional dependence. General error estimators are derived for any given functional of the flux and applied to keff to acquire the driving force for the adaptive procedure. The error estimators require the solution of an appropriately formed dual equation. Forward and dual error indicators are calculated by weighting the Hessian of each solution with the dual and forward residual respectively. The Hessian is used as an approximation of the interpolation error in the solution which gives rise to the directional dependence. The two indicators are combined to form a single error metric that is used to adapt the finite element mesh. The residual is approximated using a novel technique arising from the sub-grid scale finite element discretisation. Two adaptive routes are demonstrated: (i) a single mesh is used to solve all energy groups, and (ii) a different mesh is used to solve each energy group. The second method aims to capture the benefit from representing the flux from each energy group on a specifically optimised mesh. The keff goal-based adaptive method was applied to three examples which illustrate the superior accuracy in criticality problems that can be obtained

  14. Evaluation of the Novel Method and the Regression Equation for Calculation of Low-Density Lipoprotein Cholesterol

    Directory of Open Access Journals (Sweden)

    Muhammad Saiedullah

    2015-01-01

    Full Text Available Background: Friedewald’s formula (FF is used worldwide to calculate low-density lipoprotein cholesterol (LDL-chol. But it has several shortcomings: overestimation at lower triglyceride (TG concentrations and underestimation at higher concentrations. In FF, TG to very low-density lipoprotein cholesterol (VLDL-chol ratio (TG/VLDL-chol is considered as constant, but practically it is not a fixed value. Recently, by analyzing lipid profiles in a large population, continuously adjustable values of TG/VLDL-chol were used to derive a novel method (NM for the calculation of LDL-chol. Objective: The aim of this study was to evaluate the performance of the novel method compared with direct measurement and regression equation (RE developed for Bangladeshi population. Materials and Methods: In this cross-sectional comparative study we used lipid profiles of 955 adult Bangladeshi subjects. Total cholesterol (TC, TG, HDL-chol and LDL-chol were measured by direct methods using automation. LDL-chol was also calculated by NM and RE. LDL-chol calculated by NM and RE were compared with measured LDL-chol by twotailed paired t test, Pearson’s correlation test, bias against measured LDL-chol by Bland-Altman test, accuracy within ±5% and ±12% of measured LDL-chol and by inter-rater agreements with measured LDL-chol at different cut-off values. Results: The mean values of LDL-chol were 110.7 ± 32.0 mg/dL for direct measurement, 111.9 ± 34.8 mg/dL for NM and 113.2 ± 31.7 mg/dL for RE. Mean values of calculated LDL-chol by both NM and RE differed from that of measured LDL-chol (p130 mg/dL were 0.816 vs 0.815, 0.637 vs 0.649 and 0.791 vs 0.791 for NM and RE respectively. Conclusion: This study reveals that NM and RE developed for Bangladeshi population have similar performance and can be used for the calculation of LDL-chol.

  15. 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. PMID:21895161

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

    International Nuclear Information System (INIS)

    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-1cm-2) and U-concertrations (100-250ppm)

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

    International Nuclear Information System (INIS)

    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

  18. 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. Ovsianko

    2014-10-01

    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. 

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

    Science.gov (United States)

    Epifanovsky, Evgeny; Klein, Kerstin; Stopkowicz, Stella; Gauss, Jürgen; Krylov, Anna I

    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. PMID:26277122

  20. 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.

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

    Science.gov (United States)

    Epifanovsky, Evgeny; Klein, Kerstin; Stopkowicz, Stella; Gauss, Jürgen; Krylov, Anna I.

    2015-08-01

    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.

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

    International Nuclear Information System (INIS)

    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

  3. Calculation of the second term of the exact Green's function of the diffusion equation for diffusion-controlled chemical reactions

    Science.gov (United States)

    Plante, Ianik

    2016-01-01

    The exact Green's function of the diffusion equation (GFDE) is often considered to be the gold standard for the simulation of partially diffusion-controlled reactions. As the GFDE with angular dependency is quite complex, the radial GFDE is more often used. Indeed, the exact GFDE is expressed as a Legendre expansion, the coefficients of which are given in terms of an integral comprising Bessel functions. This integral does not seem to have been evaluated analytically in existing literature. While the integral can be evaluated numerically, the Bessel functions make the integral oscillate and convergence is difficult to obtain. Therefore it would be of great interest to evaluate the integral analytically. The first term was evaluated previously, and was found to be equal to the radial GFDE. In this work, the second term of this expansion was evaluated. As this work has shown that the first two terms of the Legendre polynomial expansion can be calculated analytically, it raises the question of the possibility that an analytical solution exists for the other terms.

  4. A general integral form of the boundary-layer equation for incompressible flow with an application to the calculation of the separation point of turbulent boundary layers

    Science.gov (United States)

    Tetervin, Neal; Lin, Chia Chiao

    1951-01-01

    A general integral form of the boundary-layer equation, valid for either laminar or turbulent incompressible boundary-layer flow, is derived. By using the experimental finding that all velocity profiles of the turbulent boundary layer form essentially a single-parameter family, the general equation is changed to an equation for the space rate of change of the velocity-profile shape parameter. The lack of precise knowledge concerning the surface shear and the distribution of the shearing stress across turbulent boundary layers prevented the attainment of a reliable method for calculating the behavior of turbulent boundary layers.

  5. 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.

  6. A new approach to calculating the memory kernel of the generalized quantum master equation for an arbitrary system-bath coupling

    Science.gov (United States)

    Shi, Qiang; Geva, Eitan

    2003-12-01

    The Nakajima-Zwanzig generalized quantum master equation provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a quantum bath. In this equation, the memory kernel accounts for the influence of the bath on the system's dynamics. The standard approach is based on using a perturbative treatment of the system-bath coupling for calculating this kernel, and is therefore restricted to systems weakly coupled to the bath. In this paper, we propose a new approach for calculating the memory kernel for an arbitrary system-bath coupling. The memory kernel is obtained by solving a set of two coupled integral equations that relate it to a new type of two-time system-dependent bath correlation functions. The feasibility of the method is demonstrated in the case of an asymetrical two-level system linearly coupled to a harmonic bath.

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

    International Nuclear Information System (INIS)

    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 cm3, 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

  8. 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.

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

    International Nuclear Information System (INIS)

    Purpose: To propose a new method to estimate lung mean dose (LMD) using technetium-99m labeled macroaggregated albumin (99mTc-MAA) single photon emission CT (SPECT)/CT for 90Yttrium 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 99mTc-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 99mTc-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

  10. Relativistic equation-of-motion coupled-cluster calculations of photo-ionization andouble-ionization for the He and Be isoelectronic sequences

    CERN Document Server

    Pathak, Himadri; Sengupta, Turbasu; Das, B P; Vaval, Nayana; Pal, Sourav

    2014-01-01

    In this paper, we apply our recently developed four-component spinor relativistic equation-of- motion coupled-cluster method to calculate single ionization (IPs) and double ionization (DIPs) potentials values of He and Be isoelectronic sequences. The calculated results are compared with those from the National Institute of Standards and Technology (NIST) database and other available calculations using the intermediate-energy R-matrix method (IERM). Our results for DIPs are in better agreement with the NIST values than those from the IERM method [Phys. Rev. A. 88, 053413 (2013)]. We have also found the dependence of the IPs and DIPs of these ions on the ionic charge.

  11. Calculation of the equation of state of a dense hydrogen plasma by the Feynman path integral method

    International Nuclear Information System (INIS)

    A method is developed for calculating the equation of state of a system of quantum particles at a finite temperature, based on the Feynman formulation of quantum statistics. A general analytical expression is found for the virial estimator for the kinetic energy of a system with rigid boundaries at a finite pressure. An effective method is developed for eliminating the unphysical singularity in the electrostatic potential between a discretized Feynman path of an electron and a proton. It is shown that the 'refinement' of an expansion of a quantum-mechanical propagator by addition of high powers of time exacerbates, rather than eliminates, the divergence of a Feynman path integral. A brief summary of the current status of the problem is presented. The proposed new approaches are presented in relation to progress made in this field. Path integral Monte Carlo simulations are performed for nonideal hydrogen plasmas in which both indistinguishability and spin of electrons are taken into account under conditions preceding the formation of the electron shells of atoms. The electron permutation symmetry is represented in terms of Young operators. It is shown that, owing to the singularity of the Coulomb potential, quantum effects on the behavior of the electron component cannot be reduced to small corrections even if the system must be treated as a classical system according to the formal de Broglie criterion. Quantum-mechanical delocalization of electrons substantially weakens the repulsion between electrons as compared to protons. In relatively cold plasmas, many-body correlations lead to complex behavior of the potential of the average force between particles and give rise to repulsive forces acting between protons and electrons at distances of about 5 angstroms. Plasma pressure drops with decreasing plasma temperature as the electron shells of atoms begin to form, and the electron kinetic energy reaches a minimum at a temperature of about 31,000 K. The minimum point

  12. High-resolution protein structure determination starting with a global fold calculated from exact solutions to the RDC equations.

    Science.gov (United States)

    Zeng, Jianyang; Boyles, Jeffrey; Tripathy, Chittaranjan; Wang, Lincong; Yan, Anthony; Zhou, Pei; Donald, Bruce Randall

    2009-11-01

    We present a novel structure determination approach that exploits the global orientational restraints from RDCs to resolve ambiguous NOE assignments. Unlike traditional approaches that bootstrap the initial fold from ambiguous NOE assignments, we start by using RDCs to compute accurate secondary structure element (SSE) backbones at the beginning of structure calculation. Our structure determination package, called RDC-PANDA: (RDC-based SSE PAcking with NOEs for Structure Determination and NOE Assignment), consists of three modules: (1) RDC-EXACT: ; (2) PACKER: ; and (3) HANA: (HAusdorff-based NOE Assignment). RDC-EXACT: computes the global optimal solution of backbone dihedral angles for each secondary structure element by exactly solving a system of quartic RDC equations derived by Wang and Donald (Proceedings of the IEEE computational systems bioinformatics conference (CSB), Stanford, CA, 2004a; J Biomol NMR 29(3):223-242, 2004b), and systematically searching over the roots, each of which is a backbone dihedral varphi- or psi-angle consistent with the RDC data. Using a small number of unambiguous inter-SSE NOEs extracted using only chemical shift information, PACKER: performs a systematic search for the core structure, including all SSE backbone conformations. HANA: uses a Hausdorff-based scoring function to measure the similarity between the experimental spectra and the back-computed NOE pattern for each side-chain from a statistically-diverse rotamer library, and drives the selection of optimal position-specific rotamers for filtering ambiguous NOE assignments. Finally, a local minimization approach is used to compute the loops and refine side-chain conformations by fixing the core structure as a rigid body while allowing movement of loops and side-chains. RDC-PANDA: was applied to NMR data for the FF Domain 2 of human transcription elongation factor CA150 (RNA polymerase II C-terminal domain interacting protein), human ubiquitin, the ubiquitin-binding zinc

  13. Exact solutions of rate equations for the calculation of supersaturations of defects and growth rates for voids

    International Nuclear Information System (INIS)

    Exact solutions of the rate equations are discussed in detail for vanishing and nonvanishing recombination coefficient α. The existence and uniquenes of the solutions are shown for arbitrary sources and sinks and for α not= o. (orig.)

  14. 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)

    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

  15. Can Western Based Online Prostate Cancer Risk Calculators Be Used to Predict Prostate Cancer after Prostate Biopsy for the Korean Population?

    OpenAIRE

    Lee, Dong Hoon; Jung, Ha Bum; Park, Jae Won; Kim, Kyu Hyun; Kim, Jongchan; Lee, Seung Hwan; Chung, Byung Ha

    2013-01-01

    Purpose To access the predictive value of the European Randomized Screening of Prostate Cancer Risk Calculator (ERSPC-RC) and the Prostate Cancer Prevention Trial Risk Calculator (PCPT-RC) in the Korean population. Materials and Methods We retrospectively analyzed the data of 517 men who underwent transrectal ultrasound guided prostate biopsy between January 2008 and November 2010. Simple and multiple logistic regression analysis were performed to compare the result of prostate biopsy. Area u...

  16. Constraints on Skyrme equations of state from properties of doubly magic nuclei and ab-initio calculations of low-density neutron matter

    OpenAIRE

    Brown, B.Alex; Schwenk, A.

    2014-01-01

    We use properties of doubly-magic nuclei and ab-initio calculations of low-density neutron matter to constrain Skyrme equations of state for neutron-rich conditions. All of these properties are consistent with a Skyrme functional form and a neutron-matter equation of state that depends on three parameters. With a reasonable range for the neutron-matter effective mass, the values of the two other Skyrme parameters are well constrained. This leads to predictions for other quantities. The neutro...

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

    International Nuclear Information System (INIS)

    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

  18. Parallel computing for homogeneous diffusion and transport equations in neutronics; Calcul parallele pour les equations de diffusion et de transport homogenes en neutronique

    Energy Technology Data Exchange (ETDEWEB)

    Pinchedez, K

    1999-06-01

    Parallel computing meets the ever-increasing requirements for neutronic computer code speed and accuracy. In this work, two different approaches have been considered. We first parallelized the sequential algorithm used by the neutronics code CRONOS developed at the French Atomic Energy Commission. The algorithm computes the dominant eigenvalue associated with PN simplified transport equations by a mixed finite element method. Several parallel algorithms have been developed on distributed memory machines. The performances of the parallel algorithms have been studied experimentally by implementation on a T3D Cray and theoretically by complexity models. A comparison of various parallel algorithms has confirmed the chosen implementations. We next applied a domain sub-division technique to the two-group diffusion Eigen problem. In the modal synthesis-based method, the global spectrum is determined from the partial spectra associated with sub-domains. Then the Eigen problem is expanded on a family composed, on the one hand, from eigenfunctions associated with the sub-domains and, on the other hand, from functions corresponding to the contribution from the interface between the sub-domains. For a 2-D homogeneous core, this modal method has been validated and its accuracy has been measured. (author)

  19. Numerical Calculation of Transport Based on the Drift-Kinetic Equation for Plasmas in General Toroidal Magnetic Geometry: Numerical Methods

    International Nuclear Information System (INIS)

    In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs

  20. Calculations of three-dimensional flows using the isenthalpic Euler equations with implicit flux-vector splitting

    Science.gov (United States)

    Cannizzaro, Frank E.; Von Lavante, E.; Melson, N. Duane

    1988-01-01

    A numerical method for solving the isenthalpic form of the Euler equations is developed. The method is based on the concept of flux vector splitting in its implicit form applied to a cell centered finite volume scheme. Approximate factorization is implemented in solving the implicit part of the governing equations. Time marching to a steady state solution requires short computational times due to the relative efficiency of the basic method. Computational times are further reduced by the implementation of multigrid. Results for several basic cases are shown.

  1. Modeling the Treatment of Glioblastoma Multiforme and Cancer Stem Cells with Ordinary Differential Equations

    OpenAIRE

    Kristen Abernathy; Jeremy Burke

    2016-01-01

    Despite improvements in cancer therapy and treatments, tumor recurrence is a common event in cancer patients. One explanation of recurrence is that cancer therapy focuses on treatment of tumor cells and does not eradicate cancer stem cells (CSCs). CSCs are postulated to behave similar to normal stem cells in that their role is to maintain homeostasis. That is, when the population of tumor cells is reduced or depleted by treatment, CSCs will repopulate the tumor, causing recurrence. In this pa...

  2. Phenomenological extensions to APROS six-equation model. Non-condensable gas, supercritical pressure, improved CCFL and reduced numerical diffusion for scalar transport calculation

    Energy Technology Data Exchange (ETDEWEB)

    Haenninen, M. (Lappeenranta Univ. of Technology, Dept. of Nuclear Energy (Finland))

    2009-11-15

    This thesis focuses on the development of the two-fluid model of the APROS simulation program. The system of constitutive equations and how equations are related to basic equations have been presented and discussed. The new non-condensable gas model, which was implemented to the two-fluid model, has been described in detail. The extension of the non-condensable gas model to the two-fluid system and the validation of the model have also been presented. The changes made to the six-equation model when the model has been applied to supercritical pressure calculation have been depicted. Finally, the author describes how the whole complicated system is verified and validated. Through the simulations, the applicability of the two-phase model for the analyses of real plant applications is substantiated and verified. In addition to this summary, the thesis consists of four publications. The first paper deals with how the CCFL (Counter Current Flow Limitation) correlations have been implemented to the code and how these correlations have been verified. In the second paper, the non-condensable gas model and its implementation to the two-fluid model have been presented. The third paper describes how the sharp temperature distribution can be maintained in the liquid flow through the aid of simple higher order discretization. In the fourth paper, the modifications carried out to the two-fluid model when applied to the calculation of the supercritical pressure flow are described and discussed. (orig.)

  3. Phenomenological extensions to APROS six-equation model. Non-condensable gas, supercritical pressure, improved CCFL and reduced numerical diffusion for scalar transport calculation

    International Nuclear Information System (INIS)

    This thesis focuses on the development of the two-fluid model of the APROS simulation program. The system of constitutive equations and how equations are related to basic equations have been presented and discussed. The new non-condensable gas model, which was implemented to the two-fluid model, has been described in detail. The extension of the non-condensable gas model to the two-fluid system and the validation of the model have also been presented. The changes made to the six-equation model when the model has been applied to supercritical pressure calculation have been depicted. Finally, the author describes how the whole complicated system is verified and validated. Through the simulations, the applicability of the two-phase model for the analyses of real plant applications is substantiated and verified. In addition to this summary, the thesis consists of four publications. The first paper deals with how the CCFL (Counter Current Flow Limitation) correlations have been implemented to the code and how these correlations have been verified. In the second paper, the non-condensable gas model and its implementation to the two-fluid model have been presented. The third paper describes how the sharp temperature distribution can be maintained in the liquid flow through the aid of simple higher order discretization. In the fourth paper, the modifications carried out to the two-fluid model when applied to the calculation of the supercritical pressure flow are described and discussed. (orig.)

  4. Calculation of third-order signals via driven Schrödinger equations: General results and application to electronic 2D photon echo spectroscopy

    International Nuclear Information System (INIS)

    Highlights: ► Method for the calculation of optical signals via driven Schrodinger equations. ► The method accounts for arbitrary pulse durations and pulse-overlap effects. ► 2D spectra are calculated for systems with vibronic and electronic couplings - Abstract: We present the wavefunction (WF) version of the equation-of-motion phase-matching approach (EOM-PMA) for the calculation of four-wave-mixing (4WM) optical signals. For the material system, we consider a general electronic-vibrational Hamiltonian, comprising the electronic ground state, a manifold of singly-excited electronic states, and a manifold of doubly-excited electronic states. We show that the calculation of the third-order polarization for particular values of the pulse delay times and in a specific phase-matching direction requires 6 independent WF propagations within the rotating wave approximation. For material systems without optical transitions to doubly-excited electronic states, the number of WF propagations is reduced to 5. The WF EOM-PMA automatically accounts for pulse-overlap effects and allows the efficient numerical calculation of 4WM signals for vibronically coupled multimode material systems. The application of the method is illustrated for model systems with strong electron-vibrational and electronic inter-state couplings

  5. On the interpretation of the inverted kinetics equation and space-time calculations of the effectiveness of the VVER-1000 reactor scram system

    Science.gov (United States)

    Zizin, M. N.; Ivanov, L. D.

    2013-12-01

    In the present paper, an attempt is made to analyze the accuracy of calculating the effectiveness of the VVER-1000 reactor scram system by means of the inverted solution of the kinetics equation (ISKE). In the numerical studies in the intellectual ShIPR software system, the actuation of the reactor scram system with the possible jamming of one of the two most effective rods is simulated. First, the connection of functionals calculated in the space-time computation in different approximations with the kinetics equation is considered on the theoretical level. The formulas are presented in a manner facilitating their coding. Then, the results of processing of several such functions by the ISKE are presented. For estimating the effectiveness of the VVER-1000 reactor scram system, it is proposed to use the measured currents of ionization chambers (IC) jointly with calculated readings of IC imitators. In addition, the integral of the delayed neutron (DN) generation rate multiplied by the adjoint DN source over the volume of the reactor, calculated for the instant of time when insertion of safety rods ends, is used. This integral is necessary for taking into account the spatial reactivity effects. Reasonable agreement was attained for the considered example between the effectiveness of the scram system evaluated by this method and the values obtained by steady-state calculations as the difference of the reciprocal effective multiplication factors with withdrawn and inserted control rods. This agreement was attained with the use of eight-group DN parameters.

  6. The Relationship between 10-Year Cardiovascular Risk Calculated Using the Pooled Cohort Equation and the Severity of Non-Alcoholic Fatty Liver Disease

    OpenAIRE

    Lee, Jeong In; Kim, Min Chul; Moon, Byung Sub; Song, Young Seok; Han, Eun Na; Lee, Hyo Sun; Son, Yoonjeong; Kim, Jihyun; Han, Eun Jin; Park, Hye-jeong; Park, Se Eun; Park, Cheol-Young; Lee, Won-Young; Oh, Ki-Won; Park, Sung-Woo

    2016-01-01

    Background We investigated the association between the severity of non-alcoholic fatty liver disease (NAFLD) and the estimated 10-year risk of cardiovascular disease (CVD) calculated by Pooled Cohort Equation (PCE) and Framingham risk score (FRS). Methods A total of 15,913 participants (mean age, 46.3 years) in a health screening program were selected for analysis. The presence and severity of fatty liver was assessed by abdominal ultrasonogram. Subjects who drank alcohol more than three time...

  7. Calculation of the Aqueous Thermodynamic Properties of Citric Acid Cycle Intermediates and Precursors and the Estimation of High Temperature and Pressure Equation of State Parameters

    OpenAIRE

    Mitchell Schulte; Peter Dalla-Betta

    2009-01-01

    The citric acid cycle (CAC) is the central pathway of energy transfer for many organisms, and understanding the origin of this pathway may provide insight into the origins of metabolism. In order to assess the thermodynamics of this key pathway for microorganisms that inhabit a wide variety of environments, especially those found in high temperature environments, we have calculated the properties and parameters for the revised Helgeson-Kirkham-Flowers equation of state for the major component...

  8. Utilisation of the Peng-Robinson equation of state in multiphase flow pressure-gradient calculations in oil and gas wells

    Energy Technology Data Exchange (ETDEWEB)

    Sutton, R.P.; Farshad, F.F.

    1983-09-01

    An evaluation of utilising the Peng-Robinson Equation of State to perform the PVT calculations required for pressure-gradient calculations in oil and gas-condensate wells is presented. The evaluation is made using a total of 50 well tests representing 30 different wellstream molar compositions. Twenty-five of the fluid systems are gas-condensates with liquid yields ranging from 5 to 194 bbls/MMcf. The remaining five compositions are from black-oil fluid systems with gas-oil ratios ranging from 481 to 2,026 scf/bbl. The compositional and well-test data are summarised in Tables 3 and 4. Multiphase flow pressure-gradient (MFPG) calculations were made using nine well-known correlations. PVT properties required by these correlations were derived using compositional and more traditional methods. The results of the calculations were compared with measured data to ascertain the suitability of the various methods for handling PVT calculations along with the overall general applicability of the MFPG correlations. This paper is not intended to provide an in-depth discussion of the various pressure-gradient calculation methods as the information is readily available from several gradient calculations and some general observations made as a result of the calculations.

  9. Following electron impact excitations of Rn, Ra, Th, U and Pu single atom L sub-shells ionization cross section calculations by using Lotz's equation

    Science.gov (United States)

    Ayinol, M.; Aydeniz, D.

    2016-03-01

    L shell ionization cross section and Li subshells ionization cross sections of Rn, Ra, Th, U, Pu atoms calculated. For each of atoms, ten different electron impact energy values (Eo) are used. Calculations carried out by using Lotz equation in Matlab. First, calculations done for non-relativistic case by using non-relativistic Lotz equation then repeated with relativistic Lotz equation. σL total and σLi(i = 1,2,3) subshells ionisation cross section values obtained for Eo values in the energy range of ELi

  10. Predictive equations for total lung capacity and residual volume calculated from radiographs in a random sample of the Michigan population.

    OpenAIRE

    Kilburn, K H; Warshaw, R H; Thornton, J C; Thornton, K.; Miller, A

    1992-01-01

    BACKGROUND: Published predicted values for total lung capacity and residual volume are often based on a small number of subjects and derive from different populations from predicted spirometric values. Equations from the only two large studies gave smaller predicted values for total lung capacity than the smaller studies. A large number of subjects have been studied from a population which has already provided predicted values for spirometry and transfer factor for carbon monoxide. METHODS: T...

  11. 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.

  12. KOHBRA BRCA risk calculator (KOHCal): a model for predicting BRCA1 and BRCA2 mutations in Korean breast cancer patients.

    Science.gov (United States)

    Kang, Eunyoung; Park, Sue K; Lee, Jong Won; Kim, Zisun; Noh, Woo-Chul; Jung, Yongsik; Yang, Jung-Hyun; Jung, Sung Hoo; Kim, Sung-Won

    2016-05-01

    The widely used Western BRCA mutation prediction models underestimated the risk of having a BRCA mutation in Korean breast cancer patients. This study aimed to identify predictive factors for BRCA1/2 mutations and to develop a Korean BRCA risk calculator. The model was constructed by logistic regression model, and it was based on the Korean Hereditary Breast Cancer study, in which 1669 female patients were enrolled between May 2007 and December 2010. A separate data set of 402 patients, who were enrolled from Jan 2011 to August 2012, was used to test the performance of our model. In total, 264 (15.8%) and 67 (16.7%) BRCA mutation carriers were identified in the model and validation set, respectively. Multivariate analysis showed that age at breast cancer diagnosis, bilateral breast cancer, triple-negative breast cancer (TNBC) and the number of relatives with breast or ovarian cancer within third-degree relatives were independent predictors of the BRCA mutation among familial breast cancer patients. An age cancer, both breast and ovarian cancer and TNBC remained significant predictors in non-familial breast cancer cases. Our model was developed based on logistic regression models. The validation results showed no differences between the observed and expected carrier probabilities. This model will be a useful tool for providing genetic risk assessments in Korean populations. PMID:26763880

  13. External validation of the Prostate Cancer Prevention Trial and the European Randomized Study of Screening for Prostate Cancer risk calculators in a Chinese cohort

    Institute of Scientific and Technical Information of China (English)

    Yao Zhu; Ding-Wei Ye; Jin-You Wang; Yi-Jun Shen; Bo Dai; Chun-Guang Ma; Wen-Jun Xiao; Guo-Wen Lin; Xu-Dong Yao; Shi-Lin Zhang

    2012-01-01

    Several prediction models have been developed to estimate the outcomes of prostate biopsies.Most of these teels were designed for use with Western populations and have not been validated across different ethnic groups.Therefore,we evaluated the predictive value of the Prostate Cancer Prevention Trial (PCPT) and the European Randomized Study of Screening for Prostate Cancer (ERSPC) risk calculators in a Chinese cohort.Clinicopathological information was obtained from 495 Chinese men who had undergone extended prostate biopsies between January 2009 and March 2011.The estimated probabilities of prostate cancer and high-grade disease (Gleason >6) were calculated using the PCPT and ERSPC risk calculators.Overall measures,discrimination,calibration and clinical usefulness were assessed for the model evaluation.Of these patients,28.7% were diagnosed with prostate cancer and 19.4% had high-grade disease.Compared to the PCPT model and the prostate-specific antigen (PSA) threshold of 4 ng ml-1,the ERSPC risk calculator exhibited better discriminative ability for predicting positive biopsies and high-grade disease (the area under the curve was 0.831 and 0.852,respectively,P<0.01 for both).Decision curve analysis also suggested the favourable clinical utility of the ERSPC calculator in the validation dataset.Both prediction models demonstrated miscalibration:the risk of prostate cancer and high-grade disease was overestimated by approximately 20% for a wide range of predicted probabilities.In conclusion,the ERSPC risk calculator outperformed both the PCPT model and the PSA threshold of 4 ng ml-1 in predicting prostate cancer and high-grade disease in Chinese patients.However,the prediction tools derived from Western men significantly overestimated the probability of prostate cancer and high-grade disease compared to the outcomes of biopsies in a Chinese cohort.

  14. Concise calculation of the scaling function, exponents, and probability functional of the Edwards-Wilkinson equation with correlated noise

    International Nuclear Information System (INIS)

    The linear Langevin equation proposed by Edwards and Wilkinson [Proc. R. Soc. London A 381, 17 (1982)] is solved in closed form for noise of arbitrary space and time correlation. Furthermore, the temporal development of the full probability functional describing the height fluctuations is derived exactly, exhibiting an interesting evolution between two distinct Gaussian forms. We determine explicitly the dynamic scaling function for the interfacial width for any given initial condition, isolate the early-time behavior, and discover an invariance that was unsuspected in this problem of arbitrary spatiotemporal noise

  15. Calculating vibrational spectra without determining excited eigenstates: Solving the complex linear equations of damped response theory for vibrational configuration interaction and vibrational coupled cluster states.

    Science.gov (United States)

    Godtliebsen, Ian H; Christiansen, Ove

    2015-10-01

    It is demonstrated how vibrational IR and Raman spectra can be calculated from damped response functions using anharmonic vibrational wave function calculations, without determining the potentially very many eigenstates of the system. We present an implementation for vibrational configuration interaction and vibrational coupled cluster, and describe how the complex equations can be solved using iterative techniques employing only real trial vectors and real matrix-vector transformations. Using this algorithm, arbitrary frequency intervals can be scanned independent of the number of excited states. Sample calculations are presented for the IR-spectrum of water, Raman spectra of pyridine and a pyridine-silver complex, as well as for the infra-red spectrum of oxazole, and vibrational corrections to the polarizability of formaldehyde. PMID:26450293

  16. Precision therapy for lung cancer : Image processing and dose calculation in stereotactic body radiotherapy

    International Nuclear Information System (INIS)

    Stereotactic body radiotherapy (SBRT) is an effective technique in lung cancer treatment and several prerequisites are essential in order to achieve good local control. These include precise imaging of the lesion before irradiation and accurate dose calculation to account for density heterogeneities in lung tissue. Both aspects were investigated within the framework of the thesis: a new approach in imaging with a conventional electronic portal imaging device (EPID) was investigated and the performance and limits of a new Monte Carlo (MC) calculation algorithm commercially available were studied. More specifically, digitally reconstructed radiographs (DRR) of lung lesions were compared with MV portal images in a feasibility study to assess any displacement of the tumour. The precision of displacement results of three registration algorithms was tested when compared to a projection image of the tumour. The various algorithms were applied to test images, a lung simulation phantom and finally to patient data including 38 tumours and images of 113 fractions. Image guidance results of tested registration algorithms proved the accuracy in the lung phantom study whereas clinical patient data had successful registrations in about 59% of anterior-posterior (AP) and 46% of lateral projections, respectively. Excluding real patient data with a clinical target volume smaller than 10 cm3, successful registrations occurred in 90% of AP and 50% lateral projections. With respect to dose calculation accuracy, experimental verification of a commercial Monte Carlo-based planning system was performed for high-energy photon beams. Several simple and complex treatment cases were calculated and compared with measurements in different phantom types. Besides ion chamber measurements, radiochromic films were irradiated to gain 2D dose distributions which were compared to calculations applying the gamma-index criterion. The dose calculation accuracy of the Monte Carlo algorithm implemented in

  17. Accurate calculation of the x-ray absorption spectrum of water via the GW/Bethe-Salpeter equation

    Science.gov (United States)

    Gilmore, Keith; Vinson, John; Kas, Josh; Vila, Fernando; Rehr, John

    2014-03-01

    We calculate x-ray absorption spectra (XAS) of water within the OCEAN code, which combines plane-wave, pseudopotential electronic structure, PAW transition elements, GW self-energy corrections, and the NIST BSE solver. Due to the computational demands of this approach, our initial XAS calculations were limited to 17 molecule super cells. This lead to unphysical, size dependent effects in the calculated spectra. To treat larger systems, we extended the OCEAN interface to support well-parallelized codes such as QuantumESPRESSO. We also implemented an efficient interpolation scheme of Shirley. We applied this large-scale GW/BSE approach to 64 molecule unit cell structures of water obtained from classical DFT/MD and PIMD simulations. In concurrence with previous work, we find the calculated spectrum both qualitatively and quantitatively reproduces the experimental features. The agreement implies that structures based on PIMD, which are similar to the traditional distorted tetrahedral view, are consistent with experimental observations. Supported by the DOE CMCSN through DOE award DE-SC0005180 (Princeton University) and in part by DOE Grant No. DE-FG03-97ER45623 (JJR) with computer support from NERSC.

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

    Energy Technology Data Exchange (ETDEWEB)

    Han Tao; Followill, David; Repchak, Roman; Molineu, Andrea; Howell, Rebecca; Salehpour, Mohammad [Department of Radiation Physics, University of Texas MD Anderson Cancer Center, Houston, Texas 77030 (United States); Mikell, Justin [Department of Radiation Physics, the University of Texas MD Anderson Cancer Center, Houston, Texas 77030 (United States); University of Texas Graduate School of Biomedical Sciences at Houston, Houston, Texas 77030 (United States); Mourtada, Firas [Department of Radiation Physics, the University of Texas MD Anderson Cancer Center, Houston, Texas 77030 (United States); Department of Radiation Oncology, Christiana Care Health System, Newark, Delaware 19713 (United States)

    2013-05-15

    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{sub m,m}) and dose-to-water in medium (D{sub 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{sub m,m} and D{sub 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{sub Dm,m}, and AXB{sub 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

  19. Constraints on Skyrme Equations of State from Properties of Doubly Magic Nuclei and Ab-Initio Calculations of Low-Density Neutron Matter

    CERN Document Server

    Brown, B Alex

    2013-01-01

    We use properties of doubly-magic nuclei and ab-initio calculations of low-density neutron matter to constrain Skyrme equations of state for neutron-rich conditions. All of these properties are consistent with a Skyrme functional form and a neutron-matter equation of state that depends on three parameters. With a reasonable range for the neutron-matter effective mass, the values of the two other Skyrme parameters are well constrained. This leads to predictions for other quantities. The neutron skins for $^{208}$Pb and $^{48}$Ca are predicted to be 0.182(10) fm and 0.173(5) fm, respectively. Other results including the dipole polarizability are discussed.

  20. First-principles calculations for $c$-coefficients of the isobaric mass multiplet equation in the $1p0f$ shell

    CERN Document Server

    Ormand, W E; Jensen, M Hjorth

    2016-01-01

    We present the first calculations for the $c$-coefficients of the isobaric mass multiplet equation (IMME) for nuclei from $A=42$ to $A=54$ based on input from several realistic nucleon-nucleon interactions. We show that there is clear dependence on the short-ranged charge-symmetry breaking (CSB) part of the strong interaction. There is a significant variation in the CSB part between the commonly used CD-Bonn, N$^3$LO and Argonne V18 nucleon-nucleon interactions. All of them give a CSB contribution that is too large when compared to experiment.

  1. Calculation of the Aqueous Thermodynamic Properties of Citric Acid Cycle Intermediates and Precursors and the Estimation of High Temperature and Pressure Equation of State Parameters

    Directory of Open Access Journals (Sweden)

    Mitchell Schulte

    2009-06-01

    Full Text Available The citric acid cycle (CAC is the central pathway of energy transfer for many organisms, and understanding the origin of this pathway may provide insight into the origins of metabolism. In order to assess the thermodynamics of this key pathway for microorganisms that inhabit a wide variety of environments, especially those found in high temperature environments, we have calculated the properties and parameters for the revised Helgeson-Kirkham-Flowers equation of state for the major components of the CAC. While a significant amount of data is not available for many of the constituents of this fundamental pathway, methods exist that allow estimation of these missing data.

  2. Following electron impact excitations of single Os, Pt, Hg, Pb and Po atom L subshells ionization cross section calculations by using Lotz's equation

    Science.gov (United States)

    Aydinol, M.; Aydeniz, D.

    2016-03-01

    L shell ionization cross section and Li subshells ionization cross sections of Os, Pt, Hg, Pb, Po atoms calculated. For each atom, ten different electron impacty energy values Eoi used. Calculations carried out by using nonrelativistic Lotz equation in Matlab. Ionization cross section values obtained for Eoi values in the energy range of ELi ≤Eoi≤4ELi for each atom. Starting allmost from Eoi = ELi (i = 1,2,3) values of the each subshell ionization threshold energy, ionization cross section are increasing rapidly with Eoi. For a fixed Eoi = 3. ELi values, while Z increases from Z = 76 to Z = 84, ionization cross section are decrease. These results help to understand some results which obtained from other electron-sigle atom impact studies on σLi subshells.

  3. 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

  4. Coupled third-order simplified spherical harmonics and diffusion equation-based fluorescence tomographic imaging of liver cancer

    Science.gov (United States)

    Chen, Xueli; Sun, Fangfang; Yang, Defu; Liang, Jimin

    2015-09-01

    For fluorescence tomographic imaging of small animals, the liver is usually regarded as a low-scattering tissue and is surrounded by adipose, kidneys, and heart, all of which have a high scattering property. This leads to a breakdown of the diffusion equation (DE)-based reconstruction method as well as a heavy computational burden for the simplified spherical harmonics equation (SPN). Coupling the SPN and DE provides a perfect balance between the imaging accuracy and computational burden. The coupled third-order SPN and DE (CSDE)-based reconstruction method is developed for fluorescence tomographic imaging. This is achieved by doubly using the CSDE for the excitation and emission processes of the fluorescence propagation. At the same time, the finite-element method and hybrid multilevel regularization strategy are incorporated in inverse reconstruction. The CSDE-based reconstruction method is first demonstrated with a digital mouse-based liver cancer simulation, which reveals superior performance compared with the SPN and DE-based methods. It is more accurate than the DE-based method and has lesser computational burden than the SPN-based method. The feasibility of the proposed approach in applications of in vivo studies is also illustrated with a liver cancer mouse-based in situ experiment, revealing its potential application in whole-body imaging of small animals.

  5. 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)

    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 99mTc-MAG3 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 m2)=(-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)

  6. Phonon-limited resistivity of graphene by first-principles calculations: Electron-phonon interactions, strain-induced gauge field, and Boltzmann equation

    Science.gov (United States)

    Sohier, Thibault; Calandra, Matteo; Park, Cheol-Hwan; Bonini, Nicola; Marzari, Nicola; Mauri, Francesco

    2014-09-01

    We use first-principles calculations, at the density-functional-theory (DFT) and GW levels, to study both the electron-phonon interaction for acoustic phonons and the "synthetic" vector potential induced by a strain deformation (responsible for an effective magnetic field in case of a nonuniform strain). In particular, the interactions between electrons and acoustic phonon modes, the so-called gauge-field and deformation potential, are calculated at the DFT level in the framework of linear response. The zero-momentum limit of acoustic phonons is interpreted as a strain of the crystal unit cell, allowing the calculation of the acoustic gauge-field parameter (synthetic vector potential) within the GW approximation as well. We find that using an accurate model for the polarizations of the acoustic phonon modes is crucial to obtain correct numerical results. Similarly, in the presence of a strain deformation, the relaxation of atomic internal coordinates cannot be neglected. The role of electronic screening on the electron-phonon matrix elements is carefully investigated. We then solve the Boltzmann equation semianalytically in graphene, including both acoustic and optical phonon scattering. We show that, in the Bloch-Grüneisen and equipartition regimes, the electronic transport is mainly ruled by the unscreened acoustic gauge field, while the contribution due to the deformation potential is negligible and strongly screened. We show that the contribution of acoustic phonons to resistivity is doping and substrate independent, in agreement with experimental observations. The first-principles calculations, even at the GW level, underestimate this contribution to resistivity by ≈30%. At high temperature (T >270 K), the calculated resistivity underestimates the experimental one more severely, the underestimation being larger at lower doping. We show that, besides remote phonon scattering, a possible explanation for this disagreement is the electron-electron interaction

  7. Impacts of equations of state (EOS) and impurities on the volume calculation of CO2 mixtures in the applications of CO2 capture and storage (CCS) processes

    International Nuclear Information System (INIS)

    Volume property is the necessary thermodynamic property in the design and operation of the CO2 capture and storage system (CCS). Because of their simple structures, cubic equations of state (EOS) are preferable to be applied in predicting volumes for engineering applications. This paper evaluates the reliabilities of seven cubic EOS, including PR, PT, RK, SRK, MPR, MSRK and ISRK for predicting volumes of binary CO2 mixtures containing CH4, H2S, SO2, Ar and N2, based on the comparisons with the collected experimental data. Results show that for calculations on the volume properties of binary CO2 mixtures, PR and PT are generally superior to others for all of the studied mixtures. In addition, it was found that the binary interaction parameter has clear effects on the calculating accuracy of an EOS in the volume calculations of CO2 mixtures. In order to improve the accuracy, kij was calibrated for all of the EOS regarding the gas and liquid phases of all the studied binary CO2 mixtures, respectively.

  8. 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)

    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

  9. A new equation for calculation of static loss of drilling fluid%一种新的钻井液静失水量方程

    Institute of Scientific and Technical Information of China (English)

    许晓琳; 乌效鸣; 杜晶

    2013-01-01

    It is found out that the viscosity of the remaining drilling fluid is higher than before the API loss test was taken. To explain this phenomenon, the paper presents a different opinion about the filtration mode used in the derivation of equation for calculation of static loss of drilling fluid, and derived a new equation based on a new fil-tration mode, which can explain the phenomenon. According to this new equation, twice of the result of 7.5 min test can replace that of the 30 min test in the API loss test.%实验室测试钻井液的 API 失水量结束后,仪器内剩余钻井液的粘度比测试前有所增大。为了解释这一现象,对原钻井液静失水量方程推导中所采用的渗滤模式提出了不同看法,以一种不同的渗滤模式为基础提出了新的钻井液静失水量方程,此方程可以解释这一现象。依照此方程,实验室测试API失水量时仍然可用7.5 min失水量的测试结果乘以2得到的数值代替30 min失水量的测试结果。

  10. Numerical solution to the Boltzmann equation for use in calculating pumping rates in a CO sub 2 discharge laser. Master's thesis

    Energy Technology Data Exchange (ETDEWEB)

    Honey, D.A.

    1989-12-01

    The collisional Boltzmann equation was solved numerically to obtain excitation rates for use in a CO{sub 2} laser design program. The program was written in Microsoft QuickBasic for use on the IBM Personal Computer or equivalent. Program validation involved comparisons of computed transport coefficients with experimental data and previous theoretical work. Four different numerical algorithms were evaluated in terms of accuracy and efficiency. L-U decomposition was identified as the preferred approach. The calculated transport coefficients were found to agree with empirical data within one to five percent. The program was integrated into a CO{sub 2} laser design program. Studies were then performed to evaluate the effects on predicted laser output power and energy density as parameters affecting electron kinetics were changed. Plotting routines were written for both programs.

  11. A calculation of the distribution function of ICRF heated plasma in LHD using a bounce-averaged Fokker-Planck equation

    International Nuclear Information System (INIS)

    High-energy ions produced by the ion cyclotron range of frequency (ICRF) heating were observed on the Large Helical Device (LHD). The dependence of the count number of high-energy particles on pitch-angle was studied using the time-of-flight neutral particle analyzer (TOF-NPA) in the LHD. The angle of the line-of-sight was scanned at five successive discharges sustained by ICRF heating only. A unique 'rabbit-ear' structure with a large population of high-energy ions at a certain pitch-angle, was observed. A bounce-averaged Fokker-Planck equation was applied to the LHD plasma in the helical magnetic configuration in order to explain the structure of the measured distribution function. The calculation successfully reproduced the 'rabbit-ear' structure. (author)

  12. Modeling the material strength and equations of state of beta-HMX from both first-principles calculations and molecular dynamics simulations

    Science.gov (United States)

    Peng, Qing; Wang, Guangyu; Liu, G. R.; de, Suvranu

    2015-06-01

    We investigate the elastic constants and equations of state (EOS) of the β-polymorph of cyclotetramethylene tetranitramine (HMX) energetic molecular crystal using density functional theory (DFT) calculations. The combination of vdW-DF2 van der Waals functionals and PBE exchange-correlation functionals gives optimized results. The DFT results are used to optimize the Reactive Force Field (ReaxFF). The material strength and EOS of beta-HMX at finite temperatures are then predicted from ReaxFF molecular dynamics simulations. Our results suggest that the optimized ReaxFF predicts the mechanics and EOS of beta-HMX well. The authors would like to acknowledge the generous financial support from the Defense Threat Reduction Agency (DTRA) Grant # HDTRA1-13-1-0025.

  13. Application Monte Carlo code calculates dose distribution of the emitted photon beams from linear accelerator in case radiotherapy lung cancer

    International Nuclear Information System (INIS)

    The dose distribution calculation is one of major steps in cancer radiotherapy. This paper applies Monte Carlo code, MCNP5, in simulation 15 MV photon beams from linear accelerator of General Hospital of Kien Giang in a case treatment of lung cancer. The settings for beam direction, field size and isocenter position used in MCNP5 must be the same as in treatment plan at hospital to ensure the results from MCNP5 are accurate. We also built a program CODIM by using MATLAB® programming software. This program is used to construct digital voxel phantoms from lung CT images obtained from cancer treatment cases at Kien Giang hospital and then simulate the delivered dose of linac in these phantoms by using MCNP5 simulation code. The results show that there is a difference of 5% in comparison to Prowess Panther program - a semi-empirical simulation program which is being used for treatment planning in Kien Giang hospital. (author)

  14. Delivered dose to scrotum in rectal cancer radiotherapy by thermoluminescence dosimetry comparing to dose calculated by planning software

    Directory of Open Access Journals (Sweden)

    Peiman Haddad

    2014-02-01

    Conclusion: In this study, the mean testis dose of radiation was 3.77 Gy, similar to the dose calculated by the planning software (4.11 Gy. This dose could be significantly harmful for spermatogenesis, though low doses of scattered radiation to the testis in fractionated radiotherapy might be followed with better recovery. Based on above findings, careful attention to testicular dose in radiotherapy of rectal cancer for the males desiring continued fertility seems to be required.

  15. On the Dirichlet boundary controllability of the one-dimensional heat equation: semi-analytical calculations and ill-posedness degree

    International Nuclear Information System (INIS)

    The ill-posedness degree for the controllability of the one-dimensional heat equation by a Dirichlet boundary control is the purpose of this work. This problem is severely (or exponentially) ill-posed. We intend to shed more light on this assertion and the underlying mathematics. We start by discussing the framework liable to fit an efficient numerical implementation without introducing further complications into the theoretical analysis. Afterward we expose the Fourier calculations that transform the ill-posedness issue to the one related to linear algebra. This consists of investigating the singular values of some infinite structured matrices that are obtained as sums of Cauchy matrices. Utilising the Gershgorin–Hadamard theorem and the Collatz–Wielandt formula, we are able to provide the lower and upper bounds for the largest singular value of these matrices. After checking whether they are also solutions of some symmetric Lyapunov (or Sylvester) equations with a very low displacement rank, we use an estimate that improves Penzl's former result to bound the ratio's smaller/largest singular values of these matrices. Accordingly, the controllability problem is confirmed to be severely ill-posed. The bounds proved here will be supported by computations made using Matlab procedures. At last, the well-known explicit inverse of Cauchy-type matrices allows us to provide a formal exponential series representation of the Dirichlet control in a long horizon controllability. That series has to be checked afterward to discover whether it is convergent or not and to find out if the desired state can be reached. Here again, some examples ran within Matlab will be discussed and commented upon

  16. Practically acquired and modified cone-beam computed tomography images for accurate dose calculation in head and neck cancer

    International Nuclear Information System (INIS)

    On-line cone-beam computed tomography (CBCT) may be used to reconstruct the dose for geometric changes of patients and tumors during radiotherapy course. This study is to establish a practical method to modify the CBCT for accurate dose calculation in head and neck cancer. Fan-beam CT (FBCT) and Elekta's CBCT were used to acquire images. The CT numbers for different materials on CBCT were mathematically modified to match them with FBCT. Three phantoms were scanned by FBCT and CBCT for image uniformity, spatial resolution, and CT numbers, and to compare the dose distribution from orthogonal beams. A Rando phantom was scanned and planned with intensity-modulated radiation therapy (IMRT). Finally, two nasopharyngeal cancer patients treated with IMRT had their CBCT image sets calculated for dose comparison. With 360 acquisition of CBCT and high-resolution reconstruction, the uniformity of CT number distribution was improved and the otherwise large variations for background and high-density materials were reduced significantly. The dose difference between FBCT and CBCT was < 2% in phantoms. In the Rando phantom and the patients, the dose-volume histograms were similar. The corresponding isodose curves covering ≥ 90% of prescribed dose on FBCT and CBCT were close to each other (within 2 mm). Most dosimetric differences were from the setup errors related to the interval changes in body shape and tumor response. The specific CBCT acquisition, reconstruction, and CT number modification can generate accurate dose calculation for the potential use in adaptive radiotherapy.

  17. Practically acquired and modified cone-beam computed tomography images for accurate dose calculation in head and neck cancer

    Energy Technology Data Exchange (ETDEWEB)

    Hu, Chih-Chung [National Taiwan Univ. Hospital and College of Medicine, Taipei (China). Division of Radiation Oncology; Yuanpei Univ., Hsinchu (China). Dept. of Radiological Technology; Huang, Wen-Tao [Yuanpei Univ., Hsinchu (China). Dept. of Radiological Technology; Tsai, Chiao-Ling; Chao, Hsiao-Ling; Huang, Guo-Ming; Wang, Chun-Wei [National Taiwan Univ. Hospital and College of Medicine, Taipei (China). Division of Radiation Oncology; Wu, Jian-Kuen [National Taiwan Univ. Hospital and College of Medicine, Taipei (China). Division of Radiation Oncology; National Taiwan Normal Univ., Taipei (China). Inst. of Electro-Optical Science and Technology; Wu, Chien-Jang [National Taiwan Normal Univ., Taipei (China). Inst. of Electro-Optical Science and Technology; Cheng, Jason Chia-Hsien [National Taiwan Univ. Hospital and College of Medicine, Taipei (China). Division of Radiation Oncology; National Taiwan Univ. Taipei (China). Graduate Inst. of Oncology; National Taiwan Univ. Taipei (China). Graduate Inst. of Clinical Medicine; National Taiwan Univ. Taipei (China). Graduate Inst. of Biomedical Electronics and Bioinformatics

    2011-10-15

    On-line cone-beam computed tomography (CBCT) may be used to reconstruct the dose for geometric changes of patients and tumors during radiotherapy course. This study is to establish a practical method to modify the CBCT for accurate dose calculation in head and neck cancer. Fan-beam CT (FBCT) and Elekta's CBCT were used to acquire images. The CT numbers for different materials on CBCT were mathematically modified to match them with FBCT. Three phantoms were scanned by FBCT and CBCT for image uniformity, spatial resolution, and CT numbers, and to compare the dose distribution from orthogonal beams. A Rando phantom was scanned and planned with intensity-modulated radiation therapy (IMRT). Finally, two nasopharyngeal cancer patients treated with IMRT had their CBCT image sets calculated for dose comparison. With 360 acquisition of CBCT and high-resolution reconstruction, the uniformity of CT number distribution was improved and the otherwise large variations for background and high-density materials were reduced significantly. The dose difference between FBCT and CBCT was < 2% in phantoms. In the Rando phantom and the patients, the dose-volume histograms were similar. The corresponding isodose curves covering {>=} 90% of prescribed dose on FBCT and CBCT were close to each other (within 2 mm). Most dosimetric differences were from the setup errors related to the interval changes in body shape and tumor response. The specific CBCT acquisition, reconstruction, and CT number modification can generate accurate dose calculation for the potential use in adaptive radiotherapy.

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

    OpenAIRE

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

    2014-01-01

    Background 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 alg...

  19. Examinations on Applications of Manual Calculation Programs on Lung Cancer Radiation Therapy Using Analytical Anisotropic Algorithm

    International Nuclear Information System (INIS)

    There was a problem with using MU verification programs for the reasons that there were errors of MU when using MU verification programs based on Pencil Beam Convolution (PBC) Algorithm with radiation treatment plans around lung using Analytical Anisotropic Algorithm (AAA). On this study, we studied the methods that can verify the calculated treatment plans using AAA. Using Eclipse treatment planning system (Version 8.9, Varian, USA), for each 57 fields of 7 cases of Lung Stereotactic Body Radiation Therapy (SBRT), we have calculated using PBC and AAA with dose calculation algorithm. By developing MU of established plans, we compared and analyzed with MU of manual calculation programs. We have analyzed relationship between errors and 4 variables such as field size, lung path distance of radiation, Tumor path distance of radiation, effective depth that can affect on errors created from PBC algorithm and AAA using commonly used programs. Errors of PBC algorithm have showned 0.2±1.0% and errors of AAA have showned 3.5±2.8%. Moreover, as a result of analyzing 4 variables that can affect on errors, relationship in errors between lung path distance and MU, connection coefficient 0.648 (P=0.000) has been increased and we could calculate MU correction factor that is A.E=L.P 0.00903+0.02048 and as a result of replying for manual calculation program, errors of 3.5±2.8% before the application has been decreased within 0.4±2.0%. On this study, we have learned that errors from manual calculation program have been increased as lung path distance of radiation increases and we could verified MU of AAA with a simple method that is called MU correction factor.

  20. 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

  1. Klein-Gordon and square-root operator equations for two-spinors and scalars: perturbation calculations for hydrogen-like systems

    OpenAIRE

    Gleim, Tobias

    2006-01-01

    There exists a Klein-Gordon-like equation for a spin-1/2 particle in an electromagnetic field with 2-spinors as wave functions that is a direct consequence of the corresponding Dirac equation. Thus, it reproduces the same binding energies for an electron in a hydrogen atom as the Dirac equation. There is also a square-root equation for 2-spinors which can give the same binding energies up to the forth order of the fine structure constant, inclusively, what will be shown by means of a comparis...

  2. Evaluation of regional work from ECG-gated SPECT images through solution of equations of continuity for fluids–mechanical cardiac work calculated using thin wall model

    International Nuclear Information System (INIS)

    Regional contraction work (RCW) of left ventricle (LV) was evaluated from cardiac perfusion images of ECG-gated single photon emission computed tomography (ECG-SPECT). The mechanical work was computed as a product of force and displaced distance. Force was determined from Laplace's law under a rectangle pressure. Deformation of wireframe representing LV was calculated from equations of continuity for two-dimensional fluids. Experiments were performed with homemade life-sized cardiac models. Total contraction work (TCW) and stroke work (SW) were 524.0 ± 166.1 mJ/beat and 709.8 ± 169.5 mJ/beat, respectively, in normal subjects (n = 23). Moderate correlation was seen between TCW and SW (y = −43.4 + 0.779 x, r = 0.815). The regional contraction amplitude (RCA), synchronous contraction index and RCW were 35.4 ± 3.5%, 95.4 ± 3.1% and 5.58 ± 0.97 mJ cm−2/beat in normal subjects, whereas those in patients with decreased ejection raction (EF) ≤ 30% (n = 6) were 19.6 ± 7.7%, 64.4 ± 32.2% and 2.58 ± 0.82 mJ cm−2/beat (p < 0.0001, Student's t-test). There was a poor correlation between RCW and RCA (y = 1.648 ± 0.116 x, r = 0.501) in normal subjects, suggesting that it might not be suitable to use RCA as an alternative to evaluate RCW. (paper)

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

    International Nuclear Information System (INIS)

    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

  4. Phase Equilibrium Calculation of Mixtures:Use of the SAFT-BACK Equation of State for Binary Systems under Elevated Pressure

    Institute of Scientific and Technical Information of China (English)

    张志禹; 胡中桥; 杨基础; 李以圭

    2002-01-01

    The statistical associating fluid theory (SAFT)-Boublík-Alder-Chen- Kreglewshi(BACK) equation of state is employed to correlate vapor-liquid equilibria of 16 binary mixtures composed of supercritical fluids with other fluids at elevated pressures. The van der Waals mixing rules are used and the binary parameters are adjusted to experimental data. The SAFT-BACK equation of state provides a better correlation of vapor-liquid equilibrium than the original BACK equation. Consequently, the binary parameters computed from the data sets can be used to accurately predict the saturated densities of the vapor and liquid phases.

  5. Boron neutron capture therapy design calculation of a 3H(p,n reaction based BSA for brain cancer setup

    Directory of Open Access Journals (Sweden)

    Bassem Elshahat

    2015-09-01

    Full Text Available Purpose: Boron neutron capture therapy (BNCT is a promising technique for the treatment of malignant disease targeting organs of the human body. Monte Carlo simulations were carried out to calculate optimum design parameters of an accelerator based beam shaping assembly (BSA for BNCT of brain cancer setup.Methods: Epithermal beam of neutrons were obtained through moderation of fast neutrons from 3H(p,n reaction in a high density polyethylene moderator and a graphite reflector. The dimensions of the moderator and the reflector were optimized through optimization of epithermal / fast neutron intensity ratio as a function of geometric parameters of the setup. Results: The results of our calculation showed the capability of our setup to treat the tumor within 4 cm of the head surface. The calculated peak therapeutic ratio for the setup was found to be 2.15. Conclusion: With further improvement in the polyethylene moderator design and brain phantom irradiation arrangement, the setup capabilities can be improved to reach further deep-seated tumor.

  6. Recommendations for dose calculations of lung cancer treatment plans treated with stereotactic ablative body radiotherapy (SABR)

    International Nuclear Information System (INIS)

    The purpose of this study was to systematically evaluate dose distributions computed with 5 different dose algorithms for patients with lung cancers treated using stereotactic ablative body radiotherapy (SABR). Treatment plans for 133 lung cancer patients, initially computed with a 1D-pencil beam (equivalent-path-length, EPL-1D) algorithm, were recalculated with 4 other algorithms commissioned for treatment planning, including 3-D pencil-beam (EPL-3D), anisotropic analytical algorithm (AAA), collapsed cone convolution superposition (CCC), and Monte Carlo (MC). The plan prescription dose was 48 Gy in 4 fractions normalized to the 95% isodose line. Tumors were classified according to location: peripheral tumors surrounded by lung (lung-island, N=39), peripheral tumors attached to the rib-cage or chest wall (lung-wall, N=44), and centrally-located tumors (lung-central, N=50). Relative to the EPL-1D algorithm, PTV D95 and mean dose values computed with the other 4 algorithms were lowest for 'lung-island' tumors with smallest field sizes (3-5 cm). On the other hand, the smallest differences were noted for lung-central tumors treated with largest field widths (7-10 cm). Amongst all locations, dose distribution differences were most strongly correlated with tumor size for lung-island tumors. For most cases, convolution/superposition and MC algorithms were in good agreement. Mean lung dose (MLD) values computed with the EPL-1D algorithm were highly correlated with that of the other algorithms (correlation coefficient =0.99). The MLD values were found to be ∼10% lower for small lung-island tumors with the model-based (conv/superposition and MC) vs. the correction-based (pencil-beam) algorithms with the model-based algorithms predicting greater low dose spread within the lungs. This study suggests that pencil beam algorithms should be avoided for lung SABR planning. For the most challenging cases, small tumors surrounded entirely by lung tissue (lung-island type

  7. Recommendations for dose calculations of lung cancer treatment plans treated with stereotactic ablative body radiotherapy (SABR)

    Science.gov (United States)

    Devpura, S.; Siddiqui, M. S.; Chen, D.; Liu, D.; Li, H.; Kumar, S.; Gordon, J.; Ajlouni, M.; Movsas, B.; Chetty, I. J.

    2014-03-01

    The purpose of this study was to systematically evaluate dose distributions computed with 5 different dose algorithms for patients with lung cancers treated using stereotactic ablative body radiotherapy (SABR). Treatment plans for 133 lung cancer patients, initially computed with a 1D-pencil beam (equivalent-path-length, EPL-1D) algorithm, were recalculated with 4 other algorithms commissioned for treatment planning, including 3-D pencil-beam (EPL-3D), anisotropic analytical algorithm (AAA), collapsed cone convolution superposition (CCC), and Monte Carlo (MC). The plan prescription dose was 48 Gy in 4 fractions normalized to the 95% isodose line. Tumors were classified according to location: peripheral tumors surrounded by lung (lung-island, N=39), peripheral tumors attached to the rib-cage or chest wall (lung-wall, N=44), and centrally-located tumors (lung-central, N=50). Relative to the EPL-1D algorithm, PTV D95 and mean dose values computed with the other 4 algorithms were lowest for "lung-island" tumors with smallest field sizes (3-5 cm). On the other hand, the smallest differences were noted for lung-central tumors treated with largest field widths (7-10 cm). Amongst all locations, dose distribution differences were most strongly correlated with tumor size for lung-island tumors. For most cases, convolution/superposition and MC algorithms were in good agreement. Mean lung dose (MLD) values computed with the EPL-1D algorithm were highly correlated with that of the other algorithms (correlation coefficient =0.99). The MLD values were found to be ~10% lower for small lung-island tumors with the model-based (conv/superposition and MC) vs. the correction-based (pencil-beam) algorithms with the model-based algorithms predicting greater low dose spread within the lungs. This study suggests that pencil beam algorithms should be avoided for lung SABR planning. For the most challenging cases, small tumors surrounded entirely by lung tissue (lung-island type), a Monte

  8. 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.

  9. Anti-cancer properties of green Tea Probed viaquantum mechanics calculations

    Directory of Open Access Journals (Sweden)

    Azin Chitsazan

    2015-03-01

    Full Text Available 10.13005/ojc/310147Tea, from the plant camellia sinensis, is consumed in different parts of the world as green, black or oolong tea. Among all of these, however, the most significant effects on human health have been observed with the consumption of green tea. Green tea contains polyphenols, which include flavanols, flavandiols, flavonoids, and phenolic acids. Most of the green tea polyphenols (GTPs are flavonols, commonly known as catechins. There are four kinds of catechins mainly find in green tea: epicatechin, epigallocatechin, epicatechin-3-gallate, and EGCG. Green tea catechins have demonstrated significant antioxidant, anticarcinogenic, anti-inflammatory, thermogenic, probiotic, and antimicrobial properties in numerous human, animal, and in vitro studies. In the present study, four type catechins of green tea were studied. For each catechin ab initio method was employed for calculations and related parameters were computed.

  10. Critical Appraisal of Acuros XB and Anisotropic Analytic Algorithm Dose Calculation in Advanced Non-Small-Cell Lung Cancer Treatments

    Energy Technology Data Exchange (ETDEWEB)

    Fogliata, Antonella, E-mail: afc@iosi.ch [Medical Physics Unit, Oncology Institute of Southern Switzerland, Bellinzona (Switzerland); Nicolini, Giorgia; Clivio, Alessandro; Vanetti, Eugenio; Cozzi, Luca [Medical Physics Unit, Oncology Institute of Southern Switzerland, Bellinzona (Switzerland)

    2012-08-01

    Purpose: To assess the clinical impact of the Acuros XB algorithm (implemented in the Varian Eclipse treatment-planning system) in non-small-cell lung cancer (NSCLC) cases. Methods and Materials: A CT dataset of 10 patients presenting with advanced NSCLC was selected and contoured for planning target volume, lungs, heart, and spinal cord. Plans were created for 6-MV and 15-MV beams using three-dimensional conformal therapy, intensity-modulated therapy, and volumetric modulated arc therapy with RapidArc. Calculations were performed with Acuros XB and the Anisotropic Analytical Algorithm. To distinguish between differences coming from the different heterogeneity management and those coming from the algorithm and its implementation, all the plans were recalculated assigning Hounsfield Unit (HU) = 0 (Water) to the CT dataset. Results: Differences in dose distributions between the two algorithms calculated in Water were <0.5%. This suggests that the differences in the real CT dataset can be ascribed mainly to the different heterogeneity management, which is proven to be more accurate in the Acuros XB calculations. The planning target dose difference was stratified between the target in soft tissue, where the mean dose was found to be lower for Acuros XB, with a range of 0.4% {+-} 0.6% (intensity-modulated therapy, 6 MV) to 1.7% {+-} 0.2% (three-dimensional conformal therapy, 6 MV), and the target in lung tissue, where the mean dose was higher for 6 MV (from 0.2% {+-} 0.2% to 1.2% {+-} 0.5%) and lower for 15 MV (from 0.5% {+-} 0.5% to 2.0% {+-} 0.9%). Mean doses to organs at risk presented differences up to 3% of the mean structure dose in the worst case. No particular or systematic differences were found related to the various modalities. Calculation time ratios between calculation time for Acuros XB and the Anisotropic Analytical Algorithm were 7 for three-dimensional conformal therapy, 5 for intensity-modulated therapy, and 0.2 for volumetric modulated arc therapy

  11. Coefficients calculations of conversion of cancer risk for occupational exposure using Monte Carlo simulations in cardiac procedures of interventionist radiology

    International Nuclear Information System (INIS)

    Cardiac procedures are among the most common procedures in interventional radiology (IR), and can lead to high medical and occupational exposures, as in most cases are procedures complex and long lasting. In this work, conversion coefficients (CC) for the risk of cancer, normalized by kerma area product (KAP) to the patient, cardiologist and nurse were calculated using Monte Carlo simulation. The patient and the cardiologist were represented by anthropomorphic simulators MESH, and the nurse by anthropomorphic phantom FASH. Simulators were incorporated into the code of Monte Carlo MCNPX. Two scenarios were created: in the first (1), lead curtain and protective equipment suspended were not included, and in the second (2) these devices were inserted. The radiographic parameters employed in Monte Carlo simulations were: tube voltage of 60 kVp and 120 kVp; filtration of the beam and 3,5 mmAl beam area of 10 x 10 cm2. The average values of CCs to eight projections (in 10-4 / Gy.cm2 were 1,2 for the patient, 2,6E-03 (scenario 1) and 4,9E-04 (scenario 2) for cardiologist and 5,2E-04 (scenario 1) and 4,0E-04 (Scenario 2) to the nurse. The results show a significant reduction in CCs for professionals, when the lead curtain and protective equipment suspended are employed. The evaluation method used in this work can provide important information on the risk of cancer patient and professional, and thus improve the protection of workers in cardiac procedures of RI

  12. Influence of dose calculation algorithms on isotoxic dose-escalation of non-small cell lung cancer radiotherapy

    International Nuclear Information System (INIS)

    Background and purpose: A series of phase I/II clinical trials are being initiated in several UK centres to explore the use of dose-escalated schedules for the treatment of non-small cell lung cancer (NSCLC). Among them the IDEAL-CRT trial (ISRCTN12155469) will investigate the introduction of individualised 'isotoxic' treatment schedules based on the relative mean lung normalised total dose (rNTDmean), an estimator related to lung toxicity. Since treatment planning will be performed using different treatment planning systems (TPSs), for the quality assurance of the trial we have carried out work to quantify the influence of dose calculation algorithms based on the determination of rNTDmean and on the choice of individualised prescription doses. Material and methods: Twenty-five patient plans with stage I, II and III NSCLC were calculated, with the same prescription dose, using the Adaptive Convolve (AC) and Collapsed Cone (CC) algorithms of the Pinnacle TPS, the pencil beam convolution (PBC) and AAA algorithms of Eclipse, and the CC and pencil beam (PB) algorithms of Oncentra Masterplan (OMP). For the paired-lungs-GTV structure, dose-volume histograms were obtained and used to calculate the corresponding rNTDmean values and results obtained with the different algorithms were compared. Results: For most (19 out of 25) of the patients studied, no algorithm-to-algorithm differences were seen in dose prescription based on rNTDmean. For the other 6 patients differences were within 2.3 Gy, except in one case where the difference was 4 Gy. Conclusions: For the IDEAL-CRT trial no corrections need to be applied to the value of rNTDmean calculated using any of the more advanced convolution/superposition algorithms studied in this work. For the two pencil beam algorithms analysed, no correction is necessary for the data obtained with the Eclipse-PBC, while for OMP-PB data a small correction needs to be applied, by using a scaling factor, to make prescription doses consistent

  13. Calculation of geometric phases in electric dipole searches with trapped spin-1/2 particles based on direct solution of the Schr\\"odinger equation

    CERN Document Server

    Steyerl, A; Müller, G; Malik, S S; Desai, A M; Golub, R

    2014-01-01

    Pendlebury $\\textit{et al.}$ [Phys. Rev. A $\\textbf{70}$, 032102 (2004)] were the first to investigate the role of geometric phases in searches for an electric dipole moment of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in general fields and in bounded geometries. We solve the Schr\\"odinger equation directly for cylindrical trap geometry and obtain a full description of EDM-relevant spin behavior in general fields, including the short-time transients and vertical spin oscillation in the entire range of particle velocities. We apply this method to general macroscopic fields and to the field of a microscopic magnetic dipole.

  14. Calculation of geometric phases in electric dipole searches with trapped spin-1/2 particles based on direct solution of the Schrödinger equation

    Science.gov (United States)

    Steyerl, A.; Kaufman, C.; Müller, G.; Malik, S. S.; Desai, A. M.; Golub, R.

    2014-05-01

    Pendlebury etal . [Phys. Rev. A 70, 032102 (2004), 10.1103/PhysRevA.70.032102] were the first to investigate the role of geometric phases in searches for an electric dipole moment (EDM) of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in general fields and in bounded geometries. We solve the Schrödinger equation directly for cylindrical trap geometry and obtain a full description of EDM-relevant spin behavior in general fields, including the short-time transients and vertical spin oscillation in the entire range of particle velocities. We apply this method to general macroscopic fields and to the field of a microscopic magnetic dipole.

  15. Analysis of "solution effects" injury. Equations for calculating phase diagram information for the ternary systems NaCl-dimethylsulfoxide-water and NaCl-glycerol-water.

    OpenAIRE

    Fahy, G. M.

    1980-01-01

    Slowly frozen cells are said to be subject to solution effects injury. An understanding of the mechanism of solution effects injury depends upon an understanding of the compositional changes brought about in the extracellular solution during the freezing process. To facilitate analysis of the mechanisms of freezing injury during slow cooling, empirical equations have been developed which permit a description of these changes in composition for the NaCl-dimethylsulfoxide-water ternary system a...

  16. Calculation of geometric phases in electric dipole searches with trapped spin-1/2 particles based on direct solution of the Schr\\"odinger equation

    OpenAIRE

    Steyerl, A.; Kaufman, C.; Müller, G.; Malik, S. S.; Desai, A. M.; Golub, R.

    2014-01-01

    Pendlebury $\\textit{et al.}$ [Phys. Rev. A $\\textbf{70}$, 032102 (2004)] were the first to investigate the role of geometric phases in searches for an electric dipole moment (EDM) of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in gene...

  17. Monte-Carlo method for multiple parametric integrals calculation and solving of linear integral Fredholm equations of a second kind, with confidence regions in uniform norm

    OpenAIRE

    Ostrovsky, E.; Sirota, L

    2011-01-01

    In this article we offer some modification of Monte-Carlo method for multiple parametric integral computation and solving of a linear integral Fredholm equation of a second kind (well posed problem). We prove that the rate of convergence of offered method is optimal under natural conditions still in the uniform norm, and construct an asymptotical and non-asymptotical confidence region, again in the uniform norm.

  18. Semi-analytical calculations for parameters of boiling layer in isetropic expansion of warm dense matter with van der Waals equation of state

    OpenAIRE

    Borovikov, Dmitry; Iosilevskiy, Igor

    2012-01-01

    Features and parameters of \\boiling" liquid layer, which arises under conditions of isentropic expansion of warm dense matter (WDM), are stud- ied with the use of simplest van der Waals equation of state (EOS). Advan- tage of this EOS is possibility of demonstrable and semi-analytical descrip- tion of thermo- and hydrodynamics of the process. Idealized self-similar case of behavior of matter on interception of equilibrium (not metastable) isoentropic curve and boundary of gas-liquid coexisten...

  19. Eilenberger equation for rotating superfluid /sup 3/He and calculation of the upper critical angular velocity. cap omega. /sub c/2

    Energy Technology Data Exchange (ETDEWEB)

    Schopohl, N.

    1980-11-01

    On the basis of Gorkov's formulation of superconductivity theory, generalized Eilenberger equations are derived which apply to rotating superfluid /sup 3/He in the presence of a magnetic field h and finite superflow v. In analyogy to conventional type II superconductors, the possibility of vortex solutions in discussed. An implicit equation determining the upper critical angular velocity ..cap omega../sub c/2 as a function of temperature T, magnetic field h, and superflow v parallel to the rotation axis is-inferred from the linearized Eilenberger equations. In contrast to the case of slowly rotating /sup 3/He-A, the solution of the eigenvalue problem determining the order parameter ..delta.. near the the upper critical angular velocity admits no coreless vortex no coreless solutions. The space-dependent amplitude of the order parameter is analogous to Abrikosov's vortex array solution, while the spin-orbit part is given either by a polar-state type or an Anderson-Brinkman-Morel (ABM)-state-type eigensolution. Among the possible eigensolutions the polar-state type yields for vanishing superflow v the highest critical rotation frequency. For finite superflow v parallel to the rotation axis, however, the ABM-state-type solution is stabilized in comparison to the polar state for Vertical BarvVertical Bar> or approx. =0.2..pi..(Tc/sub c/0/T/sub F/)v/sub f/ at zero temperature.

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

    OpenAIRE

    Myint, P. C.; Hao, Y.; Firoozabadi, A.

    2015-01-01

    Thermodynamic property calculations of mixtures containing carbon dioxide (CO$_2$) 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 ...

  1. Deterministic methods for the relativistic Vlasov-Maxwell equations and the Van Allen belts dynamics; Methodes deterministes de resolution des equations de Vlasov-Maxwell relativistes en vue du calcul de la dynamique des ceintures de Van Allen

    Energy Technology Data Exchange (ETDEWEB)

    Le Bourdiec, S

    2007-03-15

    Artificial satellites operate in an hostile radiation environment, the Van Allen radiation belts, which partly condition their reliability and their lifespan. In order to protect them, it is necessary to characterize the dynamics of the energetic electrons trapped in these radiation belts. This dynamics is essentially determined by the interactions between the energetic electrons and the existing electromagnetic waves. This work consisted in designing a numerical scheme to solve the equations modelling these interactions: the relativistic Vlasov-Maxwell system of equations. Our choice was directed towards methods of direct integration. We propose three new spectral methods for the momentum discretization: a Galerkin method and two collocation methods. All of them are based on scaled Hermite functions. The scaling factor is chosen in order to obtain the proper velocity resolution. We present in this thesis the discretization of the one-dimensional Vlasov-Poisson system and the numerical results obtained. Then we study the possible extensions of the methods to the complete relativistic problem. In order to reduce the computing time, parallelization and optimization of the algorithms were carried out. Finally, we present 1Dx-3Dv (mono-dimensional for x and three-dimensional for velocity) computations of Weibel and whistler instabilities with one or two electrons species. (author)

  2. Amendment of Master equation and its calculation for degree distribution of the model BA%Master方程的修正及其对BA模型度分布的计算

    Institute of Scientific and Technical Information of China (English)

    王双进; 李凌云; 张建

    2011-01-01

    An amendment to the original Master equation was put forward, and a mechanism for node increases was introduced. The modified Master equation was of discreteness, which was more accurate, more efficient to calculate the evolution law of degree distribution of real complex network. The analysis formula of degree distribution of model BA and its calculation by the modified Master equation were discussed. From this. the logarithmic figure of degree distribution of model BA was gotlen. Then a compassion was made between the discrete Master equation and mean - field theory, and logarithmic figure was gotten, that of degree distribution of model BA wich two kinds calculative theory in the same coordinate system.%Master方程是计算无标度网络度分布演化规律的一种常用方法.提出了对原始的Master方程进行修正,加入了节点增长机制,修正后的Master方程具有离散性,能够更精确、更有效的计算真实复杂网络的度分布演化规律.用修正的Master方程分析BA模型度分布的解析武并计算,由此得到BA模型度分布对数图.把离散性的Master方程与连续性的平均场理论进行对比分析,并在同一坐标系下分别做出用两种理论计算的BA模型度分布的对数图.

  3. Calculation for Degree Distribution of the Model BA by Amendment of Master Equation%用修正后的主方程计算BA模型度分布的探讨

    Institute of Scientific and Technical Information of China (English)

    王双进; 李凌云; 李佳

    2011-01-01

    An amendment to the original Master equation and add a mechanism for node increases is be put for ward. The modified Master equation is of discreteness, which is more accurate, more efficient to calculate the evo lution law of degree distribution of real complex network. The analysis formula of degree distribution of model BA and its calculation by the modified Master equation is discussed. From this we get the logarithmic figure of degree distribution of model BA. Then we make a compassion between the discrete Master equation and mean-field theory, and get logarithmic figure of degree distribution of model BA with two kinds calculative theory in the same coor dinate system.%提出了对原始的Master方程进行修正,加入了节点增长机制,修正后的Master方程具有离散性,能够更精确、更有效地计算真实复杂网络的度分布演化规律.用修正的Master方程分析BA模型度分布的解析式并计算,由此得出BA模型度分布对数图.把离散性的Master方程与连续性的平均场理论进行对比分析,并在同一坐标系下分别作出用2种理论计算的BA模型度分布的对数图.

  4. The influence of the carbon surface chemical composition on Dubinin-Astakhov equation parameters calculated from SF{sub 6} adsorption data-grand canonical Monte Carlo simulation

    Energy Technology Data Exchange (ETDEWEB)

    Furmaniak, Sylwester; Terzyk, Artur P; Gauden, Piotr A [Department of Chemistry, Physicochemistry of Carbon Materials Research Group, N Copernicus University, Gagarin Street 7, 87-100 Torun (Poland); Kowalczyk, Piotr [Nanochemistry Research Institute, Curtin University, PO Box U1987, Perth, WA 6845 (Australia); Harris, Peter J F, E-mail: aterzyk@chem.uni.torun.pl [Centre for Advanced Microscopy, University of Reading, Whiteknights, Reading RG6 6AF (United Kingdom)

    2011-10-05

    Using grand canonical Monte Carlo simulation we show, for the first time, the influence of the carbon porosity and surface oxidation on the parameters of the Dubinin-Astakhov (DA) adsorption isotherm equation. We conclude that upon carbon surface oxidation, the adsorption decreases for all carbons studied. Moreover, the parameters of the DA model depend on the number of surface oxygen groups. That is why in the case of carbons containing surface polar groups, SF{sub 6} adsorption isotherm data cannot be used for characterization of the porosity. (paper)

  5. Monte Carlo calculations support organ sparing in Deep-Inspiration Breath-Hold intensity-modulated radiotherapy for locally advanced lung cancer

    DEFF Research Database (Denmark)

    Ottosson, Wiviann; Sibolt, Patrik; Larsen, Christina;

    2015-01-01

    Background and purpose: Studies indicate that Deep-Inspiration Breath-Hold (DIBH) is advantageous over Free-Breathing (FB) for locally advanced lung cancer radiotherapy. However, these studies were based on simplified dose calculation algorithms, potentially critical due to the heterogeneous nature...... of the lung region. Using detailed Monte-Carlo (MC) calculations, a comparative study of DIBH vs. FB was therefore designed. Material and methods: Eighteen locally advanced lung cancer patients underwent FB and DIBH CT imaging and treatment planning with the Anisotropic-Analytical-Algorithm (AAA......) for intensity-modulated-radio therapy or volumetric-modulated-arc-therapy using 66 Gy in 33 fractions. All plans were re-calculated with MC. Results: Relative to FB, the total lung volume increased 86.8% in DIBH, while the gross tumor volume decreased 14.8%. MC revealed equally under- and over...

  6. Calculations of loads and doses delivered, from radiochemistry and human spectrometry experimental results in a case of internal contamination in man. (Validity of Morrow's test and retention equations)

    International Nuclear Information System (INIS)

    The results of a previous study giving fecal and urinary excretion curves of five radioelements (cesium 137, cobalt 60, cerium 144, strontium 90, and plutonium 239) after radioactive aerosol inhalation by a man were interpreted. It is tried to draw conclusions on the validity of the theoretical parameters needed for calculating the load and the dose in man

  7. 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)

  8. The influence of carbon surface oxygen groups on Dubinin-Astakhov equation parameters calculated from CO{sub 2} adsorption isotherm

    Energy Technology Data Exchange (ETDEWEB)

    Furmaniak, Sylwester; Terzyk, Artur P; Gauden, Piotr A [N Copernicus University, Department of Chemistry, Physicochemistry of Carbon Materials Research Group, Gagarin Street 7, 87-100 Torun (Poland); Harris, Peter J F [Centre for Advanced Microscopy, University of Reading, Whiteknights, Reading RG6 6AF (United Kingdom); Kowalczyk, Piotr, E-mail: aterzyk@chem.uni.torun.p, E-mail: p.j.f.harris@rdg.ac.u [Applied Physics, RMIT University, GPO Box 2476V, Victoria 3001 (Australia)

    2010-03-03

    We present the results of a systematic study of the influence of carbon surface oxidation on Dubinin-Astakhov isotherm parameters obtained from the fitting of CO{sub 2} adsorption data. Using GCMC simulations of adsorption on realistic VPC models differing in porosity and containing the most frequently occurring carbon surface functionalities (carboxyls, hydroxyls and carbonyls) and their mixtures, it is concluded that the maximum adsorption calculated from the DA model is not strongly affected by the presence of oxygen groups. Unfortunately, the same cannot be said of the remaining two parameters of this model i.e. the heterogeneity parameter (n) and the characteristic energy of adsorption (E{sub 0}). Since from the latter the pore diameters of carbons are usually calculated, by inverse-type relationships, it is concluded that they are questionable for carbons containing surface oxides, especially carboxyls.

  9. Effect of deformable registration on the dose calculated in radiation therapy planning CT scans of lung cancer patients

    Energy Technology Data Exchange (ETDEWEB)

    Cunliffe, Alexandra R.; Armato, Samuel G.; White, Bradley; Justusson, Julia [Department of Radiology, The University of Chicago, 5841 South Maryland Avenue, Chicago, Illinois 60637 (United States); Contee, Clay; Malik, Renuka; Al-Hallaq, Hania A., E-mail: hal-hallaq@radonc.uchicago.edu [Department of Radiation and Cellular Oncology, The University of Chicago, 5841 South Maryland Avenue, Chicago, Illinois 60637 (United States)

    2015-01-15

    Purpose: To characterize the effects of deformable image registration of serial computed tomography (CT) scans on the radiation dose calculated from a treatment planning scan. Methods: Eighteen patients who received curative doses (≥60 Gy, 2 Gy/fraction) of photon radiation therapy for lung cancer treatment were retrospectively identified. For each patient, a diagnostic-quality pretherapy (4–75 days) CT scan and a treatment planning scan with an associated dose map were collected. To establish correspondence between scan pairs, a researcher manually identified anatomically corresponding landmark point pairs between the two scans. Pretherapy scans then were coregistered with planning scans (and associated dose maps) using the demons deformable registration algorithm and two variants of the Fraunhofer MEVIS algorithm (“Fast” and “EMPIRE10”). Landmark points in each pretherapy scan were automatically mapped to the planning scan using the displacement vector field output from each of the three algorithms. The Euclidean distance between manually and automatically mapped landmark points (d{sub E}) and the absolute difference in planned dose (|ΔD|) were calculated. Using regression modeling, |ΔD| was modeled as a function of d{sub E}, dose (D), dose standard deviation (SD{sub dose}) in an eight-pixel neighborhood, and the registration algorithm used. Results: Over 1400 landmark point pairs were identified, with 58–93 (median: 84) points identified per patient. Average |ΔD| across patients was 3.5 Gy (range: 0.9–10.6 Gy). Registration accuracy was highest using the Fraunhofer MEVIS EMPIRE10 algorithm, with an average d{sub E} across patients of 5.2 mm (compared with >7 mm for the other two algorithms). Consequently, average |ΔD| was also lowest using the Fraunhofer MEVIS EMPIRE10 algorithm. |ΔD| increased significantly as a function of d{sub E} (0.42 Gy/mm), D (0.05 Gy/Gy), SD{sub dose} (1.4 Gy/Gy), and the algorithm used (≤1 Gy). Conclusions: An

  10. Burnout calculation

    International Nuclear Information System (INIS)

    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

  11. Calculation of lung cancer incidence in the Netherlands by smoking and radon exposure. Implications for the effect of radon

    International Nuclear Information System (INIS)

    Although the main cause of lung cancer is smoking cigarettes, part of the cases are subscribed to radon exposure, in particular α-radiation from daughter products. However, the relation between lung cancer and radon exposure is rather insecure. Based on international reports (e.g. BEIR VI) and extrapolation of lung cancer incidence in uranium mine workers to the population of the USA and subsequently to the Netherlands, the number of lung cancer cases in the Netherlands is estimated to be circa 800 per year, varying between 200-2000. Results of the analysis are summarized in this article. 10 refs

  12. Calculation of NaCl, KCl and LiCl Salts Activity Coefficients in Polyethylene Glycol (PEG4000)-Water System Using Modified PHSC Equation of State, Extended Debye-Hückel Model and Pitzer Model

    Science.gov (United States)

    Marjani, Azam

    2016-07-01

    For biomolecules and cell particles purification and separation in biological engineering, besides the chromatography as mostly applied process, aqueous two-phase systems (ATPS) are of the most favorable separation processes that are worth to be investigated in thermodynamic theoretically. In recent years, thermodynamic calculation of ATPS properties has attracted much attention due to their great applications in chemical industries such as separation processes. These phase calculations of ATPS have inherent complexity due to the presence of ions and polymers in aqueous solution. In this work, for target ternary systems of polyethylene glycol (PEG4000)-salt-water, thermodynamic investigation for constituent systems with three salts (NaCl, KCl and LiCl) has been carried out as PEG is the most favorable polymer in ATPS. The modified perturbed hard sphere chain (PHSC) equation of state (EOS), extended Debye-Hückel and Pitzer models were employed for calculation of activity coefficients for the considered systems. Four additional statistical parameters were considered to ensure the consistency of correlations and introduced as objective functions in the particle swarm optimization algorithm. The results showed desirable agreement to the available experimental data, and the order of recommendation of studied models is PHSC EOS > extended Debye-Hückel > Pitzer. The concluding remark is that the all the employed models are reliable in such calculations and can be used for thermodynamic correlation/predictions; however, by using an ion-based parameter calculation method, the PHSC EOS reveals both reliability and universality of applications.

  13. Semi-analytical calculations for parameters of boiling layer in isetropic expansion of warm dense matter with van der Waals equation of state

    CERN Document Server

    Borovikov, Dmitry

    2012-01-01

    Features and parameters of \\boiling" liquid layer, which arises under conditions of isentropic expansion of warm dense matter (WDM), are stud- ied with the use of simplest van der Waals equation of state (EOS). Advan- tage of this EOS is possibility of demonstrable and semi-analytical descrip- tion of thermo- and hydrodynamics of the process. Idealized self-similar case of behavior of matter on interception of equilibrium (not metastable) isoentropic curve and boundary of gas-liquid coexistence curve (binodal) is analyzed. The possibility of formation of such "liquid layer" was studied previously in [1] during solving the problem of ablation of metal surface under the action of strong laser radiation. Peculiarity of such "freezing" of finite portion of expanding matter in the state, which corresponds to the binodal of gas-liquid or/and other phase transitions|so called "phase freezeout"and prospects of applications of this phenomenon for intended generation of uniform and extensive zone of previously unexplor...

  14. Dose per unit cumulated activity (S-values) for e− and beta emitting radionuclides in cancer cell models calculated by Monte Carlo simulation

    International Nuclear Information System (INIS)

    Cell dosimetry is relevant regarding new efforts in specific molecular radiotherapy using Auger, CE and beta emitters. Absorbed dose in cells can be obtained by means of the dose per unit cumulated activity (S-values), together with the activity distribution. In this work, Monte Carlo simulation codes PENELOPE and MCNPX were used to obtain cellular S-values for point and extended sources of electrons and beta emitting radionuclides in the nucleus of breast (MDA-MB231, MCF7) and prostate (PC3) cancer cell models. - Highlights: • Cellular S-values were calculated using Penelope and MCPNX Monte Carlo codes. • S-values were obtained for e− and beta emitting radionuclides in cancer cell models. • Breast (MDA-MB231, MCF7) and prostate (PC3) cancer cell models were investigated. • Results are relevant for specific targeted molecular radiotherapy cell dosimetry

  15. Calculation of 1/m^{2}_{b} corrections to {\\Lambda}_b\\rightarrow{\\Lambda}_c decay widths in the Bethe-Salpeter equation approach

    CERN Document Server

    Zhang, L; Weng, M -H

    2016-01-01

    The matrix element of the weak transition {\\Lambda}_b\\rightarrow{\\Lambda}_c can be expressed in terms of six form factors. {\\Lambda}_Q(Q = b;c) can be regarded as composed of a heavy quark Q(Q = b;c) and a diquark which is made up of the remaining two light quarks. In this picture, we express these six form factors in terms of Bethe-Salpeter wave functions to second order in the 1/m_Q expansion. With the kernel containing both the scalar confinement and the one-gluon-exchange terms we calculate the form factors and the decay widths of the semileptonic decay {\\Lambda}_b\\rightarrow{\\Lambda}_clv as well as nonleptonic decays {\\Lambda}_b\\rightarrow{\\Lambda}_cP(V) numerically. We also add QCD corrections since they are comparable with 1/m_Q corrections.

  16. Tumor control probability and the utility of 4D vs 3D dose calculations for stereotactic body radiotherapy for lung cancer

    Energy Technology Data Exchange (ETDEWEB)

    Valdes, Gilmer, E-mail: gilmer.valdes@uphs.upenn.edu [Department of Radiation Oncology, Perelman Center for Advanced Medicine, University of Pennsylvania, Philadelphia, PA (United States); Robinson, Clifford [Department of Radiation Oncology, Siteman Cancer Center, Washington University in St. Louis, St. Louis, MO (United States); Lee, Percy [Department of Radiation Oncology, David Geffen School of Medicine, UCLA, Los Angeles, CA (United States); Morel, Delphine [Department of Biomedical Engineering, AIX Marseille 2 University, Marseille (France); Department of Medical Physics, Joseph Fourier University, Grenoble (France); Low, Daniel; Iwamoto, Keisuke S.; Lamb, James M. [Department of Radiation Oncology, David Geffen School of Medicine, UCLA, Los Angeles, CA (United States)

    2015-04-01

    Four-dimensional (4D) dose calculations for lung cancer radiotherapy have been technically feasible for a number of years but have not become standard clinical practice. The purpose of this study was to determine if clinically significant differences in tumor control probability (TCP) exist between 3D and 4D dose calculations so as to inform the decision whether 4D dose calculations should be used routinely for treatment planning. Radiotherapy plans for Stage I-II lung cancer were created for 8 patients. Clinically acceptable treatment plans were created with dose calculated on the end-exhale 4D computed tomography (CT) phase using a Monte Carlo algorithm. Dose was then projected onto the remaining 9 phases of 4D-CT using the Monte Carlo algorithm and accumulated onto the end-exhale phase using commercially available deformable registration software. The resulting dose-volume histograms (DVH) of the gross tumor volume (GTV), planning tumor volume (PTV), and PTV{sub setup} were compared according to target coverage and dose. The PTV{sub setup} was defined as a volume including the GTV and a margin for setup uncertainties but not for respiratory motion. TCPs resulting from these DVHs were estimated using a wide range of alphas, betas, and tumor cell densities. Differences of up to 5 Gy were observed between 3D and 4D calculations for a PTV with highly irregular shape. When the TCP was calculated using the resulting DVHs for fractionation schedules typically used in stereotactic body radiation therapy (SBRT), the TCP differed at most by 5% between 4D and 3D cases, and in most cases, it was by less than 1%. We conclude that 4D dose calculations are not necessary for most cases treated with SBRT, but they might be valuable for irregularly shaped target volumes. If 4D calculations are used, 4D DVHs should be evaluated on volumes that include margin for setup uncertainty but not respiratory motion.

  17. Tumor control probability and the utility of 4D vs 3D dose calculations for stereotactic body radiotherapy for lung cancer

    International Nuclear Information System (INIS)

    Four-dimensional (4D) dose calculations for lung cancer radiotherapy have been technically feasible for a number of years but have not become standard clinical practice. The purpose of this study was to determine if clinically significant differences in tumor control probability (TCP) exist between 3D and 4D dose calculations so as to inform the decision whether 4D dose calculations should be used routinely for treatment planning. Radiotherapy plans for Stage I-II lung cancer were created for 8 patients. Clinically acceptable treatment plans were created with dose calculated on the end-exhale 4D computed tomography (CT) phase using a Monte Carlo algorithm. Dose was then projected onto the remaining 9 phases of 4D-CT using the Monte Carlo algorithm and accumulated onto the end-exhale phase using commercially available deformable registration software. The resulting dose-volume histograms (DVH) of the gross tumor volume (GTV), planning tumor volume (PTV), and PTVsetup were compared according to target coverage and dose. The PTVsetup was defined as a volume including the GTV and a margin for setup uncertainties but not for respiratory motion. TCPs resulting from these DVHs were estimated using a wide range of alphas, betas, and tumor cell densities. Differences of up to 5 Gy were observed between 3D and 4D calculations for a PTV with highly irregular shape. When the TCP was calculated using the resulting DVHs for fractionation schedules typically used in stereotactic body radiation therapy (SBRT), the TCP differed at most by 5% between 4D and 3D cases, and in most cases, it was by less than 1%. We conclude that 4D dose calculations are not necessary for most cases treated with SBRT, but they might be valuable for irregularly shaped target volumes. If 4D calculations are used, 4D DVHs should be evaluated on volumes that include margin for setup uncertainty but not respiratory motion

  18. Numerical Calculation of Transport Based on the Drift Kinetic Equation for plasmas in General Toroidal Magnetic Geometry; Calculo Numerico del Transporte mediante la Ecuacion Cinetica de Deriva para Plasmas en Geometria Magnetica Toroidal: Preliminares

    Energy Technology Data Exchange (ETDEWEB)

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

    2009-12-11

    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.

  19. Variational-average-atom-in-quantum-plasmas (VAAQP) code and virial theorem: equation-of-state and shock-Hugoniot calculations for warm dense Al, Fe, Cu, and Pb.

    Science.gov (United States)

    Piron, R; Blenski, T

    2011-02-01

    The numerical code VAAQP (variational average atom in quantum plasmas), which is based on a fully variational model of equilibrium dense plasmas, is applied to equation-of-state calculations for aluminum, iron, copper, and lead in the warm-dense-matter regime. VAAQP does not impose the neutrality of the Wigner-Seitz ion sphere; it provides the average-atom structure and the mean ionization self-consistently from the solution of the variational equations. The formula used for the electronic pressure is simple and does not require any numerical differentiation. In this paper, the virial theorem is derived in both nonrelativistic and relativistic versions of the model. This theorem allows one to express the electron pressure as a combination of the electron kinetic and interaction energies. It is shown that the model fulfills automatically the virial theorem in the case of local-density approximations to the exchange-correlation free-energy. Applications of the model to the equation-of-state and Hugoniot shock adiabat of aluminum, iron, copper, and lead in the warm-dense-matter regime are presented. Comparisons with other approaches, including the inferno model, and with available experimental data are given. This work allows one to understand the thermodynamic consistency issues in the existing average-atom models. Starting from the case of aluminum, a comparative study of the thermodynamic consistency of the models is proposed. A preliminary study of the validity domain of the inferno model is also included. PMID:21405914

  20. Application of deformable registration and empirical method to calculate the accumulated dose for normal tissues and organs at risks in lung cancer radiotherapy plans

    International Nuclear Information System (INIS)

    Objective: To evaluate the accumulated doses to normal tissues and organs at risks (OARs) of patients with lung cancer in radiotherapy plans by using the deformable registration method, and make comparison with the empirical calculation method. Methods: Ten patients with lung cancer were analyzed retrospectively. 3D-CRT or IMRT plans were designed before treatment. CT to simulator was rescanned and the same treatment plan was redesigned during radiotherapy. Based on the deformable registration method, the Mimvista software was used to calculate the accumulated doses to normal tissues and OARs in two CT images respectively. The empirical estimation algorithm was calculated by the linear relationship between the fractions and the total prescribed dose. Results: The target coverage of patients had no significant difference in two plans. There were no significant differences in all the dose volume parameters for normal tissues and OARs, except the mean dose to right lung (t=2.98, P<0.05) when the the same plan was conducted in position-setting and reposition CT images. Conclusions: The empirical estimation for the accumulated dose could be used to evaluate the dose and volume parameters for normal tissues and OARs in lung cancer by the same plan. (authors)

  1. Hepatic arterial phase and portal venous phase computed tomography for dose calculation of stereotactic body radiation therapy plans in liver cancer: a dosimetric comparison study

    International Nuclear Information System (INIS)

    To investigate the effect of computed tomography (CT) using hepatic arterial phase (HAP) and portal venous phase (PVP) contrast on dose calculation of stereotactic body radiation therapy (SBRT) for liver cancer. Twenty-one patients with liver cancer were studied. HAP, PVP and non-enhanced CTs were performed on subjects scanned in identical positions under active breathing control (ABC). SBRT plans were generated using seven-field three-dimensional conformal radiotherapy (7 F-3D-CRT), seven-field intensity-modulated radiotherapy (7 F-IMRT) and single-arc volumetric modulated arc therapy (VMAT) based on the PVP CT. Plans were copied to the HAP and non-enhanced CTs. Radiation doses calculated from the three phases of CTs were compared with respect to the planning target volume (PTV) and the organs at risk (OAR) using the Friedman test and the Wilcoxon signed ranks test. SBRT plans calculated from either PVP or HAP CT, including 3D-CRT, IMRT and VMAT plans, demonstrated significantly lower (p <0.05) minimum absorbed doses covering 98%, 95%, 50% and 2% of PTV (D98%, D95%, D50% and D2%) than those calculated from non-enhanced CT. The mean differences between PVP or HAP CT and non-enhanced CT were less than 2% and 1% respectively. All mean dose differences between the three phases of CTs for OARs were less than 2%. Our data indicate that though the differences in dose calculation between contrast phases are not clinically relevant, dose underestimation (IE, delivery of higher-than-intended doses) resulting from CT using PVP contrast is larger than that resulting from CT using HAP contrast when compared against doses based upon non-contrast CT in SBRT treatment of liver cancer using VMAT, IMRT or 3D-CRT

  2. Cubic Equation

    Institute of Scientific and Technical Information of China (English)

    2004-01-01

    At the beginning of 16th century, mathematicians found it easy to solve equations of the first degree(linear equations, involving x) and of the second degree(quadratic equatiorts, involving x2). Equations of the third degree(cubic equations, involving x3)defeated them.

  3. Relationship between renal volume calculated by using multislice computed tomography and glomerular filtration rate calculated by using the Cockcroft-Gault and modification of diet in renal disease equations in living kidney donors.

    Science.gov (United States)

    Adibi, Atoosa; Mortazavi, Mojgan; Shayganfar, Azin; Kamal, Sima; Azad, Roya; Aalinezhad, Marzieh

    2016-01-01

    It is essential to ascertain the state of health and renal function of potential kidney donors before organ removal. In this regard, one of the primary steps is to estimate the donor's glomerular filtration rate (GFR). For this purpose, the modification of diet in renal disease (MDRD) and the Cockcroft-Gault (CG) formulas has been used. However, these two formulas produce different results and finding new techniques with greater accuracy is required. Measuring the renal volume from computed tomography (CT) scan may be a valuable index to assess the renal function. This study was conducted to investigate the correlation between renal volume and the GFR values in potential living kidney donors referred to the multislice imaging center at Alzahra Hospital during 2014. The study comprised 66 subjects whose GFR was calculated using the two aforementioned formulas. Their kidney volumes were measured by using 64-slice CT angiography and the correlation between renal volume and GFR values were analyzed using the Statistical Package for the Social Science software. There was no correlation between the volume of the left and right kidneys and the MDRD-based estimates of GFR (P = 0.772, r = 0.036, P = 0.251, r = 0.143, respectively). A direct linear correlation was found between the volume of the left and right kidneys and the CG-based GFR values (P = 0.001, r = 0.397, P kidney volume derived from multislice CT scan can help predict the GFR value in kidney donors with normal renal function. The limitations of our study include the small sample size and the medium resolution of 64-slice multislice scanners. Further studies with larger sample size and using higher resolution scanners are warranted to determine the accuracy of this method in potential kidney donors. PMID:27424682

  4. Measurement and calculation of evaporation

    OpenAIRE

    Plesničar, Leja

    2015-01-01

    The thesis presents three selected methods of measurement and calculation of the evapotranspiration on research plot at Hajdrihova 28 in Ljubljana. First method is measurement by evaporation pan type A and the other two methods are empirical equations for potential evapotranspiration calculation: FAO Penman-Monteith equation and Thornthwait equation. The results obtained for all three methods are compared with each other. Calculated results according to the FAO Penman-Monteith equation wer...

  5. Monte Carlo calculation of changes in the doses due to the contrast medium in the partial irradiation for the breast cancer

    International Nuclear Information System (INIS)

    In this work the results of calculating by Monte Carlo simulation with the Penelope code are presented, the changes that are presented in the dose, when modeling a system of treatment of partial irradiation of breast cancer. The system consists of a globe plastic with a radioactive source of 192Ir in his interior. This technique is used when it is carried out the extraction of incipient cancerous tumors and it is wanted to irradiate the tissue surrounding to the tumor extracted to make sure that sick tissue does not remain. This technique was patented about 5 years ago and it is known as partial irradiation by MammoSite(R). When the plastic ball is implanted in the cavity of the surgery, it is filled with a radio opaque solution. This substance is a solution whose concentration can to vary. One of the main components of this solution is the iodine. The on-line dose calculations, carried out by the programs associated to the brachytherapy sources and, in particular for this technique, they are very good; however, the calculations are made supposing that to have an homogeneous medium. They have been carried out studies for MC simulation with the EGSNRC code and it has been that when it takes into account the presence of the contrast solution, the results change considerably. In this work we carry out dose calculations with Penelope for different solution concentrations in the ball. The results agree in general way with those carried out in other works. (Author)

  6. Calculation of Single Scattering Parameters in Vector Radiative Transfer Equation%辐射传输方程中的单次散射参数计算

    Institute of Scientific and Technical Information of China (English)

    王海华; 孙贤明; 刘万强; 申晋; 刘伟

    2011-01-01

    Based on Mie theory, the single scattering characteristics of a cluster of polydisperse spherical aerosols are calculated. The size distribution of particles is Gamma distribution and effective radii are 5.56, 7, 11 μm,respectively. The average extinction coefficients, average scattering coefficients, single scattering albedos,asymmetry parameters and elements of single scattering phase matrix in the spectral range of 0.4 ~ 100 μm are analyzed. The numerical results show that the single scattering properties of aerosols are seldom affected by particle effective radius in visual light waveband, but greater at higher waveband. The single scattering albedo approximately equals 1 at visual light waveband and the characteristics of single scattering albedo are opposite to the imagery part of refraction index. The polarization ratios of single scattering phase matrix are more sensitive to particle size than phase functions.%根据米氏(Mie)理论,计算了多分散球形气溶胶粒子的单次散射特性.粒子的尺寸分布为伽马分布,有效半径分别为5.56.7和11 μm,分析了0.4-100 μm光谱范围内气溶胶粒子的平均消光系数、平均散射系数、单次散射反照率、不对称因子以及相矩阵与粒子的尺寸参数以及折射率的关系.结果表明,在可见光波段,粒子的有效半径对粒子的散射特性影响较小,在更长的波段上其影响较大;单次散射反照率在可见光范围内近似为1,随波长的变化和水滴折射率虚部随波长的变化曲线正好相反,这说明影响其大小的主要因素为粒子的折射率,即虚部越大则反照率越小;且极化率对粒子的尺寸比相函数更敏感.

  7. 常微分方程光滑性解的求取过程改进分析%Analysis of Calculating Process Improvement for Ordinary Differential Equations Smooth Solution

    Institute of Scientific and Technical Information of China (English)

    刘艳梅

    2015-01-01

    Smoothness in order to optimize the differential equations of calculating process, put forward a kind of Laplace transform and the wavelet matching calculate the smoothness of ordinary differential equation solution method and Laplace transform method is used to convert ordinary differential equation (group) to the algebraic equation (group) of complex variable, by some algebraic operation and Laplace transform table, get initial smoothness solution of ordinary differential equations, the arbitrary function expansion ChengXiaoBo basis function, through the fast discrete wavelet transform technology, shape the smoothness of approximate solution of ordinary differential equations, in the process of operation, in wavelet levels, as well as the independent variable interval, using multilayer adaptive method, adaptive and interval section to solve the problems of the long time, ensure in each time period to achieve the required accuracy and smoothness of solution to solve and improve efficiency and accuracy. The result of numerical experiment shows that the proposed method for solving ordinary differential equations of smooth solution accuracy and timeliness is better than the traditional state long time propulsion method.%为了优化常微分方程光滑性解的求取过程,提出一种拉普拉斯变换以及小波匹配的常微分方程光滑性解求取方法,采用拉普拉斯变换方法将常微分方程(组)转换成复变数的代数方程(组),通过一些代数运算和拉普拉斯变换表,获取常微分方程的初始光滑性解,将任意函数展开成小波基函数,通过快速离散小波转换技术,塑造常微分方程的近似光滑性解,在运算过程中,在小波展开层次以及自变量区间,使用多层自适应以及多区间自适应方法,对长时间问题进行分段求解,保证在每个时间段上达到所要求的数值精度,提高光滑性解求解的效率和精度。数值实验结果说

  8. Dosimetric Verification Using Monte Carlo Calculations for Tissue Heterogeneity-Corrected Conformal Treatment Plans Following RTOG 0813 Dosimetric Criteria for Lung Cancer Stereotactic Body Radiotherapy

    International Nuclear Information System (INIS)

    Purpose: The recently activated Radiation Therapy Oncology Group (RTOG) studies of stereotactic body radiation therapy (SBRT) for non-small-cell lung cancer (NSCLC) require tissue density heterogeneity correction, where the high and intermediate dose compliance criteria were established based on superposition algorithm dose calculations. The study was aimed at comparing superposition algorithm dose calculations with Monte Carlo (MC) dose calculations for SBRT for NSCLC and to evaluate whether compliance criteria need to be adjusted for MC dose calculations. Methods and Materials: Fifteen RTOG 0236 study sets were used. The planning tumor volumes (PTV) ranged from 10.7 to 117.1 cm3. SBRT conformal treatment plans were generated using XiO (CMS Inc.) treatment planning software with superposition algorithm to meet the dosimetric high and intermediate compliance criteria recommended by the RTOG 0813 protocol. Plans were recalculated using the MC algorithm of a Monaco (CMS, Inc.) treatment planning system. Tissue density heterogeneity correction was applied in both calculations. Results: Overall, the dosimetric quantities of the MC calculations have larger magnitudes than those of the superposition calculations. On average, R100% (ratio of prescription isodose volume to PTV), R50% (ratio of 50% prescription isodose volume to PTV), D2cm (maximal dose 2 cm from PTV in any direction as a percentage of prescription dose), and V20 (percentage of lung receiving dose equal to or larger than 20 Gy) increased by 9%, 12%, 7%, and 18%, respectively. In the superposition plans, 3 cases did not meet criteria for R50% or D2cm. In the MC-recalculated plans, 8 cases did not meet criteria for R100%, R50%, or D2cm. After reoptimization with MC calculations, 5 cases did not meet the criteria for R50% or D2cm. Conclusions: Results indicate that the dosimetric criteria, e.g., the criteria for R50% recommended by RTOG 0813 protocol, may need to be adjusted when the MC dose calculation

  9. String equation from field equation

    CERN Document Server

    Gurovich, V T

    1996-01-01

    It is shown that the string equation can be obtain from field equations. Such work is performed to scalar field. The equation obtained in nonrelativistic limit describes the nonlinear string. Such string has the effective elasticity connencted with the local string curvature. Some examples of the movement such nonlinear elastic string are considered.

  10. Calculation of wing-body junction flow using Gao-Yong turbulence equations%使用Gao-Yong湍流方程计算翼体角偶流动

    Institute of Scientific and Technical Information of China (English)

    高歌; 江立军; 高琳

    2012-01-01

    The derivation of Gao-Yong turbulence equations was based on a partial statistical average scheme proposed in the past by the first author in an attempt to capture the drift flow, a first-order statistical moment of turbulent fluctuations. Continuity and momentum equations of turbulent fluctuations were obtained as a result of this valuable first statistical information. Orthotropic turbulence and momentum transfer chain were formulated in the modeling of correlation terms, eventually, led to a complete set of equations of turbu- lent flow with no empirical coefficients and wall functions. Numerical simulations in the past preliminarily veri- fied the adaptability of Gao-Yong equations to a wide range of complex benchmark turbulent flows. In order to further application of these equations to engineering flows, the Gao-Yong turbulence equations were implemen- ted into OpenFOAM and applied to the calculation of wing-body junction flow. The wing-body junction flow in- volves very complex feathers, such as a 3-D separation and a horseshoe vortex. The results of numerical simu- lation of this flow compared to experimental data show that all these main characteristics have been captured, both qualitatively and quantitatively.%Gao—Yong湍流方程基于侧偏统计平均方法保留了湍流脉动量的一阶统计信息,并引入加权漂移速度对称性及正交各向异性,导出漂移流连续方程、动量方程和机械能方程,最后依据湍流物理的唯象论,使用动量传输链概念模化封闭了整个方程组.大量算例验证了此方程对广泛范围的复杂湍流问题的适定性.为了进一步的工程应用,将其加入开源计算流体力学软件OpenFOAM(OpenFieldOperationandManipulation)中,并就翼体角偶流动进行了数值模拟.翼体角偶流动具有三维分离、马蹄涡等十分复杂的流动特征,通过与实验测量结果的对比研究表明,Gao—Yong湍流方程不论在定性还是定

  11. SU-E-I-05: A Correction Algorithm for Kilovoltage Cone-Beam Computed Tomography Dose Calculations in Cervical Cancer Patients

    International Nuclear Information System (INIS)

    Purpose: To investigate the accuracy and feasibility of dose calculations using kilovoltage cone beam computed tomography in cervical cancer radiotherapy using a correction algorithm. Methods: The Hounsfield units (HU) and electron density (HU-density) curve was obtained for both planning CT (pCT) and kilovoltage cone beam CT (CBCT) using a CIRS-062 calibration phantom. The pCT and kV-CBCT images have different HU values, and if the HU-density curve of CBCT was directly used to calculate dose in CBCT images may have a deviation on dose distribution. It is necessary to normalize the different HU values between pCT and CBCT. A HU correction algorithm was used for CBCT images (cCBCT). Fifteen intensity-modulated radiation therapy (IMRT) plans of cervical cancer were chosen, and the plans were transferred to the pCT and cCBCT data sets without any changes for dose calculations. Phantom and patient studies were carried out. The dose differences and dose distributions were compared between cCBCT plan and pCT plan. Results: The HU number of CBCT was measured by several times, and the maximum change was less than 2%. To compare with pCT, the CBCT and cCBCT has a discrepancy, the dose differences in CBCT and cCBCT images were 2.48%±0.65% (range: 1.3%∼3.8%) and 0.48%±0.21% (range: 0.1%∼0.82%) for phantom study, respectively. For dose calculation in patient images, the dose differences were 2.25%±0.43% (range: 1.4%∼3.4%) and 0.63%±0.35% (range: 0.13%∼0.97%), respectively. And for the dose distributions, the passing rate of cCBCT was higher than the CBCTs. Conclusion: The CBCT image for dose calculation is feasible in cervical cancer radiotherapy, and the correction algorithm offers acceptable accuracy. It will become a useful tool for adaptive radiation therapy

  12. SU-E-I-05: A Correction Algorithm for Kilovoltage Cone-Beam Computed Tomography Dose Calculations in Cervical Cancer Patients

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, J; Zhang, W; Lu, J [Cancer Hospital of Shantou University Medical College, Shantou, Guangdong (China)

    2015-06-15

    Purpose: To investigate the accuracy and feasibility of dose calculations using kilovoltage cone beam computed tomography in cervical cancer radiotherapy using a correction algorithm. Methods: The Hounsfield units (HU) and electron density (HU-density) curve was obtained for both planning CT (pCT) and kilovoltage cone beam CT (CBCT) using a CIRS-062 calibration phantom. The pCT and kV-CBCT images have different HU values, and if the HU-density curve of CBCT was directly used to calculate dose in CBCT images may have a deviation on dose distribution. It is necessary to normalize the different HU values between pCT and CBCT. A HU correction algorithm was used for CBCT images (cCBCT). Fifteen intensity-modulated radiation therapy (IMRT) plans of cervical cancer were chosen, and the plans were transferred to the pCT and cCBCT data sets without any changes for dose calculations. Phantom and patient studies were carried out. The dose differences and dose distributions were compared between cCBCT plan and pCT plan. Results: The HU number of CBCT was measured by several times, and the maximum change was less than 2%. To compare with pCT, the CBCT and cCBCT has a discrepancy, the dose differences in CBCT and cCBCT images were 2.48%±0.65% (range: 1.3%∼3.8%) and 0.48%±0.21% (range: 0.1%∼0.82%) for phantom study, respectively. For dose calculation in patient images, the dose differences were 2.25%±0.43% (range: 1.4%∼3.4%) and 0.63%±0.35% (range: 0.13%∼0.97%), respectively. And for the dose distributions, the passing rate of cCBCT was higher than the CBCTs. Conclusion: The CBCT image for dose calculation is feasible in cervical cancer radiotherapy, and the correction algorithm offers acceptable accuracy. It will become a useful tool for adaptive radiation therapy.

  13. Water vapor pressure calculation.

    Science.gov (United States)

    Hall, J R; Brouillard, R G

    1985-06-01

    Accurate calculation of water vapor pressure for systems saturated with water vapor can be performed using the Goff-Gratch equation. A form of the equation that can be adapted for computer programming and for use in electronic databases is provided. PMID:4008425

  14. Integral equations

    CERN Document Server

    Moiseiwitsch, B L

    2005-01-01

    Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco

  15. Cancer

    Science.gov (United States)

    ... Blood tests (which look for chemicals such as tumor markers) Bone marrow biopsy (for lymphoma or leukemia) Chest ... the case with skin cancers , as well as cancers of the lung, breast, and colon. If the tumor has spread ...

  16. Cancer

    Science.gov (United States)

    Cancer begins in your cells, which are the building blocks of your body. Normally, your body forms ... be benign or malignant. Benign tumors aren't cancer while malignant ones are. Cells from malignant tumors ...

  17. TH-E-BRE-01: A 3D Solver of Linear Boltzmann Transport Equation Based On a New Angular Discretization Method with Positivity for Photon Dose Calculation Benchmarked with Geant4

    International Nuclear Information System (INIS)

    Purpose: The Linear Boltzmann Transport Equation (LBTE) solved through statistical Monte Carlo (MC) method provides the accurate dose calculation in radiotherapy. This work is to investigate the alternative way for accurately solving LBTE using deterministic numerical method due to its possible advantage in computational speed from MC. Methods: Instead of using traditional spherical harmonics to approximate angular scattering kernel, our deterministic numerical method directly computes angular scattering weights, based on a new angular discretization method that utilizes linear finite element method on the local triangulation of unit angular sphere. As a Result, our angular discretization method has the unique advantage in positivity, i.e., to maintain all scattering weights nonnegative all the time, which is physically correct. Moreover, our method is local in angular space, and therefore handles the anisotropic scattering well, such as the forward-peaking scattering. To be compatible with image-guided radiotherapy, the spatial variables are discretized on the structured grid with the standard diamond scheme. After discretization, the improved sourceiteration method is utilized for solving the linear system without saving the linear system to memory. The accuracy of our 3D solver is validated using analytic solutions and benchmarked with Geant4, a popular MC solver. Results: The differences between Geant4 solutions and our solutions were less than 1.5% for various testing cases that mimic the practical cases. More details are available in the supporting document. Conclusion: We have developed a 3D LBTE solver based on a new angular discretization method that guarantees the positivity of scattering weights for physical correctness, and it has been benchmarked with Geant4 for photon dose calculation

  18. Transport equation solving methods

    International Nuclear Information System (INIS)

    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

  19. A hybrid framework of first principles molecular orbital calculations and a three-dimensional integral equation theory for molecular liquids: Multi-center molecular Ornstein–Zernike self-consistent field approach

    Energy Technology Data Exchange (ETDEWEB)

    Kido, Kentaro, E-mail: kido.kentaro@jaea.go.jp [Nuclear Safety Research Center, Japan Atomic Energy Agency, 2-4 Shirane, Shirakata, Tokai-mura, Naka-gun, Ibaraki 319-1195 (Japan); Kasahara, Kento [Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510 (Japan); Yokogawa, Daisuke [Department of Chemistry, Graduate School of Science, Nagoya University, Chikusa, Nagoya 464-8602 (Japan); Institute of Transformative Bio-Molecules (WPI-ITbM), Nagoya University, Chikusa, Nagoya 464-8062 (Japan); Sato, Hirofumi [Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510 (Japan); Elements Strategy Institute for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520 (Japan)

    2015-07-07

    In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein–Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple S{sub N}2 reaction (Cl{sup −} + CH{sub 3}Cl → ClCH{sub 3} + Cl{sup −}) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.

  20. A hybrid framework of first principles molecular orbital calculations and a three-dimensional integral equation theory for molecular liquids: Multi-center molecular Ornstein–Zernike self-consistent field approach

    International Nuclear Information System (INIS)

    In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein–Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple SN2 reaction (Cl− + CH3Cl → ClCH3 + Cl−) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF

  1. Differential equations

    CERN Document Server

    Tricomi, FG

    2012-01-01

    Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and differential

  2. Red bone marrow dose calculations in radiotherapy of prostate cancer based on the updated VCH adult male phantom

    Science.gov (United States)

    Ai, Jinqin; Xie, Tianwu; Sun, Wenjuan; Liu, Qian

    2014-04-01

    Red bone marrow (RBM) is an important dose-limiting tissue that has high radiosensitivity but is difficult to identify on clinical medical images. In this study, we investigated dose distribution in RBM for prostate cancer radiotherapy. Four suborgans were identified in the skeleton of the visible Chinese human phantom: cortical bone (CB), trabecular bone (TB), RBM, and yellow bone marrow (YBM). Dose distributions in the phantom were evaluated by the Monte Carlo method. When the left os coxae was taken as the organ-at-risk (OAR), the difference in absorbed dose between RBM and each CB and TB was up to 20%, but was much less (≤3.1%) between RBM and YBM. When the left os coxae and entire bone were both taken as OARs, RBM dose also increased with increasing planning target volume size. The results indicate the validity of using dose to homogeneous bone marrow mixture for estimating dose to RBM when RBM is not available in computational phantoms. In addition, the human skeletal system developed in this study provides a model for considering RBM dose in radiotherapy planning.

  3. Red bone marrow dose calculations in radiotherapy of prostate cancer based on the updated VCH adult male phantom

    International Nuclear Information System (INIS)

    Red bone marrow (RBM) is an important dose-limiting tissue that has high radiosensitivity but is difficult to identify on clinical medical images. In this study, we investigated dose distribution in RBM for prostate cancer radiotherapy. Four suborgans were identified in the skeleton of the visible Chinese human phantom: cortical bone (CB), trabecular bone (TB), RBM, and yellow bone marrow (YBM). Dose distributions in the phantom were evaluated by the Monte Carlo method. When the left os coxae was taken as the organ-at-risk (OAR), the difference in absorbed dose between RBM and each CB and TB was up to 20%, but was much less (≤3.1%) between RBM and YBM. When the left os coxae and entire bone were both taken as OARs, RBM dose also increased with increasing planning target volume size. The results indicate the validity of using dose to homogeneous bone marrow mixture for estimating dose to RBM when RBM is not available in computational phantoms. In addition, the human skeletal system developed in this study provides a model for considering RBM dose in radiotherapy planning. (paper)

  4. Thiazole-based nitrogen mustards: Design, synthesis, spectroscopic studies, DFT calculation, molecular docking, and antiproliferative activity against selected human cancer cell lines

    Science.gov (United States)

    Łączkowski, Krzysztof Z.; Świtalska, Marta; Baranowska-Łączkowska, Angelika; Plech, Tomasz; Paneth, Agata; Misiura, Konrad; Wietrzyk, Joanna; Czaplińska, Barbara; Mrozek-Wilczkiewicz, Anna; Malarz, Katarzyna; Musioł, Robert; Grela, Izabela

    2016-09-01

    Synthesis, characterization and investigation of antiproliferative activity of ten thiazole-based nitrogen mustard against human cancer cells lines (MV4-11, A549, MCF-7 and HCT116) and normal mouse fibroblast (BALB/3T3) is presented. The structures of novel compounds were determined using 1H and 13C NMR, FAB(+)-MS, and elemental analyses. Among the derivatives, 5b, 5c, 5e, 5f and 5i were found to exhibit high activity against human leukaemia MV4-11 cells with IC50 values of 2.17-4.26 μg/ml. The cytotoxic activity of compound 5c and 5f against BALB/3T3 cells is up to 20 times lower than against cancer cell lines. Our results also show that compounds 5e and 5i have very strong activity against MCF-7 and HCT116 with IC50 values of 3.02-4.13 μg/ml. Moreover, spectroscopic characterization and cellular localization for selected compound were performed. In order to identify potential drug targets we perform computer simulations with DNA-binding site of hTopoI and hTopoII and quantum chemical calculation of interaction and binding energies in complexes of the five most active compounds with guanine.

  5. Comparison of Acuros (AXB) and Anisotropic Analytical Algorithm (AAA) for dose calculation in treatment of oesophageal cancer: effects on modelling tumour control probability

    International Nuclear Information System (INIS)

    To investigate systematic changes in dose arising when treatment plans optimised using the Anisotropic Analytical Algorithm (AAA) are recalculated using Acuros XB (AXB) in patients treated with definitive chemoradiotherapy (dCRT) for locally advanced oesophageal cancers. We have compared treatment plans created using AAA with those recalculated using AXB. Although the Anisotropic Analytical Algorithm (AAA) is currently more widely used in clinical routine, Acuros XB (AXB) has been shown to more accurately calculate the dose distribution, particularly in heterogeneous regions. Studies to predict clinical outcome should be based on modelling the dose delivered to the patient as accurately as possible. CT datasets from ten patients were selected for this retrospective study. VMAT (Volumetric modulated arc therapy) plans with 2 arcs, collimator rotation ± 5-10° and dose prescription 50 Gy / 25 fractions were created using Varian Eclipse (v10.0). The initial dose calculation was performed with AAA, and AXB plans were created by re-calculating the dose distribution using the same number of monitor units (MU) and multileaf collimator (MLC) files as the original plan. The difference in calculated dose to organs at risk (OAR) was compared using dose-volume histogram (DVH) statistics and p values were calculated using the Wilcoxon signed rank test. The potential clinical effect of dosimetric differences in the gross tumour volume (GTV) was evaluated using three different TCP models from the literature. PTV Median dose was apparently 0.9 Gy lower (range: 0.5 Gy - 1.3 Gy; p < 0.05) for VMAT AAA plans re-calculated with AXB and GTV mean dose was reduced by on average 1.0 Gy (0.3 Gy −1.5 Gy; p < 0.05). An apparent difference in TCP of between 1.2% and 3.1% was found depending on the choice of TCP model. OAR mean dose was lower in the AXB recalculated plan than the AAA plan (on average, dose reduction: lung 1.7%, heart 2.4%). Similar trends were seen for CRT plans

  6. [Cancer].

    Science.gov (United States)

    de la Peña-López, Roberto; Remolina-Bonilla, Yuly Andrea

    2016-09-01

    Cancer is a group of diseases which represents a significant public health problem in Mexico and worldwide. In Mexico neoplasms are the second leading cause of death. An increased morbidity and mortality are expected in the next decades. Several preventable risk factors for cancer development have been identified, the most relevant including tobacco use, which accounts for 30% of the cancer cases; and obesity, associated to another 30%. These factors, in turn, are related to sedentarism, alcohol abuse and imbalanced diets. Some agents are well knokn to cause cancer such as ionizing radiation, viruses such as the papilloma virus (HPV) and hepatitis virus (B and C), and more recently environmental pollution exposure and red meat consumption have been pointed out as carcinogens by the International Agency for Research in Cancer (IARC). The scientific evidence currently available is insufficient to consider milk either as a risk factor or protective factor against different types of cancer. PMID:27603890

  7. Monte Carlo simulations for thermodynamical properties calculations of plasmas at thermodynamical equilibrium. Applications to opacity and equation of state calculations; Apport d'un code de simulation Monte Carlo pour l'etude des proprietes thermodynamiques d'un plasma a l'equilibre et application au calcul de l'elargissement des profils de raies ioniques emises dans les plasmas denses, aux opacites spectrales et aux equations d'etat de systemes fluides

    Energy Technology Data Exchange (ETDEWEB)

    Gilles, D

    2005-07-01

    This report is devoted to illustrate the power of a Monte Carlo (MC) simulation code to study the thermodynamical properties of a plasma, composed of classical point particles at thermodynamical equilibrium. Such simulations can help us to manage successfully the challenge of taking into account 'exactly' all classical correlations between particles due to density effects, unlike analytical or semi-analytical approaches, often restricted to low dense plasmas. MC simulations results allow to cover, for laser or astrophysical applications, a wide range of thermodynamical conditions from more dense (and correlated) to less dense ones (where potentials are long ranged type). Therefore Yukawa potentials, with a Thomas-Fermi temperature- and density-dependent screening length, are used to describe the effective ion-ion potentials. In this report we present two MC codes ('PDE' and 'PUCE') and applications performed with these codes in different fields (spectroscopy, opacity, equation of state). Some examples of them are discussed and illustrated at the end of the report. (author)

  8. Uncertainty of empirical correlation equations

    Science.gov (United States)

    Feistel, R.; Lovell-Smith, J. W.; Saunders, P.; Seitz, S.

    2016-08-01

    The International Association for the Properties of Water and Steam (IAPWS) has published a set of empirical reference equations of state, forming the basis of the 2010 Thermodynamic Equation of Seawater (TEOS-10), from which all thermodynamic properties of seawater, ice, and humid air can be derived in a thermodynamically consistent manner. For each of the equations of state, the parameters have been found by simultaneously fitting equations for a range of different derived quantities using large sets of measurements of these quantities. In some cases, uncertainties in these fitted equations have been assigned based on the uncertainties of the measurement results. However, because uncertainties in the parameter values have not been determined, it is not possible to estimate the uncertainty in many of the useful quantities that can be calculated using the parameters. In this paper we demonstrate how the method of generalised least squares (GLS), in which the covariance of the input data is propagated into the values calculated by the fitted equation, and in particular into the covariance matrix of the fitted parameters, can be applied to one of the TEOS-10 equations of state, namely IAPWS-95 for fluid pure water. Using the calculated parameter covariance matrix, we provide some preliminary estimates of the uncertainties in derived quantities, namely the second and third virial coefficients for water. We recommend further investigation of the GLS method for use as a standard method for calculating and propagating the uncertainties of values computed from empirical equations.

  9. Differential equations

    CERN Document Server

    Hochstadt, Harry

    2012-01-01

    Modern approach to differential equations presents subject in terms of ideas and concepts rather than special cases and tricks which traditional courses emphasized. No prerequisites needed other than a good calculus course. Certain concepts from linear algebra used throughout. Problem section at end of each chapter.

  10. Beautiful equations

    Science.gov (United States)

    Viljamaa, Panu; Jacobs, J. Richard; Chris; JamesHyman; Halma, Matthew; EricNolan; Coxon, Paul

    2014-07-01

    In reply to a Physics World infographic (part of which is given above) about a study showing that Euler's equation was deemed most beautiful by a group of mathematicians who had been hooked up to a functional magnetic-resonance image (fMRI) machine while viewing mathematical expressions (14 May, http://ow.ly/xHUFi).

  11. Step-and-Shoot versus Compensator-based IMRT: Calculation and Comparison of Integral Dose in Non-tumoral and Target Organs in Prostate Cancer

    Directory of Open Access Journals (Sweden)

    Kaveh Shirani Tak Abi

    2015-05-01

    Full Text Available Introduction Intensity-Modulated Radiotherapy (IMRT is becoming an increasingly routine treatment method. IMRT can be delivered by use of conventional Multileaf Collimators (MLCs and/or physical compensators. One of the most important factors in selecting an appropriate IMRT technique is integral dose. Integral dose is equal to the mean energy deposited in the total irradiated volume of the patient. The aim of the present study was to calculate and compare the integral dose in normal and target organs in two different procedures of IMRT: Step-and-Shoot (SAS and compensator-based IMRT. Materials and Methods In this comparative study, five patients with prostate cancer were selected. Module Integrated Radiotherapy System was applied, using three energy ranges. In both treatment planning methods, the integral dose dramatically decreased by increasing energy. Results Comparison of two treatment methods showed that on average, the integral dose of body in SAS radiation therapy was about 1.62% lower than that reported in compensator-based IMRT. In planning target volume, rectum, bladder, and left and right femoral heads, the integral doses for SAS method were 1.01%, 1.02%, 1.11%, 1.47%, and 1.40% lower than compensator-based IMRT, respectively. Conclusion Considering the treatment conditions, the definition of dose volume constraints for healthy tissues, and the equal volume of organs in both treatment methods, SAS radiation therapy by providing a lower integral dose seems to be more advantageous and efficient for prostate cancer treatment, compared to compensator-based IMRT.

  12. The Use of the Health Disparities Calculator in Analysis of the Lung Cancer Burden in Urban and Rural Populations in the Świętokrzyskie Province (Poland: 1999–2010

    Directory of Open Access Journals (Sweden)

    Krzyżak Michalina

    2015-12-01

    Full Text Available The purpose of the study was a comparative analysis of the burden of lung cancer in urban and rural areas in the Świętokrzyskie Province in the years 1999–2010. The material for the study accounted for information about the number of new cases of lung cancer obtained from the Świętokrzyskie Cancer Registration Office in Kielce and data from the Central Statistical Office concerning the number of deaths due to lung cancer in the years 1999–2010. Crude and age-standardized incidence, mortality, and potential years of life lost rates were calculated separately for groups of men and women in urban and rural areas. A comparative analysis of coefficients in urban and rural areas based on Rate Ratio (RR and Rate Difference (RD was performed by using the Health Disparities Calculator. The average annual incidence of lung cancer among men was 18% lower in the urban population than in the rural, while the mortality rate was 16% lower. For women, the incidence and mortality rates were higher in urban areas as opposed to rural areas – by 48% and 54% respectively. The comparative analysis of the burden of lung cancer showed great diversity between urban and rural populations in the Świętokrzyskie Province.

  13. Electronic representation of wave equation

    Science.gov (United States)

    Veigend, Petr; Kunovský, Jiří; Kocina, Filip; Nečasová, Gabriela; Šátek, Václav; Valenta, Václav

    2016-06-01

    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.

  14. Calculations of reactivity based in the solution of the Neutron transport equation in X Y geometry and Lineal perturbation theory; Calculos de reactividad basados en la solucion de la Ecuacion de transporte de neutrones en geometria XY y Teoria de perturbacion lineal

    Energy Technology Data Exchange (ETDEWEB)

    Valle G, E. del; Mugica R, C.A. [IPN, ESFM, Departamento de Ingenieria Nuclear, 07738 Mexico D.F. (Mexico)]. e-mail: cmugica@ipn.mx

    2005-07-01

    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)

  15. Nuclear equation of state

    International Nuclear Information System (INIS)

    We present part of our (direct or indirect) knwoledge of the equation of state of nuclear matter in a density-temperature domain for which nucleonic effects are dominant (densities smaller than 2-4 times the saturation density and temperatures smaller than 10-20 MeV). The lectures are divided into three parts corresponding, respectiveley, to direct studies close to the saturation, to the astrophysical case and to the studies involving heavy-ion collisions. In chapter one, after a brief introduction to the concept of equation of state, we discuss the saturation property of nuclear matter. The notion of incompressibility modulus is also introduced and its value is discussed in detail. Nuclear matter calculations trying to reproduce saturation from a nucleon-nucleon interaction are also briefly presented. In chapter two we study the equation of state in the astrophysical context. The role of the nuclear component is discussed in detail for the final phase of the collapse of supernovae cores. A brief presentation of calculations of dense matter constituting neutron stars is also given. Chapter three is devoted to heavy-ion collisions below 500-600 MeV per nucleon. After a brief presentation of both theoretical and experimental frameworks, we focus on three particular aspects which could have a link with the nuclear matter equation of state: the formation of intermediate mass fragments, flow effects and subthreshold particle production

  16. Marcus equation

    Science.gov (United States)

    1998-09-21

    In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.

  17. Target volume coverage and dose to organs at risk in prostate cancer patients. Dose calculation on daily cone-beam CT data sets

    International Nuclear Information System (INIS)

    On the basis of correct Hounsfield unit to electron density calibration, cone-beam computed tomography (CBCT) data provide the opportunity for retrospective dose recalculation in the patient. Therefore, the consequences of translational positioning corrections and of morphological changes in the patient anatomy can be quantified for prostate cancer patients. The organs at risk were newly contoured on the CBCT data sets of 7 patients so as to evaluate the actual applied dose. The daily dose to the planning target volume (PTV) was recalculated with and without the translation data, which result from the real patient repositioning. A CBCT-based dose recalculation with uncertainties less than 3 % is possible. The deviations between the planning CT and the CBCT without the translational positioning correction vector show an average dose difference of - 8 % inside the PTV. An inverse proportional relation between the mean bladder dose and the actual volume of the bladder could be established. The daily applied dose to the rectum is about 1-54 % higher than predicted by the planning CT. A dose calculation based on CBCT data is possible. The daily positioning correction of the patient is necessary to avoid an underdosage in the PTV. The new contouring of the organs at risk - the bladder and rectum - allows a better appraisal to be made of the total applied dose to these organs. (orig.)

  18. Dosimetric calculation of I-131 activity for the treatment to patients having differentiated thyroid cancer. Benefits and limitations; Calculo dosimetrico de la actividad de I-131 para tratamiento de pacientes con cancer diferenciado de tiroides (CADT). Beneficios y limitaciones

    Energy Technology Data Exchange (ETDEWEB)

    Cabrejas, R. C.; Chebel, G. M.; Fadel, A. M.; Rojo, A. M.; Deluca, G.; Degross, O. J.; Valdivieso, C. M.; Carbejas, M. L.

    2006-07-01

    Maximum safe activity calculation, that has to be administered for treatment to patients having Differentiated Thyroid Cancer (CADT). No important side effects should be produced. Post treatment evolution was analysed. 23 Dosimetric studies were performed determining blood and whole body uptake curves (CE)during 5 days. Using the MIRDOSE software, the maximum safe activity in the whole body (CE)was calculated. The retained activity in the body (AR), 48 hs. post tracer dose. Should have been less than 2.96 GBq so as to avoid lung fibrosis. 17 patients that received activities<11.1 GBq, had no side effects. Three patients presents special situations: high AR, users in the mouth, and plaque to and leucopenia. This methodology has benefits because AT can be estimated. This was possible for 85% of the patients. When AR was high at 48 hr, AT was diminished to avoid pulmonary lesions. Tumor absorbed dose estimation, will allow the administration of AT>11.1 GBq in the future. (Author)

  19. Reactor lattice transport calculations

    International Nuclear Information System (INIS)

    The present lecture is a continuation of the lecture on Introduction to the Neutron Transport Phenomena. It comprises three aspects of lattice calculations. First the idea of a reactor lattice is introduced. Then the main definitions used in reactor lattice analysis are given, and finally two basic methods applied for solution of the transport equations are defined. Several remarks on secondary results from lattice transport calculations are added. (author)

  20. Integral equations

    CERN Document Server

    Tricomi, Francesco Giacomo

    1957-01-01

    This classic text on integral equations by the late Professor F. G. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, well-written treatment of the subject at the graduate or advanced undergraduate level. To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the reader to a minimum; a solid foundation in differential and integral calculus, together with some knowledge of the theory of functions is sufficient. The book is divided into four chapters, with two useful

  1. Prostate cancer is not breast cancer

    Directory of Open Access Journals (Sweden)

    Ajit Venniyoor

    2016-01-01

    Full Text Available Cancers of the prostate and breast are hormone dependent cancers. There is a tendency to equate them and apply same algorithms for treatment. It is pointed out that metastatic prostate cancer with bone-only disease is a potentially fatal condition with a much poorer prognosis than metastatic breast cancer and needs a more aggressive approach.

  2. Prostate cancer is not breast cancer

    OpenAIRE

    Ajit Venniyoor

    2016-01-01

    Cancers of the prostate and breast are hormone dependent cancers. There is a tendency to equate them and apply same algorithms for treatment. It is pointed out that metastatic prostate cancer with bone-only disease is a potentially fatal condition with a much poorer prognosis than metastatic breast cancer and needs a more aggressive approach.

  3. New models and online calculator for predicting non-sentinel lymph node status in sentinel lymph node positive breast cancer patients

    Directory of Open Access Journals (Sweden)

    Johnson Denise L

    2008-03-01

    Full Text Available Abstract Background Current practice is to perform a completion axillary lymph node dissection (ALND for breast cancer patients with tumor-involved sentinel lymph nodes (SLNs, although fewer than half will have non-sentinel node (NSLN metastasis. Our goal was to develop new models to quantify the risk of NSLN metastasis in SLN-positive patients and to compare predictive capabilities to another widely used model. Methods We constructed three models to predict NSLN status: recursive partitioning with receiver operating characteristic curves (RP-ROC, boosted Classification and Regression Trees (CART, and multivariate logistic regression (MLR informed by CART. Data were compiled from a multicenter Northern California and Oregon database of 784 patients who prospectively underwent SLN biopsy and completion ALND. We compared the predictive abilities of our best model and the Memorial Sloan-Kettering Breast Cancer Nomogram (Nomogram in our dataset and an independent dataset from Northwestern University. Results 285 patients had positive SLNs, of which 213 had known angiolymphatic invasion status and 171 had complete pathologic data including hormone receptor status. 264 (93% patients had limited SLN disease (micrometastasis, 70%, or isolated tumor cells, 23%. 101 (35% of all SLN-positive patients had tumor-involved NSLNs. Three variables (tumor size, angiolymphatic invasion, and SLN metastasis size predicted risk in all our models. RP-ROC and boosted CART stratified patients into four risk levels. MLR informed by CART was most accurate. Using two composite predictors calculated from three variables, MLR informed by CART was more accurate than the Nomogram computed using eight predictors. In our dataset, area under ROC curve (AUC was 0.83/0.85 for MLR (n = 213/n = 171 and 0.77 for Nomogram (n = 171. When applied to an independent dataset (n = 77, AUC was 0.74 for our model and 0.62 for Nomogram. The composite predictors in our model were the product of

  4. New models and online calculator for predicting non-sentinel lymph node status in sentinel lymph node positive breast cancer patients

    International Nuclear Information System (INIS)

    Current practice is to perform a completion axillary lymph node dissection (ALND) for breast cancer patients with tumor-involved sentinel lymph nodes (SLNs), although fewer than half will have non-sentinel node (NSLN) metastasis. Our goal was to develop new models to quantify the risk of NSLN metastasis in SLN-positive patients and to compare predictive capabilities to another widely used model. We constructed three models to predict NSLN status: recursive partitioning with receiver operating characteristic curves (RP-ROC), boosted Classification and Regression Trees (CART), and multivariate logistic regression (MLR) informed by CART. Data were compiled from a multicenter Northern California and Oregon database of 784 patients who prospectively underwent SLN biopsy and completion ALND. We compared the predictive abilities of our best model and the Memorial Sloan-Kettering Breast Cancer Nomogram (Nomogram) in our dataset and an independent dataset from Northwestern University. 285 patients had positive SLNs, of which 213 had known angiolymphatic invasion status and 171 had complete pathologic data including hormone receptor status. 264 (93%) patients had limited SLN disease (micrometastasis, 70%, or isolated tumor cells, 23%). 101 (35%) of all SLN-positive patients had tumor-involved NSLNs. Three variables (tumor size, angiolymphatic invasion, and SLN metastasis size) predicted risk in all our models. RP-ROC and boosted CART stratified patients into four risk levels. MLR informed by CART was most accurate. Using two composite predictors calculated from three variables, MLR informed by CART was more accurate than the Nomogram computed using eight predictors. In our dataset, area under ROC curve (AUC) was 0.83/0.85 for MLR (n = 213/n = 171) and 0.77 for Nomogram (n = 171). When applied to an independent dataset (n = 77), AUC was 0.74 for our model and 0.62 for Nomogram. The composite predictors in our model were the product of angiolymphatic invasion and size of SLN

  5. Numerical Calculation of Transport Based on the Drift-Kinetic Equation for Plasmas in General Toroidal Magnetic Geometry: Numerical Methods; Calculo Numerico de Transporte mediante la Ecuacion Cinetica de Deriva para Plasmas en Geometria Magnetica Toroidal: Metodos Numericos

    Energy Technology Data Exchange (ETDEWEB)

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

    2009-10-12

    In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs.

  6. Non RG logarithms via RG equations

    OpenAIRE

    Malyshev, Dmitry

    2004-01-01

    We compute complete leading logarithms in $\\Phi^4$ theory with the help of Connes and Kreimer RG equations. These equations are defined in the Lie algebra dual to the Hopf algebra of graphs. The results are compared with calculations in parquet approximation. An interpretation of the new RG equations is discussed.

  7. Multidimensional quasilinear first-order equations and multivalued solutions of the elliptic and hyperbolic equations

    Science.gov (United States)

    Zhuravlev, V. M.

    2016-03-01

    We discuss an extension of the theory of multidimensional second-order equations of the elliptic and hyperbolic types related to multidimensional quasilinear autonomous first-order partial differential equations. Calculating the general integrals of these equations allows constructing exact solutions in the form of implicit functions. We establish a connection with hydrodynamic equations. We calculate the number of free functional parameters of the constructed solutions. We especially construct and analyze implicit solutions of the Laplace and d'Alembert equations in a coordinate space of arbitrary finite dimension. In particular, we construct generalized Penrose-Rindler solutions of the d'Alembert equation in 3+1 dimensions.

  8. Radioactivity Calculations

    Science.gov (United States)

    Onega, Ronald J.

    1969-01-01

    Three problems in radioactive buildup and decay are presented and solved. Matrix algebra is used to solve the second problem. The third problem deals with flux depression and is solved by the use of differential equations. (LC)

  9. Boltzmann equation and hydrodynamic fluctuations.

    Science.gov (United States)

    Colangeli, Matteo; Kröger, Martin; Ottinger, Hans Christian

    2009-11-01

    We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed in the special case of Maxwell molecules. We investigate, through the comparison with experimental data and former approaches, the spectrum of density fluctuations and address the regime of finite Knudsen numbers and finite frequencies hydrodynamics. PMID:20364972

  10. Boltzmann equation and hydrodynamic fluctuations

    OpenAIRE

    Colangeli, M.; Kroger, M.; Ottinger, H. C.

    2009-01-01

    We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed in the special case of Maxwell molecules. We investigate, through the comparison with experimental data and former approaches, the spectrum of density fluctuations and address the regime of finite Knudsen numbers and finite frequencies hydrodynamics.

  11. CANCER

    Directory of Open Access Journals (Sweden)

    N. Kavoussi

    1973-09-01

    Full Text Available There are many carcinogenetic elements in industry and it is for this reason that study and research concerning the effect of these materials is carried out on a national and international level. The establishment and growth of cancer are affected by different factors in two main areas:-1 The nature of the human or animal including sex, age, point and method of entry, fat metabolism, place of agglomeration of carcinogenetic material, amount of material absorbed by the body and the immunity of the body.2 The different nature of the carcinogenetic material e.g. physical, chemical quality, degree of solvency in fat and purity of impurity of the element. As the development of cancer is dependent upon so many factors, it is extremely difficult to determine whether a causative element is principle or contributory. Some materials are not carcinogenetic when they are pure but become so when they combine with other elements. All of this creates an industrial health problem in that it is almost impossible to plan an adequate prevention and safety program. The body through its system of immunity protects itself against small amounts of carcinogens but when this amount increases and reaches a certain level the body is not longer able to defend itself. ILO advises an effective protection campaign against cancer based on the Well –equipped laboratories, Well-educated personnel, the establishment of industrial hygiene within factories, the regular control of safety systems, and the implementation of industrial health principles and research programs.

  12. 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

  13. Study of 201 Non-Small Cell Lung Cancer Patients Given Stereotactic Ablative Radiation Therapy Shows Local Control Dependence on Dose Calculation Algorithm

    International Nuclear Information System (INIS)

    Purpose: Pencil beam (PB) and collapsed cone convolution (CCC) dose calculation algorithms differ significantly when used in the thorax. However, such differences have seldom been previously directly correlated with outcomes of lung stereotactic ablative body radiation (SABR). Methods and Materials: Data for 201 non-small cell lung cancer patients treated with SABR were analyzed retrospectively. All patients were treated with 50 Gy in 5 fractions of 10 Gy each. The radiation prescription mandated that 95% of the planning target volume (PTV) receive the prescribed dose. One hundred sixteen patients were planned with BrainLab treatment planning software (TPS) with the PB algorithm and treated on a Novalis unit. The other 85 were planned on the Pinnacle TPS with the CCC algorithm and treated on a Varian linac. Treatment planning objectives were numerically identical for both groups. The median follow-up times were 24 and 17 months for the PB and CCC groups, respectively. The primary endpoint was local/marginal control of the irradiated lesion. Gray's competing risk method was used to determine the statistical differences in local/marginal control rates between the PB and CCC groups. Results: Twenty-five patients planned with PB and 4 patients planned with the CCC algorithms to the same nominal doses experienced local recurrence. There was a statistically significant difference in recurrence rates between the PB and CCC groups (hazard ratio 3.4 [95% confidence interval: 1.18-9.83], Gray's test P=.019). The differences (Δ) between the 2 algorithms for target coverage were as follows: ΔD99GITV = 7.4 Gy, ΔD99PTV = 10.4 Gy, ΔV90GITV = 13.7%, ΔV90PTV = 37.6%, ΔD95PTV = 9.8 Gy, and ΔDISO = 3.4 Gy. GITV = gross internal tumor volume. Conclusions: Local control in patients receiving who were planned to the same nominal dose with PB and CCC algorithms were statistically significantly different. Possible alternative explanations are described in

  14. The dirac equation in the algebraic approximation : VIII. Comparison of finite basis set and finite element molecular Dirac-Hartree-Fock calculations for the H-2, LiH, and BH ground states

    NARCIS (Netherlands)

    Quiney, HM; Glushkov, VN; Wilson, S

    2002-01-01

    Using basis sets of distributed s-type Gaussian functions with positions and exponents optimized so as to support Hartree-Fock total energies with an accuracy approaching the sub-muHartree level, Dirac-Hartree-Fock-Coulomb calculations are reported for the ground states of the H-2, LiH, and BH molec

  15. Calculation of two Belyi pairs

    OpenAIRE

    Dremov, V. A.

    2008-01-01

    We calculate two Belyi pairs using the properties of Mulase-Penkava differential. Details are provided including accurate construction of coordinates, variables and equations. The calculation is a part of the work which results in a catalogue arXiv:0710.2658

  16. SU-E-J-100: The Combination of Deformable Image Registration and Regions-Of-Interest Mapping Technique to Accomplish Accurate Dose Calculation On Cone Beam Computed Tomography for Esophageal Cancer

    Energy Technology Data Exchange (ETDEWEB)

    Huang, B-T; Lu, J-Y [Cancer Hospital of Shantou University Medical College, Shantou (China)

    2015-06-15

    Purpose: We introduce a new method combined with the deformable image registration (DIR) and regions-of-interest mapping (ROIM) technique to accurately calculate dose on daily CBCT for esophageal cancer. Methods: Patients suffered from esophageal cancer were enrolled in the study. Prescription was set to 66 Gy/30 F and 54 Gy/30 F to the primary tumor (PTV66) and subclinical disease (PTV54) . Planning CT (pCT) were segmented into 8 substructures in terms of their differences in physical density, such as gross target volume (GTV), venae cava superior (SVC), aorta, heart, spinal cord, lung, muscle and bones. The pCT and its substructures were transferred to the MIM software to readout their mean HU values. Afterwards, a deformable planning CT to daily KV-CBCT image registration method was then utilized to acquire a new structure set on CBCT. The newly generated structures on CBCT were then transferred back to the treatment planning system (TPS) and its HU information were overridden manually with mean HU values obtained from pCT. Finally, the treatment plan was projected onto the CBCT images with the same beam arrangements and monitor units (MUs) to accomplish dose calculation. Planning target volume (PTV) and organs at risk (OARs) from both of the pCT and CBCT were compared to evaluate the dose calculation accuracy. Results: It was found that the dose distribution in the CBCT showed little differences compared to the pCT, regardless of whether PTV or OARs were concerned. Specifically, dose variation in GTV, PTV54, PTV66, SVC, lung and heart were within 0.1%. The maximum dose variation was presented in the spinal cord, which was up to 2.7% dose difference. Conclusion: The proposed method combined with DIR and ROIM technique to accurately calculate dose distribution on CBCT for esophageal cancer is feasible.

  17. SU-E-J-100: The Combination of Deformable Image Registration and Regions-Of-Interest Mapping Technique to Accomplish Accurate Dose Calculation On Cone Beam Computed Tomography for Esophageal Cancer

    International Nuclear Information System (INIS)

    Purpose: We introduce a new method combined with the deformable image registration (DIR) and regions-of-interest mapping (ROIM) technique to accurately calculate dose on daily CBCT for esophageal cancer. Methods: Patients suffered from esophageal cancer were enrolled in the study. Prescription was set to 66 Gy/30 F and 54 Gy/30 F to the primary tumor (PTV66) and subclinical disease (PTV54) . Planning CT (pCT) were segmented into 8 substructures in terms of their differences in physical density, such as gross target volume (GTV), venae cava superior (SVC), aorta, heart, spinal cord, lung, muscle and bones. The pCT and its substructures were transferred to the MIM software to readout their mean HU values. Afterwards, a deformable planning CT to daily KV-CBCT image registration method was then utilized to acquire a new structure set on CBCT. The newly generated structures on CBCT were then transferred back to the treatment planning system (TPS) and its HU information were overridden manually with mean HU values obtained from pCT. Finally, the treatment plan was projected onto the CBCT images with the same beam arrangements and monitor units (MUs) to accomplish dose calculation. Planning target volume (PTV) and organs at risk (OARs) from both of the pCT and CBCT were compared to evaluate the dose calculation accuracy. Results: It was found that the dose distribution in the CBCT showed little differences compared to the pCT, regardless of whether PTV or OARs were concerned. Specifically, dose variation in GTV, PTV54, PTV66, SVC, lung and heart were within 0.1%. The maximum dose variation was presented in the spinal cord, which was up to 2.7% dose difference. Conclusion: The proposed method combined with DIR and ROIM technique to accurately calculate dose distribution on CBCT for esophageal cancer is feasible

  18. Lithium equation-of-state

    International Nuclear Information System (INIS)

    In 1977, Dave Young published an equation-of-state (EOS) for lithium. This EOS was used by Lew Glenn in his AFTON calculations of the HYLIFE inertial-fusion-reactor hydrodynamics. In this paper, I summarize Young's development of the EOS and demonstrate a computer program (MATHSY) that plots isotherms, isentropes and constant energy lines on a P-V diagram

  19. Quadratic field equations on the brane

    International Nuclear Information System (INIS)

    It is shown that four-dimensional vacuum Einstein solutions simply embedded in five dimensions obey the Gauss-Bonnet-Einstein field equations: Gab+ αGBab + δ55abαexp[-2χ/√α]GB4 = 0 and the Pauli-Einstein equations Gab - 3αPab/5 = 0, and the Bach-Einstein equations Bab = 0. General equations are calculated for which these and similar results follow. It is briefly argued that such field equations could be significant on large distance scales.

  20. MEMS Calculator

    Science.gov (United States)

    SRD 166 MEMS Calculator (Web, free access)   This MEMS Calculator determines the following thin film properties from data taken with an optical interferometer or comparable instrument: a) residual strain from fixed-fixed beams, b) strain gradient from cantilevers, c) step heights or thicknesses from step-height test structures, and d) in-plane lengths or deflections. Then, residual stress and stress gradient calculations can be made after an optical vibrometer or comparable instrument is used to obtain Young's modulus from resonating cantilevers or fixed-fixed beams. In addition, wafer bond strength is determined from micro-chevron test structures using a material test machine.

  1. Prediction of crude fat content of longissimus muscle of beef using the ratio of fat area calculated from computer image analysis: Comparison of regression equations for prediction using different input devices at different stations

    OpenAIRE

    KUCHIDA, Keigo; Kono, S.; KONISHI, Kazuyuki; Van, Vleck LD; SUZUKI, Mitsuyoshi; Miyoshi, Syunzou; 口田, 圭吾; 小西, 一之; 鈴木, 三義; 三好, 俊三

    2000-01-01

    Crude fat content of longissimus (ribeye) muscle of beef cattle was predicted from a ratio of fat area (RFA) to area of ribeye muscle calculated from computer image analysis (CIA). Cross sections of 64 ribeyes taken from the 6-7(th) rib from cattle at experiment station A and cross sections of 94 ribeyes taken from the 6-7(th) rib from cattle at Experiment Station B were used in this study. Slices (1 to 1.5 cm in thickness) of just the Longissimus dorsi were homogenized and sampled for chemic...

  2. Partial Differential Equations

    CERN Document Server

    1988-01-01

    The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.

  3. 立方型状态方程结合Eyring理论在液体混合物黏度计算中的应用%Calculation of Viscosities of Liquid Mixtures Using Eyring's Theory in Combination with Cubic Equations of State

    Institute of Scientific and Technical Information of China (English)

    计伟荣; D.A.Lempe

    2006-01-01

    Cubic equations of state (EOS) have been combined with the absolute rate theory of Eyring to calculate viscosities of liquid mixtures. A modified Huron-Vidal gE-mixing rule is employed in the calculation and in comparison with the van Laar and the Redlich-Kister-type mixing rule. The EOS method gives an accurate correlation of liquid viscosities with an overall average deviation less than 1% for 67 binary systems including aqueous solutions. It is also successful in extrapolating viscosity data over a certain temperature range using parameters obtained from the isotherm at a given temperature and in predicting viscosities of ternary solutions from binary parameters for either polar or associated systems.

  4. Calculation of longitudinal stiffness of mid-tower in multi-span suspension bridges based on catenary equation%主缆为悬链线的多塔悬索桥的中塔刚度计算

    Institute of Scientific and Technical Information of China (English)

    张学义; 谭红梅; 肖汝诚; 柴生波

    2014-01-01

    The main cable was treated as springs in considering its constraint on the tower .The for-mula of the longitudinal constraint stiffness of springs was derived by variational method based on cat-enary equation ,and a finite element model was established for verification .The results show that the tower stiffness formula based on catenary has higher accuracy ;the cable spring stiffness is mainly re-lated to the unit length weight of the bridge as well as the horizontal and vertical components of the main cable in the overhead of the mid-tower ,while the unstressed length of the main cable is deter-mined .%以悬链线方程为基础,将主缆对桥塔的约束等效为弹簧,通过变分方法推导了主缆对多塔悬索桥中塔纵向弹簧约束刚度的表达式,并建立有限元模型对公式进行验证。研究结果表明:基于悬链线的中塔刚度公式比已有文献具有更高的精度,在主缆无应力长度确定的情况下,主缆弹簧刚度主要与荷载集度、主缆在塔顶的水平及竖向分力有关。

  5. 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.

  6. The Boltzmann equation in the difference formulation

    International Nuclear Information System (INIS)

    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.

  7. Reliability Calculations

    DEFF Research Database (Denmark)

    Petersen, Kurt Erling

    1986-01-01

    probabilistic approaches have been introduced in some cases for the calculation of the reliability of structures or components. A new computer program has been developed based upon numerical integration in several variables. In systems reliability Monte Carlo simulation programs are used especially in analysis...... of very complex systems. In order to increase the applicability of the programs variance reduction techniques can be applied to speed up the calculation process. Variance reduction techniques have been studied and procedures for implementation of importance sampling are suggested....

  8. Soliton equations solved by the boundary CFT

    OpenAIRE

    SAITO, Satoru; Sato, Ryuichi

    2003-01-01

    Soliton equations are derived which characterize the boundary CFT a la Callan et al. Soliton fields of classical soliton equations are shown to appear as a neutral bound state of a pair of soliton fields of BCFT. One soliton amplitude under the influence of the boundary is calculated explicitly and is shown that it is frozen at the Dirichlet limit.

  9. Cancer Basics

    Science.gov (United States)

    ... Cancer? Breast Cancer Colon/Rectum Cancer Lung Cancer Prostate Cancer Skin Cancer Show All Cancer Types News and Features Cancer Glossary ACS Bookstore Cancer Information Cancer Basics Cancer Prevention & Detection Signs & Symptoms of Cancer Treatments & Side Effects ...

  10. A New Route to the Majorana Equation

    Directory of Open Access Journals (Sweden)

    Eckart Marsch

    2013-09-01

    Full Text Available In this paper, we suggest an alternative strategy to derive the complex two-component Majorana equation with a mass term and elucidate the related Lorentz transformation. The Majorana equation is established completely on its own, rather than derived from the chiral Dirac equation. Thereby, use is made of the complex conjugation operator and Pauli spin matrices only. The eigenfunctions of the two-component complex Majorana equation are also calculated. The associated quantum fields are found to describe particles and antiparticles, which have opposite mean helicities and are not their own antiparticles, but correspond to two independent degrees of freedom. The four-component real Dirac equation in its Majorana representation is shown to be the natural outcome of the two-component complex Majorana equation. Both types of equations come in two forms, which correspond to the irreducible left- and right-chiral representations of the Lorentz group.

  11. SU-E-T-85: Comparison of Treatment Plans Calculated Using Ray Tracing and Monte Carlo Algorithms for Lung Cancer Patients Having Undergone Radiotherapy with Cyberknife

    International Nuclear Information System (INIS)

    Purpose: The latest publications indicate that the Ray Tracing algorithm significantly overestimates the dose delivered as compared to the Monte Carlo (MC) algorithm. The purpose of this study is to quantify this overestimation and to identify significant correlations between the RT and MC calculated dose distributions. Methods: Preliminary results are based on 50 preexisting RT algorithm dose optimization and calculation treatment plans prepared on the Multiplan treatment planning system (Accuray Inc., Sunnyvale, CA). The analysis will be expanded to include 100 plans. These plans are recalculated using the MC algorithm, with high resolution and 1% uncertainty. The geometry and number of beams for a given plan, as well as the number of monitor units, is constant for the calculations for both algorithms and normalized differences are compared. Results: MC calculated doses were significantly smaller than RT doses. The D95 of the PTV was 27% lower for the MC calculation. The GTV and PTV mean coverage were 13 and 39% less for MC calculation. The first parameter of conformality, as defined as the ratio of the Prescription Isodose Volume to the PTV Volume was on average 1.18 for RT and 0.62 for MC. Maximum doses delivered to OARs was reduced in the MC plans. The doses for 1000 and 1500 cc of total lung minus PTV, respectively were reduced by 39% and 53% for the MC plans. The correlation of the ratio of air in PTV to the PTV with the difference in PTV coverage had a coefficient of −0.54. Conclusion: The preliminary results confirm that the RT algorithm significantly overestimates the dosages delivered confirming previous analyses. Finally, subdividing the data into different size regimes increased the correlation for the smaller size PTVs indicating the MC algorithm improvement verses the RT algorithm is dependent upon the size of the PTV

  12. Difference equations by differential equation methods

    CERN Document Server

    Hydon, Peter E

    2014-01-01

    Most well-known solution techniques for differential equations exploit symmetry in some form. Systematic methods have been developed for finding and using symmetries, first integrals and conservation laws of a given differential equation. Here the author explains how to extend these powerful methods to difference equations, greatly increasing the range of solvable problems. Beginning with an introduction to elementary solution methods, the book gives readers a clear explanation of exact techniques for ordinary and partial difference equations. The informal presentation is suitable for anyone who is familiar with standard differential equation methods. No prior knowledge of difference equations or symmetry is assumed. The author uses worked examples to help readers grasp new concepts easily. There are 120 exercises of varying difficulty and suggestions for further reading. The book goes to the cutting edge of research; its many new ideas and methods make it a valuable reference for researchers in the field.

  13. Alternative to the Kohn-Sham equations: The Pauli potential differential equation

    Science.gov (United States)

    Levämäki, H.; Nagy, Á.; Kokko, K.; Vitos, L.

    2015-12-01

    A recently developed theoretical framework of performing self-consistent orbital-free (OF) density functional theory (DFT) calculations at Kohn-Sham DFT level accuracy is tested in practice. The framework is valid for spherically symmetric systems. Numerical results for the Beryllium atom are presented and compared to accurate Kohn-Sham data. These calculations make use of a differential equation that we have developed for the so called Pauli potential, a key quantity in OF-DFT. The Pauli potential differential equation and the OF Euler equation form a system of two coupled differential equations, which have to be solved simultaneously within the DFT self-consistent loop.

  14. Recent calculational work at Department of Reactor Physics CTH

    International Nuclear Information System (INIS)

    Short presentations are given on various ANISN calculations, on studies of the Xe reactivity effect, on some Monte Carlo calculations, and on benchmark calculations of eigenvalues to the Boltzmann transport equation. (author)

  15. Random diophantine equations, I

    OpenAIRE

    Brüdern, Jörg; Dietmann, Rainer

    2012-01-01

    We consider additive diophantine equations of degree $k$ in $s$ variables and establish that whenever $s\\ge 3k+2$ then almost all such equations satisfy the Hasse principle. The equations that are soluble form a set of positive density, and among the soluble ones almost all equations admit a small solution. Our bound for the smallest solution is nearly best possible.

  16. SPEI Calculator

    OpenAIRE

    Beguería, Santiago; Vicente Serrano, Sergio M.

    2009-01-01

    [EN] *Objectives: The program calculates time series of the Standardised Precipitation-Evapotransporation Index (SPEI). *Technical Characteristics: The program is executed from the Windows console. From an input data file containing monthly time series of precipitation and mean temperature, plus the geographic coordinates of the observatory, the program computes the SPEI accumulated at the time interval specified by the user, and generates a new data file with the SPEI time serie...

  17. Confidence interval in Kirsch equations

    Directory of Open Access Journals (Sweden)

    Morteza Khodabin

    2014-09-01

    Full Text Available Rocks at depth are affected by stresses resulting from the weight of the overlying strata and tectonic stresses. When a tunnel is excavated in this rock, the stress field is locally disordered and radial, tangential and shear stresses are induced in the rock around the tunnel. Knowledge of the magnitudes and directions of these induced stresses is essential. Since the measuring of specific gravity and depth are inevitably affected by environmental noise, we consider a random version of P2 in Kirsch equations. By doing this, we define random version of the Kirsch equations. Then we introduce an algorithm to calculate confidence intervals for the Kirsch parameters. Finally we use Alborz tunnel characteristics for creating these confidence intervals as a case study. The results show that the proposed amounts of radial, tangential and shear stresses lie in desired range. Keywords: Kirsch equations; Confidence interval; confidence level; Alborz tunnel; normal distribution.

  18. Calculations of turbulent separated flows

    Science.gov (United States)

    Zhu, J.; Shih, T. H.

    1993-01-01

    A numerical study of incompressible turbulent separated flows is carried out by using two-equation turbulence models of the K-epsilon type. On the basis of realizability analysis, a new formulation of the eddy-viscosity is proposed which ensures the positiveness of turbulent normal stresses - a realizability condition that most existing two-equation turbulence models are unable to satisfy. The present model is applied to calculate two backward-facing step flows. Calculations with the standard K-epsilon model and a recently developed RNG-based K-epsilon model are also made for comparison. The calculations are performed with a finite-volume method. A second-order accurate differencing scheme and sufficiently fine grids are used to ensure the numerical accuracy of solutions. The calculated results are compared with the experimental data for both mean and turbulent quantities. The comparison shows that the present model performs quite well for separated flows.

  19. The Generalized Jacobi Equation

    OpenAIRE

    Chicone, C.; Mashhoon, B.

    2002-01-01

    The Jacobi equation in pseudo-Riemannian geometry determines the linearized geodesic flow. The linearization ignores the relative velocity of the geodesics. The generalized Jacobi equation takes the relative velocity into account; that is, when the geodesics are neighboring but their relative velocity is arbitrary the corresponding geodesic deviation equation is the generalized Jacobi equation. The Hamiltonian structure of this nonlinear equation is analyzed in this paper. The tidal accelerat...

  20. Numerical Solutions of Fractional Boussinesq Equation

    Institute of Scientific and Technical Information of China (English)

    WANG Qi

    2007-01-01

    Based upon the Adomian decomposition method,a scheme is developed to obtain numerical solutions of a fractional Boussinesq equation with initial condition,which is introduced by replacing some order time and space derivatives by fractional derivatives.The fractional derivatives are described in the Caputo sense.So the traditional Adomian decomposition method for differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional differential equations.The solutions of our model equation are calculated in the form of convergent series with easily computable components.

  1. Equations for calculation of NaCl/( NaCl + CaCl2 ) ratios and salinities from hydrohalite-melting and ice-melting temperatures in the H2O-NaCl-CaCl2 system%利用H2O-NaCl-CaCl2体系水盐化合物和冰的融化温度计算NaCl/(NaCl+CaCl2)比值和盐度的方程

    Institute of Scientific and Technical Information of China (English)

    Guoxiang Chi; Pei Ni

    2007-01-01

    The composition of fluid inclusions in the H2O-NaCl-CaCl2 system has been generally graphically estimated using the melting temperatures of hydrohalite ( Tm-HH ) and ice ( Tm-ice ). Here we present two equations that can be used to calculate the relative proportion of NaCl ( i. e. , NaCt/[ NaCl + CaCl2 ], or XNaCl) and the total salinity ( i. e. , NaCl + CaCl2, wt% ) for fluid inclusions with ice as the last melting phase. XNaCl can be calculated from Tm-HH using the following equation:y= ( a + bx)-1/c where y is XNaCl, x is Tm-HH, a =0. 33124402, b = -0.031518028, and c =0. 22932736. In the cases where only Tm-ice is measured and Tm-HH is not known, Tm-ice can be used as the maximum possible Tm-HH to calculate the maximum value of XNaCl using the above equation. In these cases, the following equation can be used to calculate the maximum total salinity: y = (a +bx +cx2) -1 where y is salinity, x is Tm-HH, a = 0. 057184817, b = 0. 00078565757, and c = 5. 7262766E-6. Because the isothems in the field of ice are sub-parallel to the NaCl-CaCl2 binary side in the H2O-NaCl-CaCl2 ternary system, the errors in salinity calculation introduced by the above approximation are small ( less than 2 wt% ). A Windows program for calculation of XNacl and salinity is available at: http ://uregina. ca/~ chiguox.

  2. Get Tested for Colon Cancer: Here's How

    Medline Plus

    Full Text Available ... Offices Close + - Text Size Get Tested for Colon Cancer [Video] This free video explains the most commonly ... Tools and Calculators Information for Health Care Professionals Cancer Information Cancer Basics Cancer Prevention & Detection Signs & Symptoms ...

  3. Get Tested for Colon Cancer: Here's How

    Medline Plus

    Full Text Available ... You Stay Well Tools and Calculators Information for Health Care Professionals Cancer Information Cancer Basics Cancer Prevention & ... Sites Bookstore ACS CAN Marketplace Cancer Atlas Global Health Finish the Fight Press Room Mobile Site Help ...

  4. Get Tested for Colon Cancer: Here's How

    Medline Plus

    Full Text Available ... You Stay Well Tools and Calculators Information for Health Care Professionals Cancer Information Cancer Basics Cancer Prevention & ... Sites Bookstore ACS CAN Shop Cancer Atlas Global Health Finish the Fight Press Room Mobile Site Help ...

  5. Hydraulic calculation of pressure pipes

    OpenAIRE

    Mikhalev, M. A.

    2012-01-01

    In the present time there is only one classic method for hydraulic calculation of pressure pipes. In it fluid flow velocity and pipeline diameter are considered as given values.The paper proposes a procedure for physical modeling and hydraulic calculation of pressure pipes, based on the theory of similarity. Methods for obtaining similarity criteria from combinations of similarity numbers were discussed. Similarity numbers and criteria and criteria equations were defined.

  6. BMN correlators by loop equations

    International Nuclear Information System (INIS)

    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)

  7. Thermohydraulic calculation of WWER-type NPP

    International Nuclear Information System (INIS)

    Technique of thermohydraulic calculation of the WWER-type NPP in unsteady processes is described. Effective algorithm for solving hydrodynamics equations without regard for acoustic effects permitting to use enough large time integration step is given. Calculation of two-dimensional temperature fields in fuel element is considered. Method for calculating a pressurizer, steam generators and pumps is described as well

  8. Calculator calculus

    CERN Document Server

    McCarty, George

    1982-01-01

    How THIS BOOK DIFFERS This book is about the calculus. What distinguishes it, however, from other books is that it uses the pocket calculator to illustrate the theory. A computation that requires hours of labor when done by hand with tables is quite inappropriate as an example or exercise in a beginning calculus course. But that same computation can become a delicate illustration of the theory when the student does it in seconds on his calculator. t Furthermore, the student's own personal involvement and easy accomplishment give hi~ reassurance and en­ couragement. The machine is like a microscope, and its magnification is a hundred millionfold. We shall be interested in limits, and no stage of numerical approximation proves anything about the limit. However, the derivative of fex) = 67.SgX, for instance, acquires real meaning when a student first appreciates its values as numbers, as limits of 10 100 1000 t A quick example is 1.1 , 1.01 , 1.001 , •••• Another example is t = 0.1, 0.01, in the functio...

  9. Reliability calculations

    International Nuclear Information System (INIS)

    Risk and reliability analysis is increasingly being used in evaluations of plant safety and plant reliability. The analysis can be performed either during the design process or during the operation time, with the purpose to improve the safety or the reliability. Due to plant complexity and safety and availability requirements, sophisticated tools, which are flexible and efficient, are needed. Such tools have been developed in the last 20 years and they have to be continuously refined to meet the growing requirements. Two different areas of application were analysed. In structural reliability probabilistic approaches have been introduced in some cases for the calculation of the reliability of structures or components. A new computer program has been developed based upon numerical integration in several variables. In systems reliability Monte Carlo simulation programs are used especially in analysis of very complex systems. In order to increase the applicability of the programs variance reduction techniques can be applied to speed up the calculation process. Variance reduction techniques have been studied and procedures for implementation of importance sampling are suggested. (author)

  10. Internal Dosimetric Calculations for Occupationally Exposed Workers

    International Nuclear Information System (INIS)

    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

  11. Calculated risks

    International Nuclear Information System (INIS)

    This book is a clear, practical, and balanced view of toxicology and risk management. The introduction argues the case for risks assessment and outlines the benefits and problems associated with chemical exposure. The first part of the book covers the basic science and the sources of human exposure to chemicals. Absorption, distribution, metabolism, and excretion are covered in some detail. The subsequent chapter gives a lively discussion of toxicity studies and then describes slow and fast poisons. The author gives the arguments for as well as against animal testing. There is much public bewilderment caused by reports of cancer-causing pesticides in apple juice and poisons emanating from nearby hazardous waste sites. The author believes that too much has been written in an attempt to expose governmental and corporate ignorance, negligence, and corruption. This book is less of a polemic, and more of a clear, unbiased clarification of the scientific basis for our concerns and uncertainties. It should serve to refocus the debate

  12. Delay Equation for Charged Brown Particle

    OpenAIRE

    Vlasov, Alexander A.

    2001-01-01

    In previous work (physics/0004026) was shown, with the help of numerical calculations, that the effective Brown temperature for charged particle is lower than that for particle without charge. Here we derive this result without numerical calculations, integrating the delay equation analytically, as for zero, so for nonzero viscosity.

  13. Relative Hazard Calculation Methodology

    International Nuclear Information System (INIS)

    The methodology presented in this document was developed to provide a means of calculating the RH ratios to use in developing useful graphic illustrations. The RH equation, as presented in this methodology, is primarily a collection of key factors relevant to understanding the hazards and risks associated with projected risk management activities. The RH equation has the potential for much broader application than generating risk profiles. For example, it can be used to compare one risk management activity with another, instead of just comparing it to a fixed baseline as was done for the risk profiles. If the appropriate source term data are available, it could be used in its non-ratio form to estimate absolute values of the associated hazards. These estimated values of hazard could then be examined to help understand which risk management activities are addressing the higher hazard conditions at a site. Graphics could be generated from these absolute hazard values to compare high-hazard conditions. If the RH equation is used in this manner, care must be taken to specifically define and qualify the estimated absolute hazard values (e.g., identify which factors were considered and which ones tended to drive the hazard estimation)

  14. Monte Carlo calculation of changes in the doses due to the contrast medium in the partial irradiation for the breast cancer; Calculo Monte Carlo de cambios en la dosis debidos al medio de contraste en la irradiacion parcial para el cancer de seno

    Energy Technology Data Exchange (ETDEWEB)

    Rojas C, E.L. [ININ, Km. 36.5 Carretera Mexico-Toluca, 52750 La Marquesa Ocoyoacac, Estado de Mexico (Mexico)]. e-mail: elrc@nuclear.inin.mx

    2007-07-01

    In this work the results of calculating by Monte Carlo simulation with the Penelope code are presented, the changes that are presented in the dose, when modeling a system of treatment of partial irradiation of breast cancer. The system consists of a globe plastic with a radioactive source of {sup 192}Ir in his interior. This technique is used when it is carried out the extraction of incipient cancerous tumors and it is wanted to irradiate the tissue surrounding to the tumor extracted to make sure that sick tissue does not remain. This technique was patented about 5 years ago and it is known as partial irradiation by MammoSite(R). When the plastic ball is implanted in the cavity of the surgery, it is filled with a radio opaque solution. This substance is a solution whose concentration can to vary. One of the main components of this solution is the iodine. The on-line dose calculations, carried out by the programs associated to the brachytherapy sources and, in particular for this technique, they are very good; however, the calculations are made supposing that to have an homogeneous medium. They have been carried out studies for MC simulation with the EGSNRC code and it has been that when it takes into account the presence of the contrast solution, the results change considerably. In this work we carry out dose calculations with Penelope for different solution concentrations in the ball. The results agree in general way with those carried out in other works. (Author)

  15. Sparsifying preconditioner for soliton calculations

    Science.gov (United States)

    Lu, Jianfeng; Ying, Lexing

    2016-06-01

    We develop a robust and efficient method for soliton calculations for nonlinear Schrödinger equations. The method is based on the recently developed sparsifying preconditioner combined with Newton's iterative method. The performance of the method is demonstrated by numerical examples of gap solitons in the context of nonlinear optics.

  16. Sparsifying preconditioner for soliton calculations

    CERN Document Server

    Lu, Jianfeng

    2015-01-01

    We develop a robust and efficient method for soliton calculations for nonlinear Schr\\"odinger equations. The method is based on the recently developed sparsifying preconditioner combined with Newton's iterative method. The performance of the method is demonstrated by numerical examples of gap solitons in the context of nonlinear optics.

  17. The Modified Magnetohydrodynamical Equations

    Institute of Scientific and Technical Information of China (English)

    EvangelosChaliasos

    2003-01-01

    After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similar fashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is done by replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vector potential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vector analysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHD equations.

  18. 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.)

  19. Proteomic patterns analysis with multivariate calculations as a promising tool for prompt differentiation of early stage lung tissue with cancer and unchanged tissue material

    Directory of Open Access Journals (Sweden)

    Grodzki Tomasz

    2011-03-01

    Full Text Available Abstract Background Lung cancer diagnosis in tissue material with commonly used histological techniques is sometimes inconvenient and in a number of cases leads to ambiguous conclusions. Frequently advanced immunostaining techniques have to be employed, yet they are both time consuming and limited. In this study a proteomic approach is presented which may help provide unambiguous pathologic diagnosis of tissue material. Methods Lung tissue material found to be pathologically changed was prepared to isolate proteome with fast and non selective procedure. Isolated peptides and proteins in ranging from 3.5 to 20 kDa were analysed directly using high resolution mass spectrometer (MALDI-TOF/TOF with sinapic acid as a matrix. Recorded complex spectra of a single run were then analyzed with multivariate statistical analysis algorithms (principle component analysis, classification methods. In the applied protocol we focused on obtaining the spectra richest in protein signals constituting a pattern of change within the sample containing detailed information about its protein composition. Advanced statistical methods were to indicate differences between examined groups. Results Obtained results indicate changes in proteome profiles of changed tissues in comparison to physiologically unchanged material (control group which were reflected in the result of principle component analysis (PCA. Points representing spectra of control group were located in different areas of multidimensional space and were less diffused in comparison to cancer tissues. Three different classification algorithms showed recognition capability of 100% regarding classification of examined material into an appropriate group. Conclusion The application of the presented protocol and method enabled finding pathological changes in tissue material regardless of localization and size of abnormalities in the sample volume. Proteomic profile as a complex, rich in signals spectrum of proteins

  20. On the Raychaudhuri equation

    Indian Academy of Sciences (India)

    George F R Ellis

    2007-07-01

    The Raychaudhuri equation is central to the understanding of gravitational attraction in astrophysics and cosmology, and in particular underlies the famous singularity theorems of general relativity theory. This paper reviews the derivation of the equation, and its significance in cosmology.

  1. Ordinary differential equations

    CERN Document Server

    Greenberg, Michael D

    2014-01-01

    Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps

  2. Testing Price Equations

    OpenAIRE

    Ray C. Fair

    2007-01-01

    How inflation and unemployment are related in both the short run and long run is perhaps the key question in macroeconomics. This paper tests various price equations using quarterly U.S. data from 1952 to the present. Issues treated are the following. 1) Estimating price and wage equations in which wages affect prices and vice versa versus estimating "reduced form" price equations with no wage explanatory variables. 2) Estimating price equations in (log) level terms, first difference (i.e., i...

  3. New unified evolution equation

    OpenAIRE

    Lim, Jyh-Liong; Li, Hsiang-nan

    1998-01-01

    We propose a new unified evolution equation for parton distribution functions appropriate for both large and small Bjorken variables $x$, which is an improved version of the Ciafaloni-Catani-Fiorani-Marchesini equation. In this new equation the cancellation of soft divergences between virtual and real gluon emissions is explicit without introducing infrared cutoffs, next-to-leading contributions to the Sudakov resummation can be included systematically. It is shown that the new equation reduc...

  4. Universality of KPZ equation

    CERN Document Server

    Goncalves, Patricia

    2010-01-01

    We introduce the notion of energy solutions of the KPZ equation. Under minimal assumptions, we prove that the density fluctuations of one-dimensional, weakly asymmetric, conservative particle systems with respect to the stationary states are given by energy solutions of the KPZ equation. As a consequence, we prove that the Cole-Hofp solutions are also energy solutions of the KPZ equation.

  5. Diophantine equations and identities

    Directory of Open Access Journals (Sweden)

    Malvina Baica

    1985-01-01

    Full Text Available The general diophantine equations of the second and third degree are far from being totally solved. The equations considered in this paper are    i  x2−my2=±1 ii  x3+my3+m2z3−3mxyz=1iii  Some fifth degree diopantine equations

  6. Una ecuación diferencial para el cálculo de las funciones de Jost para potenciales regulares Aplicación al sistema e‾+ H(1s A differential equation for the calculation of the functions de jost for regular potentials Application to the system e

    Directory of Open Access Journals (Sweden)

    Héctor Maya Taboada

    2011-06-01

    matrix S. In most of the existent methods in theory of collisions for the calculation of the function Fl first is necessary to know the regular solution of the treated system, which is obtained of the solution of the radial equation of Schrodinger, to be able to find the function Fl later. With the methodology proposed in this work an ordinary lineal differential equation of second order it is obtained whose solution in the asymptotic boundary coincides with the function Fl. The advantage of the present work is that solving the differential equation mentioned before one can obtain in a direct way the function Fl without having to find the regular solution of the problem. Another advantage is that not caring the initial conditions (real that are chosen for the solution of the differential equation, the same elements of the matrix S, are always obtained. As an example and test of the methodology, it is solved this differential equation numerically for the elastic scattering of electrons by hydrogen atoms in the ground state to low energy (e− + H(1s, obtaining for this system the function Fl, the elements of the matrix S and the phase shifts. The data obtained for the phase shifts are compared with the calculated by Klaus Bartschat.

  7. Critical dose and toxicity index of organs at risk in radiotherapy: Analyzing the calculated effects of modified dose fractionation in non–small cell lung cancer

    Energy Technology Data Exchange (ETDEWEB)

    Pedicini, Piernicola, E-mail: ppiern@libero.it [Service of Medical Physics, I.R.C.C.S. Regional Cancer Hospital C.R.O.B, Rionero in Vulture (Italy); Strigari, Lidia [Laboratory of Medical Physics and Expert Systems, Regina Elena National Cancer Institute, Rome (Italy); Benassi, Marcello [Service of Medical Physics, Scientific Institute of Tumours of Romagna I.R.S.T., Meldola (Italy); Caivano, Rocchina [Service of Medical Physics, I.R.C.C.S. Regional Cancer Hospital C.R.O.B, Rionero in Vulture (Italy); Fiorentino, Alba [U.O. of Radiotherapy, I.R.C.C.S. Regional Cancer Hospital C.R.O.B., Rionero in Vulture (Italy); Nappi, Antonio [U.O. of Nuclear Medicine, I.R.C.C.S. Regional Cancer Hospital C.R.O.B., Rionero in Vulture (Italy); Salvatore, Marco [U.O. of Nuclear Medicine, I.R.C.C.S. SDN Foundation, Naples (Italy); Storto, Giovanni [U.O. of Nuclear Medicine, I.R.C.C.S. Regional Cancer Hospital C.R.O.B., Rionero in Vulture (Italy)

    2014-04-01

    To increase the efficacy of radiotherapy for non–small cell lung cancer (NSCLC), many schemes of dose fractionation were assessed by a new “toxicity index” (I), which allows one to choose the fractionation schedules that produce less toxic treatments. Thirty-two patients affected by non resectable NSCLC were treated by standard 3-dimensional conformal radiotherapy (3DCRT) with a strategy of limited treated volume. Computed tomography datasets were employed to re plan by simultaneous integrated boost intensity-modulated radiotherapy (IMRT). The dose distributions from plans were used to test various schemes of dose fractionation, in 3DCRT as well as in IMRT, by transforming the dose-volume histogram (DVH) into a biological equivalent DVH (BDVH) and by varying the overall treatment time. The BDVHs were obtained through the toxicity index, which was defined for each of the organs at risk (OAR) by a linear quadratic model keeping an equivalent radiobiological effect on the target volume. The less toxic fractionation consisted in a severe/moderate hyper fractionation for the volume including the primary tumor and lymph nodes, followed by a hypofractionation for the reduced volume of the primary tumor. The 3DCRT and IMRT resulted, respectively, in 4.7% and 4.3% of dose sparing for the spinal cord, without significant changes for the combined-lungs toxicity (p < 0.001). Schedules with reduced overall treatment time (accelerated fractionations) led to a 12.5% dose sparing for the spinal cord (7.5% in IMRT), 8.3% dose sparing for V{sub 20} in the combined lungs (5.5% in IMRT), and also significant dose sparing for all the other OARs (p < 0.001). The toxicity index allows to choose fractionation schedules with reduced toxicity for all the OARs and equivalent radiobiological effect for the tumor in 3DCRT, as well as in IMRT, treatments of NSCLC.

  8. Test of Information Theory on the Boltzmann Equation

    OpenAIRE

    Hyeon-Deuk, Kim; Hayakawa, Hisao

    2002-01-01

    We examine information theory using the steady-state Boltzmann equation. In a nonequilibrium steady-state system under steady heat conduction, the thermodynamic quantities from information theory are calculated and compared with those from the steady-state Boltzmann equation. We have found that information theory is inconsistent with the steady-state Boltzmann equation.

  9. Test of Information Theory on the Boltzmann Equation

    OpenAIRE

    Kim, Hyeon-Deuk; Hayakawa, Hisao

    2003-01-01

    We examine information theory using the steady-state Boltzmann equation. In a nonequilibrium steady-state system under steady heat conduction, the thermodynamic quantities from information theory are calculated and compared with those from the steady-state Boltzmann equation. We have found that information theory is inconsistent with the steady-state Boltzmann equation.

  10. Calcul des paramètres de l'équation de Wilson. Analyse comparative des représentations d'équilibres liquide-vapeur isothermes par les modèles de Wilson et NRTL Computing Parameters in the Wilson Equation. Comparatrice Analysis of Representations of Isothermal Liquid-Vapor Equilibria by Wilson and Nrtl Models

    Directory of Open Access Journals (Sweden)

    Desplanches H.

    2006-11-01

    Full Text Available Un programme de calcul des paramètres de l'équation de Wilson est mis au point. II utilise une méthode itérative de minimisation des écarts sur la pression et la composition de vapeur ou sur chaque grandeur prise séparément. Les méthodes utilisées sont testées sur neuf équilibres liquide-vapeur isothermes de mélanges binaires à déviations positives ou négatives. Les écarts moyens entre les valeurs expérimentales : - de la pression; - de la composition de la vapeur; - de l'enthalpie libre d'excès; et les valeurs calculées à partir des paramètres de Wilson sont comparés à ceux obtenus d'après le modèle NRTL. A program has been developed for computing the parameters in the Wilson equation. It uses an iterative method of minimizing the differences in pressure and steam composition or in each magnitude token separately. The methods used are tried out on nine isothermal liquid-vapor equilibria of binary mixtures with positive or negative deviations. The mean differences between experimental values of the : - pressure; - vapor composition; - excess free enthalpy; and values computed from Wilson parameters are compared with those obtained from an NRTL model.

  11. Surface Tension Calculation of Undercooled Alloys

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Based on the Butler equation and extrapolated thermodynamic data of undercooled alloys from those of liquid stable alloys, a method for surface tension calculation of undercooled alloys is proposed. The surface tensions of liquid stable and undercooled Ni-Cu (xNi=0.42) and Ni-Fe (xNi=0.3 and 0.7) alloys are calculated using STCBE (Surface Tension Calculation based on Butler Equation) program. The agreement between calculated values and experimental data is good enough, and the temperature dependence of the surface tension can be reasonable down to 150-200 K under the liquid temperature of the alloys.

  12. The Modified Magnetohydrodynamical Equations

    Institute of Scientific and Technical Information of China (English)

    Evangelos Chaliasos

    2003-01-01

    After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similarfashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is doneby replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vectorpotential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vectoranalysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHDequations.

  13. Sonar equations for planetary exploration.

    Science.gov (United States)

    Ainslie, Michael A; Leighton, Timothy G

    2016-08-01

    The set of formulations commonly known as "the sonar equations" have for many decades been used to quantify the performance of sonar systems in terms of their ability to detect and localize objects submerged in seawater. The efficacy of the sonar equations, with individual terms evaluated in decibels, is well established in Earth's oceans. The sonar equations have been used in the past for missions to other planets and moons in the solar system, for which they are shown to be less suitable. While it would be preferable to undertake high-fidelity acoustical calculations to support planning, execution, and interpretation of acoustic data from planetary probes, to avoid possible errors for planned missions to such extraterrestrial bodies in future, doing so requires awareness of the pitfalls pointed out in this paper. There is a need to reexamine the assumptions, practices, and calibrations that work well for Earth to ensure that the sonar equations can be accurately applied in combination with the decibel to extraterrestrial scenarios. Examples are given for icy oceans such as exist on Europa and Ganymede, Titan's hydrocarbon lakes, and for the gaseous atmospheres of (for example) Jupiter and Venus. PMID:27586766

  14. Encapsulation of cisplatin as an anti-cancer drug into boron-nitride and carbon nanotubes: Molecular simulation and free energy calculation.

    Science.gov (United States)

    Roosta, Sara; Hashemianzadeh, Seyed Majid; Ketabi, Sepideh

    2016-10-01

    Encapsulation of cisplatin anticancer drug into the single walled (10, 0) carbon nanotube and (10, 0) boron-nitride nanotube was investigated by quantum mechanical calculations and Monte Carlo Simulation in aqueous solution. Solvation free energies and complexation free energies of the cisplatin@ carbon nanotube and cisplatin@ boron-nitride nanotube complexes was determined as well as radial distribution functions of entitled compounds. Solvation free energies of cisplatin@ carbon nanotube and cisplatin@ boron-nitride nanotube were -4.128kcalmol(-1) and -2457.124kcalmol(-1) respectively. The results showed that cisplatin@ boron-nitride nanotube was more soluble species in water. In addition electrostatic contribution of the interaction of boron- nitride nanotube complex and solvent was -281.937kcalmol(-1) which really more than Van der Waals and so the electrostatic interactions play a distinctive role in the solvation free energies of boron- nitride nanotube compounds. On the other hand electrostatic part of the interaction of carbon nanotube complex and solvent were almost the same as Van der Waals contribution. Complexation free energies were also computed to study the stability of related structures and the free energies were negative (-374.082 and -245.766kcalmol(-1)) which confirmed encapsulation of drug into abovementioned nanotubes. However, boron-nitride nanotubes were more appropriate for encapsulation due to their larger solubility in aqueous solution. PMID:27287103

  15. The degeneracy of the free Dirac equation

    International Nuclear Information System (INIS)

    Parity-mixed solutions of the free Dirac equation with the same 4-momentum are considered. The first-order EM energy has an electric dipole moment term whose value depends on the mixing angle. Further implications of this degeneracy to perturbative calculations are discussed. It is argued that the properties of the Dirac equation with the Coulomb potential can be used to decide the mixing angle, which should be zero

  16. Non-perturbative background field calculations

    International Nuclear Information System (INIS)

    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

  17. On separable Pauli equations

    International Nuclear Information System (INIS)

    We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A0(t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field

  18. A new type of loop equations

    International Nuclear Information System (INIS)

    We derive a new form of loop equations for light-like Wilson loops. In bosonic theories those loop equations close only for straight light-like Wilson lines. In the case of N=1 in ten dimensions they close for any light-like Wilson loop. Upon dimensional reduction to N=4 SYM in four dimensions, these loops become exactly the chiral loops which can be evaluated semiclassically, in the strong coupling limit, by a minimal surface in anti de-Sitter space. We show that the AdS calculation satisfies those loop equations. We also find a new fermionic loop equation derived from the gauge theory fermionic equation of motion. (author)

  19. Comparison between CT-based volumetric calculations and ICRU reference-point estimates of radiation doses delivered to bladder and rectum during intracavitary radiotherapy for cervical cancer

    International Nuclear Information System (INIS)

    Purpose: To compare CT-based volumetric calculations and International Commission on Radiation Units and Measurements (ICRU) reference-point estimates of radiation doses to the bladder and rectum in patients with carcinoma of the uterine cervix treated with definitive low-dose-rate intracavitary radiotherapy (ICRT). Methods and Materials: Between November 2001 and March 2003, 60 patients were prospectively enrolled in a pilot study of ICRT with CT-based dosimetry. Most patients underwent two ICRT insertions. After insertion of an afterloading ICRT applicator, intraoperative orthogonal films were obtained to ensure proper positioning of the system and to facilitate subsequent planning. Treatments were prescribed using standard two-dimensional dosimetry and planning. Patients also underwent helical CT of the pelvis for three-dimensional reconstruction of the radiation dose distributions. The systems were loaded with 137Cs sources using the Selectron remote afterloading system according to institutional practice for low-dose-rate brachytherapy. Three-dimensional dose distributions were generated using the Varian BrachyVision treatment planning system. The rectum was contoured from the bottom of the ischial tuberosities to the sigmoid flexure. The entire bladder was contoured. The minimal doses delivered to the 2 cm3 of bladder and rectum receiving the highest dose (DBV2 and DRV2, respectively) were determined from dose-volume histograms, and these estimates were compared with two-dimensionally derived estimates of the doses to the corresponding ICRU reference points. Results: A total of 118 unique intracavitary insertions were performed, and 93 were evaluated and the subject of this analysis. For the rectum, the estimated doses to the ICRU reference point did not differ significantly from the DRV2 (p = 0.561); the mean (± standard deviation) difference was 21 cGy (± 344 cGy). The median volume of the rectum that received at least the ICRU reference-point dose was 2

  20. Functional equations with causal operators

    CERN Document Server

    Corduneanu, C

    2003-01-01

    Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.

  1. Scattering equations and global duality of residues

    Science.gov (United States)

    Søgaard, Mads; Zhang, Yang

    2016-05-01

    We examine the polynomial form of the scattering equations by means of computational algebraic geometry. The scattering equations are the backbone of the Cachazo-He-Yuan (CHY) representation of the S-matrix. We explain how the Bezoutian matrix facilitates the calculation of amplitudes in the CHY formalism, without explicitly solving the scattering equations or summing over the individual residues. Since for n -particle scattering the size of the Bezoutian matrix grows only as (n -3 )×(n -3 ), our algorithm is very efficient for analytic and numeric amplitude computations.

  2. Differential equations for dummies

    CERN Document Server

    Holzner, Steven

    2008-01-01

    The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.

  3. Nonlinear Dirac Equations

    Directory of Open Access Journals (Sweden)

    Wei Khim Ng

    2009-02-01

    Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.

  4. Elliptic partial differential equations

    CERN Document Server

    Volpert, Vitaly

    If we had to formulate in one sentence what this book is about it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Mathematical anaylsis of reaction-diffusion equations will be based on the theory of Fredholm operators presented in the first volume. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equ...

  5. Equilibrium calculations for helical axis stellarators

    International Nuclear Information System (INIS)

    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

  6. Fundamental Equation of Economics

    OpenAIRE

    Wayne, James J.

    2013-01-01

    Recent experience of the great recession of 2008 has renewed one of the oldest debates in economics: whether economics could ever become a scientific discipline like physics. This paper proves that economics is truly a branch of physics by establishing for the first time a fundamental equation of economics (FEOE), which is similar to many fundamental equations governing other subfields of physics, for example, Maxwell’s Equations for electromagnetism. From recently established physics laws of...

  7. Solving Ordinary Differential Equations

    Science.gov (United States)

    Krogh, F. T.

    1987-01-01

    Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

  8. Differential equations I essentials

    CERN Document Server

    REA, Editors of

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.

  9. Ordinary differential equations

    CERN Document Server

    Pontryagin, Lev Semenovich

    1962-01-01

    Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.

  10. On separable Pauli equations

    OpenAIRE

    Zhalij, Alexander

    2002-01-01

    We classify (1+3)-dimensional Pauli equations for a spin-1/2 particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the eleven classes of vector-potentials of the electro-magnetic field A(t,x) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is...

  11. A new evolution equation

    International Nuclear Information System (INIS)

    A new evolution equation is proposed for the gluon density relevant (GLR) for the region of small xB. It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists of taking shadowing effects more comprehensively into account by including multi gluon correlations, and allowing for an arbitrary initial gluon distribution in a hadron. We solve the new equation for fixed αs. It is found that the effects of multi gluon correlations on the deep-inelastic structure function are small. (author) 15 refs, 5 figs, 2 tabs

  12. BMN Correlators by Loop Equations

    OpenAIRE

    Eynard, B.; Kristjansen, C.

    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...

  13. Cosmology calculations almost without general relativity

    CERN Document Server

    Jordan, T F

    2003-01-01

    The Friedmann equation can be derived for a Newtonian universe. Changing mass density to energy density gives exactly the Friedmann equation of general relativity. Accounting for work done by pressure then yields the two Einstein equations that govern the expansion of the universe. Descriptions and explanations of radiation pressure and vacuum pressure are added to complete a basic kit of cosmology tools. It provides a basis for teaching cosmology to undergraduates in a way that quickly equips them to do basic calculations. This is demonstrated with calculations involving: characteristics of the expansion for densities dominated by radiation, matter, or vacuum; the closeness of the density to the critical density; how much vacuum energy compared to matter energy is needed to make the expansion accelerate; and how little is needed to make it stop. Travel time and luninosity distance are calculated in terms of the redshift and the densities of matter and vacuum energy, using a scaled Friedmann equation with the...

  14. Stochastic Runge-Kutta Software Package for Stochastic Differential Equations

    CERN Document Server

    Gevorkyan, M N; Korolkova, A V; Kulyabov, D S; Sevastyanov, L A

    2016-01-01

    As a result of the application of a technique of multistep processes stochastic models construction the range of models, implemented as a self-consistent differential equations, was obtained. These are partial differential equations (master equation, the Fokker--Planck equation) and stochastic differential equations (Langevin equation). However, analytical methods do not always allow to research these equations adequately. It is proposed to use the combined analytical and numerical approach studying these equations. For this purpose the numerical part is realized within the framework of symbolic computation. It is recommended to apply stochastic Runge--Kutta methods for numerical study of stochastic differential equations in the form of the Langevin. Under this approach, a program complex on the basis of analytical calculations metasystem Sage is developed. For model verification logarithmic walks and Black--Scholes two-dimensional model are used. To illustrate the stochastic "predator--prey" type model is us...

  15. Clinical evaluation of X-ray voxel Monte Carlo versus pencil beam-based dose calculation in stereotactic body radiotherapy of lung cancer under normal and deep inspiration breath hold.

    Science.gov (United States)

    Landoni, V; Borzì, G R; Strolin, S; Bruzzaniti, V; Soriani, A; D'Alessio, D; Ambesi, F; Di Grazia, A M; Strigari, L

    2015-06-01

    The purpose of this study is to evaluate the differences between dose distributions calculated with the pencil beam (PB) and X-ray voxel Monte Carlo (MC) algorithms for patients with lung cancer using intensity-modulated radiotherapy (IMRT) or HybridArc techniques. The 2 algorithms were compared in terms of dose-volume histograms, under normal and deep inspiration breath hold, and in terms of the tumor control probability (TCP). The dependence of the differences in tumor volume and location was investigated. Dosimetric validation was performed using Gafchromic EBT3 (International Specialty Products, ISP, Wayne, NJ). Forty-five Computed Tomography (CT) data sets were used for this study; 40 Gy at 8 Gy/fraction was prescribed with 5 noncoplanar 6-MV IMRT beams or 3 to 4 dynamic conformal arcs with 3 to 5 IMRT beams distributed per arc. The plans were first calculated with PB and then recalculated with MC. The difference between the mean tumor doses was approximately 10% ± 4%; these differences were even larger under deep inspiration breath hold. Differences between the mean tumor dose correlated with tumor volume and path length of the beams. The TCP values changed from 99.87% ± 0.24% to 96.78% ± 4.81% for both PB- and MC-calculated plans (P = .009). When a fraction of hypoxic cells was considered, the mean TCP values changed from 76.01% ± 5.83% to 34.78% ± 18.06% for the differently calculated plans (P < .0001). When the plans were renormalized to the same mean dose at the tumor, the mean TCP for oxic cells was 99.05% ± 1.59% and for hypoxic cells was 60.20% ± 9.53%. This study confirms that the MC algorithm adequately accounts for inhomogeneities. The inclusion of the MC in the process of IMRT optimization could represent a further step in the complex problem of determining the optimal treatment plan. PMID:25223324

  16. Numerical calculation of Casimir forces

    OpenAIRE

    Kilen, Isak Ragnvald

    2012-01-01

    In this thesis a set of regularized boundary integral equation are introduced that can be used to calculate the Casimir force induced by a two dimensional scalar field. The boundary integral method is compared to the functional integral method and mode summation where possible. Comparisons are done for the case of two parallel plates, two concentric circles and two adjacent circles. The results indicate that the boundary integral method correctly predicts the geometry dependence of the C...

  17. Configuration space Faddeev calculations

    International Nuclear Information System (INIS)

    The detailed study of few-body systems provides one of the most effective means for studying nuclear physics at subnucleon distance scales. For few-body systems the model equations can be solved numerically with errors less than the experimental uncertainties. We have used such systems to investigate the size of relativistic effects, the role of meson-exchange currents, and the importance of quark degrees of freedom in the nucleus. Complete calculations for momentum-dependent potentials have been performed, and the properties of the three-body bound state for these potentials have been studied. Few-body calculations of the electromagnetic form factors of the deuteron and pion have been carried out using a front-form formulation of relativistic quantum mechanics. The decomposition of the operators transforming convariantly under the Poincare group into kinematical and dynamical parts has been studies. New ways for constructing interactions between particles, as well as interactions which lead to the production of particles, have been constructed in the context of a relativistic quantum mechanics. To compute scattering amplitudes in a nonperturbative way, classes of operators have been generated out of which the phase operator may be constructed. Finally, we have worked out procedures for computing Clebsch-Gordan and Racah coefficients on a computer, as well as giving procedures for dealing with the multiplicity problem

  18. Multilayer optical calculations

    CERN Document Server

    Byrnes, Steven J

    2016-01-01

    When light hits a multilayer planar stack, it is reflected, refracted, and absorbed in a way that can be derived from the Fresnel equations. The analysis is treated in many textbooks, and implemented in many software programs, but certain aspects of it are difficult to find explicitly and consistently worked out in the literature. Here, we derive the formulas underlying the transfer-matrix method of calculating the optical properties of these stacks, including oblique-angle incidence, absorption-vs-position profiles, and ellipsometry parameters. We discuss and explain some strange consequences of the formulas in the situation where the incident and/or final (semi-infinite) medium are absorptive, such as calculating $T>1$ in the absence of gain. We also discuss some implementation details like complex-plane branch cuts. Finally, we derive modified formulas for including one or more "incoherent" layers, i.e. very thick layers in which interference can be neglected. This document was written in conjunction with ...

  19. Linear Equations: Equivalence = Success

    Science.gov (United States)

    Baratta, Wendy

    2011-01-01

    The ability to solve linear equations sets students up for success in many areas of mathematics and other disciplines requiring formula manipulations. There are many reasons why solving linear equations is a challenging skill for students to master. One major barrier for students is the inability to interpret the equals sign as anything other than…

  20. Gauge invariant flow equation

    CERN Document Server

    Wetterich, C

    2016-01-01

    We propose a gauge invariant flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations, corresponding to a particular gauge fixing. The freedom in the precise choice of the macroscopic field can be exploited in order to keep the flow equation simple.

  1. Braneworld flow equations

    OpenAIRE

    Ramirez, Erandy; Liddle, Andrew

    2004-01-01

    We generalize the flow equations approach to inflationary model building to the Randall–Sundrum Type II braneworld scenario. As the flow equations are quite insensitive to the expansion dynamics, we find results similar to, though not identical to, those found in the standard cosmology.

  2. On the Diophantine equation

    Science.gov (United States)

    Zahari, N. M.; Sapar, S. H.; Mohd Atan, K. A.

    2013-04-01

    This paper discusses an integral solution (a, b, c) of the Diophantine equations x3n+y3n = 2z2n for n ≥ 2 and it is found that the integral solution of these equation are of the form a = b = t2, c = t3 for any integers t.

  3. Some classical Diophantine equations

    Directory of Open Access Journals (Sweden)

    Nikita Bokarev

    2014-09-01

    Full Text Available An attempt to find common solutions complete some Diophantine equations of the second degree with three variables, traced some patterns, suggest a common approach, which being elementary, however, lead to a solution of such equations. Using arithmetic functions allowed to write down the solutions in a single formula with no restrictions on the parameters used.

  4. Applied singular integral equations

    CERN Document Server

    Mandal, B N

    2011-01-01

    The book is devoted to varieties of linear singular integral equations, with special emphasis on their methods of solution. It introduces the singular integral equations and their applications to researchers as well as graduate students of this fascinating and growing branch of applied mathematics.

  5. Alternative equations of gravitation

    International Nuclear Information System (INIS)

    It is shown, trough a new formalism, that the quantum fluctuation effects of the gravitational field in Einstein's equations are analogs to the effects of a continuum medium in Maxwell's Electrodynamics. Following, a real example of the applications of these equations is studied. Qunatum fluctuations effects as perturbation sources in Minkowski and Friedmann Universes are examined. (L.C.)

  6. Reduced Braginskii equations

    International Nuclear Information System (INIS)

    A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that we solve the perpendicular component of Ohm's law to conserve the physical energy while ensuring the relation ∇ · j = 0

  7. Hamming generalized corrector for reactivity calculation

    Energy Technology Data Exchange (ETDEWEB)

    Suescun-Diaz, Daniel; Ibarguen-Gonzalez, Maria C.; Figueroa-Jimenez, Jorge H. [Pontificia Universidad Javeriana Cali, Cali (Colombia). Dept. de Ciencias Naturales y Matematicas

    2014-06-15

    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{sup 5}, where h is the time step. (orig.)

  8. Hamming generalized corrector for reactivity calculation

    International Nuclear Information System (INIS)

    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 h5, where h is the time step. (orig.)

  9. The relativistic Pauli equation

    CERN Document Server

    Delphenich, David

    2012-01-01

    After discussing the way that C2 and the algebra of complex 2x2 matrices can be used for the representation of both non-relativistic rotations and Lorentz transformations, we show that Dirac bispinors can be more advantageously represented as 2x2 complex matrices. One can then give the Dirac equation a form for such matrix-valued wave functions that no longer necessitates the introduction of gamma matrices or a choice for their representation. The minimally-coupled Dirac equation for a charged spinning particle in an external electromagnetic field then implies a second order equation in the matrix-valued wave functions that is of Klein-Gordon type and represents the relativistic analogue of the Pauli equation. We conclude by presenting the Lagrangian form for the relativistic Pauli equation.

  10. The generalized Jacobi equation

    International Nuclear Information System (INIS)

    The Jacobi equation in pseudo-Riemannian geometry determines the linearized geodesic flow. The linearization ignores the relative velocity of the geodesics. The generalized Jacobi equation takes the relative velocity into account; that is, when the geodesics are neighbouring but their relative velocity is arbitrary the corresponding geodesic deviation equation is the generalized Jacobi equation. The Hamiltonian structure of this nonlinear equation is analysed in this paper. The tidal accelerations for test particles in the field of a plane gravitational wave and the exterior field of a rotating mass are investigated. In the latter case, the existence of an attractor of uniform relative radial motion with speed 2-1/2c ∼ 0.7c is pointed out. The astrophysical implication of this result for the terminal speed of a relativistic jet is briefly explored

  11. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2004-01-01

    This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...

  12. Extended MHD equations

    International Nuclear Information System (INIS)

    The direct use of enlarged subsets of mathematically exact equations of change in moments of the velocity distribution function, each equation corresponding to one of the macroscopic variables to be retained, produces extended MHD models. The first relevant level of closure provides 'ten moment' equations in the density ρ, velocity v, scalar pressure p, and the traceless component of the pressure tensor t. The next 'thirteen moment' level also includes the thermal flux vector q, and further extended MHD models could be developed by including even higher level basic equations of change. Explicit invariant forms for the tensor t and the heat flux vector defining q follow from their respective basic equations of change. Except in the neighbourhood of a magnetic null, in magnetised plasma these forms may be resolved into known sums of their parallel, cross (or transverse) and perpendicular components. Parallel viscosity in an electron-ion plasma is specifically discussed. (author)

  13. Nuclear fission with a Langevin equation

    International Nuclear Information System (INIS)

    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

  14. Approximation equation for EW receiver sensitivity

    International Nuclear Information System (INIS)

    A set of equations is presented for the calculation of the signal-to-noise ratio in decibels for required operational sensitivity of a microwave receiver. Given RF bandwidth and video bandwidth for an EW receiver, along with probability of detection and false alarm rate, S/N in decibels may be obtained. The method is less time-consuming than calculating sensitivity from curves, and the results obtained are within 1 dB of values obtained from curves. 8 references

  15. Landau levels from the Bethe Ansatz equations

    OpenAIRE

    Hoshi, K.; Hatsugai, Y.

    2000-01-01

    The Bethe ansatz (BA) equations for the two-dimensional Bloch electrons in a uniform magnetic field are treated in the weak-field limit. We have calculated energies near the lower boundary of the energy spectrum up to the first nontrivial order. It corresponds to calculating a finite size correction for the excitation energies of the BA solvable lattice models and gives the Landau levels in the present problem.

  16. Landau Levels from the Bethe Ansatz Equations

    OpenAIRE

    Hoshi, K.; Hatsugai, Y.

    1999-01-01

    The Bethe ansatz (BA) equations for the two-dimensional Bloch electrons in a uniform magnetic field are treated in the weak field limit. We have calculated energies near the lower boundary of the energy spectrum up to the first nontrivial order. It corresponds to calculating a finite size correction for the excitation energies of the BA solvable lattice models and gives the Landau levels in the present problem.

  17. Some Calculations for Cold Fusion Superheavy Elements

    OpenAIRE

    X. H. Zhong; Li, L.; Ning, P. Z.

    2004-01-01

    The Q value and optimal exciting energy of the hypothetical superheavy nuclei in cold fusion reaction are calculated with relativistic mean field model and semiemperical shell model mass equation(SSME) and the validity of the two models is tested. The fusion barriers are also calculated with two different models and reasonable results are obtained. The calculations can give useful references for the experiments in the superheavy nuclei synthesized in cold fusion reactions.

  18. First principles phonon calculations in materials science

    OpenAIRE

    Togo, Atsushi; Tanaka, Isao

    2015-01-01

    Phonon plays essential roles in dynamical behaviors and thermal properties, which are central topics in fundamental issues of materials science. The importance of first principles phonon calculations cannot be overly emphasized. Phonopy is an open source code for such calculations launched by the present authors, which has been world-widely used. Here we demonstrate phonon properties with fundamental equations and show examples how the phonon calculations are applied in materials science.

  19. Calculation of plasma characteristics of the sun

    Institute of Scientific and Technical Information of China (English)

    Muhammad Abbas Bari; Zhong Jia-Yong; Chen Miu; Zhao Jing; Zhang Jie

    2006-01-01

    The ionization level and free electron density of most abundant elements (C, N, O, Mg, Al, Si, S, and Fe) in the sun are calculated from the centre of the sun to the surface of the photosphere. The model and computations are made under the assumption of local thermodynamic equilibrium (LTE). The Saha equation has been used to calculate the ionization level of elements and the electron density. Temperature values for calculations along the solar radius are taken from referebces.

  20. Nonlinear gyrokinetic equations

    International Nuclear Information System (INIS)

    Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed

  1. Nonlinear gyrokinetic equations

    Energy Technology Data Exchange (ETDEWEB)

    Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.

    1983-03-01

    Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.

  2. Standardized Referente Evapotranspiration Equation

    OpenAIRE

    M.D. Mundo–Molina

    2009-01-01

    In this paper is presented a discussion on the necessity to standardize the Penman–Monteith equations in order to estimate ETo. The proposal is to define an accuracy and standarize equation based in Penman–Monteith. The automated weather station named CIANO (27° 22 ' 144 North latitude and 109" 55' west longitude) it was selected tomake comparisons. The compared equations we re: a) CIANO weat her station, b) Penman–Monteith ASCE (PMA), Penman–Monteith FAO 56 (PM FAO 56), Penman–Monteith estan...

  3. Stochastic Schroedinger equations

    International Nuclear Information System (INIS)

    A derivation of Belavkin's stochastic Schroedinger equations is given using quantum filtering theory. We study an open system in contact with its environment, the electromagnetic field. Continuous observation of the field yields information on the system: it is possible to keep track in real time of the best estimate of the system's quantum state given the observations made. This estimate satisfies a stochastic Schroedinger equation, which can be derived from the quantum stochastic differential equation for the interaction picture evolution of system and field together. Throughout the paper we focus on the basic example of resonance fluorescence

  4. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2011-01-01

    A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres

  5. Uncertain differential equations

    CERN Document Server

    Yao, Kai

    2016-01-01

    This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.

  6. Partial differential equations

    CERN Document Server

    Friedman, Avner

    2008-01-01

    This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists.Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of we

  7. Hyperbolic partial differential equations

    CERN Document Server

    Witten, Matthew

    1986-01-01

    Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M

  8. Ordinary differential equations

    CERN Document Server

    Miller, Richard K

    1982-01-01

    Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,

  9. Differential equations problem solver

    CERN Document Server

    Arterburn, David R

    2012-01-01

    REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and

  10. Path Integral Methods for Stochastic Differential Equations

    OpenAIRE

    Chow, Carson C.; Buice, Michael A.

    2015-01-01

    Stochastic differential equations (SDEs) have multiple applications in mathematical neuroscience and are notoriously difficult. Here, we give a self-contained pedagogical review of perturbative field theoretic and path integral methods to calculate moments of the probability density function of SDEs. The methods can be extended to high dimensional systems such as networks of coupled neurons and even deterministic systems with quenched disorder.

  11. 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…

  12. Adaptive Rendering Based on Visual Acuity Equations

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    A new method of adaptable rendering for interaction in Virtual Environment(VE) through different visual acuity equations is proposed. An acuity factor equation of luminance vision is first given. Secondly, five equations which calculate the visual acuity through visual acuity factors are presented, and adaptive rendering strategy based on different visual acuity equations is given. The VE system may select one of them on the basis of the host's load, hereby select LOD for each model which would be rendered. A coarser LOD is selected where the visual acuity is lower, and a better LOD is used where it is higher. This method is tested through experiments and the experimental results show that it is effective.

  13. Modern introduction to differential equations

    CERN Document Server

    Ricardo, Henry J

    2009-01-01

    A Modern Introduction to Differential Equations, Second Edition, provides an introduction to the basic concepts of differential equations. The book begins by introducing the basic concepts of differential equations, focusing on the analytical, graphical, and numerical aspects of first-order equations, including slope fields and phase lines. The discussions then cover methods of solving second-order homogeneous and nonhomogeneous linear equations with constant coefficients; systems of linear differential equations; the Laplace transform and its applications to the solution of differential equat

  14. A Comparison of IRT Equating and Beta 4 Equating.

    Science.gov (United States)

    Kim, Dong-In; Brennan, Robert; Kolen, Michael

    Four equating methods were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional mean squared error (CMSE) difference, and the equipercentile equating property. The four methods were: (1) three parameter logistic (3PL) model true score equating; (2) 3PL observed score equating; (3) beta 4 true…

  15. The Numerical Calculation of Wind Effect on Sea Level Elevations

    OpenAIRE

    Uusitalo, S.

    2011-01-01

    An iteration method has been developed which uses finite differences for calculating water level elevation and water transport. To this end, the equations of motion were integrated over the depth and transformed into an implicit difference equation system. The equations were solved by the aid of an electronic computer. Two main cases were calculated, and in one instance the water levels were checked with the real ones.DOI: 10.1111/j.2153-3490.1960.tb01329.x

  16. 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.

  17. Nonlinear differential equations

    International Nuclear Information System (INIS)

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics

  18. Exciton laser rate equations

    OpenAIRE

    Garkavenko A. S.

    2011-01-01

    The rate equations of the exciton laser in the system of interacting excitons have been obtained and the inverted population conditions and generation have been derived. The possibility of creating radically new gamma-ray laser has been shown.

  19. On Dust Charging Equation

    OpenAIRE

    Tsintsadze, Nodar L.; Tsintsadze, Levan N.

    2008-01-01

    A general derivation of the charging equation of a dust grain is presented, and indicated where and when it can be used. A problem of linear fluctuations of charges on the surface of the dust grain is discussed.

  20. Diophantine Equations and Computation

    Science.gov (United States)

    Davis, Martin

    Unless otherwise stated, we’ll work with the natural numbers: N = \\{0,1,2,3, dots\\}. Consider a Diophantine equation F(a1,a2,...,an,x1,x2,...,xm) = 0 with parameters a1,a2,...,an and unknowns x1,x2,...,xm For such a given equation, it is usual to ask: For which values of the parameters does the equation have a solution in the unknowns? In other words, find the set: \\{ mid exists x_1,ldots,x_m [F(a_1,ldots,x_1,ldots)=0] \\} Inverting this, we think of the equation F = 0 furnishing a definition of this set, and we distinguish three classes: a set is called Diophantine if it has such a definition in which F is a polynomial with integer coefficients. We write \\cal D for the class of Diophantine sets.

  1. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2015-01-01

    This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.  Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...

  2. A clinical study of lung cancer dose calculation accuracy by using Monte Carlo simulation%蒙特卡罗系统验证PBC和CCC算法精确度的临床研究

    Institute of Scientific and Technical Information of China (English)

    赵艳群; 尹刚; 王先良; 王培; 祁国海; 吴大可; 肖明勇; 黎杰; 康盛伟

    2016-01-01

    .00,0.00,0.00,0.00,0.00),but the effect is not obvious in 3DCRT plans (P =0.18,0.08,0.62,0.08,0.97),similarly,the same effect was found in the differences between PBC and MC for IMRT plans,and the differences of dose volume are lager than that of CCC and MC.For the dose of ipsilateral lung,CCC algorithm overestimated dose for all lung,PBC algorithm overestimated V20(P=0.00,0.00),but underestimated V5(P=0.00,0.00),the difference of V10 have no statistical significant (P=0.47).Conclusions It is recommended that the treatment plan of lung cancer should be calculated by an advanced algorithm other than PBC.MC can calculate dose distribution of lung cancer accurately and can provide a very good tool for benchmarking the performance of other dose calculation algorithms.

  3. Hedin Equations for Superconductors

    OpenAIRE

    Linscheid, A.; Essenberger, F.

    2015-01-01

    We generalize Hedin equations to a system of superconducting electrons coupled with a system of phonons. The electrons are described by an electronic Pauli Hamiltonian which includes the Coulomb interaction among electrons and an external vector and scalar potential. We derive the continuity equation in the presence of the superconducting condensate and point out how to cast vertex corrections in the form of a non-local effective interaction that can be used to describe both fluctuations of s...

  4. Resistive ballooning mode equation

    Energy Technology Data Exchange (ETDEWEB)

    Bateman, G.; Nelson, D. B.

    1978-10-01

    A second-order ordinary differential equation on each flux surface is derived for the high mode number limit of resistive MHD ballooning modes in tokamaks with arbitrary cross section, aspect ratio, and shear. The equation is structurally similar to that used to study ideal MHD ballooning modes computationally. The model used in this paper indicates that all tokamak plasmas are unstable, with growth rate proportional to resistivity when the pressure gradient is less than the critical value needed for ideal MHD stability.

  5. Relativistic Guiding Center Equations

    Energy Technology Data Exchange (ETDEWEB)

    White, R. B. [PPPL; Gobbin, M. [Euratom-ENEA Association

    2014-10-01

    In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.

  6. SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER

    Science.gov (United States)

    Collier, D.M.; Meeks, L.A.; Palmer, J.P.

    1960-05-10

    A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.

  7. Simple Improvement of Momentum Interpolation Equation for Navier-Stoke Equation Solver on Unstructured Grid

    OpenAIRE

    Adek Tasri

    2010-01-01

    Problem statement: Pressure and velocity decoupling have been source of problem in solving Navier-Stokes and continuity equation particularly in complex collocated grid. The problem of pressure velocity decoupling is usually reduced by using momentum interpolation to calculate mass flux at face of control volume. Equation of momentum interpolation was derived by assumption that the face of cell is equidistant from two neighbor cell centers and face of cell is collinear with two neighbor cell ...

  8. Derivation of Bloch equations from the time convolution less generalized master equation

    International Nuclear Information System (INIS)

    The generalized Bloch equations (GBE) describing the temporal evolution of a single two-level atom interacting with a classical external field of arbitrary intensity and with a thermodynamic bath are obtained from the time convolutionless generalized master equation or equivalently from the Tokuyama-Mori identity. These GBE are then used to calculate the absorption spectrum of a single two-level atom with frequency modulated by dichotomic noise with time-dependent transition probability. (author)

  9. Zero Temperature Hope Calculations

    International Nuclear Information System (INIS)

    The primary purpose of the HOPE code is to calculate opacities over a wide temperature and density range. It can also produce equation of state (EOS) data. Since the experimental data at the high temperature region are scarce, comparisons of predictions with the ample zero temperature data provide a valuable physics check of the code. In this report we show a selected few examples across the periodic table. Below we give a brief general information about the physics of the HOPE code. The HOPE code is an ''average atom'' (AA) Dirac-Slater self-consistent code. The AA label in the case of finite temperature means that the one-electron levels are populated according to the Fermi statistics, at zero temperature it means that the ''aufbau'' principle works, i.e. no a priory electronic configuration is set, although it can be done. As such, it is a one-particle model (any Hartree-Fock model is a one particle model). The code is an ''ion-sphere'' model, meaning that the atom under investigation is neutral within the ion-sphere radius. Furthermore, the boundary conditions for the bound states are also set at the ion-sphere radius, which distinguishes the code from the INFERNO, OPAL and STA codes. Once the self-consistent AA state is obtained, the code proceeds to generate many-electron configurations and proceeds to calculate photoabsorption in the ''detailed configuration accounting'' (DCA) scheme. However, this last feature is meaningless at zero temperature. There is one important feature in the HOPE code which should be noted; any self-consistent model is self-consistent in the space of the occupied orbitals. The unoccupied orbitals, where electrons are lifted via photoexcitation, are unphysical. The rigorous way to deal with that problem is to carry out complete self-consistent calculations both in the initial and final states connecting photoexcitations, an enormous computational task. The Amaldi correction is an attempt to address this problem by distorting the

  10. Insertion device calculations with mathematica

    Energy Technology Data Exchange (ETDEWEB)

    Carr, R. [Stanford Synchrotron Radiation Lab., CA (United States); Lidia, S. [Univ. of California, Davis, CA (United States)

    1995-02-01

    The design of accelerator insertion devices such as wigglers and undulators has usually been aided by numerical modeling on digital computers, using code in high level languages like Fortran. In the present era, there are higher level programming environments like IDL{reg_sign}, MatLab{reg_sign}, and Mathematica{reg_sign} in which these calculations may be performed by writing much less code, and in which standard mathematical techniques are very easily used. The authors present a suite of standard insertion device modeling routines in Mathematica to illustrate the new techniques. These routines include a simple way to generate magnetic fields using blocks of CSEM materials, trajectory solutions from the Lorentz force equations for given magnetic fields, Bessel function calculations of radiation for wigglers and undulators and general radiation calculations for undulators.

  11. VLW equation of state of detonation products

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    Based on the virial theory, we proposed VLW equation of state of detonation products (VLW EOS). Its basic theory and applications were described. The distinct features of the VLW EOS were:First, the detonation performance of the new high energy density materials could be predicted more reliably. Second, it had extensive application. The detonation parameters of both the condensed high energy density materials and the gaseous fuel air explosives could be calculated. Moreover, combustion performance of propellants could also be precisely calculated. The calculation results were satisfactory.

  12. Cancer Statistics: Endometrial Cancer

    Science.gov (United States)

    ... a third party. HPF: Did You Know? Endometrial Cancer Endometrial Cancer - Did you know that endometrial cancer ... mfhs0vbvWi8?rel=0 SEER Stat Fact Sheets: Endometrial Cancer Expand All Collapse All Lifetime risk estimates are ...

  13. Functional Equations and Fourier Analysis

    OpenAIRE

    Yang, Dilian

    2010-01-01

    By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson equation, and the d'Alembert long equation, on compact groups.

  14. Efficient pulsed CO2 laser calculations

    Science.gov (United States)

    Stone, David H.; Honey, David A.

    1991-02-01

    A computationally efficient scheme for generating pumping rates was developed for use with a pulsed CO2 laser model. A steady-state solution of the Boltzmann electron transport equation generates the rates. Vibrational temperatures for the CO2 and N2 populations are determined by iterating the Boltzmann solver with the rate equation model. Rapid convergence and coarse grids allow quick calculations of pulse shape, peak power, and total energy. Results compare well with a fully time-dependent Boltzmann solver.

  15. HENRY'S LAW CALCULATOR

    Science.gov (United States)

    On-Site was developed to provide modelers and model reviewers with prepackaged tools ("calculators") for performing site assessment calculations. The philosophy behind OnSite is that the convenience of the prepackaged calculators helps provide consistency for simple calculations,...

  16. Sensitivity of rocky planet structures to the equation of state

    International Nuclear Information System (INIS)

    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.

  17. Sensitivity of rocky planet structures to the equation of state

    Energy Technology Data Exchange (ETDEWEB)

    Swift, D C

    2009-06-10

    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.

  18. Cancer Statistics

    Science.gov (United States)

    ... What Is Cancer? Cancer Statistics Cancer Disparities Cancer Statistics Cancer has a major impact on society in ... success of efforts to control and manage cancer. Statistics at a Glance: The Burden of Cancer in ...

  19. Configuration space Faddeev calculations

    International Nuclear Information System (INIS)

    The detailed study of few-body systems provides one of the most precise tools for studying the dynamics of nuclei. Our research program consists of a careful theoretical study of the nuclear few-body systems. During the past year we have completed several aspects of this program. We have continued our program of using the trinucleon system to investigate the validity of various realistic nucleon-nucleon potentials. Also, the effects of meson-exchange currents in nuclear systems have been studied. Initial calculations using the configuration-space Faddeev equations for nucleon-deuteron scattering have been completed. With modifications to treat relativistic systems, few-body methods can be applied to phenomena that are sensitive to the structure of the individual hadrons. We have completed a review of Relativistic Hamiltonian Dynamics in Nuclear and Particle Physics for Advances in Nuclear Physics. Although it is called a review, it is a large document that contains a significant amount of new research

  20. Relativistic few body calculations

    International Nuclear Information System (INIS)

    A modern treatment of the nuclear few-body problem must take into account both the quark structure of baryons and mesons, which should be important at short range, and the relativistic exchange of mesons, which describes the long range, peripheral interactions. A way to model both of these aspects is described. The long range, peripheral interactions are calculated using the spectator model, a general approach in which the spectators to nucleon interactions are put on their mass-shell. Recent numerical results for a relativistic OBE model of the NN interaction, obtained by solving a relativistic equation with one-particle on mass-shell, will be presented and discussed. Two meson exchange models, one with only four mesons (π,σ,/rho/,ω) but with a 25% admixture of γ5 coupling for the pion, and a second with six mesons (π,σ,/rho/,ω,δ,/eta/) but pure γ5γ/sup μ/ pion coupling, are shown to give very good quantitative fits to the NN scattering phase shifts below 400 MeV, and also a good description of the /rvec p/ 40Ca elastic scattering observables. Applications of this model to electromagnetic interactions of the two body system, with emphasis on the determination of relativistic current operators consistent with the dynamics and the exact treatment of current conservation in the presence of phenomenological form factors, will be described. 18 refs., 8 figs

  1. The retention index calculated with dual-phase F-18 FDG PET by the primary tumor as a predictor for lymph node involvement in patients with non small cell lung cancer

    Energy Technology Data Exchange (ETDEWEB)

    Kim, S. E.; Chung, H. C.; Lee, S. Y. [Korea University College of Medicine, Seoul (Korea, Republic of)] (and others)

    2005-07-01

    F-18 FDG uptake within primary tumor has been shown to correlate with aggressiveness and survival on PET studies of patients with NSCLC (Vesselle H, 2003). We investigated whether F-18 FDG uptake by primary tumor is a predictor of lymph node (LN) involvement in patients with non small cell lung cancer (NSCLC). A total of 51 consecutive patients with pathologically proven NSCLC were underwent dual-phase FDG PET. All of patients was underwent a thoracotomy within 1 month of F-18 FDG PET study. Maximum standard uptake values at 1 hour (SUV1) and 2 hour (SUV 2) following the injection of F-18 FDG were determined, and the retention index (RI) was calculated by dividing the difference between SUV2 and SUV1 by SUV1 (RI=(SUV2-SUV1)/SUV X 100%). The predictive values of SUV1, SUV2 and RI were analyzed, along with the clinical parameters. (age(=60 vs 60<), Sex(M vs F), tumor size(>3cm vs 3cm<), histology (adenocarcinoma vs nondenocaricnoma), and tumor differentiation (well/moderately vs poorly). The LN involvements were founded in 49%. In univariate analysis the tumor size, RI and histology were factors significantly associated with LN involvement (p<0.05). The best cut-off value for RI was 17. In multivariate analysis the tumor size and RI (>17) were factors significantly associated with LN involvement (P<0.001). SUV2 and RI from dual-phase FDG-PET by the primary tumor was significant predictors for LN involvement. High RI in the primary tumor at presentation should prompt high suspicion and an aggressive search for lymph node metastasis.

  2. Target Heart Rate Calculator

    Science.gov (United States)

    ... Local Offices Volunteer Employment Become a Supplier Report Fraud or ... reserved. The American Cancer Society is a qualified 501(c)(3) tax-exempt organization. Cancer.org is provided courtesy of ...

  3. Scaling Equation for Invariant Measure

    Institute of Scientific and Technical Information of China (English)

    LIU Shi-Kuo; FU Zun-Tao; LIU Shi-Da; REN Kui

    2003-01-01

    An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.

  4. Integral equations and computation problems

    International Nuclear Information System (INIS)

    Volterra's Integral Equations and Fredholm's Integral Equations of the second kind are discussed. Computational problems are found in the derivations and the computations. The theorem of the solution of the Fredholm's Integral Equation is discussed in detail. (author)

  5. The Use of the Health Disparities Calculator in Analysis of the Lung Cancer Burden in Urban and Rural Populations in the Świętokrzyskie Province (Poland): 1999–2010

    OpenAIRE

    Krzyżak Michalina; Piotrowska Katarzyna; Maślach Dominik; Sowa Paweł; Pędziński Bartosz; Macek Paweł; Karczewski Jan

    2015-01-01

    The purpose of the study was a comparative analysis of the burden of lung cancer in urban and rural areas in the Świętokrzyskie Province in the years 1999–2010. The material for the study accounted for information about the number of new cases of lung cancer obtained from the Świętokrzyskie Cancer Registration Office in Kielce and data from the Central Statistical Office concerning the number of deaths due to lung cancer in the years 1999–2010. Crude and age-standardized incidence, mortality,...

  6. A Generalized Equation of State for High-Pressure Liquids

    Institute of Scientific and Technical Information of China (English)

    LIANG Yan-bo; TONG Jing-shan

    2005-01-01

    An equation of state (EOS) for high-pressure liquids, I.e., Tait EOS, is deduced according to isothermal compressibility KT=-1/V·((а)V/(а)p)T·.Based on the equation, a generalized EOS for high pressure-liquids is established by using the reduced state principle and introducing a characteristic parameter-configuration factorξ.Reasonably satisfactory P-V-T data for many organic compounds, including some polar components, were calculated by using the equation.

  7. Numerical methods for solving the planar vacuum Einstein equations

    International Nuclear Information System (INIS)

    We describe a numerical code developed as a tool to investigate fully nonlinear behavior in the one-dimensional vacuum Einstein equations in plane symmetry. We use the York splitting into free and constrained variables to solve the initial-value equations. These data are then propagated in time using a fully constrained evolution scheme. We carry out a perturbative treatment of the Einstein equations and use the results as test-bed calculations for the code

  8. Numerical methods for solving the planar vacuum Einstein equations

    Energy Technology Data Exchange (ETDEWEB)

    Anninos, P.; Centrella, J. (Department of Physics and Atmospheric Science, Drexel University, Philadelphia, Pennsylvania 19104 (USA)); Matzner, R.A. (Department of Physics and Center for Relativity, The University of Texas at Austin, Austin, Texas 78712 (USA))

    1991-03-15

    We describe a numerical code developed as a tool to investigate fully nonlinear behavior in the one-dimensional vacuum Einstein equations in plane symmetry. We use the York splitting into free and constrained variables to solve the initial-value equations. These data are then propagated in time using a fully constrained evolution scheme. We carry out a perturbative treatment of the Einstein equations and use the results as test-bed calculations for the code.

  9. Exact integral equation for the renormalized Fermi surface

    OpenAIRE

    Ledowski, Sascha; Kopietz, Peter

    2002-01-01

    The true Fermi surface of a fermionic many-body system can be viewed as a fixed point manifold of the renormalization group (RG). Within the framework of the exact functional RG we show that the fixed point condition implies an exact integral equation for the counterterm which is needed for a self-consistent calculation of the Fermi surface. In the simplest approximation, our integral equation reduces to the self-consistent Hartree-Fock equation for the counterterm.

  10. Linearized Boltzmann Equation and Hydrodynamics for Granular Gases

    OpenAIRE

    Brey, J. Javier; Dufty, James W.; Ruiz-Montero, M. J.

    2003-01-01

    The linearized Boltzmann equation is considered to describe small spatial perturbations of the homogeneous cooling state. The corresponding macroscopic balance equations for the density, temperature, and flow velocity are derived from it as the basis for a hydrodynamic description. Hydrodynamics is defined in terms of the spectrum of the generator for the dynamics of the linearized Boltzmann equation. The hydrodynamic eigenfunctions and eigenvalues are calculated in the long wavelength limit....

  11. Introduction to partial differential equations

    CERN Document Server

    Greenspan, Donald

    2000-01-01

    Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.

  12. Unified derivation of evolution equations

    OpenAIRE

    Li, Hsiang-nan

    1998-01-01

    We derive the evolution equations of parton distribution functions appropriate in different kinematic regions in a unified and simple way using the resummation technique. They include the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation for large momentum transfer $Q$, the Balitskii-Fadin-Kuraev-Lipatov equation for a small Bjorken variable $x$, and the Ciafaloni-Catani-Fiorani-Marchesini equation which embodies the above two equations. The relation among these equations is explored, and p...

  13. On the monodromy group for the super Schwarzian differential equation

    International Nuclear Information System (INIS)

    We calculate the first variation of the monodromy group associated with a super Schwarzian differential equation. The relation between the monodromy period and the Fenchel-Nielsen deformation of a super Riemann surface is presented. (author)

  14. The Equations of Magnetoquasigeostrophy

    CERN Document Server

    Umurhan, O M

    2013-01-01

    The dynamics contained in magnetized layers of exoplanet atmospheres are important to understand in order to characterize what observational signatures they may provide for future observations. It is important to develop a framework to begin studying and learning the physical processes possible under those conditions and what, if any, features contained in them may be observed in future observation missions. The aims of this study is to formally derive, from scaling arguments, a manageable reduced set of equations for analysis, i.e. a magnetic formulation of the equations of quasigeostrophy appropriate for a multi-layer atmosphere. The main goal is to provide a simpler theoretical platform to explore the dynamics possible within confined magnetized layers of exoplanet atmospheres. We primarily use scaling arguments to derive the reduced equations of "magnetoquasigeostrophy" which assumes dynamics to take place in an atmospheric layer which is vertically thin compared to its horizontal scales. The derived equa...

  15. Boussinesq evolution equations

    DEFF Research Database (Denmark)

    Bredmose, Henrik; Schaffer, H.; Madsen, Per A.

    2004-01-01

    This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model...

  16. Quadratic Diophantine equations

    CERN Document Server

    Andreescu, Titu

    2015-01-01

    This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.

  17. Numerical calculation of second order perturbations

    International Nuclear Information System (INIS)

    We numerically solve the Klein-Gordon equation at second order in cosmological perturbation theory in closed form for a single scalar field, describing the method employed in detail. We use the slow-roll version of the second order source term and argue that our method is extendable to the full equation. We consider two standard single field models and find that the results agree with previous calculations using analytic methods, where comparison is possible. Our procedure allows the evolution of second order perturbations in general and the calculation of the non-linearity parameter fNL to be examined in cases where there is no analytical solution available

  18. Dressing symmetry of the uniformization solution of Liouville equation

    International Nuclear Information System (INIS)

    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

  19. The Bernoulli Equation in a Moving Reference Frame

    Science.gov (United States)

    Mungan, Carl E.

    2011-01-01

    Unlike other standard equations in introductory classical mechanics, the Bernoulli equation is not Galilean invariant. The explanation is that, in a reference frame moving with respect to constrictions or obstacles, those surfaces do work on the fluid, constituting an extra term that needs to be included in the work-energy calculation. A…

  20. 40 CFR 60.1935 - What equations must I use?

    Science.gov (United States)

    2010-07-01

    ... Small Municipal Waste Combustion Units Constructed on or Before August 30, 1999 Equations § 60.1935 What...) Percent reduction in potential hydrogen chloride emissions. Calculate the percent reduction in potential hydrogen chloride emissions (%PHC1) using equation 3 of this section: ER06DE00.005 Where: %PHC1 =...

  1. 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.

  2. A new temperature-dependent equation of state of solids

    Indian Academy of Sciences (India)

    Kamal Kapoor; Anuj Kumar; Narsingh Dass

    2014-03-01

    In the present paper, a temperature-dependent equation of state (EOS) of solids is discussed which is found to be applicable in high-pressure and high-temperature range. Present equation of state has been applied in 18 solids. The calculated data are found in very good agreement with the data available from other sources.

  3. 6 Common Cancers - Prostate Cancer

    Science.gov (United States)

    ... PSA tests. Read More "6 Common Cancers" Articles Lung Cancer / Breast Cancer / Prostate Cancer / Colorectal Cancer / Skin Cancer / Gynecologic Cancers Spring 2007 Issue: Volume 2 Number 2 Page 10 MedlinePlus | Subscribe | Magazine Information | Contact Us | Viewers & ...

  4. 6 Common Cancers - Skin Cancer

    Science.gov (United States)

    ... advanced melanoma. Read More "6 Common Cancers" Articles Lung Cancer / Breast Cancer / Prostate Cancer / Colorectal Cancer / Skin Cancer / Gynecologic Cancers Spring 2007 Issue: Volume 2 Number 2 Page 12 MedlinePlus | Subscribe | Magazine Information | Contact Us | Viewers & ...

  5. 6 Common Cancers - Colorectal Cancer

    Science.gov (United States)

    ... certain people. Read More "6 Common Cancers" Articles Lung Cancer / Breast Cancer / Prostate Cancer / Colorectal Cancer / Skin Cancer / Gynecologic Cancers Spring 2007 Issue: Volume 2 Number 2 Page 11 MedlinePlus | Subscribe | Magazine Information | Contact Us | Viewers & ...

  6. 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

  7. A New Type of Loop Equations

    OpenAIRE

    Drukker, Nadav

    1999-01-01

    We derive a new form of loop equations for light-like Wilson loops. In bosonic theories those loop equations close only for straight light-like Wilson lines. In the case of N=1 in ten dimensions they close for any light-like Wilson loop. Upon dimensional reduction to N=4 SYM in four dimensions, these loops become exactly the chiral loops which can be evaluated semiclassically, in the strong coupling limit, by a minimal surface in anti de-Sitter space. We show that the AdS calculation satisfie...

  8. Eigenvalue problems for fractional ordinary differential equations

    International Nuclear Information System (INIS)

    The eigenvalue problems are considered for the fractional ordinary differential equations with different classes of boundary conditions including the Dirichlet, Neumann, Robin boundary conditions and the periodic boundary condition. The eigenvalues and eigenfunctions are characterized in terms of the Mittag–Leffler functions. The eigenvalues of several specified boundary value problems are calculated by using MATLAB subroutine for the Mittag–Leffler functions. When the order is taken as the value 2, our results degenerate to the classical ones of the second-ordered differential equations. When the order α satisfies 1 < α < 2 the eigenvalues can be finitely many.

  9. Equations of mathematical physics

    CERN Document Server

    Tikhonov, A N

    2011-01-01

    Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri

  10. Mirce Functionability Equation

    Directory of Open Access Journals (Sweden)

    Dr Jezdimir Knezevic

    2014-08-01

    Full Text Available Scientific principles and concepts expressed through the laws, equations and formulas are the bedrock for the prediction of the deign-in functionality performance of any engineering creation. However, there is no equivalent when the in-service functionability performance predictions have to be made. Hence, Mirce Mechanics has been created at the MIRCE Akademy to fulfil the roll. The main purpose of this paper is to present the development and application of Mirce Functionability Equation which is the bedrock for the prediction of the functionability performance of maintainable systems.

  11. Obtaining Maxwell's equations heuristically

    Science.gov (United States)

    Diener, Gerhard; Weissbarth, Jürgen; Grossmann, Frank; Schmidt, Rüdiger

    2013-02-01

    Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure of the microscopic Maxwell equations for the electromagnetic fields can be deduced heuristically by using the transformation properties of the fields under space inversion and time reversal. Using the experimental facts of charge conservation and that electromagnetic waves propagate with the speed of light, together with Galilean invariance of the Lorentz force, allows us to finalize Maxwell's equations and to introduce arbitrary electrodynamics units naturally.

  12. Generalized estimating equations

    CERN Document Server

    Hardin, James W

    2002-01-01

    Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th

  13. ON A FUNCTIONAL EQUATION

    Institute of Scientific and Technical Information of China (English)

    Ding Yi

    2009-01-01

    In this article, the author derives a functional equation η(s)=[(π/4)s-1/2√2/πг(1-s)sin(πs/2)]η(1-s) of the analytic function η(s) which is defined by η(s)=1-s-3-s-5-s+7-s…for complex variable s with Re s>1, and is defined by analytic continuation for other values of s. The author proves (1) by Ramanujan identity (see [1], [3]). Her method provides a new derivation of the functional equation of Riemann zeta function by using Poisson summation formula.

  14. Kepler Equation solver

    Science.gov (United States)

    Markley, F. Landis

    1995-01-01

    Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation. This method is not iterative, and requires only four transcendental function evaluations: a square root, a cube root, and two trigonometric functions. The maximum relative error of the algorithm is less than one part in 10(exp 18), exceeding the capability of double-precision computer arithmetic. Roundoff errors in double-precision implementation of the algorithm are addressed, and procedures to avoid them are developed.

  15. Symplectic Dirac Equation

    CERN Document Server

    Amorim, R G G; Silva, Edilberto O

    2015-01-01

    Symplectic unitary representations for the Poincar\\'{e} group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space is constructed. The state of a quantum mechanics system is described by a quasi-probability amplitude that is in association with the Wigner function. As a result, the Klein-Gordon and Dirac equations are derived in phase space. As an application, we study the Dirac equation with electromagnetic interaction in phase space.

  16. The relativistic Pauli equation

    OpenAIRE

    Delphenich, David

    2012-01-01

    After discussing the way that C2 and the algebra of complex 2x2 matrices can be used for the representation of both non-relativistic rotations and Lorentz transformations, we show that Dirac bispinors can be more advantageously represented as 2x2 complex matrices. One can then give the Dirac equation a form for such matrix-valued wave functions that no longer necessitates the introduction of gamma matrices or a choice for their representation. The minimally-coupled Dirac equation for a charge...

  17. Solving Diophantine Equations

    OpenAIRE

    Cira, Octavian; Smarandache, Florentin

    2016-01-01

    In this book a multitude of Diophantine equations and their partial or complete solutions are presented. How should we solve, for example, the equation {\\eta}({\\pi}(x)) = {\\pi}({\\eta}(x)), where {\\eta} is the Smarandache function and {\\pi} is Riemann function of counting the number of primes up to x, in the set of natural numbers? If an analytical method is not available, an idea would be to recall the empirical search for solutions. We establish a domain of searching for the solutions and th...

  18. Langevin Equation for DNA Dynamics

    Science.gov (United States)

    Grych, David; Copperman, Jeremy; Guenza, Marina

    Under physiological conditions, DNA oligomers can contain well-ordered helical regions and also flexible single-stranded regions. We describe the site-specific motion of DNA with a modified Rouse-Zimm Langevin equation formalism that describes DNA as a coarse-grained polymeric chain with global structure and local flexibility. The approach has successfully described the protein dynamics in solution and has been extended to nucleic acids. Our approach provides diffusive mode analytical solutions for the dynamics of global rotational diffusion and internal motion. The internal DNA dynamics present a rich energy landscape that accounts for an interior where hydrogen bonds and base-stacking determine structure and experience limited solvent exposure. We have implemented several models incorporating different coarse-grained sites with anisotropic rotation, energy barrier crossing, and local friction coefficients that include a unique internal viscosity and our models reproduce dynamics predicted by atomistic simulations. The models reproduce bond autocorrelation along the sequence as compared to that directly calculated from atomistic molecular dynamics simulations. The Langevin equation approach captures the essence of DNA dynamics without a cumbersome atomistic representation.

  19. 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.

  20. The Statistical Drake Equation

    Science.gov (United States)

    Maccone, Claudio

    2010-12-01

    We provide the statistical generalization of the Drake equation. From a simple product of seven positive numbers, the Drake equation is now turned into the product of seven positive random variables. We call this "the Statistical Drake Equation". The mathematical consequences of this transformation are then derived. The proof of our results is based on the Central Limit Theorem (CLT) of Statistics. In loose terms, the CLT states that the sum of any number of independent random variables, each of which may be ARBITRARILY distributed, approaches a Gaussian (i.e. normal) random variable. This is called the Lyapunov Form of the CLT, or the Lindeberg Form of the CLT, depending on the mathematical constraints assumed on the third moments of the various probability distributions. In conclusion, we show that: The new random variable N, yielding the number of communicating civilizations in the Galaxy, follows the LOGNORMAL distribution. Then, as a consequence, the mean value of this lognormal distribution is the ordinary N in the Drake equation. The standard deviation, mode, and all the moments of this lognormal N are also found. The seven factors in the ordinary Drake equation now become seven positive random variables. The probability distribution of each random variable may be ARBITRARY. The CLT in the so-called Lyapunov or Lindeberg forms (that both do not assume the factors to be identically distributed) allows for that. In other words, the CLT "translates" into our statistical Drake equation by allowing an arbitrary probability distribution for each factor. This is both physically realistic and practically very useful, of course. An application of our statistical Drake equation then follows. The (average) DISTANCE between any two neighboring and communicating civilizations in the Galaxy may be shown to be inversely proportional to the cubic root of N. Then, in our approach, this distance becomes a new random variable. We derive the relevant probability density

  1. Comparison of Kernel Equating and Item Response Theory Equating Methods

    Science.gov (United States)

    Meng, Yu

    2012-01-01

    The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…

  2. On difference Riccati equations and second order linear difference equations

    OpenAIRE

    Ishizaki, Katsuya

    2011-01-01

    In this paper, we treat difference Riccati equations and second order linear difference equations in the complex plane. We give surveys of basic properties of these equations which are analogues in the differential case. We are concerned with the growth and value distributions of transcendental meromorphic solutions of these equations. Some examples are given.

  3. Test equating methods and practices

    CERN Document Server

    Kolen, Michael J

    1995-01-01

    In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...

  4. Variation principle of piezothermoelastic bodies, canonical equation and homogeneous equation

    Institute of Scientific and Technical Information of China (English)

    LIU Yan-hong; ZHANG Hui-ming

    2007-01-01

    Combining the symplectic variations theory, the homogeneous control equation and isoparametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isoparametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which are often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.

  5. Standardized Referente Evapotranspiration Equation

    Directory of Open Access Journals (Sweden)

    M.D. Mundo–Molina

    2009-04-01

    Full Text Available In this paper is presented a discussion on the necessity to standardize the Penman–Monteith equations in order to estimate ETo. The proposal is to define an accuracy and standarize equation based in Penman–Monteith. The automated weather station named CIANO (27° 22 ' 144 North latitude and 109" 55' west longitude it was selected tomake comparisons. The compared equations we re: a CIANO weat her station, b Penman–Monteith ASCE (PMA, Penman–Monteith FAO 56 (PM FAO 56, Penman–Monteith estandarizado ASCE (PM Std. ASCE. The results were: a There are important differences between PMA and CIANO weather station. The differences are attributed to the nonstandardization of the equation CIANO weather station, b The coefficient of correlation between both methods was of 0,92, with a standard deviation of 1,63 mm, an average quadratic error of 0,60 mm and one efficiency in the estimation of ETo with respect to the method pattern of 87%.

  6. Calculus & ordinary differential equations

    CERN Document Server

    Pearson, David

    1995-01-01

    Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.

  7. 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...

  8. The Equation of Causality

    OpenAIRE

    Chi, Do Minh

    1999-01-01

    We research the natural causality of the Universe. We find that the equation of causality provides very good results on physics. That is our first endeavour and success in describing a quantitative expression of the law of causality. Hence, our theoretical point suggests ideas to build other laws including the law of the Universe's evolution.

  9. Stochastic nonlinear beam equations

    Czech Academy of Sciences Publication Activity Database

    Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan

    2005-01-01

    Roč. 132, č. 1 (2005), s. 119-149. ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005

  10. On rough differential equations

    OpenAIRE

    Lejay, Antoine

    2009-01-01

    We prove that the Ito map, that is the map that gives the solution of a differential equation controlled by a rough path of finite p-variation with p in [2,3) is locally Lipschitz continuous in all its arguments and could be extended to vector fields that have only a linear growth.

  11. Exciton laser rate equations

    Directory of Open Access Journals (Sweden)

    Garkavenko A. S.

    2011-08-01

    Full Text Available The rate equations of the exciton laser in the system of interacting excitons have been obtained and the inverted population conditions and generation have been derived. The possibility of creating radically new gamma-ray laser has been shown.

  12. On the Breit Equation

    OpenAIRE

    Kasari, Hikoya; Yamaguchi, Yoshio

    2001-01-01

    Contrary to the conventional belief, it was shown that the Breit equation has the eigenvalues for bound states of two oppositely charged Dirac particles interacting through the (static) Coulomb potential. All eigenvalues reduced to those of the Sch\\"odinger case in the non-relativistic limit.

  13. Generalized reduced magnetohydrodynamic equations

    International Nuclear Information System (INIS)

    A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics

  14. Modelling by Differential Equations

    Science.gov (United States)

    Chaachoua, Hamid; Saglam, Ayse

    2006-01-01

    This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations. By analysing the problems posed by scientists in the seventeenth century, we note that physics is very important for the emergence of this theory. Taking into account this analysis, we show the…

  15. Do Differential Equations Swing?

    Science.gov (United States)

    Maruszewski, Richard F., Jr.

    2006-01-01

    One of the units of in a standard differential equations course is a discussion of the oscillatory motion of a spring and the associated material on forcing functions and resonance. During the presentation on practical resonance, the instructor may tell students that it is similar to when they take their siblings to the playground and help them on…

  16. Kinetic equation of sociodynamics

    OpenAIRE

    Володимир Олександрович Касьянов

    2014-01-01

    This article aims to build a theory of social dynamics, similar to the kinetic theory of gases. In general, given model is hybrid because off static mechanics ideas. In particular, Boltsman equation, Jaynes’s principle of entropy optimality have been applied to preference distribution of first and second type.

  17. Equational binary decision diagrams

    NARCIS (Netherlands)

    Groote, J.F.; Pol, J.C. van de

    2000-01-01

    We incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and tautology checkin

  18. Kinetic equation of sociodynamics

    Directory of Open Access Journals (Sweden)

    Володимир Олександрович Касьянов

    2014-08-01

    Full Text Available This article aims to build a theory of social dynamics, similar to the kinetic theory of gases. In general, given model is hybrid because off static mechanics ideas. In particular, Boltsman equation, Jaynes’s principle of entropy optimality have been applied to preference distribution of first and second type.

  19. Dunkl Hyperbolic Equations

    Directory of Open Access Journals (Sweden)

    Hatem Mejjaoli

    2008-12-01

    Full Text Available We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.

  20. Dual Diagonalization of Reactive Transport Equations

    Science.gov (United States)

    Yeh, G.; Tsai, C.

    2013-12-01

    One solves a system of species transport equations in the primitive approach to reactive transport modeling. This approach is not able to decouple equilibrium reaction rates from species concentrations. This problem has been overcome with the approach to diagonalizing the reaction matrix since mid 1990's, which yields the same number of transport equations for reaction-extents. In the diagonalization approach, first, a subset of reaction- extent transport equations is solved for concentrations of components and kinetic-variables. Then, the component, kinetic-variable, and mass action equations are solved for all species concentrations. Finally, the equilibrium reaction rates are posterior computed. The difficulty in this approach is that the solution of species concentrations in the second step is a stiff problem when the concentrations of master species are small compared to those of equilibrium species. To overcome the problem of stiffness, we propose a dual diagonalization approach. Here, a second diagonalization is performed on the decomposed unit matrix to yield species concentrations, each as a linear function of reaction extents. In this dual diagonalization approach, four steps are needed to complete the modeling. First, component and kinetic-variable transport equations are solved for the concentrations of components (a subset of reaction-extents) and kinetic-variables (another subset of reaction-extents). Second, the set of mass action equations written in terms of reaction extents are solved for equilibrium-variables (yet another subset of reaction-extents). Third, species concentrations are posterior obtained by solving the set of linear equations defining reaction-extents. Fourth, equilibrium rates are posterior calculated with transport equations for equilibrium-variables. Several example problems will be used to demonstrate the efficiency of this approach. Keywords: Reactive Transport, Reaction-Extent, Component, Kinetic-Variable, Equilibrium