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.
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...... 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...
Equation of State from Lattice QCD Calculations
Energy Technology Data Exchange (ETDEWEB)
Gupta, Rajan [Los Alamos National Laboratory
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 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 these lattice results of EoS are precise enough to be used in the phenomenological analysis of heavy ion experiments at RHIC and LHC.
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)
Algebraic calculation of stroboscopic maps of ordinary, nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Wackerbauer, R. (Max-Planck-Institut fuer Extraterrestrische Physik, Garching (Germany)); Huebler, A. (Illinois Univ., Urbana, IL (United States). Center for Complex Systems Research); Mayer-Kress, G. (Los Alamos National Lab., NM (United States) California Univ., Santa Cruz, CA (United States). Dept. of Mathematics)
1991-07-25
The relation between the parameters of a differential equation and corresponding discrete maps are becoming increasingly important in the study of nonlinear dynamical systems. Maps are well adopted for numerical computation and several universal properties of them are known. Therefore some perturbation methods have been proposed to deduce them for physical systems, which can be modeled by an ordinary differential equation (ODE) with a small nonlinearity. A new iterative, rigorous algebraic method for the calculation of the coefficients of a Taylor expansion of a stroboscopic map from ODE's with not necessarily small nonlinearities is presented. It is shown analytically that most of the coefficients are small for a small integration time and grow slowly in the course of time if the flow vector field of the ODE is polynomial and if the ODE has fixed point in the origin. Approximations of different orders respectively of the rest term are investigated for several nonlinear systems. 31 refs., 16 figs.
Deterministic Partial Differential Equation Model for Dose Calculation in Electron Radiotherapy
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.
Buchdahl's glass dispersion coefficients calculated from Schott equation constants.
Reardon, P J; Chipman, R A
1989-08-15
A method for the rapid evaluation of Buchdahl's dispersion coefficients at an arbitrary base wavelength given the Schott equation constants is presented. Buchdahl's chromatic coordinate transformation is performed on the Schott equation for the refractive index. A Taylor series expansion of the transformed Schott equation is then equated to the square of the Buchdahl dispersion model. Equations for Buchdahl's dispersion coefficients are then obtained for any base wavelength by matching the power of Buchdahl's chromatic coordinate omega out to fourth order.
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.
Efficient implementation of core-excitation Bethe Salpeter equation calculations
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...
Calculation of similarity solutions of partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Dresner, L.
1980-08-01
When a partial differential equation in two independent variables is invariant to a group G of stretching transformations, it has similarity solutions that can be found by solving an ordinary differential equation. Under broad conditions, this ordinary differential equation is also invariant to another stretching group G', related to G. The invariance of the ordinary differential equation to G' can be used to simplify its solution, particularly if it is of second order. Then a method of Lie's can be used to reduce it to a first-order equation, the study of which is greatly facilitated by analysis of its direction field. The method developed here is applied to three examples: Blasius's equation for boundary layer flow over a flat plate and two nonlinear diffusion equations, cc/sub t/ = c/sub zz/ and c/sub t/ = (cc/sub z/)/sub z/.
Calculation of multi frequency of Helmholtz boundary integral equation
Institute of Scientific and Technical Information of China (English)
ZHAO Zhigao; HUANG Qibai
2005-01-01
The method using series expansion is presented, and the wavenumber is separated from fundamental solution of Helmholtz boundary element equation, then the system matrices dependent of wavenumber are the matrices series associated with wavenumber, and the astringency of the method is proved. The numerical results show that combined with the CHIEFmethod, the SECHIEF (Series Expansion Combined Helmholtz Integral Equation Formulation) method can not only provide uniqueness of solution and reduce the computational time but also give accurate results under the coarse elements.
Calculation of Volterra kernels for solutions of nonlinear differential equations
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
Equations for calculating pressure loss; Ecuaciones para el calculo de perdida de carga
Energy Technology Data Exchange (ETDEWEB)
Cifre Vicens, B. [Hospital Son dureta, Plama de Mallorca, (Spain)
1995-12-31
Friction`s factor calculation is necessary for the determination of pressure loss, generally relied on the Colebrook equation which, since it is implicit, is difficult to apply using computers. A thorough review of the literature published since 1939 on the most commonly used equations is provided, establishing the validity range and relative error according to each author. The Churchill equation is recommended for use with computers as it allows calculations to be made in laminar and eddying flow areas. (Author) 17 refs.
First-principle Calculations of Equation of State for Metals at High Energy Density
Minakov, Dmitry; Levashov, Pavel; Khishchenko, Konstantin
2012-02-01
In this work, we present quantum molecular dynamics calculations of the shock Hugoniots of solid and porous samples as well as release isentropes and isentropic sound velocity behind the shock front for aluminum. Also we perform similar calculations for nickel and iron. We use the VASP code with ultrasoft and PAW pseudopotentials and GGA exchange-correlation functional. Up to 512 particles have been used in calculations. To calculate Hugoniots we solve the Hugoniot equation numerically. To obtain release isentropes, we use Zel'dovich's approach and integrate an ordinary differential equation for the temperature thus restoring all thermodynamic parameters. Isentropic sound velocity is calculated by differentiation of pressure along isentropes. The results of our calculations are in good agreement with experimental data at densities both higher and lower than the normal one. Thus, quantum molecular dynamics results can be effectively used for verification or calibration of semiempirical equations of state under conditions of lack of experimental information at high energy densities.
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico)], E-mail: paolo.amore@gmail.com; Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Division Quimica Teorica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)], E-mail: fernande@quimica.unlp.edu.ar
2008-04-28
We show that the Riccati-Pade method is suitable for the calculation of the complex eigenvalues of the Schroedinger equation with a repulsive exponential potential. The accuracy of the results is remarkable for realistic potential parameters.
Fast and accurate calculation of dilute quantum gas using Uehling-Uhlenbeck model equation
Yano, Ryosuke
2017-02-01
The Uehling-Uhlenbeck (U-U) model equation is studied for the fast and accurate calculation of a dilute quantum gas. In particular, the direct simulation Monte Carlo (DSMC) method is used to solve the U-U model equation. DSMC analysis based on the U-U model equation is expected to enable the thermalization to be accurately obtained using a small number of sample particles and the dilute quantum gas dynamics to be calculated in a practical time. Finally, the applicability of DSMC analysis based on the U-U model equation to the fast and accurate calculation of a dilute quantum gas is confirmed by calculating the viscosity coefficient of a Bose gas on the basis of the Green-Kubo expression and the shock layer of a dilute Bose gas around a cylinder.
Calculation of Wave Radiation Stress in Combination with Parabolic Mild Slope Equation
Institute of Scientific and Technical Information of China (English)
ZHENG Yonghong; SHEN Yongming; QIU Dahong
2000-01-01
A new method for the calculation of wave radiation stress is proposed by linking the expressions for wave radiation stress with the variables in the parabolic mild slope equation. The governing equations are solved numerically by the finite difference method. Numerical results show that the new method is accurate enough, can be efficiently solved with little programming effort, and can be applied to the calculation of wave radiation stress for large coastal areas.
Equation of State of Al Based on Quantum Molecular Dynamics Calculations
Minakov, Dmitry V.; Levashov, Pavel R.; Khishchenko, Konstantin V.
2011-06-01
In this work, we present quantum molecular dynamics calculations of the shock Hugoniots of solid and porous samples as well as release isentropes and values of isentropic sound velocity behind the shock front for aluminum. We use the VASP code with an ultrasoft pseudopotential and GGA exchange-correlation functional. Up to 108 particles have been used in calculations. For the Hugoniots of Al we solve the Hugoniot equation numerically. To calculate release isentropes, we use Zel'dovich's approach and integrate an ordinary differential equation for the temperature thus restoring all thermodynamic parameters. Isentropic sound velocity is calculated by differentiation along isentropes. The results of our calculations are in good agreement with experimental data. Thus, quantum molecular dynamics results can be effectively used for verification or calibration of semiempirical equations of state under conditions of lack of experimental information at high energy densities. This work is supported by RFBR, grants 09-08-01129 and 11-08-01225.
Novel Empirical Equations to Calculate the Impedance of a Strip Dipole Antenna
Directory of Open Access Journals (Sweden)
S. Keyrouz
2013-12-01
Full Text Available This paper investigates the input impedance of strip dipoles since they are the basic elements of folded strip dipole antennas. A novel, simple and accurate design algorithm is presented. Compared to state-of-the art design equations, the new proposed equations are more accurate than those found in the literature and take into consideration the antenna feeding width. These equations reduce the calculation time, when compared to commercial electromagnetic simulation software, allowing for fast antenna designs with very high accuracy. Based on the novel equations, a strip dipole antenna is designed, simulated, manufactured and measured. The simulation results are validated by measurements.
Calculation of NARM's Equilibrium with Peng-Robinson Equation of State
Institute of Scientific and Technical Information of China (English)
LI Tingxun; GUO Kaihua; WANG Ruzhu; FAN Shuanshi
2001-01-01
The liquid molar volumes of nonazeotropic refrigerant mixtures (NARM), calculated with Peng Robinson (PR)equation, were compared with vapor -liquid equilibrium experimental data in this paper. Provided with coreaction coefficient kij, the discrepancies of liquid molar volume data for R22+Rl14 and R22+R142b using PR equation are 7.7% and 8.1% , respectively. When HBT (Hankinson-Brobst-Thomson) equation was joined with PR equation, the deviations are reduced to less than 1.5% for both R22+Rl14 and R22+R142b.
Calculation of NARM's equilibrium with Peng-Robinson equation of state
Li, Tingxun; Guo, Kaihua; Wang, Ruzhu; Fan, Shuanshi
2001-04-01
The liquid molar volumes of nonazeotropic refrigerant mixtures (NARM), calculated with Peng Robinson (PR) equation, were compared with vapor -liquid equilibrium experimental data in this paper. Provided with co-reaction coefficient k ij , the discrepancies of liquid molar volume data for R22+R114 and R22+R142b using PR equation are 7.7% and 8.1%, respectively. When HBT (Hankinson-Brobst-Thomson) equation was joined with PR equation, the deviations are reduced to less than 1.5% for both R22+R114 and R22+R142b.
A deterministic partial differential equation model for dose calculation in electron radiotherapy
Energy Technology Data Exchange (ETDEWEB)
Duclous, R; Dubroca, B [CELIA and IMB Laboratories, Bordeaux University, 33405 Talence (France); Frank, M, E-mail: duclous@celia.u-bordeaux1.f, E-mail: dubroca@celia.u-bordeaux1.f, E-mail: frank@mathcces.rwth-aachen.d [Department of Mathematics and Center for Computational Engineering Science, RWTH Aachen University, Schinkelstr. 2, 52062 Aachen (Germany)
2010-07-07
High-energy ionizing radiation is a prominent modality for the treatment of many cancers. The approaches to electron dose calculation can be categorized into semi-empirical models (e.g. Fermi-Eyges, convolution-superposition) and probabilistic methods (e.g. Monte Carlo). A third approach to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. We derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on Berthon et al (2007 J. Sci. Comput. 31 347-89) that exactly preserves the key properties of the analytical solution on the discrete level. We discuss several test cases taken from the medical physics literature. A test case with an academic Henyey-Greenstein scattering kernel is considered. We compare our model to a benchmark discrete ordinate solution. A simplified model of electron interactions with tissue is employed to compute the dose of an electron beam in a water phantom, and a case of irradiation of the vertebral column. Here our model is compared to the PENELOPE Monte Carlo code. In the academic example, the fluences computed with the new model and a benchmark result differ by less than 1%. The depths at half maximum differ by less than 0.6%. In the two comparisons with Monte Carlo, our model gives qualitatively reasonable dose distributions. Due to the crude interaction model, these so far do not have the accuracy needed in clinical practice. However, the new model has a computational cost that is less than one-tenth of the cost of a Monte Carlo simulation. In addition, simulations can be set up in a similar way as a Monte Carlo simulation. If more detailed effects such as coupled electron-photon transport, bremsstrahlung
A deterministic partial differential equation model for dose calculation in electron radiotherapy
Duclous, R.; Dubroca, B.; Frank, M.
2010-07-01
High-energy ionizing radiation is a prominent modality for the treatment of many cancers. The approaches to electron dose calculation can be categorized into semi-empirical models (e.g. Fermi-Eyges, convolution-superposition) and probabilistic methods (e.g. Monte Carlo). A third approach to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. We derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on Berthon et al (2007 J. Sci. Comput. 31 347-89) that exactly preserves the key properties of the analytical solution on the discrete level. We discuss several test cases taken from the medical physics literature. A test case with an academic Henyey-Greenstein scattering kernel is considered. We compare our model to a benchmark discrete ordinate solution. A simplified model of electron interactions with tissue is employed to compute the dose of an electron beam in a water phantom, and a case of irradiation of the vertebral column. Here our model is compared to the PENELOPE Monte Carlo code. In the academic example, the fluences computed with the new model and a benchmark result differ by less than 1%. The depths at half maximum differ by less than 0.6%. In the two comparisons with Monte Carlo, our model gives qualitatively reasonable dose distributions. Due to the crude interaction model, these so far do not have the accuracy needed in clinical practice. However, the new model has a computational cost that is less than one-tenth of the cost of a Monte Carlo simulation. In addition, simulations can be set up in a similar way as a Monte Carlo simulation. If more detailed effects such as coupled electron-photon transport, bremsstrahlung
An equation for calculating the volumetric ratios required in a ligation reaction.
Cranenburgh, R M
2004-08-01
The ligation of two DNA fragments to create a new plasmid DNA molecule is a key reaction in molecular biology. Where the fragment lengths and concentrations are known, existing equations allow the desired relative molar ratio to be calculated, but this must then be related to the required volumes. Further calculations are then necessary if the maximum available volume is to consist of DNA solutions. The equation presented here allows the simple calculation of volumes of DNA solutions required to obtain a desired molar insert-to-vector ratio, and these can comprise all of the available volume in a ligation if required, thus maximising the yield of the recombinant plasmid.
Institute of Scientific and Technical Information of China (English)
朱良生; 洪广文
2001-01-01
Based on the high order nonlinear and dispersive wave equation with a dissipative term, a numerical model for nonlinear waves is developed. It is suitable to calculate wave propagation in water areas with an arbitrarily varying bottom slope and a relative depth h/L0≤1. By the application of the completely implicit stagger grid and central difference algorithm, discrete governing equations are obtained. Although the central difference algorithm of second-order accuracy both in time and space domains is used to yield the difference equations, the order of truncation error in the difference equation is the same as that of the third-order derivatives of the Boussinesq equation. In this paper, the correction to the first-order derivative is made, and the accuracy of the difference equation is improved. The verifications of accuracy show that the results of the numerical model are in good agreement with those of analytical solutions and physical models.
Institute of Scientific and Technical Information of China (English)
WANG Huai-Yu; LONG Yao; CHEN Nan-Xian
2006-01-01
In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin quantum number S. The Chebyshev equation is transformed from an ordinary differential equation obtained when we dealt with Heisenberg model, in order to calculate all three components of magnetization, by many-body Green's function under random phase approximation. The Chebyshev functions with argument being greater than 1 are discussed. This paper shows that the Chebyshev polynomials with their argument being greater than 1 have their physical application.
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)
A universal equation for calculating the energy gradient function in the energy gradient theory
Dou, Hua-Shu
2016-01-01
The relationship for the energy variation, work done, and energy dissipation in unit volumetric fluid of incompressible flow is derived. A universal equation for calculating the energy gradient function is presented for situations where both pressure driven flow and shear driven flow are present simultaneously.
A partial differential equation model of metastasized prostatic cancer.
Friedman, Avner; Jain, Harsh Vardhan
2013-06-01
Biochemically failing metastatic prostate cancer is typically treated with androgen ablation. However, due to the emergence of castration-resistant cells that can survive in low androgen concentrations, such therapy eventually fails. Here, we develop a partial differential equation model of the growth and response to treatment of prostate cancer that has metastasized to the bone. Existence and uniqueness results are derived for the resulting free boundary problem. In particular, existence and uniqueness of solutions for all time are proven for the radially symmetric case. Finally, numerical simulations of a tumor growing in 2-dimensions with radial symmetry are carried in order to evaluate the therapeutic potential of different treatment strategies. These simulations are able to reproduce a variety of clinically observed responses to treatment, and suggest treatment strategies that may result in tumor remission, underscoring our model's potential to make a significant contribution in the field of prostate cancer therapeutics.
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.
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.
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.
DEFF Research Database (Denmark)
Rindorf, Lars Henning; Mortensen, Asger
2006-01-01
We present a method for calculating the transmission spectra, dispersion, and time delay characteristics of optical-waveguide gratings based on Green's functions and Dyson's equation. Starting from the wave equation for transverse electric modes we show that the method can solve exactly both...... profile of the grating. Numerically, the method scales as O(N) where N is the number of points used to discretize the grating along the propagation axis. We consider optical fiber gratings although the method applies to all one-dimensional (1D) optical waveguide gratings including high-index contrast...
Calculation of the critical exponents by a renormalization of the Ornstein-Zernike equation
Zhang, Q.; Badiali, J. P.
1991-09-01
We calculate the critical exponents at the liquid-vapor critical point by using the classical ingredients of the liquid-state theory. Two coupling constants are defined at a microscopic level. The closure of the Ornstein-Zernike equation is given by the Callan-Symanzik equation from which we determine the position of the fixed point. The role of the three-body direct-correlation function is emphasized. A comparison between this work and the standard theory of critical phenomena based on the Landau-Ginzburg-Wilson Hamiltonian is presented.
A new way in few-body scattering calculations: discretized Faddeev equations solved on GPU
Pomerantsev, V N; Rubtsova, O A
2014-01-01
A new approach towards very fast and economic few-body scattering calculations is described. The general method is realized on three steps: (i) reformulation of the scattering equations using the convenient analytical form for the channel resolvent operator; (ii) the complete few-body continuum discretization and projection of all operators and wave functions onto the $L_2$ type basis constructed from the stationary wave packets and (iii) ultra-fast solution of the resulted matrix equations using graphics processor. The whole approach is illustrated by the calculations of the neutron-deuteron elastic scattering below and above three-body breakup threshold with fully realistic $NN$ potential which are performed on a serial PC using graphics processor for extremely short running time.
Alon, Leeor; Sodickson, Daniel K; Deniz, Cem M
2016-10-01
Deposition of radiofrequency (RF) energy can be quantified via electric field or temperature change measurements. Magnetic resonance imaging has been used as a tool to measure three dimensional small temperature changes associated with RF radiation exposure. When duration of RF exposure is long, conversion from temperature change to specific absorption rate (SAR) is nontrivial due to prominent heat-diffusion and conduction effects. In this work, we demonstrated a method for calculation of SAR via an inversion of the heat equation including heat-diffusion and conduction effects. This method utilizes high-resolution three dimensional magnetic resonance temperature images and measured thermal properties of the phantom to achieve accurate calculation of SAR. Accuracy of the proposed method was analyzed with respect to operating frequency of a dipole antenna and parameters used in heat equation inversion. Bioelectromagnetics. 37:493-503, 2016. © 2016 Wiley Periodicals, Inc.
Fast Near-Field Calculation for Volume Integral Equations for Layered Media
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Meincke, Peter; Breinbjerg, Olav
2005-01-01
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...
Water-Aromatic Liquid-Liquid-Vapour Equilibrium Calculation Using a Cubic Equation of State
Institute of Scientific and Technical Information of China (English)
无
1994-01-01
This paper presents an extension of the procedure developed in the case of water-alkane binaries to mixtures of water and benzene or toluene or xylene or ethylbenzene or diethylbenzene.The method used to calculate the equilibria is based on the Peng-Robinson cubic equation of state modified as regards the coefficient α(Tr)and on the use of a binary interaction coefficient kiw specific to binaries containing water.
Calculation of Spin Observables for Proton-Proton Elastic Scattering in the Bethe-Salpeter Equation
Kinpara, Susumu
2015-01-01
Bethe-Salpeter equation is applied to $p$-$p$ elastic scattering. The observables of spin are calculated in the framework of the M matrix using the two-body interaction potential. The parameter of the pseudovector coupling constant is adjusted so as to reproduce the spin singlet part. It is shown that the spin rotation $R(\\theta)$ and $A(\\theta)$ are improved by the resonance effect for ${}^{\\rm 1}S_{\\rm 0}$.
2009-10-01
Beattie - Bridgeman Virial expansion The above equations are suitable for moderate pressures and are usually based on either empirical constants...CR 2010-013 October 2009 A Review of Equation of State Models, Chemical Equilibrium Calculations and CERV Code Requirements for SHS Detonation...Defence R&D Canada. A Review of Equation of State Models, Chemical Equilibrium Calculations and CERV Code Requirements for SHS Detonation
Open Quantum Dynamics Calculations with the Hierarchy Equations of Motion on Parallel Computers.
Strümpfer, Johan; Schulten, Klaus
2012-08-14
Calculating the evolution of an open quantum system, i.e., a system in contact with a thermal environment, has presented a theoretical and computational challenge for many years. With the advent of supercomputers containing large amounts of memory and many processors, the computational challenge posed by the previously intractable theoretical models can now be addressed. The hierarchy equations of motion present one such model and offer a powerful method that remained under-utilized so far due to its considerable computational expense. By exploiting concurrent processing on parallel computers the hierarchy equations of motion can be applied to biological-scale systems. Herein we introduce the quantum dynamics software PHI, that solves the hierarchical equations of motion. We describe the integrator employed by PHI and demonstrate PHI's scaling and efficiency running on large parallel computers by applying the software to the calculation of inter-complex excitation transfer between the light harvesting complexes 1 and 2 of purple photosynthetic bacteria, a 50 pigment system.
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.
An analytical solution of the gyrokinetic equation for the calculation of neoclassical effects
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...
A Study on the Consistency of Discretization Equation in Unsteady Heat Transfer Calculations
Directory of Open Access Journals (Sweden)
Wenhua Zhang
2013-01-01
Full Text Available The previous studies on the consistency of discretization equation mainly focused on the finite difference method, but the issue of consistency still remains with several problems far from totally solved in the actual numerical computation. For instance, the consistency problem is involved in the numerical case where the boundary variables are solved explicitly while the variables away from the boundary are solved implicitly. And when the coefficient of discretization equation of nonlinear numerical case is the function of variables, calculating the coefficient explicitly and the variables implicitly might also give rise to consistency problem. Thus the present paper mainly researches the consistency problems involved in the explicit treatment of the second and third boundary conditions and that of thermal conductivity which is the function of temperature. The numerical results indicate that the consistency problem should be paid more attention and not be neglected in the practical computation.
BOUNDARY VALUE PROBLEMS, PARTIAL DIFFERENTIAL EQUATIONS ), (* PARTIAL DIFFERENTIAL EQUATIONS , BOUNDARY VALUE PROBLEMS), (*NUMERICAL ANALYSIS, BOUNDARY VALUE PROBLEMS), FUNCTIONS(MATHEMATICS), DIFFERENCE EQUATIONS
Total Sensitivity Index Calculation of Tool Requirement Model via Error Propagation Equation
Institute of Scientific and Technical Information of China (English)
无
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.
First-Principles Calculation of Static Equation of State and Elastic Constants for GaSe
Institute of Scientific and Technical Information of China (English)
ZHANG Dong-Wen; JIN Feng-Tao; YUAN Jian-Min
2006-01-01
@@ The all-electron full potential augmented plane-wave plus local orbital (APW+1o) method with the local-density approximation (LDA) is used to calculate the static equation of state (EOS) and elastic constants of crystalline GaSe. After the full relaxation of atomic positions, the calculated band structure at ambient pressure is consistent with the experimental data to the extent expected to give the known limits of LDA one-electron energies. The equilibrium lattice parameters found here exhibit the usual LDA-induced contraction. However, constrained with the experimental cell volume, the interlayer separation exhibits an expansion due to the LDA underestimate of the weak interlayer bonding. The calculated values of elastic constants are in good agreement with acoustic measurements. The pressure derivatives of the lattice constants derived from the theoretical elastic constants are in very good agreement with x-ray spectra measurements. Two analytical EOSs have been determined at pressures up to 4.5 GPa. The pressure evolution of the structure indicates that the layer thickness decreasesslightly under pressure.
Directory of Open Access Journals (Sweden)
S. Mattedi
2000-12-01
Full Text Available A modified form of the Hicks and Young algorithm was used with the Mattedi-Tavares-Castier lattice equation of state (MTC lattice EOS to calculate critical points of binary mixtures that exhibit several types of critical behavior. Several qualitative aspects of the critical curves, such as maxima and minima in critical pressure, and minima in critical temperature, could be predicted using the MTC lattice EOS. These results were in agreement with experimental information available in the literature, illustrating the flexibility of the functional form of the MTC lattice EOS. We observed however that the MTC lattice EOS failed to predict maxima in pressure for two of the studied systems: ethane + ethanol and methane + n-hexane. We also observed that the agreement between the calculated and experimental critical properties was at most semi-quantitative in some examples. Despite these limitations, in many ways similar to those of other EOS in common use when applied to critical point calculations, we can conclude that the MTC lattice EOS has the ability to predict several types of critical curves of complex shape.
Energy Technology Data Exchange (ETDEWEB)
Mikell, Justin K. [Department of Radiation Physics, University of Texas MD Anderson Cancer Center, Houston, Texas (United States); University of Texas Graduate School of Biomedical Sciences at Houston, Houston, Texas (United States); Klopp, Ann H. [Department of Radiation Oncology, University of Texas MD Anderson Cancer Center, Houston, Texas (United States); Gonzalez, Graciela M.N. [Department of Biostatistics, University of Texas MD Anderson Cancer Center, Houston, Texas (United States); Kisling, Kelly D. [Department of Radiation Physics-Patient Care, University of Texas MD Anderson Cancer Center, Houston, Texas (United States); University of Texas Graduate School of Biomedical Sciences at Houston, Houston, Texas (United States); Price, Michael J. [Department of Physics and Astronomy, Louisiana State University and Agricultural and Mechanical College, Baton Rouge, Louisiana, and Mary Bird Perkins Cancer Center, Baton Rouge, Louisiana (United States); Berner, Paula A. [Department of Radiation Physics, University of Texas MD Anderson Cancer Center, Houston, Texas (United States); Eifel, Patricia J. [Department of Radiation Oncology, University of Texas MD Anderson Cancer Center, Houston, Texas (United States); Mourtada, Firas, E-mail: fmourtad@christianacare.org [Department of Radiation Physics-Patient Care, University of Texas MD Anderson Cancer Center, Houston, Texas (United States); Department of Experimental Diagnostic Imaging, University of Texas MD Anderson Cancer Center, Houston, Texas (United States); Department of Radiation Oncology, Helen F. Graham Cancer Center, Newark, Delaware (United States)
2012-07-01
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 {sup 192}Ir 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/cm{sup 3} muscle, and with and without overriding contrast materials to muscle or 2.25 g/cm{sup 3} 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 {sub D2cm3} to the bladder, rectum, and sigmoid. Results: Points A and B, D{sub 2} cm{sup 3} 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 D{sub 2cm3} rectum (n = 3), D{sub 2cm3} 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
A Transport Equation Approach to Green Functions and Self-force Calculations
Wardell, Barry
2010-01-01
In a recent work, we presented the first application of the Poisson-Wiseman-Anderson method of `matched expansions' to compute the self-force acting on a point particle moving in a curved spacetime. The method employs two expansions for the Green function which are respectively valid in the `quasilocal' and `distant past' regimes, and which may be matched together within the normal neighbourhood. In this article, we introduce the method of matched expansions and discuss transport equation methods for the calculation of the Green function in the quasilocal region. These methods allow the Green function to be evaluated throughout the normal neighborhood and are also relevant to a broad range of problems from radiation reaction to quantum field theory in curved spacetime and quantum gravity.
Energy Technology Data Exchange (ETDEWEB)
Tominaka, Toshiharu [Ministry of Education, Culture, Sports, Science and Technology (MEXT), 2-5-1, Marunouchi, Chiyoda-ku, Tokyo 100-8959 (Japan)
2006-10-15
The current distributions of untwisted infinitely long superconductors have been studied during the current sweep and under an external field, using the inductance matrix among superconducting finite elements which are generated from a superconductor. The self- and mutual inductances of general polygonal conductors with a uniform current density over each cross section are precisely calculated from the analytical expressions for the geometrical mean distances. The current distributions among each superconducting element are obtained by solving the circuit equation with the Bean model and a nonlinear E-J relation based on the power law. In addition, the magnetic field and vector potential distributions of an untwisted superconducting composite are also obtained, using the analytical expressions for the magnetic field and vector potential due to polygonal conductors.
Numerical Calculation and Exergy Equations of Spray Heat Exchanger Attached to a Main Fan Diffuser
Cui, H.; Wang, H.; Chen, S.
2015-04-01
In the present study, the energy depreciation rule of spray heat exchanger, which is attached to a main fan diffuser, is analyzed based on the second law of thermodynamics. Firstly, the exergy equations of the exchanger are deduced. The equations are numerically calculated by the fourth-order Runge-Kutta method, and the exergy destruction is quantitatively effected by the exchanger structure parameters, working fluid (polluted air, i.e., PA; sprayed water, i.e., SW) initial state parameters and the ambient reference parameters. The results are showed: (1) heat transfer is given priority to latent transfer at the bottom of the exchanger, and heat transfer of convection and is equivalent to that of condensation in the upper. (2) With the decrease of initial temperature of SW droplet, the decrease of PA velocity or the ambient reference temperature, and with the increase of a SW droplet size or initial PA temperature, exergy destruction both increase. (3) The exergy efficiency of the exchanger is 72.1 %. An approach to analyze the energy potential of the exchanger may be provided for engineering designs.
DEFF Research Database (Denmark)
Budtz-Jørgensen, Esben; Keiding, Niels; Grandjean, P.
2003-01-01
observational epidemiology; measurement error; multiple endpoints structural equation models; safety standard......observational epidemiology; measurement error; multiple endpoints structural equation models; safety standard...
Efficient implementation of core-excitation Bethe-Salpeter equation calculations
Gilmore, K.; Vinson, John; Shirley, E. L.; Prendergast, D.; Pemmaraju, C. D.; Kas, J. J.; Vila, F. D.; Rehr, J. J.
2015-12-01
We present an efficient implementation of the Bethe-Salpeter equation (BSE) method for obtaining core-level spectra including X-ray absorption (XAS), X-ray emission (XES), and both resonant and non-resonant inelastic X-ray scattering spectra (N/RIXS). Calculations are based on density functional theory (DFT) electronic structures generated either by ABINIT or QuantumESPRESSO, both plane-wave basis, pseudopotential codes. This electronic structure is improved through the inclusion of a GW self energy. The projector augmented wave technique is used to evaluate transition matrix elements between core-level and band states. Final two-particle scattering states are obtained with the NIST core-level BSE solver (NBSE). We have previously reported this implementation, which we refer to as OCEAN (Obtaining Core Excitations from Ab initio electronic structure and NBSE) (Vinson et al., 2011). Here, we present additional efficiencies that enable us to evaluate spectra for systems ten times larger than previously possible; containing up to a few thousand electrons. These improvements include the implementation of optimal basis functions that reduce the cost of the initial DFT calculations, more complete parallelization of the screening calculation and of the action of the BSE Hamiltonian, and various memory reductions. Scaling is demonstrated on supercells of SrTiO3 and example spectra for the organic light emitting molecule Tris-(8-hydroxyquinoline)aluminum (Alq3) are presented. The ability to perform large-scale spectral calculations is particularly advantageous for investigating dilute or non-periodic systems such as doped materials, amorphous systems, or complex nano-structures.
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.
Calculating the renormalisation group equations of a SUSY model with Susyno
Fonseca, Renato M.
2012-10-01
Susyno is a Mathematica package dedicated to the computation of the 2-loop renormalisation group equations of a supersymmetric model based on any gauge group (the only exception being multiple U(1) groups) and for any field content. Program summary Program title: Susyno Catalogue identifier: AEMX_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMX_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 30829 No. of bytes in distributed program, including test data, etc.: 650170 Distribution format: tar.gz Programming language: Mathematica 7 or higher. Computer: All systems that Mathematica 7+ is available for (PC, Mac). Operating system: Any platform supporting Mathematica 7+ (Windows, Linux, Mac OS). Classification: 4.2, 5, 11.1. Nature of problem: Calculating the renormalisation group equations of a supersymmetric model involves using long and complicated general formulae [1, 2]. In addition, to apply them it is necessary to know the Lagrangian in its full form. Building the complete Lagrangian of models with small representations of SU(2) and SU(3) might be easy but in the general case of arbitrary representations of an arbitrary gauge group, this task can be hard, lengthy and error prone. Solution method: The Susyno package uses group theoretical functions to calculate the super-potential and the soft-SUSY-breaking Lagrangian of a supersymmetric model, and calculates the two-loop RGEs of the model using the general equations of [1, 2]. Susyno works for models based on any representation(s) of any gauge group (the only exception being multiple U(1) groups). Restrictions: As the program is based on the formalism of [1, 2], it shares its limitations. Running time can also be a significant restriction, in particular for models with many fields. Unusual features
Usang, M. D.; Ivanyuk, F. A.; Ishizuka, C.; Chiba, S.
2016-10-01
Nuclear fission is treated by using the Langevin dynamical description with macroscopic and microscopic transport coefficients (mass and friction tensors), and it is elucidated how the microscopic (shell and pairing) effects in the transport coefficients, especially their dependence on temperature, affects various fission observables. We found that the microscopic transport coefficients, calculated by linear response theory, change drastically as a function of temperature: in general, the friction increases with growing temperature while the mass tensor decreases. This temperature dependence brings a noticeable change in the mass distribution and kinetic energies of fission fragments from nuclei around 236U at an excitation energy of 20 MeV. The prescission kinetic energy decreases from 25 MeV at low temperature to about 2.5 MeV at high temperature. In contrast, the Coulomb kinetic energy increases as the temperature increases. Interpolating the microscopic transport coefficients among the various temperatures enabled our Langevin equation to use the microscopic transport coefficients at a deformation-dependent local temperature of the dynamical evolution. This allowed us to compare directly the fission observables of both macroscopic and microscopic calculations, and we found almost identical results under the conditions considered in this work.
Directory of Open Access Journals (Sweden)
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
Kidon, Lyran; Wilner, Eli Y; Rabani, Eran
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Benedict, L; Ogitsu, T
2008-07-24
We describe the construction of a three-phase equation of state (EOS) for elemental beryllium. The phases considered are: the ambient hcp phase, the high-temperature bcc phase, and the liquid. The free energies of the solid phases are constructed from cold, ion-thermal, and electron-thermal components derived from ab initio electronic structure-based calculations. We find that the bcc phase is unstable near ambient conditions, and that even at high pressures at which the bcc phase is stable, the bcc-hcp energy barrier can be as small as a few hundred Kelvins. The liquid free energy is based on a model of Chisolm and Wallace and is constrained by using the melt curve (determined by ab initio 2-phase simulations) as a reference. The high-temperature plasma limit is addressed with an average-atom-in-jellium model. Comparisons to experimental results, both for the ambient hcp phase, and for the phase diagram as a whole, are discussed.
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.
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.
Calculation of Equation of State of QCD at Finite Chemical Potential and Temperature
Institute of Scientific and Technical Information of China (English)
QIAO Qing-Peng; ZONG Hong-Shi; TANG Jian; HOU Feng-Yao; LI Xue-Qian; SUN Wei-Min; L(U) Xiao-Fu
2008-01-01
In this paper, using path integral techniques we derive a model-independent formula for the pressure density (μ, T) (or equivalently the partition function) of Quantum Chromodynamics (QCD), which gives the equation of state (EOS) of QCD at finite chemical potential and temperature. In this formula the pressure density (μ, T) consists of two terms: the first term (μ,T) T=0) is a #-independent (but T-dependent) constant; the second term is totally determined by G[μ, T] (p ωn) (the dressed quark propagator at finite μ and finite T), which contains all the nontrivial μ-dependence. Then, in the framework of the rainbow-ladder approximation of the Dyson-Schwinger (DS) approach and under the approximation of neglecting the μ-dependence of the dressed gluon propagator, we show that G[μ, T] (p, ωn) can be obtained from G[T] (p, ωn) (the dressed quark propagator at μ = 0) by the substitution ωn →ωn + iμ. This result facilitates numerical calculations considerably. By this result, once G[T](p, ωn) is known, one can determine the EOS of QCD under the above approximations (up to the additive term (μ, T)[T=0). Finally, a comparison of the present EOS of QCD and the EOS obtained in the previous literatures in the framework of the rainbow-ladder approximation of the DS approach is given. It is found that the EOS given in the previous literatures does not satisfy the thermodynamic relation p(μ, T) = T.
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.
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...
Calculating the renormalisation group equations of a SUSY model with Susyno
Fonseca, Renato M
2011-01-01
Susyno is a Mathematica package dedicated to the computation of the 2-loop renormalisation group equations of a supersymmetric model based on any gauge group (the only exception being multiple U(1) groups) and for any field content.
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.
Institute of Scientific and Technical Information of China (English)
无
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.
A nodal collocation method for the calculation of the lambda modes of the P {sub L} equations
Energy Technology Data Exchange (ETDEWEB)
Capilla, M. [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, Camino de Vera 14, E-46022 Valencia (Spain)]. E-mail: tcapilla@mat.upv.es; Talavera, C.F. [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, Camino de Vera 14, E-46022 Valencia (Spain)]. E-mail: talavera@mat.upv.es; Ginestar, D. [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, Camino de Vera 14, E-46022 Valencia (Spain)]. E-mail: dginesta@mat.upv.es; Verdu, G. [Departamento de Ingenieria Quimica y Nuclear, Universidad Politecnica de Valencia, Camino de Vera 14, E-46022 Valencia (Spain)]. E-mail: gverdu@iqn.upv.es
2005-11-15
P {sub L} equations are classical approximations to the neutron transport equation admitting a diffusive form. Using this property, a nodal collocation method is developed for the P {sub L} approximations, which is based on the expansion of the flux in terms of orthonormal Legendre polynomials. This method approximates the differential lambda modes problem by an algebraic eigenvalue problem from which the fundamental and the subcritical modes of the system can be calculated. To test the performance of this method, two problems have been considered, a homogeneous slab, which admits an analytical solution, and a seven-region slab corresponding to a more realistic problem.
Calculation of the Dirac equation in curved spacetimes with possible torsion using MAPLE and REDUCE
Vulcanov, Dumitru N.
2003-08-01
The article presents computer algebra procedures and routines applied to the study of the Dirac field on curved spacetimes. The main part of the procedures is devoted to the construction of Pauli and Dirac matrices algebra on an anholonomic orthonormal reference frame. Then these procedures are used to compute the Dirac equation on curved spacetimes in a sequence of special dedicated routines. A comparative review of such procedures obtained for two computer algebra platforms (REDUCE+EXCALC and MAPLE+GRTensorII) is carried out. Applications for the calculus of Dirac equation on specific examples of spacetimes with or without torsion are pointed out.
Two Approaches to the Calculation of Approximate Symmetry of Ostrovsky Equation with Small Parameter
Mahdavi, Abolhassan; Nadjafikhah, Mehdi; Toomanian, Megerdich
2015-12-01
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.
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.
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.
GENERALIZATION OF MOVEMENT EQUATIONS OF VEHICLES FOR CALCULATION OF THE FREE MOTION VELOCITY
N. Smirnovа; D. Leontiev
2014-01-01
The basic equations of vehicles motion have been analyzed and summarized; the solving algorithm for the analysis of free movement under road conditions that are defined by the parameters of the roads technical level and its operational state was made up. The results of modeling are given.
Kinetic Formulation of the Kohn-Sham Equations for ab initio Electronic Structure Calculations
Mendoza, M; Herrmann, H J
2013-01-01
We introduce a new approach to density functional theory based on kinetic theory, showing that the Kohn-Sham equations can be derived as a macroscopic limit of a suitable Boltzmann kinetic equation in the limit of small mean free path versus the typical scale of density gradients (Chapman-Enskog expansion). To derive the approach, we first write the Schr\\"odinger equation as a special case of a Boltzmann equation for a gas of quasi-particles, with the potential playing the role of an external source that generates and destroys particles, so as to drive the system towards the ground state. The ions are treated as classical particles, using the Born-Oppenheimer dynamics, or by imposing concurrent evolution with the electronic orbitals. In order to provide quantitative support to our approach, we implement a discrete (lattice) model and compute, the exchange and correlation energies of simple atoms, and the geometrical configuration of the methane molecule. Excellent agreement with values in the literature is fo...
Energy Technology Data Exchange (ETDEWEB)
Song, T., E-mail: songting_lzjtu@yeah.net [School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070 (China); School of Material Science and Engineering, Lanzhou University of Technology, Lanzhou 730050 (China); Ma, Q. [School of Material Science and Engineering, Lanzhou University of Technology, Lanzhou 730050 (China); Sun, X.W., E-mail: xsun@carnegiescience.edu [School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070 (China); Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC 20015 (United States); Liu, Z.J., E-mail: liuzj_lzcu@163.com [School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070 (China); Department of Physics, Lanzhou City University, Lanzhou 730070 (China); Fu, Z.J. [School of Electrical and Electronic Engineering, Chongqing University of Arts and Sciences, Chongqing 402160 (China); Wei, X.P.; Wang, T.; Tian, J.H. [School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070 (China)
2016-09-07
The phase transition, electronic band structure, and equation of state (EOS) of cubic TcN are investigated by first-principles pseudopotential method based on density-functional theory. The calculated enthalpies show that TcN has a transformation between zincblende and rocksalt phases and the pressure determined by the relative enthalpy is 32 GPa. The calculated band structure indicates the metallic feature and it might make cubic TcN a better candidate for hard materials. Particular attention is paid to the predictions of volume, bulk modulus and its pressure derivative which play a central role in the formulation of approximate EOSs using the quasi-harmonic Debye model. - Highlights: • The phase transition pressure and electronic band structure for cubic TcN are determined. • Particular attention is paid to investigate the equation of state parameters for cubic TcN. • The thermodynamic properties up to 80 GPa and 3000 K are successfully predicted.
Directory of Open Access Journals (Sweden)
Zadnik Vesna
2016-06-01
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.
PREDICTION AND CALCULATION OF AZEOTROPIC’S BEHAVIOURS ON THE BASIS OF CUBIC EQUATION OF STATE
Троценко, А. В.
2015-01-01
The azeotropic binary mixtures are effective working substances for various refrigerators, including low-temperature ones. Their experimental finding and investigation is the complicated and labour-intensive problem. That problemrestrains more practical application of azeotropic mixtures in cooling systems. The problems of prediction and modeling of azeotropic behaviours with the help of two-parametric cubic equations of a state are considered. Using the maxwell line method, the conditions of...
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...
Rogers, G; Oosthuyse, T
2000-02-01
The standard equation used to calculate mean arterial pressure (MAP) assumes that diastole persists for 2/3 and systole for 1/3 of each cardiac cycle. This ratio is altered when heart rate increases, and therefore we investigated the efficacy of predicting MAP during exercise using non-invasive indirect methods. Eight subjects exercised on a cycle ergometer for 3 minute intervals to elicit heart rates between 100-110, 120-130, 140-150, 160-170, and 180-190 beats/min. In the last minute of each 3 min interval an ECG recording was taken and systolic (SP) and diastolic (DP) blood pressure was measured by manual auscultation. MAP was calculated for each heart rate interval by: MAP=DP+1/3(SP-DP) (method A), and MAP= DP + Fs(SP- DP) (method B), where Fs is the fraction of the cardiac cycle comprising systole, measured from the ECG. Fs increased from 0.35+/-0.049 at rest to 0.47+/-0.039 at a heart rate of 180-190 beats/min. MAP measured by method B was consistently greater than MAP calculated by method A at all heart rates greater than resting heart rate (pequation (method A) to derive MAP during exercise (measured as the percentage difference between method A and B) increased linearly with heart rate (r=0.98). The standard MAP equation should not be applied during exercise, as it does not account for the change in the systolic: diastolic period ratio as heart rate increases.
Yoon, Sungroh; Park, Man Sik; Choi, Hoon; Bae, Jae Hyun; Moon, Du Geon; Hong, Sung Kyu; Lee, Sang Eun; Park, Chanwang
2017-01-01
Purpose We developed the Korean Prostate Cancer Risk Calculator for High-Grade Prostate Cancer (KPCRC-HG) that predicts the probability of prostate cancer (PC) of Gleason score 7 or higher at the initial prostate biopsy in a Korean cohort (http://acl.snu.ac.kr/PCRC/RISC/). In addition, KPCRC-HG was validated and compared with internet-based Western risk calculators in a validation cohort. Materials and Methods Using a logistic regression model, KPCRC-HG was developed based on the data from 602 previously unscreened Korean men who underwent initial prostate biopsies. Using 2,313 cases in a validation cohort, KPCRC-HG was compared with the European Randomized Study of Screening for PC Risk Calculator for high-grade cancer (ERSPCRC-HG) and the Prostate Cancer Prevention Trial Risk Calculator 2.0 for high-grade cancer (PCPTRC-HG). The predictive accuracy was assessed using the area under the receiver operating characteristic curve (AUC) and calibration plots. Results PC was detected in 172 (28.6%) men, 120 (19.9%) of whom had PC of Gleason score 7 or higher. Independent predictors included prostate-specific antigen levels, digital rectal examination findings, transrectal ultrasound findings, and prostate volume. The AUC of the KPCRC-HG (0.84) was higher than that of the PCPTRC-HG (0.79, pcancer prediction model in Korea. It had higher predictive accuracy than PCPTRC-HG in a Korean population and showed similar performance with ERSPCRC-HG in a Korean population. This prediction model could help avoid unnecessary biopsy and reduce overdiagnosis and overtreatment in clinical settings. PMID:28046017
Faster G0W0 calculations using Lanczos algorithm and Sternheimer equation
2011-01-01
G0W0 corrections to DFT band structures are a popular way to go beyond the accuracy DFT is able to provide. However, the calculation of such corrections with the ABINIT code is currently prohibitive for systems with more than a few hundreds of electrons. What limits the calculations to this system size is the need in the current implementation to invert the dielectric matrix and to carry out some summation over conduction bands. This poster presents a strategy to avoid both of these limitatio...
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.
Zhao, Sipei; Qiu, Xiaojun; Cheng, Jianchun
2015-09-01
This paper proposes a different method for calculating a sound field diffracted by a rigid barrier based on the integral equation method, where a virtual boundary is assumed above the rigid barrier to divide the whole space into two subspaces. Based on the Kirchhoff-Helmholtz equation, the sound field in each subspace is determined with the source inside and the boundary conditions on the surface, and then the diffracted sound field is obtained by using the continuation conditions on the virtual boundary. Simulations are carried out to verify the feasibility of the proposed method. Compared to the MacDonald method and other existing methods, the proposed method is a rigorous solution for whole space and is also much easier to understand.
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.
Mirzadeh, Mohammad; Squires, Todd; Gibou, Frederic
2010-11-01
We present a finite difference discretization of the non-linear Poisson-Boltzmann (PB) equation over complex geometries that has second order accurracy. The level-set method is adopted to represent the interface and Octree (in three dimensions) or Quadtree (in two dimensions) data stuructures are used to generate adaptive grids. Such an approach garanties that the finest grid resolution is located near the interface where EDL forms and creates very large electric field. Several numerical experiments are carried which indicate the second order accuracy both in the case of Dirichlet and Neumann boundary conditions in L2 and L∞ norms. Finally, we use our method to study the electrostatic interaction of double layers between charged particles in an unbounded bulk electrolyte as well as in a channel where the channel width is of the order of Debye length.
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.
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.
Simpson, Jamesina J.; Taflove, Allen
2005-05-01
We report what we believe to be the first three-dimensional computational solution of the full-vector Maxwell's equations for hypothesized pre-seismic electromagnetic phenomena propagated within the entire Earth-ionosphere cavity. Periodic boundary conditions are used in conjunction with a variable-cell finite-difference time-domain (FDTD) space lattice wrapping around the complete Earth-sphere and extending +/-100 km radially from sea level. This technique permits a direct time-domain calculation of round-the-world ULF/ELF propagation accounting for arbitrary horizontal as well as vertical geometrical and electrical inhomogeneities/anisotropies of the excitation, ionosphere, lithosphere, and oceans. In this study, we model electrokinetic currents at depths of 2.5 km and 17 km near the hypocenter of the Loma Prieta earthquake and compare the FDTD-calculated surface magnetic field to analytical results and measurements previously reported in the literature. We accommodate the complete physics introduced by impulsive electromagnetic wave propagation through the conductive Earth, and hence illustrate the importance of solving the full Maxwell's equations when modeling current sources within the Earth's crust. Our calculated spectra agree qualitatively with those reported by Fraser-Smith et al. (1990).
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)
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.
Otiniano Cáceres, Manuel Eduardo; Facultad de Química e Ingeniería Química, Universidad Nacional Mayor de San Marcos,Lima,Perú.
2014-01-01
This paper presents a simple method for calculation on a column of binary batch rectification with rectification, using the Rayleigh equation in the two main operating modes: constant, variable reflux reflux. En este trabajo se presenta un método simple para realizar los cálculos en una columna de rectificación discontinua binaria con rectificación, utilizando la ecuación de Rayleigh en los dos principales modos de operación: reflujo constante y reflujo variable.
Iitaka, T.; Nomura, S.; Hirayama, H.; Zhao, X. W.; Aoyagi, Y.; Sugano, T.
1997-08-01
We introduce a new linear scaling( ( O(N) ) ) algorithm [1] for calculating linear response functions of non-interacting electrons. It requires only ( O(N) ) computational efforts where ( N ) is the dimension of the statevector, because it avoids ( O(N^3) ) computational effort for calculating large number of eigenstates, i.e., the occupied one-electron states up to the Fermi energy and the unoccupied states with higher energy. The advantage of this method compared to the Chebyshev polynomial method recently developed by Wang [2] is that it does not need any storage of huge statevectors on hard disks. The application of this method to photonic band structures [3], and silicon nanocrystalites [3,4] will be also presented. [ 1 ] T. Iitaka, S. Nomura, H. Hirayama, X.W. Zhao, Y. Aoyagi, T. Sugano, to appear in Phys. Rev. E, preprint is available at xxx.lanl.gov/abs/cond-mat/9703224>cond- mat/9703224. See also http://espero.riken.go.jp/. [ 2 ] L.W. Wang, Phys. Rev. B 49, 10154 (1994); L.W. Wang, Phys. Rev. Lett. 73, 1039 (1994) . [ 3 ] H. Hirayama et al., S. Nomura et al., and T. Iitaka et al., in LDSD97, Lisbon, Portugal 19-20 May 1997. The proceedings will appear in Materials Science & Engineering B. [ 4 ] S. Nomura et al., (submitted to Phys. Rev. B).
Calculating the vertex unknowns of nine point scheme on quadrilateral meshes for diffusion equation
Institute of Scientific and Technical Information of China (English)
YUAN GuangWei; SHENG ZhiQiang
2008-01-01
In the construction of nine point scheme, both vertex unknowns and cell-centered unknowns are introduced, and the vertex unknowns are usually eliminated by using the interpolation of neighboring cell-centered unknowns, which often leads to lose accuracy. Instead of using interpolation,here we propose a different method of calculating the vertex unknowns of nine point scheme, which are solved independently on a new generated mesh. This new mesh is a Voronoi mesh based on the vertexes of primary mesh and some additional points on the interface. The advantage of this method is that it is particularly suitable for solving diffusion problems with discontinuous coefficients on highly distorted meshes, and it leads to a symmetric positive definite matrix. We prove that the method has first-order convergence on distorted meshes. Numerical experiments show that the method obtains nearly second-order accuracy on distorted meshes.
Calculating the vertex unknowns of nine point scheme on quadrilateral meshes for diffusion equation
Institute of Scientific and Technical Information of China (English)
2008-01-01
In the construction of nine point scheme,both vertex unknowns and cell-centered unknowns are introduced,and the vertex unknowns are usually eliminated by using the interpolation of neighboring cell-centered unknowns,which often leads to lose accuracy.Instead of using interpolation,here we propose a different method of calculating the vertex unknowns of nine point scheme,which are solved independently on a new generated mesh.This new mesh is a Vorono¨i mesh based on the vertexes of primary mesh and some additional points on the interface.The advantage of this method is that it is particularly suitable for solving diffusion problems with discontinuous coeffcients on highly distorted meshes,and it leads to a symmetric positive definite matrix.We prove that the method has first-order convergence on distorted meshes.Numerical experiments show that the method obtains nearly second-order accuracy on distorted meshes.
Ichino, Takatoshi; Cheng, Lan; Stanton, John F.
2016-06-01
The innovative application of the ion-trap technique by Wester and coworkers has yielded definitive experimental values of photodetachment cross sections for the atomic oxygen radical anion (Obullet -) [Hlavenka et al., J. Chem. Phys. 130, 061105 (2009)]. In the present study, equation-of-motion coupled-cluster (EOM-CC) calculations have been performed to derive theoretical values of photodetachment cross sections for the negative ions of atoms in the first two periods of the periodic table as well as of those which belong to the alkali metal and halogen groups. Two methods have been employed to derive the cross sections. One involves the Dyson orbitals obtained from EOM-CC calculations and plane wave functions for the detached electron in the transition dipole moment integrals. The other method utilizes the moment theory following EOM-CC calculations of transition dipole moments for a large number of pseudo-states. The cross sections so evaluated for Obullet - match the experimental values very well. Generally good agreement has been found between the theoretical and experimental values of the cross sections for the atoms in the first two periods, while the present calculations cast some doubt on reported experimental values for some atoms beyond the second period. Substantial relativistic effects on the cross section have been observed for heavy elements in the alkali metal and halogen groups.
DEFF Research Database (Denmark)
Christiansen, Rasmus Lübeck; Jensen, Henrik R.; Brink, Carsten
2017-01-01
Background: Current state of the art radiotherapy planning of prostate cancer utilises magnetic resonance (MR) for soft tissue delineation and computed tomography (CT) to provide an electron density map for dose calculation. This dual scan workflow is prone to setup and registration error....... This study evaluates the feasibility of an MR-only workflow and the validity of dose calculation from an MR derived pseudo CT. Material and methods: Thirty prostate cancer patients were CT and MR scanned. Clinical treatment plans were generated on CT using a single 18 MV arc volumetric modulated arc therapy...
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.
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.
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.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In order to predict the conductance for dilute 1-1 valent electrolyte solutions,a new conductance equation was proposed based on the Onsager and Onsagar-Fuoss-Chen conductance equation.It has only one parameter A,which can be obtained directly from the data of ionic limiting molar conductivity Λ∞m,and its expression is very simple.The new equation has been verified by the experimental molar conductivities of some single strong electrolyte and mixed electrolyte solutions at 298.15 K reported in literatures.The results are in good agreement with the experimental data.Meanwhile the ionization constants of some weak electrolyte solutions were calculated by a modified equation of this new equation,and it was also found that the calculation results are in good agreement with the data in the literature.
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.
Dąbrowska, Barbara
2000-03-01
The Deiters equation of state and the Redlich-Kwong equation of state were used for calculations of low-temperature vapour-liquid phase equilibria and related thermodynamic properties in binary systems containing halogenhydrocarbons. In all calculations, standard mixing rules for the Deiters equation of state as well as the modified mixing rules (including the repulsion function and density-dependent weight factors or the repulsion function and modified mean density approximation with density-dependent weight factors) were used. The calculations were done for the following systems: CF 4/CHF 3, CF 3Cl/CF 2Cl 2, CH 4/CHF 2Cl, CH 4/CF 2Cl 2, CHF 3/CFCl 3, N 2/CF 2Cl 2. The best results were achieved with the Deiters equation of state, especially with modified mixing rules. For higher pressures and lower temperatures the Redlich-Kwong equation of state is not able to predict the phase equilibria in halogenhydrocarbon systems accurately. It fails too in the case of strongly polar substances. The best parameter sets for the Redlich-Kwong equation of state and the Deiters equation of state for the systems investigated were collected.
Directory of Open Access Journals (Sweden)
V. Ovsianko
2012-01-01
Full Text Available The paper reveals a brand-new direction in simulation of frame and continual structures while calculating static and dynamic loads and stability. An electronic model has been synthesized for an investigated object and then it has been analyzed not with the help of specialized analog computing techniques but by means of high-performance software package for electronic circuit calculation using a personal computer.The given paper contains exact algebraic equations corresponding to differential equations for lateral bending calculation of frame structures without and with due account of viscoelastic material properties in compliance with the Kelvin model.The exact algebraic equation for a beam on elastic supports (or elastic Winkler foundation has been derived for quartic differential equation.The paper presents a number of exact algebraic equations which are equivalent to differential equations for transverse-longitudinal bending calculation of frame structures without and with due account of viscoelastic material properties when lateral and longitudinal loads are applied in the form of impulses with any periods of their duration and any interchangeability.
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Kondo,Yoshiro
2006-12-01
Full Text Available To develop a new method for evaluating the intensity of workers’ exposures to toluene alone or toluene in mixed solvents, regression equations were calculated between the concentrations of toluene to which workers were exposed and the concentrations of hippuric acid or toluene in workers’ urine samples taken at the end of their shifts. Thereafter, the discriminant exposure concentration of the solvents in air, which was the concentration considered to discriminate exposure from non-exposure within a fi xed level of error using fi ducial ranges of individual specimens (DEC-I or using confi dence ranges of regression equation (DEC-R, was measured by a scale. The devised equations were applied to calculate DEC-I or DEC-R accurately using the formulas expressing a regression line and its fi ducial ranges or confi dence ranges. The equations can calculate not only more precise values of DEC-I or DEC-R than can be measured by a scale, but can also calculate values corresponding to any level of error. Moreover, DEC-I and DEC-R can be defi ned by the equations. The concentration capable of discriminating TLV (threshold limit value exposure from non-TLV exposure was estimated using fi ducial ranges (DTL-I and then using confi dence ranges of the regression equation (DTL-R.
Miller, M L; Cornish, R E; Pomatto, C B
1999-05-01
The Uranium Mill Tailings Remedial Action Project has completed remedial action at 22 uranium mill tailings sites and about 5,000 properties ("vicinity properties") where tailings were used in construction, at a total cost of $1.45 billion. This paper uses existing data from Environmental Impact Statements and Environmental Assessments, and vicinity property calculations, to determine the total number of cancer deaths averted by the Uranium Mill Tailings Remedial Action Project. The cost-effectiveness of remediating each site, the vicinity properties, and the entire project is calculated. The cost per cancer death averted was four orders of magnitude higher at the least cost-effective site than at the most cost-effective site.
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Suresh Rana
2013-01-01
Full Text Available Purpose: The purpose of this study is to assess the dosimetric impact of Acuros XB dose calculation algorithm (AXB, in comparisons with Anisotropic Analytical Algorithm (AAA calculations in prostate cancer treatment using RapidArc. Materials and Methods: A computed tomography (CT dataset of low-risk prostate cancer patients treated at Arizona Center for Cancer Care was selected and contoured for prostate, seminal vesicles, and organs at risk (OARs(rectum, bladder, and femur heads. Plans were created for 6 MV photon beam using RapidArc technique in Eclipse treatment planning system. Dose calculations were performed with AAA and AXB for same number of monitor units and identical beam setup. Mean and maximum doses to planning target volume (PTV and OARs were analyzed. Additionally, minimum dose to PTV and V100 was analyzed. Finally, point-dose difference between planar dose distributions of AAA and AXB plans was investigated. Results: The highest dose difference was up to 0.43% (range: 0.05−0.43%, P> 0.05 for PTV and 1.98% (range: 0.22−1.98%, P> 0.05 for OARs with AAA predicting higher dose than AXB. The V100 values of AAA plans (95 % and AXB plans (range: 93.1−97.9 % had an average difference of 0.89±1.47% with no statistical significance (P = 0.25411. The point-dose difference analysis showed that AAA predicted higher dose than AXB at significantly higher percentage (in average 94.15 of total evaluated points. Conclusion: The dosimetric results of this study suggest that the AXB can perform the dose computation comparable to AAA in RapidArc prostate cancer treatment plans that are generated by a partial single-arc technique.
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.
Ender, I A; Flegontova, E Yu; Gerasimenko, A B
2016-01-01
An algorithm for sequential calculation of non-isotropic matrix elements of the collision integral which are necessary for the solution of the non-linear Boltzmann equation by moment method is proposed. Isotropic matrix elements that we believe are known, are starting ones. The procedure is valid for any interaction law and any mass ratio of the colliding particles.
Quiney, H. M.; Glushkov, V. N.; Wilson, S.; Sabin,; Brandas, E
2001-01-01
A comparison is made of the accuracy achieved in finite difference and finite basis set approximations to the Dirac equation for the ground state of the hydrogen molecular ion. The finite basis set calculations are carried out using a distributed basis set of Gaussian functions the exponents and pos
Energy Technology Data Exchange (ETDEWEB)
Goto, H. [Dept. of Mathematics and Physical Science, Graduate School of Science and Technology, Chiba Univ. (Japan); Natsume, Y. [Chiba Univ. (Japan). Dept. of Physics
1995-04-01
The estimation of Tc for the superconducting phase under the ultra-high magnetic feild is discussed on the basis of numerical calculation by the use of the expression of Eliashberg equations for strong coupling theory. The essenthial effect of the retardation of the interaction by phonons on making the gap is pointed out in comparison between 2 and 3 dimensinal systems. (orig.)
2010-07-01
... 40 Protection of Environment 12 2010-07-01 2010-07-01 true Equations To Calculate Organic HAP Emissions Factors for Specific Open Molding and Centrifugal Casting Process Streams 1 Table 1 to Subpart... Specific Open Molding and Centrifugal Casting Process Streams ER25AU05.020 ER25AU05.021...
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.
Ferenczy, György G
2013-04-05
The application of the local basis equation (Ferenczy and Adams, J. Chem. Phys. 2009, 130, 134108) in mixed quantum mechanics/molecular mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) methods is investigated. This equation is suitable to derive local basis nonorthogonal orbitals that minimize the energy of the system and it exhibits good convergence properties in a self-consistent field solution. These features make the equation appropriate to be used in mixed QM/MM and QM/QM methods to optimize orbitals in the field of frozen localized orbitals connecting the subsystems. Calculations performed for several properties in divers systems show that the method is robust with various choices of the frozen orbitals and frontier atom properties. With appropriate basis set assignment, it gives results equivalent with those of a related approach [G. G. Ferenczy previous paper in this issue] using the Huzinaga equation. Thus, the local basis equation can be used in mixed QM/MM methods with small size quantum subsystems to calculate properties in good agreement with reference Hartree-Fock-Roothaan results. It is shown that bond charges are not necessary when the local basis equation is applied, although they are required for the self-consistent field solution of the Huzinaga equation based method. Conversely, the deformation of the wave-function near to the boundary is observed without bond charges and this has a significant effect on deprotonation energies but a less pronounced effect when the total charge of the system is conserved. The local basis equation can also be used to define a two layer quantum system with nonorthogonal localized orbitals surrounding the central delocalized quantum subsystem.
Naqvi, K R
2005-01-01
Ornstein and his coauthors, who constructed a dynamical theory of Brownian motion, taking the equation $mdv/dt =-\\zeta v+X$ as their starting point, usually named the equation after Einstein alone or after both Einstein and Langevin; furthermore, Ornstein, who was the first to extract from this equation the correct expression for $\\bar{\\Delta^2}$, the mean-squared distance covered by a Brownian particle, credited de Haas-Lorentz, rather than Langevin, for finding the stationary limit of $\\bar{\\Delta^2}$. A glance at Einstein's 1907 paper, titled ``Theoretical remarks on Brownian motion'', should suffice to convince one that it is not unfair to attribute the {\\it conception} of the above equation, now universally known as the Langevin equation, to Einstein. Langevin's avowed aim in his 1908 article was to recover, through a route that was `infinitely more simple', Einstein's 1905 expression for the diffusion coefficient, but a careful reading of Langevin's paper shows that--depending on how one interprets his ...
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)
Koc, Ramazan; Olgar, Eser
2010-01-01
A novel method is proposed to determine an analytical expression for eigenfunctions and numerical result for eigenvalues of the Schr\\"odinger type equations, within the context of Taylor expansion of a function. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical result for eigenvalues.
Fulazzaky, Mohamad Ali
2013-01-01
Anaerobic treatment processes to remove organic matter from palm oil mill effluent (POME) have been used widely in Malaysia. Still the amounts of total organic and total mineral released from POME that may cause degradation of the receiving environment need to be verified. This paper proposes the use of the hydrodynamic equations to estimate performance of the cascaded anaerobic ponds (CAP) and to calculate amounts of total organic matter and total mineral released from POME. The CAP efficiencies to remove biochemical oxygen demands, chemical oxygen demands, total solids and volatile solids (VS) as high as 94.5, 93.6, 96.3 and 98.2 %, respectively, are estimated. The amounts of total organic matter and total mineral as high as 538 kg VS/day and 895 kg FS/day, respectively, released from POME to the receiving water are calculated. The implication of the proposed hydrodynamic equations contributes to more versatile environmental assessment techniques, sometimes replacing laboratory analysis.
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.
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...
Directory of Open Access Journals (Sweden)
Grazziela P Figueredo
Full Text Available 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 when contrasted with stochastic versions of ODE models using early-stage cancer examples. We seek answers to the following questions: (1 Does this new stochastic formulation produce similar results to the agent-based version? (2 Can these methods be used interchangeably? (3 Do agent-based models outcomes reveal any benefit when compared to the Gillespie results? To answer these research questions we investigate three well-established mathematical models describing interactions between tumour cells and immune elements. These case studies were re-conceptualised under an agent-based perspective and also converted to the Gillespie algorithm formulation. Our interest in this work, therefore, is to establish a methodological discussion regarding the usability of different simulation approaches, rather than provide further biological insights into the investigated case studies. Our results show that it is possible to obtain equivalent models that implement the same mechanisms; however, the incapacity of the Gillespie algorithm to retain individual memory of past events affects the similarity of some results. Furthermore, the emergent behaviour of ABMS produces extra patters of behaviour in the system, which was not obtained by the Gillespie algorithm.
Figueredo, Grazziela P; Siebers, Peer-Olaf; Owen, Markus R; Reps, Jenna; Aickelin, Uwe
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 when contrasted with stochastic versions of ODE models using early-stage cancer examples. We seek answers to the following questions: (1) Does this new stochastic formulation produce similar results to the agent-based version? (2) Can these methods be used interchangeably? (3) Do agent-based models outcomes reveal any benefit when compared to the Gillespie results? To answer these research questions we investigate three well-established mathematical models describing interactions between tumour cells and immune elements. These case studies were re-conceptualised under an agent-based perspective and also converted to the Gillespie algorithm formulation. Our interest in this work, therefore, is to establish a methodological discussion regarding the usability of different simulation approaches, rather than provide further biological insights into the investigated case studies. Our results show that it is possible to obtain equivalent models that implement the same mechanisms; however, the incapacity of the Gillespie algorithm to retain individual memory of past events affects the similarity of some results. Furthermore, the emergent behaviour of ABMS produces extra patters of behaviour in the system, which was not obtained by the Gillespie algorithm.
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 (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 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 CO_{2} 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 CO_{2}, pure water, and both CO_{2}-rich and aqueous (H_{2}O-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 CO_{2}. It can be combined with another model for the brine enthalpy to calculate the molar enthalpy of H_{2}O-CO_{2}-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.
Volpe, Donna A; Hamed, Salaheldin S; Zhang, Lei K
2014-01-01
Drug interactions due to efflux transporters may result in one drug increasing or decreasing the systemic exposure of a second drug. The potential for in vivo drug interactions is estimated through in vitro cell assays. Variability in in vitro parameter determination (e.g., IC₅₀ values) among laboratories may lead to different conclusions in in vivo interaction predictions. The objective of this study was to investigate variability in in vitro inhibition potency determination that may be due to calculation methods. In a Caco-2 cell assay, the absorptive and secretive permeability of digoxin was measured in the presence of spironolactone, itraconazole and vardenafil. From the permeability data, the efflux ratio and net secretory flux where calculated for each inhibitor. IC₅₀ values were then calculated using a variety of equations and software programs. All three drugs decreased the secretory transport of digoxin in a concentration-dependent manner while increasing digoxin's absorption to a lesser extent. The resulting IC₅₀ values varied according to the parameter evaluated, whether percent inhibition or percent control was applied, and the computational IC₅₀ equation. This study has shown that multiple methods used to quantitate the inhibition of drug efflux in a cell assay can result in different IC₅₀ values. The variability in the results in this study points to a need to standardize any transporter assay and calculation methods within a laboratory and to validate the assay with a set of known inhibitors and non-inhibitors against a clinically relevant substrate.
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Veronica Fibbi
2015-01-01
Full Text Available Aim. We investigated the predictors of tissue Doppler left ventricular (LV longitudinal indexes in a healthy Italian pediatric population and established normative data and regression equations for the calculation of z scores. Methods and Results. A total of 369 healthy subjects aged 1–17 years (age of 6.4 ± 1.1 years, 49.1% female underwent echocardiography. LV peak longitudinal velocity at systole (s', early diastole (e', and late diastole (a' was determined by tissue Doppler. The ratio of peak early diastolic LV filling velocity to e' was calculated. Age was the only independent determinant of s' (β=0.491, p<0.0001 and the strongest determinant of e' (β=0.334, p<0.0001 and E/e' (β=-0.369, p<0.0001. Heart rate was the main determinant of a' (β=0.265, p<0.0001. Male gender showed no effects except for a weak association with lateral s', suggesting no need of gender-specific reference ranges. Age-specific reference ranges, regression equations, and scatterplots for the calculation of z scores were determined for each index. Conclusion. In a pediatric Italian population, age was the strongest determinant of LV longitudinal dynamics. The availability of age-specific normality data for the calculation of z scores may allow for correctly detecting LV dysfunction in pediatric pathological populations.
Godtliebsen, Ian H; Christiansen, Ove
2015-10-07
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.
Levashov, P R; Sin'ko, G V; Smirnov, N A; Minakov, D V; Shemyakin, O P; Khishchenko, K V
2010-12-22
In the present work, we compare the thermal contribution of electrons to thermodynamic functions of metals in different models at high densities and electron temperatures. One of the theoretical approaches, the full-potential linear-muffin-tin-orbital method, treats all electrons in the framework of density functional theory (DFT). The other approach, VASP, uses projector-augmented-wave pseudopotentials for the core electrons and considers the valent electrons also in the context of DFT. We analyze the limitations of the pseudopotential approach and compare the DFT results with a finite-temperature Thomas-Fermi model and two semiempirical equations of state.
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.
Directory of Open Access Journals (Sweden)
M. Krawczyk
2012-01-01
Full Text Available The calculation of the magnonic spectra using the plane-wave method has limitations, the origin of which lies in the formulation of the effective magnetic field term in the equation of motion (the Landau-Lifshitz equation for composite media. According to ideas of the plane-wave method the system dynamics is described in terms of plane waves (a superposition of a number of plane waves, which are continuous functions and propagate throughout the medium. Since in magnonic crystals the sought-for superposition of plane waves represents the dynamic magnetization, the magnetic boundary conditions on the interfaces between constituent materials should be inherent in the Landau-Lifshitz equations. In this paper we present the derivation of the two expressions for the exchange field known from the literature. We start from the Heisenberg model and use a linear approximation and take into account the spacial dependence of saturation magnetization and exchange constant present in magnetic composites. We discuss the magnetic boundary conditions included in the presented formulations of the exchange field and elucidate their effect on spin-wave modes and their spectra in one- and two-dimensional planar magnonic crystals from plane-wave calculations.
Ermakova, Olga; López-Solano, Javier; Minikayev, Roman; Carlson, Stefan; Kamińska, Agata; Głowacki, Michał; Berkowski, Marek; Mujica, Andrés; Muñoz, Alfonso; Paszkowicz, Wojciech
2014-06-01
Lanthanum orthovanadate (LaVO4) is the only stable monazite-type rare-earth orthovanadate. In the present paper the equation of state of LaVO4 is studied using in situ high-pressure powder diffraction at room temperature, and ab initio calculations within the framework of the density functional theory. The parameters of a second-order Birch-Murnaghan equation of state, i.e. those fitted to the experimental and theoretical data, are found to be in perfect agreement - in particular, the bulk moduli are almost identical, with values of 106 (1) and 105.8 (5) GPa, respectively. In agreement with recent reported experimental data, the compression is shown to be anisotropic. Its nature is comparable to that of some other monazite-type compounds. The softest compression direction is determined.
Staley, Dennis M.; Negri, Jacquelyn A.; Kean, Jason W.; Laber, Jayme L.; Tillery, Anne C.; Youberg, Ann M.
2016-06-30
Wildfire can significantly alter the hydrologic response of a watershed to the extent that even modest rainstorms can generate dangerous flash floods and debris flows. To reduce public exposure to hazard, the U.S. Geological Survey produces post-fire debris-flow hazard assessments for select fires in the western United States. We use publicly available geospatial data describing basin morphology, burn severity, soil properties, and rainfall characteristics to estimate the statistical likelihood that debris flows will occur in response to a storm of a given rainfall intensity. Using an empirical database and refined geospatial analysis methods, we defined new equations for the prediction of debris-flow likelihood using logistic regression methods. We showed that the new logistic regression model outperformed previous models used to predict debris-flow likelihood.
2013-08-01
2 x Dose (2) CAMI (3) Medication Max Hrs Hrs Half-lives Interv Hrs Half-lives Eq Hrs Half-lives Codeine 4.0 24 6.0 8.0 2.0 15 3.6 Morphine 7.0 24...return-to-duty time, even for individuals on the extreme metabolic margins of the general population. The variation in t½ (calculated by the CAMI
Ferenczy, György G
2013-04-05
Mixed quantum mechanics/quantum mechanics (QM/QM) and quantum mechanics/molecular mechanics (QM/MM) methods make computations feasible for extended chemical systems by separating them into subsystems that are treated at different level of sophistication. In many applications, the subsystems are covalently bound and the use of frozen localized orbitals at the boundary is a possible way to separate the subsystems and to ensure a sensible description of the electronic structure near to the boundary. A complication in these methods is that orthogonality between optimized and frozen orbitals has to be warranted and this is usually achieved by an explicit orthogonalization of the basis set to the frozen orbitals. An alternative to this approach is proposed by calculating the wave-function from the Huzinaga equation that guaranties orthogonality to the frozen orbitals without basis set orthogonalization. The theoretical background and the practical aspects of the application of the Huzinaga equation in mixed methods are discussed. Forces have been derived to perform geometry optimization with wave-functions from the Huzinaga equation. Various properties have been calculated by applying the Huzinaga equation for the central QM subsystem, representing the environment by point charges and using frozen strictly localized orbitals to connect the subsystems. It is shown that a two to three bond separation of the chemical or physical event from the frozen bonds allows a very good reproduction (typically around 1 kcal/mol) of standard Hartree-Fock-Roothaan results. The proposed scheme provides an appropriate framework for mixed QM/QM and QM/MM methods.
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.
Dalla-Betta, Peter; Schulte, Mitchell
2009-06-22
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.
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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.
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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
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Ali Ghaffari
2014-01-01
Full Text Available The main objective of this paper is to propose an optimal finite duration treatment method for cancer. A mathematical model is proposed to show the interactions between healthy and cancerous cells in the human body. To extend the existing models, the effect of vaccine therapy and chemotherapy are also added to the model. The equilibrium points and the related local stability are derived and discussed. It is shown that the dynamics of the cancer model must be changed and modified for finite treatment duration. Therefore, the vaccine therapy is used to change the parameters of the system and the chemotherapy is applied for pushing the system to the domain of attraction of the healthy state. For optimal chemotherapy, an optimal control is used based on state dependent Riccati equation (SDRE. It is shown that, in spite of eliminating the treatment, the system approaches the healthy state conditions. The results show that the development of optimal vaccine-chemotherapy protocols for removing tumor cells would be an appropriate strategy in cancer treatment. Also, the present study states that a proper treatment method not only reduces the population of the cancer cells but also changes the dynamics of the cancer.
Amend, Jan P.; Helgeson, Harold C.
1997-01-01
Group additivity equations of state for aqueous organic molecules have been generated by combining the revised Helgeson-Kirkham-Flowers (HKF) equations of state ( Shock and Helgeson, 1988, 1990; Tanger and Helgeson, 1988; Shock et al., 1989, 1992) with experimental values of the standard molal properties of aqueous alkanes, alkanols, alkylbenzenes, car☐ylic acids, amides, and amines. Equations of state parameters for the groups represented by -CH 2-, -CH 3, -CHCH 3-, -C 6H 5, -CH 2OH, -COOH, -CONH 2, and -CH 2NH 2 were determined by regression of the experimental data. This procedure permits calculation of the standard molal thermodynamic properties of these groups at elevated temperatures and pressures. Although curves representing the apparent standard molal Gibbs free energies (Δ G°) and enthalpies (Δ H°) of formation, and the standard molal entropies ( S°) of the groups as a function of temperature and pressure are respectively similar for each of them, the temperature dependence of the standard molal heat capacities ( Cp°) and volumes ( V°) of a number of the groups are quite different from one another. For example, the standard molal heat capacities of the hydrocarbon groups minimize with increasing temperature, but those of -CH 2OH and -CH 2NH 2 maximize. Computed values of Δ G°, Δ H°, S°, Cp°, V°, and the equations of state parameters for the various groups were used together with group additivity relations to generate corresponding values of these properties for aqueous n-alkanes, 2-methylalkanes, n-alkylbenzenes, n-alkanols, n-car☐ylic acids, n-amides, and n-amines at temperatures ≤ 250°C and pressures ≤ 1 kbar. The validity and generality of the equations of state are supported by the fact that predicted equilibrium constants for liquid n-alkane solubility reactions in water compare favorably with experimental values reported in the literature for temperatures as high as 200°C. Furthermore, equilibrium constants for aqueous ethane
Chen, Qianghua; Zhang, Mengce; Liu, Shuaijie; He, Yongxi; Luo, Huifu; Luo, Jun; Lv, Weiwei
2016-12-01
At present the formulae proposed by G Boensch and E Potulski in 1998 (Boensch and Potulski 1998 Metrologia 35 133-9) are mostly used to calculate the air refractive index. However, the humidity correction equation in the formulae is derived by using the light source of a Cd lamp whose light frequency stability is poor and at a narrow temperature range, around 20 °C. So it is no longer suitable in present optical precision measurements. To solve this problem, we propose a refractive index measurement system based on phase step interferometer with three frequency stabilized lasers (532 nm, 633 nm, 780 nm), corrected coefficients of the humidity are measured and a corresponding revised humidity correction equation is acquired. Meanwhile, the application temperature range is extended from 14.6 °C to 25.0 °C. The experiment comparison results at the temperature of 22.2-23.2 °C show the accuracy by the presented equation is better than that of Boensch and Potulski.
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Nelson H. T. Lemes
2010-01-01
Full Text Available Analytical solutions of a cubic equation with real coefficients are established using the Cardano method. The method is first applied to simple third order equation. Calculation of volume in the van der Waals equation of state is afterwards established. These results are exemplified to calculate the volumes below and above critical temperatures. Analytical and numerical values for the compressibility factor are presented as a function of the pressure. As a final example, coexistence volumes in the liquid-vapor equilibrium are calculated. The Cardano approach is very simple to apply, requiring only elementary operations, indicating an attractive method to be used in teaching elementary thermodynamics.
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...
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Ivone Patrão
Full Text Available Objective: Women diagnosed with breast cancer are confronted with different stressors throughout the illness trajectory, e.g. awaiting diagnosis, having surgery, anticipating the possibility that the cancer has spread and coping with side effects. The aim of this study was to assess the impact of the psychosocial pathway of breast cancer. Methods: A total of 360 women diagnosed with breast cancer were evaluated, on 3 separate occasions, regarding: distress, emotional control, neuroticism, social support, coping, quality of life (QoL and demographic characteristics. We used structural equation modeling (SEM to examine the relationships among all the variables. Results: The emotional, cognitive response, and the QoL suffered significant changes concerning diagnosis (time 1, surgery (time 2 and treatments (time 3. Furthermore, results indicate that an adapted emotional response is associated to efficient coping strategy, and satisfaction with the perceived social support and good QoL. This is particularly the case when women are undergoing a psychological intervention. Conclusion: To help breast cancer patients adjust to their situation the clinical psychologist should encourage the patient to adopt more efficient coping strategies. By doing so, patients may indeed experience less psychological distress and a higher quality of life, thereby increasing their overall sense of well-being.
S-K Equations of Calculating Formatiom Water Density%计算地层水密度的S-K方程
Institute of Scientific and Technical Information of China (English)
康志勇; 谢开宁
2012-01-01
通过对现有地层水密度确定方法的分析对比,结合渤海湾地区已有地层水高压物性分析成果,证实Schowalter诺谟图能客观地反映地层水密度的变化规律.提出影响地层水密度变化的五大因素:地层温度、地层压力、地层水矿化度、气水比及盐与水的质量比.系统建立了求取地层水密度通用方程(简称S-K方程),改变了依靠查图版求地层水密度的传统方法,并为利用压汞资料确定原始含油饱和度奠定了基础.%Now known methods of determining formation water density have been compared and analysed, density vary property of formation water is approved by Schowaller' s Nomograph and Bohai Gulf area' s PVT analysis data of formation water to determine density of formation water at subsurface conditions. At the same time, put forward five influence factors for density of formation water,they are temperature and pressure and mineralization and GWR and mass concentration of salts. The equations calculating density of formation water have been established, for short S-K equations. It changed the tradition method to determine density of formation water depending on Nomograph, and laid a foundation for S-K equations to determine original oil saleralion by mercury injection curve.
Dahms, Rainer N
2015-05-01
The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phase components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. The new model preserves the accuracy of previous temperature
Bassem Elshahat; Akhtar Naqvi; Nabil Maalej
2015-01-01
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 dimensio...
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.
[Model calculations of the effect of demographic changes on the incidence of cancer in Saarland].
Brenner, H; Ziegler, H
1989-12-01
Resulting from the population structure and current fertility and mortality rates, a rapid aging of the West German society is to be expected. The impact of these demographic changes on numbers of cancer cases and incidence rates is quantitatively assessed for the Saarland, which is the only state with reliable population-based cancer registration in the FRG. Despite a projected decrease in population size during the next decades, numbers of incident cases are expected to rise substantially in males and to remain almost constant in females for all of the most common forms of cancer. The projected changes have model character for other parts of the FRG.
Yepes, Pablo; Randeniya, Sharmalee; Taddei, Phillip J; Newhauser, Wayne D
2009-01-07
The Monte Carlo method is used to provide accurate dose estimates in proton radiation therapy research. While it is more accurate than commonly used analytical dose calculations, it is computationally intense. The aim of this work was to characterize for a clinical setup the fast dose calculator (FDC), a Monte Carlo track-repeating algorithm based on GEANT4. FDC was developed to increase computation speed without diminishing dosimetric accuracy. The algorithm used a database of proton trajectories in water to calculate the dose of protons in heterogeneous media. The extrapolation from water to 41 materials was achieved by scaling the proton range and the scattering angles. The scaling parameters were obtained by comparing GEANT4 dose distributions with those calculated with FDC for homogeneous phantoms. The FDC algorithm was tested by comparing dose distributions in a voxelized prostate cancer patient as calculated with well-known Monte Carlo codes (GEANT4 and MCNPX). The track-repeating approach reduced the CPU time required for a complete dose calculation in a voxelized patient anatomy by more than two orders of magnitude, while on average reproducing the results from the Monte Carlo predictions within 2% in terms of dose and within 1 mm in terms of distance.
... cancer Non-Hodgkin lymphoma Ovarian cancer Pancreatic cancer Testicular cancer Thyroid cancer Uterine cancer Symptoms Symptoms of cancer ... tumor Obesity Pancreatic cancer Prostate cancer Stomach cancer Testicular cancer Throat or larynx cancer Thyroid cancer Patient Instructions ...
A Fortran program for the calculation of estrogen receptor contents in human breast cancer.
Zayas, A; Lage, A
1981-01-01
A computer program in Fortran-IV for the processing of data from estradiol receptor assays in human breast cancer is described. The program prints the results in two tables together with the Saturation graph and the Scatchard's Plot. It includes a systematic, operator-independent, method for the elimination of "deviated points".
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
Institute of Scientific and Technical Information of China (English)
李春喜; 宋红燕; 李以圭; 陆九芳
2001-01-01
An equation of state for electrolyte aqueous solution is developed by treating the ion-ion electrostatic and ion-solvent molecule interactions with primitive MSA and perturbation theory, respectively. The effect of the dielectric constant on the ionic chemical potential and the calculation accuracy of ionic mean activity coefficients for 2∶1 and 1∶1 type halide aqueous solution are discussed.By taking ionic Pauling diameter as ionic hard sphere diameter for anions and treating the cation hard sphere diameter as ionic strength dependent, the equation can be used to calculate ionic activity coefficients in the moderate concentration range with good accuracy.
Ferreira, José Alexandre; Peixoto, Andreia; Neves, Manuel; Gaiteiro, Cristiana; Reis, Celso A; Assaraf, Yehuda G; Santos, Lúcio Lara
2016-01-01
Cisplatin-based chemotherapeutic regimens are the most frequently used (neo)adjuvant treatments for the majority of solid tumors. While platinum-based chemotherapeutic regimens have proven effective against highly proliferative malignant tumors, significant relapse and progression rates as well as decreased overall survival are still observed. Currently, it is known that sub-populations of chemoresistant cells share biological properties with cancer stem cells (CSC), which are believed to be responsible for tumor relapse, invasion and ultimately disease dissemination through acquisition of mesenchymal cell traits. In spite of concentrated efforts devoted to decipher the mechanisms underlying CSC chemoresistance and to design targeted therapeutics to these cells, proteomics has failed to unveil molecular signatures capable of distinguishing between malignant and non-malignant stem cells. This has hampered substantial developments in this complex field. Envisaging a novel rationale for an effective therapy, the current review summarizes the main cellular and molecular mechanisms underlying cisplatin resistance and the impact of chemotherapy challenge in CSC selection and clinical outcome. It further emphasizes the growing amount of data supporting a role for protein glycosylation in drug resistance. The dynamic and context-dependent nature of protein glycosylation is also comprehensively discussed, hence highlighting its potentially important role as a biomarker of CSC. As the paradigm of cancer therapeutics shifts towards precision medicine and patient-tailored therapeutics, we bring into focus the need to introduce glycomics and glycoproteomics in holistic pan-omics models, in order to integrate diverse, multimodal and clinically relevant information towards more effective cancer therapeutics.
Maeda, Hisatoshi
2012-03-01
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.
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Jin, L; Wang, L; Li, J; Luo, W; Feigenberg, S J; Ma, C-M [Department of Radiation Oncology, Fox Chase Cancer Center, Philadelphia, PA 19111 (United States)
2007-07-21
This work investigated the selection of beam margins in lung-cancer stereotactic body radiotherapy (SBRT) with 6 MV photon beams. Monte Carlo dose calculations were used to systematically and quantitatively study the dosimetric effects of beam margins for different lung densities (0.1, 0.15, 0.25, 0.35 and 0.5 g cm{sup -3}), planning target volumes (PTVs) (14.4, 22.1 and 55.3 cm{sup 3}) and numbers of beam angles (three, six and seven) in lung-cancer SBRT in order to search for optimal beam margins for various clinical situations. First, a large number of treatment plans were generated in a commercial treatment planning system, and then recalculated using Monte Carlo simulations. All the plans were normalized to ensure that 95% of the PTV at least receives the prescription dose and compared quantitatively. Based on these plans, the relationships between the beam margin and quantities such as the lung toxicity (quantified by V{sub 20}, the percentage volume of the two lungs receiving at least 20 Gy) and the maximum target (PTV) dose were established for different PTVs and lung densities. The impact of the number of beam angles on the relationship between V{sub 20} and the beam margin was assessed. Quantitative information about optimal beam margins for lung-cancer SBRT was obtained for clinical applications.
Chang, Young Woo; Kim, Hwan Soo; Jung, Seung Pil; Kim, Hoon Yub; Lee, Jae Bok; Bae, Jeoung Won
2017-01-01
Purpose The lymph node ratio (LNR) is an important prognostic factor in papillary thyroid carcinoma (PTC), but micrometastases in cervical lymph nodes (LNs) are not of great clinical importance. In this study, we analyzed the accuracy of prediction of the prognosis depending on whether micrometastases were included in the number of metastatic LNs when calculating LNR. Methods The study included 353 PTC patients who underwent total thyroidectomy with neck LN dissection, and calculated LNR by 2 methods according to whether micrometastases were included in the number of metastatic LNs: Method 1 did not and method 2 did include. To compare the predictive values of LNR by the 2 methods, correlation coefficients and receiver operating characteristic (ROC) curves were analyzed. Results Positive correlations were found between LNR and preablation stimulated thyroglobulin (sTg) levels in both methods, but the correlation between method 1 LNR and preablation sTg level was significantly stronger than that for method 2 (Fisher z = 1.7, P = 0.045). The areas under these 2 independent ROC curves were analyzed; the prognostic efficacy of method 1 LNR was more accurate than that of method 2 LNR, and the difference was statistically significant (P = 0.0001). Conclusion Regional recurrence of PTC can be predicted more accurately by not including micrometastases in the number of metastatic LNs when calculating LNR.
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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.
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.
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.
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Chiriva-Internati Maurizio
2006-03-01
Full Text Available Abstract Background Although impacts upon gastric cancer incidence of race, age, sex, and Lauren type have been individually explored, neither their importance when evaluated together nor the presence or absence of interactions among them have not been fully described. Methods This study, derived from SEER (Surveillance, Epidemiology, and End Results (SEER Program of the National Cancer Institute data, analyzed the incidences of gastric cancer between the years 1992–2001. There were 7882 patients who had developed gastric cancer. The total denominator population was 145,155, 669 persons (68,395,787 for 1992–1996, 78,759,882 for 1997–2001. Patients with multiple tumors were evaluated as per the default of the SEER*Stat program. 160 age-, five year period (1992–1996 vs 1997–2001-, sex-, race (Asian vs non-Asian-, Lauren type- specific incidences were derived to form the stratified sample evaluated by linear regression. (160 groups = 2 five year periods × 2 race groups × 2 sexes × 2 Lauren types × 10 age groups. Linear regression was used to analyze the importance of each of these explanatory variables and to see if there were interactions among the explanatory variables. Results Race, sex, age group, and Lauren type were found to be important explanatory variables, as were interactions between Lauren type and each of the other important explanatory variables. In the final model, the contribution of each explanatory variable was highly statistically significant (t > 5, d.f. 151, P Conclusion The change of the incidence of stomach cancer with respect to age for Lauren type 1 stomach cancer differs from that for Lauren type 2 stomach cancers. The relationships between age and Lauren type do not differ across gender or race. The results support the notion that Lauren type 1 and Lauren type 2 gastric cancers have different etiologies and different patterns of progression from pre-cancer to cancer. The results should be validated by
Leontev, K. L.
1981-07-01
An expression is obtained for heat capacity differences of materials at a constant pressure and volume, on the basis of the rigorous thermodynamic equation (Kittel, 1976), and by using the Grueneisen law (Kikoin and Kikoin, 1976) of constancy of the ratio of the cubic expansion coefficient to the molar heat capacity. Conditions are determined, where the empirical Nernst and Lindemann (Filippov, 1967) equation is regarded as rigorous.
Anti-cancer properties of green Tea Probed viaquantum mechanics calculations
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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.
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Thiyagarajan, Rajesh; Vikraman, S; Karrthick, KP; Ramu, M; Sambasivaselli, R; Senniandavar, V; Kataria, Tejinder [Medanta The Medicity, Gurgaon, Haryana (India); Nambiraj, N Arunai; Sigamani, Ashokkumar [VIT University, Vellore, Tamil Nadu (India); Subbarao, Bargavan [Elekta India, Chennai, Tamil Nadu (India)
2015-06-15
Purpose: To evaluate the impact of dose calculation algorithm on the dose distribution of biologically optimized Volumatric Modulated Arc Therapy (VMAT) plans for Esophgeal cancer. Methods: Eighteen retrospectively treated patients with carcinoma esophagus were studied. VMAT plans were optimized using biological objectives in Monaco (5.0) TPS for 6MV photon beam (Elekta Infinity). These plans were calculated for final dose using Monte Carlo (MC), Collapsed Cone Convolution (CCC) & Pencil Beam Convolution (PBC) algorithms from Monaco and Oncentra Masterplan TPS. A dose grid of 2mm was used for all algorithms and 1% per plan uncertainty maintained for MC calculation. MC based calculations were considered as the reference for CCC & PBC. Dose volume histogram (DVH) indices (D95, D98, D50 etc) of Target (PTV) and critical structures were compared to study the impact of all three algorithms. Results: Beam models were consistent with measured data. The mean difference observed in reference with MC calculation for D98, D95, D50 & D2 of PTV were 0.37%, −0.21%, 1.51% & 1.18% respectively for CCC and 3.28%, 2.75%, 3.61% & 3.08% for PBC. Heart D25 mean difference was 4.94% & 11.21% for CCC and PBC respectively. Lung Dmean mean difference was 1.5% (CCC) and 4.1% (PBC). Spinal cord D2 mean difference was 2.35% (CCC) and 3.98% (PBC). Similar differences were observed for liver and kidneys. The overall mean difference found for target and critical structures was 0.71±1.52%, 2.71±3.10% for CCC and 3.18±1.55%, 6.61±5.1% for PBC respectively. Conclusion: We observed a significant overestimate of dose distribution by CCC and PBC as compared to MC. The dose prediction of CCC is closer (<3%) to MC than that of PBC. This can be attributed to poor performance of CCC and PBC in inhomogeneous regions around esophagus. CCC can be considered as an alternate in the absence of MC algorithm.
Energy Technology Data Exchange (ETDEWEB)
Sano, Y.; Yamamoto, S. [Yamaguchi University, Yamaguchi (Japan). Faculty of Engineering
1997-01-10
The integral form of the diffusion equation for a slab with a constant surface concentration based on the dissolved solid coordinate is derived, which presents the relation between desorption rate and integral average diffusion coefficient by the ratio of the 0 and 1st moments of concentration distribution. The relation between the 0 and 1st moments is quite insensitive to the concentration distribution governed by the diffusion equation with the concentration dependent diffusion coefficients and is satisfactorily estimated by the ratio of average to center concentration at the starting point of the regular regime. From these equations, one desorption curve is quantitatively transformed to the integral average diffusion coefficients as a function of center concentrations. The diffusion coefficient is calculated as a function of concentration by differentiating the integral average diffusion coefficients. As an example, the isothermal drying data of skim-milk aqueous solution are analyzed. 11 refs., 11 figs., 2 tabs.
Chang, T. S.
1974-01-01
A numerical scheme using the method of characteristics to calculate the flow properties and pressures behind decaying shock waves for materials under hypervelocity impact is developed. Time-consuming double interpolation subroutines are replaced by a technique based on orthogonal polynomial least square surface fits. Typical calculated results are given and compared with the double interpolation results. The complete computer program is included.
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.
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)
Institute of Scientific and Technical Information of China (English)
仇军
2013-01-01
Based on the modified equation of water hammer,the method for solving the water hammer using the characteristic line is researched. The relevant calculating program with C++language is worked out. The simulation calculation of water hammer in the horizontally simple pipeline is made when the valve is gradually closed,and the rationality of the calculation results is proved.%基于改进的水击方程，用矩形网格差分格式及其算法原理，研究了特征线求解水击的方法，用C++语言编制程序，对水平放置的简单管道在阀门逐渐关闭时的水击进行了模拟计算，并分析了计算结果的合理性。
Abdallah, Omar; Natsheh, Mohammed; Abo Alam, Kawther; Qananwah, Qasem; Al Nabulsi, Ahmed; Bolz, Armin
2010-04-01
Based on the optical methods, it could be able to identify the concentrations of the hemoglobin fractions in a few seconds. An array of Light Emitting Diodes "LEDs" with different wavelengths and a photo detector were used to detect the transmitted or reflected light intensities. A system of equations was built according to the modified Lambert-Beer Law to be solved as an inverse problem. Typically practical inverse problems are all ill-posed. Even well-posed problems may be unstable or ill-conditioned when they digitalized. Also, applications in tissue spectroscopy and optical imaging result in an ill-posed problems. The difficulties involved in solving ill-posed systems are known, where large changes in the solution result from small perturbations in the right hand members of the system that can be caused by measurement tolerance or noise. A good numerical method to solve it may be beneficial in the applications to the optimization problems including linear programming and nonlinear programming. To account for the sensitivity to noise, a regularization method is usually applied to solve this sort of ill-posed problem, where a suitable regularized parameter is used to depress the bias in the computed solution by a better balance of approximation error and propagated data error. The Method has better computational efficiency and accuracy even for the highly ill-conditioned linear equations with a large disturbance on the given data. Comparing the results with that obtained from a direct solution of the system of equations, we prove well-posedness, stability and convergence of the method. The estimated hemoglobin fractions were highly correlated to the reference laboratory measurements.
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)
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)
Institute of Scientific and Technical Information of China (English)
刘世兴; 李娜; 刘畅
2015-01-01
In this paper,the numerical algorithms of Whittaker equation,which is a non-Hamiltonian system, are researched by using the discrete variational method in the framework of Birkhoffian.Compared with Runge-Kutta method,the numerical results show that the more reliable and accurate numerical results are obtained when the non-Hamilton systems without simple symplectic structure are studied in the Birkhoffian framework.%本文在 Birkhoff 框架下，采用离散变分方法研究了非 Hamilton 系统-Whittaker 方程的数值解法，并通过和传统的 Runge-Kutta 方法进行比较，说明了在 Birkhoff 框架下研究非 Hamilton 系统可以得到更加可靠和精确的数值结果。
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
Li, Heng; Liu, Wei; Park, Peter; Matney, Jason; Liao, Zhongxing; Chang, Joe; Zhang, Xiaodong; Li, Yupeng; Zhu, Ronald X
2014-09-08
The objective of this study was to evaluate and understand the systematic error between the planned three-dimensional (3D) dose and the delivered dose to patient in scanning beam proton therapy for lung tumors. Single-field and multifield optimized scanning beam proton therapy plans were generated for ten patients with stage II-III lung cancer with a mix of tumor motion and size. 3D doses in CT datasets for different respiratory phases and the time-weighted average CT, as well as the four-dimensional (4D) doses were computed for both plans. The 3D and 4D dose differences for the targets and different organs at risk were compared using dose-volume histogram (DVH) and voxel-based techniques, and correlated with the extent of tumor motion. The gross tumor volume (GTV) dose was maintained in all 3D and 4D doses, using the internal GTV override technique. The DVH and voxel-based techniques are highly correlated. The mean dose error and the standard deviation of dose error for all target volumes were both less than 1.5% for all but one patient. However, the point dose difference between the 3D and 4D doses was up to 6% for the GTV and greater than 10% for the clinical and planning target volumes. Changes in the 4D and 3D doses were not correlated with tumor motion. The planning technique (single-field or multifield optimized) did not affect the observed systematic error. In conclusion, the dose error in 3D dose calculation varies from patient to patient and does not correlate with lung tumor motion. Therefore, patient-specific evaluation of the 4D dose is important for scanning beam proton therapy for lung tumors.
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.
Calculation on empirical formula for evaporation in nearby tropic of cancer%计算北回归线附近蒸发量的经验公式
Institute of Scientific and Technical Information of China (English)
李文斌; 史成; 杨森槐; 刘祖健; 张兴铃
2012-01-01
利用四会新气象观测站2009～2011年小型蒸发皿蒸发量的资料,选取30个气象样本资料,建立日照、相对湿度、水汽压、风速与蒸发量之间对应的多元线性关系式[1],采用潮州气象站已有的样本资料回代蒸发经验公式,得出潮州日平均蒸发估算值是实际蒸发值的1.2倍,说明此经验公式配上适当的修正系数,适用于岭南北回归线内陆和沿海附近地区蒸发量的理论估算值计算,其值可作为判断因降水引起蒸发误差是否偏大的主要依据,同时为科研机构研究近地面蒸发量提供参考数据。%By means of evaporation data from mini evaporator of new Sihui meteorological station in 2009-2011, this paper selects 30 meteorological samples in order to build up a corresponding plural linear equation among sunlight, relative humidity, vapor pressure, wind speed and evaporation. According to back substitution of the known samples in Chaozhou meteorological station to empirical formula of evaporation,the estimated value of daily average evaporation in Chaozhou city is 1.2 times than the actual values. Therefore, this empirical formula with a relevant correction coefficient is compatibly applied to calculate the theoretical value of evaporative capacity in Lingnan in-land tropic of cancer and nearby regions along the coast. This theoretical value could be used as the base to judge whether there is a big difference in the evaporation caused by the rainfall, meanwhile it gives the reference data to the study on evaporative capacity of the earth surface.
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...
Directory of Open Access Journals (Sweden)
Tatiana Petrova
2016-08-01
Full Text Available An extremely interesting problem in aero-hydrodynamics is the sound radiation of a single vortical structure. Currently, this type of problem is mainly considered for an incompressible medium. In this paper a method was developed to take into account the viscosity and thermal conductivity of gas. The acoustic radiation frequency of a cylindrical vortex on a flat wall in viscous heat-conducting gas (air has been investigated. The problem is solved on the basis of the Navier–Stokes equations using the small initial vorticity approach. The power expansion of unknown functions in a series with a small parameter (vorticity is used. It is shown that there are high-frequency oscillations modulated by a low-frequency signal. The value of the high frequency remains constant for a long period of time. Thus the high frequency can be considered a natural frequency of the vortex radiation. The value of the natural frequency depends only on the initial radius of the cylindrical vortex, and does not depend on the intensity of the initial vorticity. As expected from physical considerations, the natural frequency decreases exponentially as the initial radius of the cylinder increases. Furthermore, the natural frequency differs from that of the oscillations inside the initial cylinder and in the outer domain. The results of the paper may be of interest for aeroacoustics and tornado modeling.
Sokolova, Tatiana S.; Dorogokupets, Peter I.; Dymshits, Anna M.; Danilov, Boris S.; Litasov, Konstantin D.
2016-09-01
We present Microsoft Excel spreadsheets for calculation of thermodynamic functions and P-V-T properties of MgO, diamond and 9 metals, Al, Cu, Ag, Au, Pt, Nb, Ta, Mo, and W, depending on temperature and volume or temperature and pressure. The spreadsheets include the most common pressure markers used in in situ experiments with diamond anvil cell and multianvil techniques. The calculations are based on the equation of state formalism via the Helmholtz free energy. The program was developed using Visual Basic for Applications in Microsoft Excel and is a time-efficient tool to evaluate volume, pressure and other thermodynamic functions using T-P and T-V data only as input parameters. This application is aimed to solve practical issues of high pressure experiments in geosciences and mineral physics.
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.
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......) 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...
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.
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.
Equation of state of solid krypton from correlated quantum chemistry calculations%固氪物态方程的关联量子化学计算
Institute of Scientific and Technical Information of China (English)
武娜; 杨皎; 肖芬; 蔡灵仓; 田春玲
2014-01-01
The two-, three- and four-body interaction energies in face-centered cubic (fcc) krypton are evaluated using the many-body expansion method and the coupled cluster theory with full single and double excitations plus perturbative treatment of triples, and both self-consistent-field (SCF) Hartree-Fock energy and correlation one are accurately deter-mined in a wide volume range (from 27 to 4 cm3/mol). All different three- and four-atom clusters existing in the first three and two nearest and two neighbor shells of fcc lattice are considered. It is found that the three-body interaction energy is positive at low compression, where the dispersive forces play a dominant role, with increasing the compression the three-body contribution becomes attractive, and the SCF energy overwhelms the dispersive one. At pressures higher than 30 GPa, the four-body contribution becomes important and significantly cancels the over-softening effects of the three-body potential. It shows that the combination of the four-body effects with two- and three-body interactions leads to an excellent agreement with the measurements from the equation of state in the whole experimental range of 0-130 GPa.%运用多体展开理论和量子化学方法--超分子单、双(三重)激发微扰处理耦合簇CCSD (T)方法，首次系统地计算了面心立方固氪在较宽(从晶格平衡位置到体积压缩率超过3倍)区间的两体、三体和四体相互作用对结合能和物态方程的贡献大小，包括Hartree-Fock自洽场项和范德瓦耳斯长程关联作用项；并与实验数据进行比较。结果表明，在考虑到两体、三体、四体相互作用能后，多体展开理论以及CCSD (T)方法对平衡位置结合能测量数据0-130 GPa整个研究区间的实验物态方程数据都做出令人满意的描述。
Baltar, V.T.; Xun, W.W.; Johansson, M.; Bueno-de-Mesquita, B.; Boshuizen, H.C.; Gils, van C.H.; Onland-Moret, C.N.
2013-01-01
The one-carbon metabolism (OCM) is considered key in maintaining DNA integrity and regulating gene expression, and may be involved in the process of carcinogenesis. Several B-vitamins and amino acids have been implicated in lung cancer risk, via the OCM directly as well as immune system activation.
Institute of Scientific and Technical Information of China (English)
季振义; 吴文渊; 冯勇
2013-01-01
针对一类特殊的非线性方程组雅克比矩阵奇异的问题,提出了一种基于对偶空间的牛顿迭代方法.给出了一个显式的计算对偶空间的公式,在此基础上利用对偶空间作用于原方程组构造新的方程,使扩充后的方程组在近似值点的雅可比矩阵满秩,从而恢复牛顿迭代算法的二次收敛性.实验结果表明,改进后的算法一般迭代3次计算精度就可以达到10-15.所提算法丰富了代数几何中关于理想的对偶空间理论,也为工程应用中的数值计算提供了一种新方法.%To resolve the peculiar problem of the Jacobian matrix for a special class of nonlinear equations, an improved Newton mtheod was proposed based on the dual space. This paper proposed an explicit formula to compute the dual space of an ideal in a point through polynomial multiplication, and constructed augmented equations using the dual space. Meanwhile, the Jacobian matrix of augmented equations at initial point was full rank, and then the algorithm recovered quadratical convergence of Newton's iteration. The experimental results show that after three iterations, the accuracy of computation can achieve 10 ~15. The proposed method further enriches the theories of the dual space of ideal in algebra geometry and provides a new method for the numerical calculation in engineering applications.
Institute of Scientific and Technical Information of China (English)
杨帆; 陈保东; 姜文全; 石宇; 李理; 刘赫铭
2013-01-01
With the development of new energy liquefied natural gas (LNG) industry, natural gas plays more and more important role in energy structure in China. High accuracy simulation of process flow, such as natural gas liquefaction, LNG storage and transportation, LNG gasification, is required. The accuracy of natural gas thermodynamic properties calculation is an important part of process flow simulation. It is necessary to prove its accuracy in order to provide theoretical foundations for process flow simulation. In this article, density and viscosity were calculated by P-R state equation,which can provide a theoretical basis for LNG process flow simulation.% 随着液化天然气（LNG）产业的兴起，天然气在我国能源结构中占有越来越重要的位置，对于天然气液化流程、LNG储存运输以及气化流程模拟的要求越来越高，天然气热物性质计算的精度在流程模拟中至关重要。采用P-R方程计算了密度和粘度的精度，为天然气的流程模拟提供进一步的理论基础。
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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.
Porru, Stefano; Pavanello, Sofia; Carta, Angela; Arici, Cecilia; Simeone, Claudio; Izzotti, Alberto; Mastrangelo, Giuseppe
2014-01-01
DNA adducts are considered an integrate measure of carcinogen exposure and the initial step of carcinogenesis. Their levels in more accessible peripheral blood lymphocytes (PBLs) mirror that in the bladder tissue. In this study we explore whether the formation of PBL DNA adducts may be associated with bladder cancer (BC) risk, and how this relationship is modulated by genetic polymorphisms, environmental and occupational risk factors for BC. These complex interrelationships, including direct and indirect effects of each variable, were appraised using the structural equation modeling (SEM) analysis. Within the framework of a hospital-based case/control study, study population included 199 BC cases and 213 non-cancer controls, all Caucasian males. Data were collected on lifetime smoking, coffee drinking, dietary habits and lifetime occupation, with particular reference to exposure to aromatic amines (AAs) and polycyclic aromatic hydrocarbons (PAHs). No indirect paths were found, disproving hypothesis on association between PBL DNA adducts and BC risk. DNA adducts were instead positively associated with occupational cumulative exposure to AAs (p = 0.028), whereas XRCC1 Arg 399 (poccupational cumulative exposure to AAs with DNA adducts and BC risk, strengthening the central role of AAs in bladder carcinogenesis. However the lack of an association between PBL DNA adducts and BC risk advises that these snapshot measurements are not representative of relevant exposures. This would envisage new scenarios for biomarker discovery and new challenges such as repeated measurements at different critical life stages.
Magnus, Wilhelm
2004-01-01
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period
Institute of Scientific and Technical Information of China (English)
张晓霞; 钟文生; 姚远
2012-01-01
A torsional vibration dynamic model of double - cardan shaft is established with tools of constraint e-quation and finite element method. Numerical simulation shows that angular accelerations of the model are identical with calculation results, verifying the correctness of double - cardan shaft. Trie fluctuation of mid - shaft due to comer angle of cardan and high frequencies of torsional vibration are considered in this model and it is suited for torsional vibration analysis of cardan shaft drive system.%万向轴传动由于附加力矩会对传动系统产生强迫振动,为了避开传动系统扭转共振,需要对万向轴传动系统进行计算分析,合理选取结构参数.利用约束方程表示万向铰传动特点,并用有限单元法建立双万向轴扭转振动动力学模型,通过数值仿真得到万向轴传动系统扭转振动数值解.计算结果表明:模型能够计算万向轴附加力矩引起的强迫振动,可用于万向轴传动系统扭转振动分析.
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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.
Directory of Open Access Journals (Sweden)
Pavlos A. Kassomenos
2009-02-01
Full Text Available The objective of the current study was the development of a reliable modeling platform to calculate in real time the personal exposure and the associated health risk for filling station employees evaluating current environmental parameters (traffic, meteorological and amount of fuel traded determined by the appropriate sensor network. A set of Artificial Neural Networks (ANNs was developed to predict benzene exposure pattern for the filling station employees. Furthermore, a Physiology Based Pharmaco-Kinetic (PBPK risk assessment model was developed in order to calculate the lifetime probability distribution of leukemia to the employees, fed by data obtained by the ANN model. Bayesian algorithm was involved in crucial points of both model sub compartments. The application was evaluated in two filling stations (one urban and one rural. Among several algorithms available for the development of the ANN exposure model, Bayesian regularization provided the best results and seemed to be a promising technique for prediction of the exposure pattern of that occupational population group. On assessing the estimated leukemia risk under the scope of providing a distribution curve based on the exposure levels and the different susceptibility of the population, the Bayesian algorithm was a prerequisite of the Monte Carlo approach, which is integrated in the PBPK-based risk model. In conclusion, the modeling system described herein is capable of exploiting the information collected by the environmental sensors in order to estimate in real time the personal exposure and the resulting health risk for employees of gasoline filling stations.
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Stefano Porru
Full Text Available DNA adducts are considered an integrate measure of carcinogen exposure and the initial step of carcinogenesis. Their levels in more accessible peripheral blood lymphocytes (PBLs mirror that in the bladder tissue. In this study we explore whether the formation of PBL DNA adducts may be associated with bladder cancer (BC risk, and how this relationship is modulated by genetic polymorphisms, environmental and occupational risk factors for BC. These complex interrelationships, including direct and indirect effects of each variable, were appraised using the structural equation modeling (SEM analysis. Within the framework of a hospital-based case/control study, study population included 199 BC cases and 213 non-cancer controls, all Caucasian males. Data were collected on lifetime smoking, coffee drinking, dietary habits and lifetime occupation, with particular reference to exposure to aromatic amines (AAs and polycyclic aromatic hydrocarbons (PAHs. No indirect paths were found, disproving hypothesis on association between PBL DNA adducts and BC risk. DNA adducts were instead positively associated with occupational cumulative exposure to AAs (p = 0.028, whereas XRCC1 Arg 399 (p<0.006 was related with a decreased adduct levels, but with no impact on BC risk. Previous findings on increased BC risk by packyears (p<0.001, coffee (p<0.001, cumulative AAs exposure (p = 0.041 and MnSOD (p = 0.009 and a decreased risk by MPO (p<0.008 were also confirmed by SEM analysis. Our results for the first time make evident an association between occupational cumulative exposure to AAs with DNA adducts and BC risk, strengthening the central role of AAs in bladder carcinogenesis. However the lack of an association between PBL DNA adducts and BC risk advises that these snapshot measurements are not representative of relevant exposures. This would envisage new scenarios for biomarker discovery and new challenges such as repeated measurements at different
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.
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
DEFF Research Database (Denmark)
Bahr, Patrick; Hutton, Graham
2015-01-01
In this article, we present a new approach to the problem of calculating compilers. In particular, we develop a simple but general technique that allows us to derive correct compilers from high-level semantics by systematic calculation, with all details of the implementation of the compilers...... falling naturally out of the calculation process. Our approach is based upon the use of standard equational reasoning techniques, and has been applied to calculate compilers for a wide range of language features and their combination, including arithmetic expressions, exceptions, state, various forms...
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)
Lim, Sara N.; Pradhan, Anil K.; Nahar, Sultana N.
2013-06-01
When used with X-ray radiotherapy, heavy elements (high atomic number Z or HZ) such as gold(Au) and platinum(Pt) have the potential to greatly sensitize and enhance the damage to tumor tissues. While HZ radiosensitization has been shown to be higly effective in reducing tumor sizes, much work still needs to be done to determine the ideal X-ray energy/energy spectrum. The likelihood of photoelectric absorption of X-rays that result in the production of cell-killing Auger electrons relative to the photon scatter in an HZ sensitized tumor has to be determined for treatments using X-rays from various sources and energies to assess their efficacy. In this report, we present computations that outline the dependence of photoelectric absorption on X-ray energy. The relative X-ray absorption by a radiosensitized tumor was calculated to contrast the efficacy of different X-ray sources in Auger electron production at different tumor depths. Enhanced photoabsorption of low-energy X-rays from broadband sources in the keV range is shown to be much higher than from those in the MeV range. In addition, with the use of the Monte Carlo code package Geant4, we present the total X-ray energy deposited into a radiosensitized tumor located at different depths in a phantom. The enhancement in radiation dose deposition will also be analysed at the microscopic cellular level to determine the HZ radiosensitizer concentration required. Potential use of monochromatic X-rays for more precise HZ radiosensitization will also be described.
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GarcIa-Lastra, J M [Departamento de Fisica Moderna, Universidad de Cantabria, Avenida de los Castros s/n, 39005 Santander (Spain); Wesolowski, T [Departement de Chimie, Universite de Geneve, 30, quai Ernest-Ansermet, CH-1211 Geneva 4 (Switzerland); Barriuso, M T [Departamento de Fisica Moderna, Universidad de Cantabria, Avenida de los Castros s/n, 39005 Santander (Spain); Aramburu, J A [Departamento de Ciencias de la Tierra y Fisica de la Materia Condensada, Universidad de Cantabria, Avenida de los Castros s/n, 39005 Santander (Spain); Moreno, M [Departamento de Ciencias de la Tierra y Fisica de la Materia Condensada, Universidad de Cantabria, Avenida de los Castros s/n, 39005 Santander (Spain)
2006-02-08
The local structure and optical and vibrational properties associated with Mn{sup 2+}-doped cubic AMF{sub 3} (A = K, Rb; M = Mg, Zn, Cd) fluoroperovskites are studied by means of embedding calculations using Kohn-Sham equations with constrained electron density. It is shown that while an electronic parameter like 10Dq essentially depends on the Mn{sup 2+}-F{sup -} distance, the local vibration frequencies {omega}{sub i} (i = a{sub 1g}, e{sub g} modes) are dominated by the interaction between F{sup -} ligands and nearest M{sup 2+} ions lying along bonding directions. The high {omega}{sub a} values observed for KMgF{sub 3}:Mn{sup 2+} and KZnF{sub 3}:Mn{sup 2+}, the huge variations of {omega}{sub e} and {omega}{sub a} frequencies when the host lattice is changed, as well as the increase of Huang-Rhys factors and the Stokes shift following the host lattice parameter, are shown to be related to this elastic coupling of the MnF{sub 6}{sup 4-} complex to the rest of the host lattice. The present results support the conclusion that the Stokes shift is determined by the interaction of the excited {sup 4}T{sub 1g} state with a{sub 1g} and e{sub g} local modes while the coupling with the t{sub 2g} shear mode is not relevant. The variations of local vibrational frequencies and the Stokes shift induced by a hydrostatic pressure on a given system are shown to be rather different to those produced by the chemical pressure associated with distinct host lattices.
Institute of Scientific and Technical Information of China (English)
曾强; 王利生
2005-01-01
本文基于P-V-T-与T-μ-P关系的相似性,结合Peng-Robinson立方型状态方程(PR EOS),建立了一个预测纯烷烃气液相粘度的统一模型.新模型首先运用PR EOS方程来计算指定温度下物质的饱和蒸汽压,然后以温度和饱和蒸汽压为独立变量,计算饱和气液相粘度.采用大量实测数据对新模型进行考核的结果表明,新模型在亚临界和超临界范围内,都有较好的计算结果.%This work presents a viscosity model based on Peng-Robinson (PR) cubic equation of state (EOS) for a better description of viscosity. A viscosity model has been developed based on the similarity between PVTand Tμ (viscosity)P relationship and the PR EOS.At a specified temperature, prediction for the saturated vapor pressure based on the PR EOS with Twu's α-function can be carried out at first, and then using the specified temperature and the predicted vapor pressure as independent variables, the saturated liquid and vapor viscosities of pure hydrocarbons based on the new viscosity model can be calculated. The new viscosity model is applicable to both sub and supercritical regions for pure hydrocarbons.
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Lloyd K. Williams
1987-01-01
Full Text Available In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second-order ordinary differential equations which are solved herewith.
Prentis, Jeffrey J.
1996-05-01
One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.
Tricomi, FG
2013-01-01
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 diff
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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.
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
A new supersymmetric classical Boussinesq equation
Institute of Scientific and Technical Information of China (English)
Zhang Meng-Xia; Liu Qing-Ping; Wang Juan; Wu Ke
2008-01-01
In this paper,we obtain a supersymmetric generalization for the classical Boussinesq equation.We show that the supersymmetric equation system passes the Painlevé test and we also calculate its one- and two-soliton solutions.
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 ...
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)
Directory of Open Access Journals (Sweden)
TAKURO ISODA
2017-01-01
.2% for lung cancer. The corresponding possibility were 14.7% for osteoblastic metastases, 23.9% for mildly osteoblastic metastases, 7.14% for mixedtype metastases, and 16.0% for osteolytic metastases.Conclusion: The lesion-based ANN values calculated by BONENAVI can be influenced by the type of primary cancer and bone metastasis.
National Oceanic and Atmospheric Administration, Department of Commerce — Declination is calculated using the current International Geomagnetic Reference Field (IGRF) model. Declination is calculated using the current World Magnetic Model...
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)
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)
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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
Al-Jaroudi, Said S; Altaf, Muhammad; Al-Saadi, Abdulaziz A; Kawde, Abdel-Nasser; Altuwaijri, Saleh; Ahmad, Saeed; Isab, Anvarhusein A
2015-10-01
The gold(III) complexes of the type (1,2-diaminocyclohexane)(1,3-diaminopropane)gold(III) chloride, [(DACH)Au(pn)]Cl3, [where DACH = cis-, trans-1,2- and S,S-1,2-diaminocyclohexane and pn = 1,3-diaminopropane] have been synthesized and characterized using various spectroscopic and analytical techniques including elemental analysis, UV-Vis and FTIR spectroscopy; solution as well as solid-state NMR measurements. The solid-state (13)C NMR shows that 1,2-diaminocyclohexane (1,2-DACH) and 1,3-diaminopropane (pn) are strongly bound to the gold(III) center via N donor atoms. The stability of the mixed diamine ligand gold(III) was checked by UV-Vis spectroscopy and NMR measurements. The molecular structure of compound 1 (containing cis-1,2-DACH) was determined by X-ray diffraction analysis. The structure of 1 consists of [(cis-DACH)Au(pn)](3+) complex ion and chloride counter ions. Each gold atom in the complex ion adopts a distorted square-planar geometry. The structural details and relative stabilities of the four possible isomers of the complexes were also estimated at the B3LYP/LANL2DZ level of theoretical calculations. The computational study demonstrates that trans- conformations are slightly more stable than the cis- conformations. The antiproliferative effects and cytotoxic properties of the mixed ligand gold(III) complexes were evaluated in vitro on human gastric SGC7901 and prostate PC3 cancer cells using MTT assay. The antiproliferative study of the gold(III) complexes on PC3 and SGC7901 cells indicate that complex 3 (containing 1S,2S-(+)-1,2-(DACH)) is the most effective antiproliferative agent. The IC50 data reveal that the in vitro cytotoxicity of complex 3 against SGC7901 cancer cells manifested similar and very pronounced cytotoxic effects with respect to cisplatin. Moreover, the electrochemical behavior, and the interaction of complex 3 with two well-known model proteins, namely, hen egg white lysozyme and bovine serum albumin is also reported.
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.
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Florian Ion Tiberiu Petrescu
2015-09-01
Full Text Available This paper presents the dynamic, original, machine motion equations. The equation of motion of the machine that generates angular speed of the shaft (which varies with position and rotation speed is deduced by conservation kinetic energy of the machine. An additional variation of angular speed is added by multiplying by the coefficient dynamic D (generated by the forces out of mechanism and or by the forces generated by the elasticity of the system. Kinetic energy conservation shows angular speed variation (from the shaft with inertial masses, while the dynamic coefficient introduces the variation of w with forces acting in the mechanism. Deriving the first equation of motion of the machine one can obtain the second equation of motion dynamic. From the second equation of motion of the machine it determines the angular acceleration of the shaft. It shows the distribution of the forces on the mechanism to the internal combustion heat engines. Dynamic, the velocities can be distributed in the same way as forces. Practically, in the dynamic regimes, the velocities have the same timing as the forces. Calculations should be made for an engine with a single cylinder. Originally exemplification is done for a classic distribution mechanism, and then even the module B distribution mechanism of an Otto engine type.
Spin Resonance Strength Calculations
Courant, E. D.
2009-08-01
In calculating the strengths of depolarizing resonances it may be convenient to reformulate the equations of spin motion in a coordinate system based on the actual trajectory of the particle, as introduced by Kondratenko, rather than the conventional one based on a reference orbit. It is shown that resonance strengths calculated by the conventional and the revised formalisms are identical. Resonances induced by radiofrequency dipoles or solenoids are also treated; with rf dipoles it is essential to consider not only the direct effect of the dipole but also the contribution from oscillations induced by it.
Spin resonance strength calculations
Energy Technology Data Exchange (ETDEWEB)
Courant,E.D.
2008-10-06
In calculating the strengths of depolarizing resonances it may be convenient to reformulate the equations of spin motion in a coordinate system based on the actual trajectory of the particle, as introduced by Kondratenko, rather than the conventional one based on a reference orbit. It is shown that resonance strengths calculated by the conventional and the revised formalisms are identical. Resonances induced by radiofrequency dipoles or solenoids are also treated; with rf dipoles it is essential to consider not only the direct effect of the dipole but also the contribution from oscillations induced by it.
A reformulation of an ordinary differential equation
Barraza, Oscar A.
2013-01-01
The purpose of this note is to present a formulation of a given nonlinear ordinary differential equation into an equivalent system of linear ordinary differential equations. It is evident that the easiness of a such procedure would be able to open a new way in order to calculate or approximate the solution of an ordinary differential equation. Some examples are presented.
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.
... uses a surgical tool to remove the tumor.Mohs' surgery. Layers of cancer cells are removed one ... usually have not been approved by the U.S. Food and Drug Administration (FDA). The medicine may have ...
Energy Technology Data Exchange (ETDEWEB)
Latifi, Kujtim, E-mail: Kujtim.Latifi@Moffitt.org [Department of Radiation Oncology, Moffitt Cancer Center, Tampa, Florida (United States); Oliver, Jasmine [Department of Radiation Oncology, Moffitt Cancer Center, Tampa, Florida (United States); Department of Physics, University of South Florida, Tampa, Florida (United States); Baker, Ryan [University of South Florida School of Medicine, Tampa, Florida (United States); Dilling, Thomas J.; Stevens, Craig W. [Department of Radiation Oncology, Moffitt Cancer Center, Tampa, Florida (United States); Kim, Jongphil; Yue, Binglin [Department of Biostatics and Bioinformatics, Moffitt Cancer Center, Tampa, Florida (United States); DeMarco, MaryLou; Zhang, Geoffrey G.; Moros, Eduardo G.; Feygelman, Vladimir [Department of Radiation Oncology, Moffitt Cancer Center, Tampa, Florida (United States)
2014-04-01
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: ΔD99{sub GITV} = 7.4 Gy, ΔD99{sub PTV} = 10.4 Gy, ΔV90{sub GITV} = 13.7%, ΔV90{sub PTV} = 37.6%, ΔD95{sub PTV} = 9.8 Gy, and ΔD{sub ISO} = 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
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
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.
Integration of quantum hydrodynamical equation
Ulyanova, Vera G.; Sanin, Andrey L.
2007-04-01
Quantum hydrodynamics equations describing the dynamics of quantum fluid are a subject of this report (QFD).These equations can be used to decide the wide class of problem. But there are the calculated difficulties for the equations, which take place for nonlinear hyperbolic systems. In this connection, It is necessary to impose the additional restrictions which assure the existence and unique of solutions. As test sample, we use the free wave packet and study its behavior at the different initial and boundary conditions. The calculations of wave packet propagation cause in numerical algorithm the division. In numerical algorithm at the calculations of wave packet propagation, there arises the problem of division by zero. To overcome this problem we have to sew together discrete numerical and analytical continuous solutions on the boundary. We demonstrate here for the free wave packet that the numerical solution corresponds to the analytical solution.
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
Institute of Scientific and Technical Information of China (English)
张克武; 张宇英
2006-01-01
提出气体不平衡状态方程后,将其移植应用于气体平衡性质的研究,建立气体定压比热理论方程和两个定理;经用各种结构类型的538种气体纯质2398个实验数据检验,平均误差0.38%,显著优于文献中各式,尤其突出的是物理意义明晰,有一定的理论意义与实际应用价值,在基础理论研究中取得重要进展.%According to differential equation of Argon model the author has proposed a theoretical equation for the nonequilibrium state of gases (TENSG), that is extended here to the theoretical calculation of gaseous heat capacity. Thus an equation of the heat capacity of gases at constant pressure is derived. This equation applies to both polar and nonpolar gases, the average error from 2398 experimental values being 0. 38% based on 538 compounds. The method is far better than the other published methods. These results show that this work makes a great progress in basic research.
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 modelthe energy master equation...... (EME)is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...
Radar equations for modern radar
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
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.
Stiffness of cancer cells measured with an AFM indentation method.
Hayashi, Kozaburo; Iwata, Mayumi
2015-09-01
The stiffness of cancer cells and its changes during metastasis are very important for understanding the pathophysiology of cancer cells and the mechanisms of metastasis of cancer. As the first step of the studies on the mechanics of cancer cells during metastasis, we determined the elasticity and stiffness of cancer cells with an indentation method using an atomic force microscope (AFM), and compared with those of normal cells. In most of the past AFM studies, Young׳s elastic moduli of cells have been calculated from force-indentation data using Hertzian model. As this model is based on several important assumptions including infinitesimal strain and Hooke׳s linear stress-strain law, in the exact sense it cannot be applied to cells that deform very largely and nonlinearly. To overcome this problem, we previously proposed an equation F=a[exp(bδ)-1] to describe relations between force (F) and indentation (δ), where a and b are parameters relating with cellular stiffness. In the present study, we applied this method to cancer cells instead of Young׳s elastic modulus. The conclusions obtained are: 1) AFM indentation test data of cancer cells can be very well described by the above equation, 2) cancer cells are softer than normal cells, and 3) there are no significant locational differences in the stiffness of cancer cells between the central and the peripheral regions. These methods and results are useful for studying the mechanics of cancer cells and the mechanisms of metastasis.
Institute of Scientific and Technical Information of China (English)
蒋伟; 何正耀; 王冬海
2006-01-01
提出了一种计算无界声媒质空间中任意形状辐射体辐射声场的新方法--综合Helmholtz积分公式法(Synthetic Helmholtz Integral Equation Formulation,SHIEF).该方法将关于辐射体的内部、表面和外部Helmholtz积分方程有机地组合在一起,在已知辐射体表面法向振速的条件下,求出辐射体表面的声压分布,进而求其辐射声场分布.运用该方法计算分析了脉动球相对辐射阻抗随相对半径的变化情况,通过与理论值以及已有的其他方法(例如联立Helmholtz积分公式法(CHIEF)、超定外部Helmholtz积分公式法等)的比较,证明了该方法的正确性、准确性以及快速性,该方法有效地克服了CHIEF法和超定外部Helmholtz积分公式法的缺点.
Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation
Karney, C. F. F.
1977-01-01
Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.
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.
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.
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...
Constraint-Preserving Scheme for Maxwell's Equations
Tsuchiya, Takuya
2016-01-01
We derive the discretized Maxwell's equations using the discrete variational derivative method (DVDM), calculate the evolution equation of the constraint, and confirm that the equation is satisfied at the discrete level. Numerical simulations showed that the results obtained by the DVDM are superior to those obtained by the Crank-Nicolson scheme. In addition, we study the two types of the discretized Maxwell's equations by the DVDM and conclude that if the evolution equation of the constraint is not conserved at the discrete level, then the numerical results are also unstable.
A New Perturbed Hard-Sphere Equation of State
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A new equation of state based on hard-sphere perturbed theory was developed. This equation combined the CS repulsive term and Guo-Du attractive term. Parameters of 38 substances were estimated, the pressure-volume-temperature properties were calculated and compared with two other equations. The results show that this equation is more accurate.
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.)
Partial Differential Equations
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.
Infrared Evolution Equations: Method and Applications
Ermolaev, B. I.; Greco, M; Troyan, S. I.
2007-01-01
It is a brief review on composing and solving Infrared Evolution Equations. They can be used in order to calculate amplitudes of high-energy reactions in different kinematic regions in the double-logarithmic approximation.
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.
Low-density lipoprotein cholesterol and the risk of cancer: a mendelian randomization study
DEFF Research Database (Denmark)
Benn, Marianne; Tybjærg-Hansen, Anne; Stender, Stefan;
2011-01-01
cholesterol was calculated using the Friedewald equation in samples in which the triglyceride level was less than 354 mg/dL and measured directly by colorimetry for samples with higher triglyceride levels. Risk of cancer was estimated prospectively using Cox proportional hazards regression analyses and cross...
Wave Equations in Bianchi Space-Times
Directory of Open Access Journals (Sweden)
S. Jamal
2012-01-01
Full Text Available We investigate the wave equation in Bianchi type III space-time. We construct a Lagrangian of the model, calculate and classify the Noether symmetry generators, and construct corresponding conserved forms. A reduction of the underlying equations is performed to obtain invariant solutions.
Symmetrized solutions for nonlinear stochastic differential equations
Directory of Open Access Journals (Sweden)
G. Adomian
1981-01-01
Full Text Available Solutions of nonlinear stochastic differential equations in series form can be put into convenient symmetrized forms which are easily calculable. This paper investigates such forms for polynomial nonlinearities, i.e., equations of the form Ly+ym=x where x is a stochastic process and L is a linear stochastic operator.
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.
Surface Tension Calculation of Undercooled Alloys
Institute of Scientific and Technical Information of China (English)
无
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.
Exact solutions for nonlinear partial fractional differential equations
Institute of Scientific and Technical Information of China (English)
Khaled A.Gepreel; Saleh Omran
2012-01-01
In this article,we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations.We use the improved (G’/G)-expansion function method to calculate the exact solutions to the time-and space-fractional derivative foam drainage equation and the time-and space-fractional derivative nonlinear KdV equation.This method is efficient and powerful for solving wide classes of nonlinear evolution fractional order equations.
Sherman-Morrison-Woodbury Formula for Linear Integrodifferential Equations
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Feng Wu
2016-01-01
Full Text Available The well-known Sherman-Morrison-Woodbury formula is a powerful device for calculating the inverse of a square matrix. The paper finds that the Sherman-Morrison-Woodbury formula can be extended to the linear integrodifferential equation, which results in an unified scheme to decompose the linear integrodifferential equation into sets of differential equations and one integral equation. Two examples are presented to illustrate the Sherman-Morrison-Woodbury formula for the linear integrodifferential equation.
Directory of Open Access Journals (Sweden)
Jin F
2016-05-01
Full Text Available Feng Jin,1,2 Hui Zhu,2 Zheng Fu,3 Li Kong,2 Jinming Yu2 1School of Medicine and Life Sciences, University of Jinan-Shandong Academy of Medical Sciences, 2Department of Radiation Oncology, Shandong Cancer Hospital Affiliated to Shandong University, Shandong Academy of Medical Sciences, 3Department of Nuclear Medicine, Shandong Cancer Hospital Affiliated to Shandong University, Shandong Academy of Medical Sciences, Jinan, People’s Republic of China Purpose: The purpose of this study was to investigate the prognostic value of the standardized uptake value maximum (SUVmax change calculated by dual-time-point 18F-fluorodeoxyglucose positron emission tomography (PET imaging in patients with advanced non-small-cell lung cancer (NSCLC.Patients and methods: We conducted a retrospective review of 115 patients with advanced NSCLC who underwent pretreatment dual-time-point 18F-fluorodeoxyglucose PET acquired at 1 and 2 hours after injection. The SUVmax from early images (SUVmax1 and SUVmax from delayed images (SUVmax2 were recorded and used to calculate the SUVmax changes, including the SUVmax increment (ΔSUVmax and percent change of the SUVmax (%ΔSUVmax. Progression-free survival (PFS and overall survival (OS were determined by the Kaplan–Meier method and were compared with the studied PET parameters, and the clinicopathological prognostic factors in univariate analyses and multivariate analyses were constructed using Cox proportional hazards regression.Results: One hundred and fifteen consecutive patients were reviewed, and the median follow-up time was 12.5 months. The estimated median PFS and OS were 3.8 and 9.6 months, respectively. In univariate analysis, SUVmax1, SUVmax2, ΔSUVmax, %ΔSUVmax, clinical stage, and Eastern Cooperative Oncology Group (ECOG scores were significant prognostic factors for PFS. Similar results were significantly correlated with OS, except %ΔSUVmax. In multivariate analysis, ΔSUVmax and %ΔSUVmax were significant
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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
Directory of Open Access Journals (Sweden)
S.I. Denisov
2013-10-01
Full Text Available Using the modified stochastic Landau-Lifshitz equation driven by Poisson white noise, we derive the generalized Fokker-Planck equation for the probability density function of the nanoparticle magnetic moment. In our calculations we employ the Ito interpretation of stochastic equations and take into account the fact that the magnetic moment direction can be changed by this noise instantaneously. The analysis of the stationary solution of the generalized Fokker-Planck equation shows that the distribution of the free magnetic moment in Poisson white noise is not uniform. This feature of the stationary distribution arises from using the Ito interpretation of the stochastic Landau-Lifshitz equation.
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.
Germanium multiphase equation of state
Crockett, S. D.; De Lorenzi-Venneri, G.; Kress, J. D.; Rudin, S. P.
2014-05-01
A new SESAME multiphase germanium equation of state (EOS) has been developed utilizing the best available experimental data and density functional theory (DFT) calculations. The equilibrium EOS includes the Ge I (diamond), the Ge II (β-Sn) and the liquid phases. The foundation of the EOS is based on density functional theory calculations which are used to determine the cold curve and the Debye temperature. Results are compared to Hugoniot data through the solid-solid and solid-liquid transitions. We propose some experiments to better understand the dynamics of this element.
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.
Kinetic energy equations for the average-passage equation system
Johnson, Richard W.; Adamczyk, John J.
1989-01-01
Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.
Research on Nuclear Reaction Network Equation for Fission Product Nuclides
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
Nuclear Reaction Network Equation calculation system for fission product nuclides was developed. With the system, the number of the fission product nuclides at different time can be calculated in the different neutron field intensity and neutron energy spectra
Cosmology calculations almost without general relativity
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...
Solving Nonlinear Wave Equations by Elliptic Equation
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
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.
Multilayer optical calculations
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 ...
Calculation of cohesive energy of actinide metals
Institute of Scientific and Technical Information of China (English)
钱存富; 陈秀芳; 余瑞璜; 耿平; 段占强
1997-01-01
According to empirical electron theory of solids and molecules (EET), an equation for calculating the cohesive energy of actinide metals is given, the cohesive energy of 9 actinide metals with known crystal structure is calculated, which is identical with the experimental values on the whole, and the cohesive energy of 6 actinide metals with unknown crystal structure is forecast.
Calculation base of flooded type evaporators with finned tubes
Energy Technology Data Exchange (ETDEWEB)
Brod, W.; Slipcevic, B.
1989-03-01
For the construction of flooded type evaporators with halogen refrigerants, the refrigeration industry is using finned tubes. Equations for thermodynamical calculations of the apparaturs are given, and explained with the aid of a calculation example.
Kleinert, H.; Zatloukal, V.
2015-01-01
The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.
Energy Technology Data Exchange (ETDEWEB)
Roosta, Sara [Molecular Simulation Research Laboratory, Department of Chemistry, Iran University of Science & Technology, Tehran (Iran, Islamic Republic of); Hashemianzadeh, Seyed Majid, E-mail: hashemianzadeh@iust.ac.ir [Molecular Simulation Research Laboratory, Department of Chemistry, Iran University of Science & Technology, Tehran (Iran, Islamic Republic of); Ketabi, Sepideh, E-mail: sepidehketabi@yahoo.com [Department of Chemistry, East Tehran Branch, Islamic Azad University, Tehran (Iran, Islamic Republic of)
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 − 4.128 kcal mol{sup −1} and − 2457.124 kcal mol{sup −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 − 281.937 kcal mol{sup −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 − 245.766 kcal mol{sup −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. - Highlights: • Solubility of cisplatin@ boron-nitride nanotube is larger than cisplatin@ carbon nanotube. • Boron- nitride nanotube complexes have larger electrostatic contribution in solvation free energy. • Complexation free energies confirm encapsulation of drug into the nanotubes in aqueous solution. • Boron- nitride nanotubes are appropriate drug delivery systems compared with carbon nanotubes.
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.)
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.
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.
Renormalizing Partial Differential Equations
Bricmont, J.; Kupiainen, A.
1994-01-01
In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Ordinary differential equations
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
Using Financial Calculators in a Business Mathematics Course.
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…
Zero Temperature Hope Calculations
Energy Technology Data Exchange (ETDEWEB)
Rozsnyai, B F
2002-07-26
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
Omekanda, Avoki; Broche, Christian; Baland, René
1992-11-01
The switched reluctance motor (SRM) is a doubly salient electrical machine carrying simple windings in which flow unidirectional currents over appropriate rotor positions[1]. Because of its simplicity, robustness, and high efficiency[2, 3], SRM is evaluated for variable speed- and traction drives. In this paper, a quadratic two-dimensional technique founded upon Lagrange curvilinear elements and coupling finite element method (FEM)- and boundary integral equation method (BIEM) is used to calculate electromagnetic parameters in a SRM. The application of this method to two SRM prototypes provides an accurate analysis of the magnetostatic field and gives good values of the electromagnetic parameters of a SRM. Le moteur à réluctance à commutations est une machine électrique à structures saillantes au stator et au rotor et qui comporte des bobinages simples dans lesquels circulent des courants unidirectionnels pour des positions appropriées du rotor[1]. Grâce à sa simplicité, sa robustesse et son rendement élevé[2, 3], ce moteur à réluctance est apprécié dans les entraînements à vitesse variable et de traction. Dans cet article, nous présentons l'application d'une méthode quadratique bidimensionnelle qui couple des éléments finis (MEF) et la méthode des équations intégrales de frontière (MEIF) en vue du calcul des paramètres électromagnétiques d'un moteur à réluctance à commutations. L'application de cette méthode à deux prototypes fournit une analyse précise de la répartition du champ magnétique ainsi qu'une bonne prédiction des paramètres électromagnétiques de ces moteurs.
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.
Sonar equations for planetary exploration.
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.
Program calculation of thermodynamic properties
Gill, Walter; Filho, Fernando Fachini; Ribeirodeoliveira, Ronaldo
1986-12-01
The determination of the thermodynamic properties are examined through the basic equations such as: state equation (Beattie-Bridgeman Form), saturation pressure equation, specific heat constant pressure or constant volume equation, and specific volume or density of liquid equation.
Generalized Bloch-Wangsness-Redfield Kinetic Equations
Fatkullin, Nail
2011-01-01
We present a compact and general derivation of the generalized Bloch-Wangsness-Redfield kinetic equations for systems with the static spin Hamiltonian utilizing the concept of the Liouville space. We show that the assumptions of short correlation times and large heat capacity of the lattice are sufficient to derive the kinetic equations without the use of perturbation theory for the spin-lattice interaction operator. The perturbation theory is only applied for calculation of the kinetic coeff...
Proposal for a running coupling JIMWLK equation
Lappi, T
2014-01-01
In the CGC framework the initial stages of a heavy ion collision at high energy are described as "glasma" field configurations. The initial condition for these evolving fields depends, in the CGC effective theory, on a probability distribution for color charges. The energy dependence of this distribution can be calculated from the JIMWLK renormalization group equation. We discuss recent work on a practical implementation of the running coupling constant in the Langevin method of solving the JIMWLK equation.
Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Jianping Zhao
2012-01-01
Full Text Available An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving fractional differential equations.
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
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.
MFTF-B performance calculations
Energy Technology Data Exchange (ETDEWEB)
Thomassen, K.I.; Jong, R.A.
1982-12-06
In this report we document the operating scenario models and calculations as they exist and comment on those aspects of the models where performance is sensitive to the assumptions that are made. We also focus on areas where improvements need to be made in the mathematical descriptions of phenomena, work which is in progress. To illustrate the process of calculating performance, and to be very specific in our documentation, part 2 of this report contains the complete equations and sequence of calculations used to determine parameters for the MARS mode of operation in MFTF-B. Values for all variables for a particular set of input parameters are also given there. The point design so described is typical, but should be viewed as a snapshot in time of our ongoing estimations and predictions of performance.
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.
Equilibrium solutions of the shallow water equations
Weichman, P B; Weichman, Peter B.; Petrich, Dean M.
2000-01-01
A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2-d fluid flow with a free surface, is described. The model contains a competing acoustic turbulent {\\it direct} energy cascade, and a 2-d turbulent {\\it inverse} energy cascade. It is shown, nonetheless that, just as in the corresponding theory of the inviscid Euler equation, the infinite number of conserved quantities constrain the flow sufficiently to produce nontrivial large-scale vortex structures which are solutions to a set of explicitly derived coupled nonlinear partial differential equations.
Giantomassi, Matteo; Huhs, Georg; Waroquiers, David; Gonze, Xavier
2014-03-01
Many-Body Perturbation Theory (MBPT) defines a rigorous framework for the description of excited-state properties based on the Green's function formalism. Within MBPT, one can calculate charged excitations using e.g. Hedin's GW approximation for the electron self-energy. In the same framework, neutral excitations are also well described through the solution of the Bethe-Salpeter equation (BSE). In this talk, we report on the recent developments concerning the parallelization of the MBPT algorithms available in the ABINIT code (www.abinit.org). In particular, we discuss how to improve the parallel efficiency thanks to a hybrid version that employs MPI for the coarse-grained parallelization and OpenMP (a de facto standard for parallel programming on shared memory architectures) for the fine-grained parallelization of the most CPU-intensive parts. Benchmark results obtained with the new implementation are discussed. Finally, we present results for the GW corrections of amorphous SiO2 in the presence of defects and the BSE absorption spectrum. This work has been supported by the Prace project (PaRtnership for Advanced Computing in Europe, http://www.prace-ri.eu).
Scaling Calculations for a Relativistic Gyrotron.
2014-09-26
a relativistic gyrotron. The results of calculations are given in Section 3. The non- linear , slow-time-scale equations of motion used for these...corresponds to a cylindrical resonator and a thin annular electron beam ;, " with the beam radius chosen to coincide with a maximum of the resonator...entering the cavity. A tractable set of non- linear equations based on a slow-time-scale formulation developed previously was used. For this
Perturbative calculation of quasi-normal modes
Siopsis, G
2005-01-01
I discuss a systematic method of analytically calculating the asymptotic form of quasi-normal frequencies. In the case of a four-dimensional Schwarzschild black hole, I expand around the zeroth-order approximation to the wave equation proposed by Motl and Neitzke. In the case of a five-dimensional AdS black hole, I discuss a perturbative solution of the Heun equation. The analytical results are in agreement with the results from numerical analysis.
Novel SVPWM based on first order equation
Directory of Open Access Journals (Sweden)
Ahmed A. Mansour
2015-09-01
Full Text Available PWM plays an important role in generating sinusoidal waveform for variable voltage variable frequency drives (VVVFD's with a minimum harmonic level. PWM techniques have many methods in implementation ranging from a relatively simple method such as modulating sine wave to the advanced Space Vector PWM technique SVPWM. The SVPWM has a dense calculation that requires considerable processor time for execution. The proposed technique requires simple calculations and can be implemented using simple microcontrollers. The calculations of the proposed SVPWM are based on first order equations rather than trigonometric functions requiring either huge lookup tables for fetching or too many instruction cycles for calculation on a digital controller.
Stochastic Runge-Kutta Software Package for Stochastic Differential Equations
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...
State-dependent neutral delay equations from population dynamics.
Barbarossa, M V; Hadeler, K P; Kuttler, C
2014-10-01
A novel class of state-dependent delay equations is derived from the balance laws of age-structured population dynamics, assuming that birth rates and death rates, as functions of age, are piece-wise constant and that the length of the juvenile phase depends on the total adult population size. The resulting class of equations includes also neutral delay equations. All these equations are very different from the standard delay equations with state-dependent delay since the balance laws require non-linear correction factors. These equations can be written as systems for two variables consisting of an ordinary differential equation (ODE) and a generalized shift, a form suitable for numerical calculations. It is shown that the neutral equation (and the corresponding ODE--shift system) is a limiting case of a system of two standard delay equations.
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Differential equations for dummies
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.
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.
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Fractional Chemotaxis Diffusion Equations
Langlands, T A M
2010-01-01
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding. The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macro-molecular crowding or other obstacles.
Developmental Partial Differential Equations
Duteil, Nastassia Pouradier; Rossi, Francesco; Boscain, Ugo; Piccoli, Benedetto
2015-01-01
In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's evolution. In other words, the manifold's evolution depends on the solution to the PDE, and vice versa the differential operator of the PDE depends on the manifold's geometry. DPDE is used to study a diffusion equation with source on a growing surface whose gro...
Directory of Open Access Journals (Sweden)
K. Banoo
1998-01-01
equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.
Differential equations I essentials
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.
Analysis of one assumption of the Navier-Stokes equations
Budarin, V A
2013-01-01
This article analyses the assumptions regarding the influence of pressure forces during the calculation of the motion of a Newtonian fluid. The purpose of the analysis is to determine the reasonableness of the assumptions and their impact on the results of the analytical calculation. The connections between equations, causes of discrepancies in exact solutions of the Navier-Stokes equations at low Reynolds numbers and the emergence of unstable solutions using computer programs are also addressed. The necessity to complement the well-known equations of motion in mechanical stress requires other equations are substantive. It is shown that there are three methods of solving such a problem and the requirements for the unknown equations are described. Keywords: Navier-Stokes, approximate equation, closing equations, holonomic system.
Ordinary differential equations
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.
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.
Difference inversion model of wave equation
Institute of Scientific and Technical Information of China (English)
WANG De-ming
2008-01-01
A numerical iterative model was derived from the difference method and a perturbation assumption to calculate the coefficient function of a wave equation.The method Was used to solve the disaccord problem of numerical precision between the direct problem model and inverse problem model,and its serial problems using the old method.Numerical simulation calculation shows that the method is feasible and effective.
Semiclassical calculation of decay rates
Bessa, A; Fraga, E S
2008-01-01
Several relevant aspects of quantum-field processes can be well described by semiclassical methods. In particular, the knowledge of non-trivial classical solutions of the field equations, and the thermal and quantum fluctuations around them, provide non-perturbative information about the theory. In this work, we discuss the calculation of the one-loop effective action from the semiclasssical viewpoint. We intend to use this formalism to obtain an accurate expression for the decay rate of non-static metastable states.
On The Ladder Bethe-Salpeter Equation
Efimov, G V
2003-01-01
The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a scalar theory: two scalar fields (constituents) with mass $m$ interacting via an exchange of a scalar field (tieon) with mass $\\mu$. The BS equation is written in the form of an integral equation in the configuration Euclidean $x$-space with the kernel which for stable bound states $M<2m$ is a self-adjoint positive operator. The solution of the BS equation is formulated as a variational problem. The nonrelativistic limit of the BS equation is considered. The role of so-called abnormal states is discussed. The analytical form of test functions for which the accuracy of calculations of bound state masses is better than 1% (the comparison with available numerical calculations is done) is determined. These test functions make it possible to calculate analytically vertex functions describing the interaction of bound states with constituents. As a by-product a simple solution of the Wick-Cutkosky model for the case of massless bound...
Multigrid Methods in Electronic Structure Calculations
Briggs, E L; Bernholc, J
1996-01-01
We describe a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods provide effective convergence acceleration and preconditioning on all length scales, thereby permitting efficient calculations for ill-conditioned systems with long length scales or high energy cut-offs. We discuss specific implementations of multigrid and real-space algorithms for electronic structure calculations, including an efficient multigrid-accelerated solver for Kohn-Sham equations, compact yet accurate discretization schemes for the Kohn-Sham and Poisson equations, optimized pseudo\\-potentials for real-space calculations, efficacious computation of ionic forces, and a complex-wavefunction implementation for arbitrary sampling of the Brillioun zone. A particular strength of a real-space multigrid approach is its ready adaptability to massively parallel computer architectures, and we present an implementation for the Cray-T3D with essen...
Hazewinkel, M.
1995-01-01
Dedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an original space-
Dissipative Boussinesq equations
Dutykh, D; Dias, Fr\\'{e}d\\'{e}ric; Dutykh, Denys
2007-01-01
The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated numerically.
Directory of Open Access Journals (Sweden)
Hannelore Breckner
2000-01-01
Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.
Shabat, A. B.
2016-12-01
We consider the class of entire functions of exponential type in relation to the scattering theory for the Schrödinger equation with a finite potential that is a finite Borel measure. These functions have a special self-similarity and satisfy q-difference functional equations. We study their asymptotic behavior and the distribution of zeros.
Applied partial differential equations
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...
National Oceanic and Atmospheric Administration, Department of Commerce — The Magnetic Field Calculator will calculate the total magnetic field, including components (declination, inclination, horizontal intensity, northerly intensity,...
Green's function calculations of light nuclei
Sun, ZhongHao; Wu, Qiang; Xu, FuRong
2016-09-01
The influence of short-range correlations in nuclei was investigated with realistic nuclear force. The nucleon-nucleon interaction was renormalized with V lowk technique and applied to the Green's function calculations. The Dyson equation was reformulated with algebraic diagrammatic constructions. We also analyzed the binding energy of 4He, calculated with chiral potential and CD-Bonn potential. The properties of Green's function with realistic nuclear forces are also discussed.
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.
Adaptive Rendering Based on Visual Acuity Equations
Institute of Scientific and Technical Information of China (English)
无
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.
Kuksin, Sergei; Maiocchi, Alberto
In this chapter we present a general method of constructing the effective equation which describes the behavior of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a hamiltonian system with a pure imaginary discrete spectrum. The effective equation is obtained by retaining only the resonant terms of the nonlinearity (which may be hamiltonian, or may be not); the assertion that it describes the limiting behavior of small-amplitude solutions is a rigorous mathematical theorem. In particular, the method applies to the three- and four-wave systems. We demonstrate that different possible types of energy transport are covered by this method, depending on whether the set of resonances splits into finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima equation), or is connected (this happens, e.g. in the case of the NLS equation if the space-dimension is at least two). For equations of the first type the energy transition to high frequencies does not hold, while for equations of the second type it may take place. Our method applies to various weakly nonlinear wave systems, appearing in plasma, meteorology and oceanography.
Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio
2014-10-01
The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.
VLW equation of state of detonation products
Institute of Scientific and Technical Information of China (English)
无
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.
Flow Field Calculations for Afterburner
Institute of Scientific and Technical Information of China (English)
ZhaoJianxing; LiuQuanzhong; 等
1995-01-01
In this paper a calculation procedure for simulating the coimbustion flow in the afterburner with the heat shield,flame stabilizer and the contracting nozzle is described and evaluated by comparison with experimental data.The modified two-equation κ-ε model is employed to consider the turbulence effects,and the κ-ε-g turbulent combustion model is used to determine the reaction rate.To take into accunt the influence of heat radiation on gas temperature distribution,heat flux model is applied to predictions of heat flux distributions,The solution domain spanned the entire region between centerline and afterburner wall ,with the heat shield represented as a blockage to the mesh.The enthalpy equation and wall boundary of the heat shield require special handling for two passages in the afterburner,In order to make the computer program suitable to engineering applications,a subregional scheme is developed for calculating flow fields of complex geometries.The computational grids employed are 100×100 and 333×100(non-uniformly distributed).The numerical results are compared with experimental data,Agreement between predictions and measurements shows that the numerical method and the computational program used in the study are fairly reasonable and appopriate for primary design of the afterburner.
Partial differential equations
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
Hyperbolic partial differential equations
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
Introduction to functional equations
Sahoo, Prasanna K
2011-01-01
Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as possible for students from a variety of disciplines, the book chooses not to focus on functional equations where the unknown functions take on values on algebraic structures such as groups, rings, or fields. However, each chapter includes sections hig
Beginning partial differential equations
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
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Pierret, Frédéric
2016-02-01
We derived the equations of Celestial Mechanics governing the variation of the orbital elements under a stochastic perturbation, thereby generalizing the classical Gauss equations. Explicit formulas are given for the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle, and the mean anomaly, which are expressed in term of the angular momentum vector H per unit of mass and the energy E per unit of mass. Together, these formulas are called the stochastic Gauss equations, and they are illustrated numerically on an example from satellite dynamics.
Differential equations problem solver
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
Ordinary differential equations
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,
Uncertain differential equations
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.
Heat pipe thermosyphon heat performance calculation
Novomestský, Marcel; Kapjor, Andrej; Papučík, Štefan; Siažik, Ján
2016-06-01
In this article the heat performance of the heat pipe thermosiphon is achieved through numerical model. The heat performance is calculated from few simplified equations which depends on the working fluid and geometry. Also the thermal conductivity is good to mentioning, because is really interesting how big differences are between heat pipes and full solid surfaces.
Sensitivity of rocky planet structures to the equation of state
Swift, Damian C
2009-01-01
Structures were calculated for Mercury, Venus, Earth, the Moon, and Mars, using a core-mantle model and adjusting the core radius to reproduce the observed mass and diameter of each body. Structures were calculated using Fe and basalt equations of state of different degrees of sophistication for the core and mantle. The choice of equation of state had a significant effect on the inferred structure. For each structure, the moment of inertia ratio was calculated and compared with observed values. Linear Grueneisen equations of state fitted to limited portions of shock data reproduced the observed moments of inertia significantly better than did more detailed equations of state incorporating phase transitions, presumably reflecting the actual compositions of the bodies. The linear Grueneisen equations of state and corresponding structures seem however to be a reasonable starting point for comparative simulations of large-scale astrophysical impacts.
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.
Regularized Structural Equation Modeling.
Jacobucci, Ross; Grimm, Kevin J; McArdle, John J
A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM's utility.
Applied partial differential equations
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...
Kinetic equations: computation
Pareschi, Lorenzo
2013-01-01
Kinetic equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity.
Institute of Scientific and Technical Information of China (English)
A.I.Arbab
2013-01-01
A unified complex model of Maxwell's equations is presented.The wave nature of the electromagnetic field vector is related to the temporal and spatial distributions and the circulation of charge and current densities.A new vacuum solution is obtained,and a new transformation under which Maxwell's equations are invariant is proposed.This transformation extends ordinary gauge transformation to include charge-current as well as scalar-vector potential.An electric dipole moment is found to be related to the magnetic charges,and Dirac's quantization is found to determine an uncertainty relation expressing the indeterminacy of electric and magnetic charges.We generalize Maxwell's equations to include longitudinal waves.A formal analogy between this formulation and Dirac's equation is also discussed.
Frédéric, Pierret
2014-01-01
The equations of celestial mechanics that govern the variation of the orbital elements are completely derived for stochastic perturbation which generalized the classic perturbation equations which are used since Gauss, starting from Newton's equation and it's solution. The six most understandable orbital element, the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle and the mean motion are express in term of the angular momentum vector $\\textbf{H}$ per unit of mass and the energy $E$ per unit of mass. We differentiate those expressions using It\\^o's theory of differential equations due to the stochastic nature of the perturbing force. The result is applied to the two-body problem perturbed by a stochastic dust cloud and also perturbed by a stochastic dynamical oblateness of the central body.
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.
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Functional Equations and Fourier Analysis
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.
Susceptibilities of QCD Vacuum from Renormalized Dyson-Schwinger Equations
Institute of Scientific and Technical Information of China (English)
CHEN Wei; QI Shi; SUN Wei-Min; ZONG Hong-Shi
2004-01-01
The pion and tensor vacuum susceptibilities are calculated in the framework of the renormalizable DysonSchwinger equations. A comparison with the results of other nonperturbative QCD approaches is given.
The Dirichlet problem for the minimal surface equation
Williams, Graham H.
1996-01-01
The minimal surface equation is an elliptic equation but it is nonlinear and is not uniformly elliptic. It is the Euler-Lagrange equation for variational problems which involve minimising the area of the graphs of functions. For the most part we will solve the variational problem with Dirichlet boundary values, that is, when the values of the function are prescribed on the boundary of some given set. We will present some existence results using the Direct Method from the Calcul...
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.
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.
Understanding synchronization from simple core of chaotic equation
Energy Technology Data Exchange (ETDEWEB)
Chen Li; Qiu Can [Department of Physics, Southeast University, Nanjing 210096 (China); Huang Hongbing, E-mail: hongbinh@seu.edu.c [Department of Physics, Southeast University, Nanjing 210096 (China); Qi Guanxiao [Research Center Juelich, Institute for Neuronscience and Medicine INM-2, D-52425 Juelich (Germany); Wang, H.J. [Department of Physics, Nanjing Xiaozhuang College, Nanjing 210017 (China)
2010-12-01
We dissect Roessler equation and give a linear core, which can capture the essence of Roessler oscillator. The maximal transversal Lyapunov exponents calculated from the core are in good agreement with those obtained from Roessler equation. The idea is also tested for coupled Chua's circuit systems. Numerical experiments are given.
Differential geometry techniques for sets of nonlinear partial differential equations
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.
Equation of State in Non-Zero Magnetic Field
Ezzelarab, Nada; Tawfik, Abdel Nasser
2015-01-01
The Polyakov linear-sigma model (PLSM) and Hadron Resonance Gas (HRG) model are considered to study the hadronic and partonic equation(s) of state, the pressure, and response to finite magnetic field, the magnetization. The results are confronted to recent lattice QCD calculations. Both models are in fairly good agreement with the lattice.
Equation of State in Non-Zero Magnetic Field
Ezzelarab, Nada; Magied Diab, Abdel; Nasser Tawfik, Abdel
2016-01-01
The Polyakov linear-sigma model (PLSM) and Hadron Resonance Gas (HRG) model are considered to study the hadronic and partonic equation(s) of state, the pressure, and response to finite magnetic field, the magnetization. The results are compared to recent lattice QCD calculations. Both models are in fairly good agreement with the lattice.
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.
Prediction Of Refrigerant Thermodynamic Properties By Equations Of State
Moshfeghian, Mahmood Moshfeghian, Mahmood
1992-01-01
The ability of three equations of state (EOS) for calculating the thermodynamic properties of refrigerants has been studied for 35 pure component refrigerants. Three equations of state studied were the Soave-Redlich-Kwong (SRK), Peng-Robinson (PR) and Parameters From Group Contribution (PFGC). For each refrigerant, the vapor pressure, saturated vapor volume, saturated liquid density, and heat of vaporization were calculated and compared with the values reported in the ASHRAE hand-book. For...
A novel lattice energy calculation technique for simple inorganic crystals
Kaya, Cemal; Kaya, Savaş; Banerjee, Priyabrata
2017-01-01
In this pure theoretical study, a hitherto unexplored equation based on Shannon radii of the ions forming that crystal and chemical hardness of any crystal to calculate the lattice energies of simple inorganic ionic crystals has been presented. To prove the credibility of this equation, the results of the equation have been compared with experimental outcome obtained from Born-Fajans-Haber- cycle which is fundamentally enthalpy-based thermochemical cycle and prevalent theoretical approaches proposed for the calculation of lattice energies of ionic compounds. The results obtained and the comparisons made have demonstrated that the new equation is more useful compared to other theoretical approaches and allows to exceptionally accurate calculation of lattice energies of inorganic ionic crystals without doing any complex calculations.
Langevin equation path integral ground state.
Constable, Steve; Schmidt, Matthew; Ing, Christopher; Zeng, Tao; Roy, Pierre-Nicholas
2013-08-15
We propose a Langevin equation path integral ground state (LePIGS) approach for the calculation of ground state (zero temperature) properties of molecular systems. The approach is based on a modification of the finite temperature path integral Langevin equation (PILE) method (J. Chem. Phys. 2010, 133, 124104) to the case of open Feynman paths. Such open paths are necessary for a ground state formulation. We illustrate the applicability of the method using model systems and the weakly bound water-parahydrogen dimer. We show that the method can lead to converged zero point energies and structural properties.
Dirac equation and the Melvin metric
Energy Technology Data Exchange (ETDEWEB)
Santos, L.C.N.; Barros, C.C. [Universidade Federal de Santa Catarina, Depto de Fisica-CFM, CP. 476, Florianopolis, SC (Brazil)
2016-10-15
A relativistic wave equation for spin 1/2 particles in the Melvin space-time, a space-time where the metric is determined by a magnetic field, is obtained. The energy levels for these particles are obtained as functions of the magnetic field and compared with the ones calculated with the Dirac equation in the flat Minkowski space-time. The numeric values for some magnetic fields of interest are shown. With these results, the effects of very intense magnetic fields on the energy levels, as intense as the ones expected to be produced in magnetars or in ultra-relativistic heavy-ion collisions, are investigated. (orig.)
A method of calculating the Jost function for analytic potentials
Energy Technology Data Exchange (ETDEWEB)
Rakityansky, S.A. [University of South Africa (UNISA), Pretoria (South Africa). Dept. of Physics; Sofianos, S.A. [Joint Inst. for Nuclear Research, Dubna (Russian Federation); Amos, K. [Melbourne Univ., Parkville, VIC (Australia). School of Physics
1995-05-10
A combination of the variable-constant and complex coordinate rotation methods is used to solve the two-body Schroedinger equation. The equation is replaced by a system of linear first-order differential equations, which enables one to perform direct calculation of the Jost function for all complex momenta of physical interest including the spectral points corresponding to bound and resonance states. 16 refs., 2 tabs., 2 figs.
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.
Kleinert, H; Zatloukal, V
2013-11-01
The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.
Introduction to partial differential equations
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.
40 CFR 98.363 - Calculating GHG emissions.
2010-07-01
... CH4). DE = CH4 destruction efficiency from flaring or burning in engine (lesser of manufacturer's... manure management facility. CH4C = CH4 flow to digester combustion device, calculated using Equation JJ-6... combustion device (CH4C) using Equation JJ-6 of this section. A fully integrated system that directly...
40 CFR 91.419 - Raw emission sampling calculations.
2010-07-01
... mass flow rate , MHCexh = Molecular weight of hydrocarbons in the exhaust; see the following equation: MHCexh = 12.01 + 1.008 × α Where: α=Hydrocarbon/carbon atomic ratio of the fuel. Mexh=Molecular weight of..., calculated from the following equation: ER04OC96.019 WCO = Mass rate of CO in exhaust, MCO = Molecular...
Geochemical Calculations Using Spreadsheets.
Dutch, Steven Ian
1991-01-01
Spreadsheets are well suited to many geochemical calculations, especially those that are highly repetitive. Some of the kinds of problems that can be conveniently solved with spreadsheets include elemental abundance calculations, equilibrium abundances in nuclear decay chains, and isochron calculations. (Author/PR)
Autistic Savant Calendar Calculators.
Patti, Paul J.
This study identified 10 savants with developmental disabilities and an exceptional ability to calculate calendar dates. These "calendar calculators" were asked to demonstrate their abilities, and their strategies were analyzed. The study found that the ability to calculate dates into the past or future varied widely among these…
Generalization of Hopf Functional Equation
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
This paper generalizes the Hopf functional equation in order to apply it to a wider class of not necessarily incompressible fluid flows. We start by defining characteristic functionals of the velocity field, the density field and the temperature field of a compressible field. Using the continuity equation, the Navier-Stokes equations and the equation of energy we derive a functional equation governing the motion of an ideal gas flow and a van der Waals gas flow, and then give some general methods of deriving a functional equation governing the motion of any compressible fluid flow. These functional equations can be considered as the generalization of the Hopf functional equation.
Energy Technology Data Exchange (ETDEWEB)
Santos, William S.; Neves, Lucio P.; Perini, Ana P.; Caldas, Linda V.E., E-mail: wssantos@ipen.br, E-mail: lpneves@ipen.br, E-mail: aperini@ipen.br, E-mail: lcaldas@ipen.br [Instituto de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil); Maia, Ana F., E-mail: afmaia@ufs.br [Universidade Federal de Sergipe (UFS), Sao Cristovao, SE (Brazil). Dept. de Fisica
2014-07-01
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 cm{sup 2}. The average values of CCs to eight projections (in 10{sup -4} / Gy.cm{sup 2} 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.
How Do Calculators Calculate Trigonometric Functions?
Underwood, Jeremy M.; Edwards, Bruce H.
How does your calculator quickly produce values of trigonometric functions? You might be surprised to learn that it does not use series or polynomial approximations, but rather the so-called CORDIC method. This paper will focus on the geometry of the CORDIC method, as originally developed by Volder in 1959. This algorithm is a wonderful…
Xia, Baoqiang; Zhou, Ruguang; Qiao, Zhijun
2016-10-01
In this paper, we propose a new approach to calculate multi-soliton solutions of Camassa-Holm (CH) equation and modified Camassa-Holm (MCH) equation with the aid of Darboux transformation (DT). The new approach simplifies the approach presented by Li and Zhang [Proc. R. Soc. London, Ser. A 460, 2617-2627 (2004)]. We first map the CH and MCH equation to a negative order KdV (NKdV) equation by a reciprocal transformation. Then we proceed to apply the DT to solve the NKdV equation in the usual way. Finally we invert the reciprocal transformation to recover the solutions of the CH equation and MCH equation.
Quasirelativistic Langevin equation.
Plyukhin, A V
2013-11-01
We address the problem of a microscopic derivation of the Langevin equation for a weakly relativistic Brownian particle. A noncovariant Hamiltonian model is adopted, in which the free motion of particles is described relativistically while their interaction is treated classically, i.e., by means of action-to-a-distance interaction potentials. Relativistic corrections to the classical Langevin equation emerge as nonlinear dissipation terms and originate from the nonlinear dependence of the relativistic velocity on momentum. On the other hand, similar nonlinear dissipation forces also appear as classical (nonrelativistic) corrections to the weak-coupling approximation. It is shown that these classical corrections, which are usually ignored in phenomenological models, may be of the same order of magnitude, if not larger than, relativistic ones. The interplay of relativistic corrections and classical beyond-the-weak-coupling contributions determines the sign of the leading nonlinear dissipation term in the Langevin equation and thus is qualitatively important.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
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 for wave...
Systematic Equation Formulation
DEFF Research Database (Denmark)
Lindberg, Erik
2007-01-01
A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....
Theory of differential equations
Gel'fand, I M
1967-01-01
Generalized Functions, Volume 3: Theory of Differential Equations focuses on the application of generalized functions to problems of the theory of partial differential equations.This book discusses the problems of determining uniqueness and correctness classes for solutions of the Cauchy problem for systems with constant coefficients and eigenfunction expansions for self-adjoint differential operators. The topics covered include the bounded operators in spaces of type W, Cauchy problem in a topological vector space, and theorem of the Phragmén-Lindelöf type. The correctness classes for the Cau
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.
Generalized estimating equations
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
Equations of mathematical physics
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
Gas Dynamics Equations: Computation
Chen, Gui-Qiang G
2012-01-01
Shock waves, vorticity waves, and entropy waves are fundamental discontinuity waves in nature and arise in supersonic or transonic gas flow, or from a very sudden release (explosion) of chemical, nuclear, electrical, radiation, or mechanical energy in a limited space. Tracking these discontinuities and their interactions, especially when and where new waves arise and interact in the motion of gases, is one of the main motivations for numerical computation for the gas dynamics equations. In this paper, we discuss some historic and recent developments, as well as mathematical challenges, in designing and formulating efficient numerical methods and algorithms to compute weak entropy solutions for the Euler equations for gas dynamics.
Nonlocal electrical diffusion equation
Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.
2016-07-01
In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.
Test equating methods and practices
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...
Comparison of Kernel Equating and Item Response Theory Equating Methods
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…
The Statistical Drake Equation
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
Energy Technology Data Exchange (ETDEWEB)
Stoenescu, M.L.
1977-06-01
The terms in Boltzmann kinetic equation corresponding to elastic short range collisions, inelastic excitational collisions, coulomb interactions and electric field acceleration are evaluated numerically for a standard distribution function minimizing the computational volume by expressing the terms as linear combinations with recalculable coefficients, of the distribution function and its derivatives. The present forms are suitable for spatial distribution calculations.
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.
Energy Technology Data Exchange (ETDEWEB)
Nagao, Yoshiharu [Japan Atomic Energy Research Inst., Oarai, Ibaraki (Japan). Oarai Research Establishment
1998-03-01
In material testing reactors like the JMTR (Japan Material Testing Reactor) of 50 MW in Japan Atomic Energy Research Institute, the neutron flux and neutron energy spectra of irradiated samples show complex distributions. It is necessary to assess the neutron flux and neutron energy spectra of an irradiation field by carrying out the nuclear calculation of the core for every operation cycle. In order to advance core calculation, in the JMTR, the application of MCNP to the assessment of core reactivity and neutron flux and spectra has been investigated. In this study, in order to reduce the time for calculation and variance, the comparison of the results of the calculations by the use of K code and fixed source and the use of Weight Window were investigated. As to the calculation method, the modeling of the total JMTR core, the conditions for calculation and the adopted variance reduction technique are explained. The results of calculation are shown. Significant difference was not observed in the results of neutron flux calculations according to the difference of the modeling of fuel region in the calculations by K code and fixed source. The method of assessing the results of neutron flux calculation is described. (K.I.)
QCD evolution equations from conformal symmetry
Braun, V M
2014-01-01
QCD evolution equations in $\\text{MS}$-like schemes can be recovered from the same equations in a modified theory, QCD in non-integer $d=4-2\\epsilon$ dimensions, which enjoys exact scale and conformal invariance at the critical point. Restrictions imposed by the conformal symmetry of the modified theory allow one to obtain complete evolution kernels in integer (physical) dimensions at the given order of perturbation theory from the spectrum of anomalous dimensions added by the calculation of the special conformal anomaly at one order less. We use this technique to derive two-loop evolution equations for flavor-nonsinglet quark-antiquark light-ray operators that encode the scale dependence of generalized hadron parton distributions.
On Gakerkin approximations for the quasigeostrophic equations
Rocha, Cesar B; Grooms, Ian
2015-01-01
We study the representation of approximate solutions of the three-dimensional quasigeostrophic (QG) equations using Galerkin series with standard vertical modes. In particular, we show that standard modes are compatible with nonzero buoyancy at the surfaces and can be used to solve the Eady problem. We extend two existing Galerkin approaches (A and B) and develop a new Galerkin approximation (C). Approximation A, due to Flierl (1978), represents the streamfunction as a truncated Galerkin series and defines the potential vorticity (PV) that satisfies the inversion problem exactly. Approximation B, due to Tulloch and Smith (2009b), represents the PV as a truncated Galerkin series and calculates the streamfunction that satisfies the inversion problem exactly. Approximation C, the true Galerkin approximation for the QG equations, represents both streamfunction and PV as truncated Galerkin series, but does not satisfy the inversion equation exactly. The three approximations are fundamentally different unless the b...
Two-body bound states & the Bethe-Salpeter equation
Energy Technology Data Exchange (ETDEWEB)
Pichowsky, M. [Argonne National Lab., IL (United States); Kennedy, M. [Univ. of New Hampshire, Durham, NH (United States). Physics Dept.; Strickland, M. [Duke Univ., Durham, NC (United States)
1995-01-18
The Bethe-Salpeter formalism is used to study two-body bound states within a scalar theory: two scalar fields interacting via the exchange of a third massless scalar field. The Schwinger-Dyson equation is derived using functional and diagrammatic techniques, and the Bethe-Salpeter equation is obtained in an analogous way, showing it to be a two-particle generalization of the Schwinger-Dyson equation. The authors also present a numerical method for solving the Bethe-Salpeter equation without three-dimensional reduction. The ground and first excited state masses and wavefunctions are computed within the ladder approximation and space-like form factors are calculated.
Transformation of equations in analysis of proportionality through referent models
Romay, E O
2006-01-01
In proportionality of objects, samples or populations, usually we work with Z score of proportionality calculated through referent models, instead directly with the variables of the objects in itself. In these studies we have the necessity to transform, the equations that use the variables of the object, in equations that directly use like variables Z score. In the present work a method is developed to transform the parametric equations, in equations in variables Z using like example the studies of human proportionality from the Phantom stratagem of Ross and Wilson.
On the hierarchy of partially invariant submodels of differential equations
Golovin, Sergey V
2007-01-01
It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. In this framework the complete classification of regular partially invariant solutions of ideal MHD equations is given.
Generalized reduced magnetohydrodynamic equations
Energy Technology Data Exchange (ETDEWEB)
Kruger, S.E.
1999-02-01
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.
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
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.
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.
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%.
Equational binary decision diagrams
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
Equation of State for physical quark masses
Cheng, M; Hegde, P; Karsch, F; Kaczmarek, O; Laermann, E; Mawhinney, R D; Miao, C; Mukherjee, S; Petreczky, P; Schmidt, C; Soeldner, W
2009-01-01
We calculate the QCD equation of state for temperatures corresponding to the transition region with physical mass values for two degenerate light quark flavors and a strange quark using an improved staggered fermion action (p4-action) on lattices with temporal extent N_tau=8. We compare our results with previous calculations performed at twice larger values of the light quark masses as well as with results obtained from a resonance gas model calculation. We also discuss the deconfining and chiral aspects of the QCD transition in terms of renormalized Polyakov loop, strangeness fluctuations and subtracted chiral condensate. We show that compared to the calculations performed at twice larger value of the light quark mass the transition region shifts by about 5 MeV toward smaller temperatures
Lie Symmetries of Ishimori Equation
Institute of Scientific and Technical Information of China (English)
SONG Xu-Xia
2013-01-01
The Ishimori equation is one of the most important (2+1)-dimensional integrable models,which is an integrable generalization of (1+1)-dimensional classical continuous Heisenberg ferromagnetic spin equations.Based on importance of Lie symmetries in analysis of differential equations,in this paper,we derive Lie symmetries for the Ishimori equation by Hirota's direct method.
Lectures on partial differential equations
Petrovsky, I G
1992-01-01
Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.
Thermodynamic analysis of fluorescence enhancement and Quenching theory equations
Institute of Scientific and Technical Information of China (English)
Manman YANG; Xiaoli XI; Pin YANG
2008-01-01
The action of the three kinds of new third generation cephalosporin,class drugs,cefepime hydrochroride,cefpiramide and ceftizoxime with HSA and BSA was studied at different temperatures through the fluorescence method. First,the binding constants were calculated by using fluorescence quenching and enhancement theoretical equations. Their thermodynamic functions were also calculated. Because the KA corresponding to the different theoretical equations are not completely the same,the thermodynamic parameters calculated are also different. In this paper,the differences among these thermodynamic data obtained from the different theoretical equations were analyzed and the results show that the thermodynamic data deduced from fluorescence enhancement are more reasonable. Thus,we propose that even when the fluorescence quenching action of the acceptorsubstrate is studied,more realistic data can be obtained by using the fluorescence enhancement equation.
Elements of partial differential equations
Sneddon, Ian N
2006-01-01
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st
Electrical installation calculations advanced
Kitcher, Christopher
2013-01-01
All the essential calculations required for advanced electrical installation workThe Electrical Installation Calculations series has proved an invaluable reference for over forty years, for both apprentices and professional electrical installation engineers alike. The book provides a step-by-step guide to the successful application of electrical installation calculations required in day-to-day electrical engineering practiceA step-by-step guide to everyday calculations used on the job An essential aid to the City & Guilds certificates at Levels 2 and 3For apprentices and electrical installatio
Electrical installation calculations basic
Kitcher, Christopher
2013-01-01
All the essential calculations required for basic electrical installation workThe Electrical Installation Calculations series has proved an invaluable reference for over forty years, for both apprentices and professional electrical installation engineers alike. The book provides a step-by-step guide to the successful application of electrical installation calculations required in day-to-day electrical engineering practice. A step-by-step guide to everyday calculations used on the job An essential aid to the City & Guilds certificates at Levels 2 and 3Fo
Radar Signature Calculation Facility
Federal Laboratory Consortium — FUNCTION: The calculation, analysis, and visualization of the spatially extended radar signatures of complex objects such as ships in a sea multipath environment and...
Electronics Environmental Benefits Calculator
U.S. Environmental Protection Agency — The Electronics Environmental Benefits Calculator (EEBC) was developed to assist organizations in estimating the environmental benefits of greening their purchase,...
Tadpole summation by Dyson-Schwinger equations
Kuester, J; Kuester, Jens; Muenster, Gernot
1996-01-01
In quantum field theory with three-point and four-point couplings the Feynman diagrams of perturbation theory contain momentum independent subdiagrams, the ``tadpoles'' and ``snails''. With the help of Dyson-Schwinger equations we show how these can be summed up completely by a suitable modification of the mass and coupling parameters. This reduces the number of diagrams significantly. The method is useful for the organisation of perturbative calculations in higher orders.
Analytical Equation for Estimating Terminal Velocities of Spheroidal Particles
Energy Technology Data Exchange (ETDEWEB)
Marshall, Douglas W.
2007-06-01
An analytical method for estimating the terminal velocities of spheroidal particles in a fluid medium has been derived form a graphical approach proposed by Haider and Levenspiel. Using an analytical equation enables the researcher to calculate the terminal velocities without resorting to graphical interpolations, thereby reducing errors and enabling terminal velocities to be estimated in automated calculations.
Stochastic differential equations and applications
Friedman, Avner
2006-01-01
This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and asymptotic es
SPECIFIC SOLUTIONS GROUNDWATER FLOW EQUATION
Syahruddin, Muhammad Hamzah
2014-01-01
Geophysic publication Groundwater flow under surface, its usually slow moving, so that in laminer flow condition can find analisys using the Darcy???s law. The combination between Darcy law and continuity equation can find differential Laplace equation as general equation groundwater flow in sub surface. Based on Differential Laplace Equation is the equation that can be used to describe hydraulic head and velocity flow distribution in porous media as groundwater. In the modeling Laplace e...
Methods for Equating Mental Tests.
1984-11-01
1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth
Differential Equations with Linear Algebra
Boelkins, Matthew R; Potter, Merle C
2009-01-01
Linearity plays a critical role in the study of elementary differential equations; linear differential equations, especially systems thereof, demonstrate a fundamental application of linear algebra. In Differential Equations with Linear Algebra, we explore this interplay between linear algebra and differential equations and examine introductory and important ideas in each, usually through the lens of important problems that involve differential equations. Written at a sophomore level, the text is accessible to students who have completed multivariable calculus. With a systems-first approach, t
SU-E-T-191: First Principle Calculation of Quantum Yield in Photodynamic Therapy
Energy Technology Data Exchange (ETDEWEB)
Abolfath, R; Guo, F; Chen, Z; Nath, R [Yale New Haven Hospital, New Haven, CT (United States)
2014-06-01
Purpose: We present a first-principle method to calculate the spin transfer efficiency in oxygen induced by any photon fields especially in MeV energy range. The optical pumping is mediated through photosensitizers, e.g., porphyrin and/or ensemble of quantum dots. Methods: Under normal conditions, oxygen molecules are in the relatively non-reactive triplet state. In the presence of certain photosensitizer compounds such as porphyrins, electromagnetic radiation of specific wavelengths can excite oxygen to highly reactive singlet state. With selective uptake of photosensitizers by certain malignant cells, photon irradiation of phosensitized tumors can lead to selective killing of cancer cells. This is the basis of photodynamic therapy (PDT). Despite several attempts, PDT has not been clinically successful except in limited superficial cancers. Many parameters such as photon energy, conjugation with quantum dots etc. can be potentially combined with PDT in order to extend the role of PDT in cancer management. The key quantity for this optimization is the spin transfer efficiency in oxygen by any photon field. The first principle calculation model presented here, is an attempt to fill this need. We employ stochastic density matrix description of the quantum jumps and the rate equation methods in quantum optics based on Markov/Poisson processes and calculate time evolution of the population of the optically pumped singlet oxygen. Results: The results demonstrate the feasibility of our model in showing the dependence of the optical yield in generating spin-singlet oxygen on the experimental conditions. The adjustable variables can be tuned to maximize the population of the singlet oxygen hence the efficacy of the photodynamic therapy. Conclusion: The present model can be employed to fit and analyze the experimental data and possibly to assist researchers in optimizing the experimental conditions in photodynamic therapy.
Road Transport Congestion Costs Calculations-Adaptation to Engineering Approach
Directory of Open Access Journals (Sweden)
Marjan Lep
2008-01-01
Full Text Available The article represents so called engineering approach for computing the total road transport congestion costs. According to economic welfare theory, the total costs of transport congestion are defined as dead weight loss (DWL of infrastructure use. With a set of equations DWL could be formulated in a mathematical way. Because such form of equation is not directly applicable for concrete road network calculations it should be transformed into engineering form, which comprises transport engineering related data as classified road links, traffic volumes, passenger unit costs, etc. The equation is well applicable on the interurban road network; adaptations are needed for the urban road network cost calculations, where time losses are not so much related to the link travel time. The final equation was derived for the purposes of national road congestion cost calculation.
Gravitationally Coupled Dirac Equation for Antimatter
Jentschura, U D
2013-01-01
The coupling of antimatter to gravity is of general interest because of conceivable cosmological consequences ("surprises") related to dark energy and the cosmological constant. Here, we revisit the derivation of the gravitationally coupled Dirac equation and find that the prefactor of a result given previously in [D.R. Brill and J.A. Wheeler, Rev. Mod. Phys., vol. 29, p. 465 (1957)] for the affine connection matrix is in need of a correction. We also discuss the conversion the curved-space Dirac equation from East-Coast to West-Coast conventions, in order to bring the gravitationally coupled Dirac equation to a form where it can easily be unified with the electromagnetic coupling as it is commonly used in modern particle physics calculations. The Dirac equation describes anti-particles as negative-energy states. We find a symmetry of the gravitationally coupled Dirac equation, which connects particle and antiparticle solutions for a general space-time metric of the Schwarzschild type and implies that particl...
On the full Boltzmann equations for Leptogenesis
Garayoa, J; Pinto, T; Rius, N; Vives, O
2009-01-01
We consider the full Boltzmann equations for standard and soft leptogenesis, instead of the usual integrated Boltzmann equations which assume kinetic equilibrium for all species. Decays and inverse decays may be inefficient for thermalising the heavy-(s)neutrino distribution function, leading to significant deviations from kinetic equilibrium. We analyse the impact of using the full kinetic equations in the case of a previously generated lepton asymmetry, and find that the washout of this initial asymmetry due to the interactions of the right-handed neutrino is larger than when calculated via the integrated equations. We also solve the full Boltzmann equations for soft leptogenesis, where the lepton asymmetry induced by the soft SUSY-breaking terms in sneutrino decays is a purely thermal effect, since at T=0 the asymmetry in leptons cancels the one in sleptons. In this case, we obtain that in the weak washout regime (K ~< 1) the final lepton asymmetry can change up to a factor four with respect to previous...
On the full Boltzmann equations for leptogenesis
Energy Technology Data Exchange (ETDEWEB)
Garayoa, J.; Pastor, S.; Pinto, T.; Rius, N.; Vives, O., E-mail: garayoa@ific.uv.es, E-mail: pastor@ific.uv.es, E-mail: teguayco@gmail.com, E-mail: nuria@ific.uv.es, E-mail: vives@ific.uv.es [Depto. de Física Teórica and IFIC, Universidad de Valencia-CSIC, Edificio de Institutos de Paterna, Apt. 22085, 46071 Valencia (Spain)
2009-09-01
We consider the full Boltzmann equations for standard and soft leptogenesis, instead of the usual integrated Boltzmann equations which assume kinetic equilibrium for all species. Decays and inverse decays may be inefficient for thermalising the heavy-(s)neutrino distribution function, leading to significant deviations from kinetic equilibrium. We analyse the impact of using the full kinetic equations in the case of a previously generated lepton asymmetry, and find that the washout of this initial asymmetry due to the interactions of the right-handed neutrino is larger than when calculated via the integrated equations. We also solve the full Boltzmann equations for soft leptogenesis, where the lepton asymmetry induced by the soft SUSY-breaking terms in sneutrino decays is a purely thermal effect, since at T = 0 the asymmetry in leptons cancels the one in sleptons. In this case, we obtain that in the weak washout regime (K ∼< 1) the final lepton asymmetry can change up to a factor four with respect to previous estimates.
Polytropic equation of state and primordial quantum fluctuations
Energy Technology Data Exchange (ETDEWEB)
Freitas, R.C.; Goncalves, S.V.B. [Universidade Federal do Espirito Santo, Departamento de Fisica, Vitoria, Espirito Santo (Brazil)
2014-12-01
We study the primordial Universe in a cosmological model where inflation is driven by a fluid with a polytropic equation of state p = αρ + ρ{sup 1+1/n}. We calculate the dynamics of the scalar factor and build a Universe with constant density at the origin. We also find the equivalent scalar field that could create such an equation of state and calculate the corresponding slow-roll parameters. We calculate the scalar perturbations, the scalar power spectrum, and the spectral index. (orig.)
Calculators and Polynomial Evaluation.
Weaver, J. F.
The intent of this paper is to suggest and illustrate how electronic hand-held calculators, especially non-programmable ones with limited data-storage capacity, can be used to advantage by students in one particular aspect of work with polynomial functions. The basic mathematical background upon which calculator application is built is summarized.…
Calculating Optimal Inventory Size
Directory of Open Access Journals (Sweden)
Ruby Perez
2010-01-01
Full Text Available The purpose of the project is to find the optimal value for the Economic Order Quantity Model and then use a lean manufacturing Kanban equation to find a numeric value that will minimize the total cost and the inventory size.
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Directory of Open Access Journals (Sweden)
Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
Transmission pipeline calculations and simulations manual
Menon, E Shashi
2014-01-01
Transmission Pipeline Calculations and Simulations Manual is a valuable time- and money-saving tool to quickly pinpoint the essential formulae, equations, and calculations needed for transmission pipeline routing and construction decisions. The manual's three-part treatment starts with gas and petroleum data tables, followed by self-contained chapters concerning applications. Case studies at the end of each chapter provide practical experience for problem solving. Topics in this book include pressure and temperature profile of natural gas pipelines, how to size pipelines for specified f
Classical Diophantine equations
1993-01-01
The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...
Carbon Footprint Calculations: An Application of Chemical Principles
Treptow, Richard S.
2010-01-01
Topics commonly taught in a general chemistry course can be used to calculate the quantity of carbon dioxide emitted into the atmosphere by various human activities. Each calculation begins with the balanced chemical equation for the reaction that produces the CO[subscript 2] gas. Stoichiometry, thermochemistry, the ideal gas law, and dimensional…
Equation of state and QCD transition at finite temperature
Bazavov, A; Cheng, M; Christ, N H; DeTar, C; Ejiri, S; Gottlieb, Steven; Gupta, R; Heller, U M; Huebner, K; Jung, C; Karsch, F; Laermann, E; Levkova, L; Miao, C; Mawhinney, R D; Petreczky, P; Schmidt, C; Soltz, R A; Söldner, W; Sugar, R; Toussaint, D; Vranas, P
2009-01-01
We calculate the equation of state in 2+1 flavor QCD at finite temperature with physical strange quark mass and almost physical light quark masses using lattices with temporal extent Nt=8. Calculations have been performed with two different improved staggered fermion actions, the asqtad and p4 actions. Overall, we find good agreement between results obtained with these two O(a^2) improved staggered fermion discretization schemes. A comparison with earlier calculations on coarser lattices is performed to quantify systematic errors in current studies of the equation of state. We also present results for observables that are sensitive to deconfining and chiral aspects of the QCD transition on Nt=6 and 8 lattices. We find that deconfinement and chiral symmetry restoration happen in the same narrow temperature interval. In an Appendix we present a simple parametrization of the equation of state that can easily be used in hydrodynamic model calculations. In this parametrization we also incorporated an estimate of c...
Arithmetic partial differential equations
Buium, Alexandru; Simanca, Santiago R.
2006-01-01
We develop an arithmetic analogue of linear partial differential equations in two independent ``space-time'' variables. The spatial derivative is a Fermat quotient operator, while the time derivative is the usual derivation. This allows us to ``flow'' integers or, more generally, points on algebraic groups with coordinates in rings with arithmetic flavor. In particular, we show that elliptic curves have certain canonical ``flows'' on them that are the arithmetic analogues of the heat and wave...
Differential equations with Mathematica
Abell, Martha L
2004-01-01
The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica
Trzetrzelewski, Maciej
2016-11-01
Starting with a Nambu-Goto action, a Dirac-like equation can be constructed by taking the square-root of the momentum constraint. The eigenvalues of the resulting Hamiltonian are real and correspond to masses of the excited string. In particular there are no tachyons. A special case of radial oscillations of a closed string in Minkowski space-time admits exact solutions in terms of wave functions of the harmonic oscillator.
Dissipative Boussinesq equations
2007-01-01
40 pages, 15 figures, published in C. R. Mecanique 335 (2007) Other author's papers can be downloaded at http://www.cmla.ens-cachan.fr/~dutykh; International audience; The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water fr...
Stability in Neutral Equations
1976-02-04
Martinez-Amores Division of Applied Mathematics Brown University Providence, Rhode Island 02912 and Universidad de Granada, Seccion de Matematicas , Spain S...XG w)1- 0 ~t)- >~~~ 0 suc ht j~<kIp, Ii 2 ~ o ~~~ X~ G (t) , y’ip X= 0 y 20 since equation (3.16) is satisfied. Since F = col(f,0), only the col
Calculation and application of liquidus projection
Institute of Scientific and Technical Information of China (English)
CHEN Shuanglin; CAO Weisheng; YANG Ying; ZHANG Fan; WU Kaisheng; DU Yong; Y.Austin Chang
2006-01-01
Liquidus projection usually refers to a two-dimensional projection of ternary liquidus univariant lines at constant pressure. The algorithms used in Pandat for the calculation of liquidus projection with isothermal lines and invariant reaction equations in a ternary system are presented. These algorithms have been extended to multicomponent liquidus projections and have also been implemented in Pandat. Some examples on ternary and quaternary liquidus projections are presented.
Configuration mixing calculations in soluble models
Cambiaggio, M. C.; Plastino, A.; Szybisz, L.; Miller, H. G.
1983-07-01
Configuration mixing calculations have been performed in two quasi-spin models using basis states which are solutions of a particular set of Hartree-Fock equations. Each of these solutions, even those which do not correspond to the global minimum, is found to contain interesting physical information. Relatively good agreement with the exact lowest-lying states has been obtained. In particular, one obtains a better approximation to the ground state than that provided by Hartree-Fock.
TINTE. Nuclear calculation theory description report
Energy Technology Data Exchange (ETDEWEB)
Gerwin, H.; Scherer, W.; Lauer, A. [Forschungszentrum Juelich GmbH (DE). Institut fuer Energieforschung (IEF), Sicherheitsforschung und Reaktortechnik (IEF-6); Clifford, I. [Pebble Bed Modular Reactor (Pty) Ltd. (South Africa)
2010-01-15
The Time Dependent Neutronics and Temperatures (TINTE) code system deals with the nuclear and the thermal transient behaviour of the primary circuit of the High-temperature Gas-cooled Reactor (HTGR), taking into consideration the mutual feedback effects in twodimensional axisymmetric geometry. This document contains a complete description of the theoretical basis of the TINTE nuclear calculation, including the equations solved, solution methods and the nuclear data used in the solution. (orig.)
Directory of Open Access Journals (Sweden)
D. Diederen
2015-06-01
Full Text Available We present a new equation describing the hydrodynamics in infinitely long tidal channels (i.e., no reflection under the influence of oceanic forcing. The proposed equation is a simple relationship between partial derivatives of water level and velocity. It is formally derived for a progressive wave in a frictionless, prismatic, tidal channel with a horizontal bed. Assessment of a large number of numerical simulations, where an open boundary condition is posed at a certain distance landward, suggests that it can also be considered accurate in the more natural case of converging estuaries with nonlinear friction and a bed slope. The equation follows from the open boundary condition and is therefore a part of the problem formulation for an infinite tidal channel. This finding provides a practical tool for evaluating tidal wave dynamics, by reconstructing the temporal variation of the velocity based on local observations of the water level, providing a fully local open boundary condition and allowing for local friction calibration.
Quantum molecular master equations
Brechet, Sylvain D.; Reuse, Francois A.; Maschke, Klaus; Ansermet, Jean-Philippe
2016-10-01
We present the quantum master equations for midsize molecules in the presence of an external magnetic field. The Hamiltonian describing the dynamics of a molecule accounts for the molecular deformation and orientation properties, as well as for the electronic properties. In order to establish the master equations governing the relaxation of free-standing molecules, we have to split the molecule into two weakly interacting parts, a bath and a bathed system. The adequate choice of these systems depends on the specific physical system under consideration. Here we consider a first system consisting of the molecular deformation and orientation properties and the electronic spin properties and a second system composed of the remaining electronic spatial properties. If the characteristic time scale associated with the second system is small with respect to that of the first, the second may be considered as a bath for the first. Assuming that both systems are weakly coupled and initially weakly correlated, we obtain the corresponding master equations. They describe notably the relaxation of magnetic properties of midsize molecules, where the change of the statistical properties of the electronic orbitals is expected to be slow with respect to the evolution time scale of the bathed system.
Directory of Open Access Journals (Sweden)
M. Paul Gough
2008-07-01
Full Text Available LandauerÃ¢Â€Â™s principle is applied to information in the universe. Once stars began forming there was a constant information energy density as the increasing proportion of matter at high stellar temperatures exactly compensated for the expanding universe. The information equation of state was close to the dark energy value, w = -1, for a wide range of redshifts, 10 > z > 0.8, over one half of cosmic time. A reasonable universe information bit content of only 1087 bits is sufficient for information energy to account for all dark energy. A time varying equation of state with a direct link between dark energy and matter, and linked to star formation in particular, is clearly relevant to the cosmic coincidence problem. In answering the Ã¢Â€Â˜Why now?Ã¢Â€Â™ question we wonder Ã¢Â€Â˜What next?Ã¢Â€Â™ as we expect the information equation of state to tend towards w = 0 in the future.c
New application to Riccati equation
Taogetusang; Sirendaoerji; Li, Shu-Min
2010-08-01
To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Bäcklund transformation of Riccati equation. Based on the tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov-Kuznetsov equation, Karamoto-Sivashinsky equation and the set of (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.
Bitsadze, A V
1963-01-01
Equations of the Mixed Type compiles a series of lectures on certain fundamental questions in the theory of equations of mixed type. This book investigates the series of problems concerning linear partial differential equations of the second order in two variables, and possessing the property that the type of the equation changes either on the boundary of or inside the considered domain. Topics covered include general remarks on linear partial differential equations of mixed type; study of the solutions of second order hyperbolic equations with initial conditions given along the lines of parab
Saluja, Tajindra Singh; Spadigam, Anita; Dhupar, Anita; Syed, Shaheen
2016-04-01
Oral squamous cell carcinoma (OSCC) is the sixth most common human malignancy. According to World Health Organization, oral cancer has been reported to have the highest morbidity and mortality and a survival rate of approximately 50 % at 5 years from diagnosis. This is attributed to the subjectivity in TNM staging and histological grading which may result in less than optimum treatment outcomes including tumour recurrence. One of the hallmarks of cancer is aerobic glycolysis also known as the Warburg effect. This glycolytic phenotype (hypoxic state) not only confers immortality to cancer cells, but also correlates with the belligerent behaviour of various malignancies and is reflected as an increase in the expression of lactate dehydrogenase 5 (LDH-5), the main isoform of LDH catalysing the conversion of pyruvate to lactate during glycolysis. The diagnostic role of salivary LDH in assessing the metabolic phenotype of oral cancer has not been studied. Since salivary LDH is mainly sourced from oral epithelial cells, any pathological changes in the epithelium should reflect diagnostically in saliva. Thus in our current research, we made an attempt to ascertain the biological behaviour and aggressiveness of OSCC by appraising its metabolic phenotype as indirectly reflected in salivary LDH activity. We found that salivary LDH can be used to assess the aggressiveness of different histological grades of OSCC. For the first time, an evidence of differing metabolic behaviour in similar histologic tumour grade is presented. Taken together, our study examines the inclusion of salivary LDH as potential diagnostic parameter and therapeutic index in OSCC.
Colorectal cancer; Cancer - colon; Rectal cancer; Cancer - rectum; Adenocarcinoma - colon; Colon - adenocarcinoma ... In the United States, colorectal cancer is one of the leading causes of deaths due to cancer. Early diagnosis can often lead to a complete cure. Almost ...
DEFF Research Database (Denmark)
Marcussen, Lis; Aasberg-Petersen, K.; Krøll, Annette Elisabeth
2000-01-01
An adsorption isotherm equation for nonideal pure component adsorption based on vacancy solution theory and the Non-Random-Two-Liquid (NRTL) equation is found to be useful for predicting pure component adsorption equilibria at a variety of conditions. The isotherm equation is evaluated successfully...... adsorption systems, spreading pressure and isosteric heat of adsorption are also calculated....
Auxiliary equation method for solving nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Sirendaoreji,; Jiong, Sun
2003-03-31
By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation.
Elliptic Equation and New Solutions to Nonlinear Wave Equations
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Kuo; LIU Shi-Da
2004-01-01
The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on.
Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating
Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen
2012-01-01
This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…
New Exact Solutions to NLS Equation and Coupled NLS Equations
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2004-01-01
A transformation is introduced on the basis of the projective Riccati equations, and it is applied as an intermediate in expansion method to solve nonlinear Schrodinger (NLS) equation and coupled NLS equations. Many kinds of envelope travelling wave solutions including envelope solitary wave solution are obtained, in which some are found for the first time.
The compressible adjoint equations in geodynamics: equations and numerical assessment
Ghelichkhan, Siavash; Bunge, Hans-Peter
2016-04-01
The adjoint method is a powerful means to obtain gradient information in a mantle convection model relative to past flow structure. While the adjoint equations in geodynamics have been derived for the conservation equations of mantle flow in their incompressible form, the applicability of this approximation to Earth is limited, because density increases by almost a factor of two from the surface to the Core Mantle Boundary. Here we introduce the compressible adjoint equations for the conservation equations in the anelastic-liquid approximation. Our derivation applies an operator formulation in Hilbert spaces, to connect to recent work in seismology (Fichtner et al (2006)) and geodynamics (Horbach et al (2014)), where the approach was used to derive the adjoint equations for the wave equation and incompressible mantle flow. We present numerical tests of the newly derived equations based on twin experiments, focusing on three simulations. A first, termed Compressible, assumes the compressible forward and adjoint equations, and represents the consistent means of including compressibility effects. A second, termed Mixed, applies the compressible forward equation, but ignores compressibility effects in the adjoint equations, where the incompressible equations are used instead. A third simulation, termed Incompressible, neglects compressibility effects entirely in the forward and adjoint equations relative to the reference twin. The compressible and mixed formulations successfully restore earlier mantle flow structure, while the incompressible formulation yields noticeable artifacts. Our results suggest the use of a compressible formulation, when applying the adjoint method to seismically derived mantle heterogeneity structure.
Interval arithmetic in calculations
Bairbekova, Gaziza; Mazakov, Talgat; Djomartova, Sholpan; Nugmanova, Salima
2016-10-01
Interval arithmetic is the mathematical structure, which for real intervals defines operations analogous to ordinary arithmetic ones. This field of mathematics is also called interval analysis or interval calculations. The given math model is convenient for investigating various applied objects: the quantities, the approximate values of which are known; the quantities obtained during calculations, the values of which are not exact because of rounding errors; random quantities. As a whole, the idea of interval calculations is the use of intervals as basic data objects. In this paper, we considered the definition of interval mathematics, investigated its properties, proved a theorem, and showed the efficiency of the new interval arithmetic. Besides, we briefly reviewed the works devoted to interval analysis and observed basic tendencies of development of integral analysis and interval calculations.
Unit Cost Compendium Calculations
U.S. Environmental Protection Agency — The Unit Cost Compendium (UCC) Calculations raw data set was designed to provide for greater accuracy and consistency in the use of unit costs across the USEPA...
DEFF Research Database (Denmark)
Frederiksen, Morten
2014-01-01
Williamson’s characterisation of calculativeness as inimical to trust contradicts most sociological trust research. However, a similar argument is found within trust phenomenology. This paper re-investigates Williamson’s argument from the perspective of Løgstrup’s phenomenological theory of trust....... Contrary to Williamson, however, Løgstrup’s contention is that trust, not calculativeness, is the default attitude and only when suspicion is awoken does trust falter. The paper argues that while Williamson’s distinction between calculativeness and trust is supported by phenomenology, the analysis needs...... to take actual subjective experience into consideration. It points out that, first, Løgstrup places trust alongside calculativeness as a different mode of engaging in social interaction, rather conceiving of trust as a state or the outcome of a decision-making process. Secondly, the analysis must take...
EFFECTIVE DISCHARGE CALCULATION GUIDE
Institute of Scientific and Technical Information of China (English)
D.S.BIEDENHARN; C.R.THORNE; P.J.SOAR; R.D.HEY; C.C.WATSON
2001-01-01
This paper presents a procedure for calculating the effective discharge for rivers with alluvial channels.An alluvial river adjusts the bankfull shape and dimensions of its channel to the wide range of flows that mobilize the boundary sediments. It has been shown that time-averaged river morphology is adjusted to the flow that, over a prolonged period, transports most sediment. This is termed the effective discharge.The effective discharge may be calculated provided that the necessary data are available or can be synthesized. The procedure for effective discharge calculation presented here is designed to have general applicability, have the capability to be applied consistently, and represent the effects of physical processes responsible for determining the channel, dimensions. An example of the calculations necessary and applications of the effective discharge concept are presented.
Magnetic Field Grid Calculator
National Oceanic and Atmospheric Administration, Department of Commerce — The Magnetic Field Properties Calculator will computes the estimated values of Earth's magnetic field(declination, inclination, vertical component, northerly...
Newnes circuit calculations pocket book with computer programs
Davies, Thomas J
2013-01-01
Newnes Circuit Calculations Pocket Book: With Computer Programs presents equations, examples, and problems in circuit calculations. The text includes 300 computer programs that help solve the problems presented. The book is comprised of 20 chapters that tackle different aspects of circuit calculation. The coverage of the text includes dc voltage, dc circuits, and network theorems. The book also covers oscillators, phasors, and transformers. The text will be useful to electrical engineers and other professionals whose work involves electronic circuitry.
Current interruption transients calculation
Peelo, David F
2014-01-01
Provides an original, detailed and practical description of current interruption transients, origins, and the circuits involved, and how they can be calculated Current Interruption Transients Calculationis a comprehensive resource for the understanding, calculation and analysis of the transient recovery voltages (TRVs) and related re-ignition or re-striking transients associated with fault current interruption and the switching of inductive and capacitive load currents in circuits. This book provides an original, detailed and practical description of current interruption transients, origins,
Source and replica calculations
Energy Technology Data Exchange (ETDEWEB)
Whalen, P.P.
1994-02-01
The starting point of the Hiroshima-Nagasaki Dose Reevaluation Program is the energy and directional distributions of the prompt neutron and gamma-ray radiation emitted from the exploding bombs. A brief introduction to the neutron source calculations is presented. The development of our current understanding of the source problem is outlined. It is recommended that adjoint calculations be used to modify source spectra to resolve the neutron discrepancy problem.
Scientific calculating peripheral
Energy Technology Data Exchange (ETDEWEB)
Ethridge, C.D.; Nickell, J.D. Jr.; Hanna, W.H.
1979-09-01
A scientific calculating peripheral for small intelligent data acquisition and instrumentation systems and for distributed-task processing systems is established with a number-oriented microprocessor controlled by a single component universal peripheral interface microcontroller. A MOS/LSI number-oriented microprocessor provides the scientific calculating capability with Reverse Polish Notation data format. Master processor task definition storage, input data sequencing, computation processing, result reporting, and interface protocol is managed by a single component universal peripheral interface microcontroller.
On the water saturation calculation in hydrocarbon sandstone reservoirs
Energy Technology Data Exchange (ETDEWEB)
Stalheim, Stein Ottar
2002-07-01
The main goal of this work was to identify the most important uncertainty sources in water saturation calculation and examine the possibility for developing new S{sub w} - equations or possibility to develop methods to remove weaknesses and uncertainties in existing S{sub w} - equations. Due to the need for industrial applicability of the equations we aimed for results with the following properties: The accuracy in S{sub w} should increase compared with existing S{sub w} - equations. The equations should be simple to use in petrophysical evaluations. The equations should be based on conventional logs and use as few as possible input parameters. The equations should be numerical stable. This thesis includes an uncertainty and sensitivity analysis of the most common S{sub w} equations. The results are addressed in chapter 3 and were intended to find the most important uncertainty sources in water saturation calculation. To increase the knowledge of the relationship between R{sub t} and S{sub w} in hydrocarbon sandstone reservoirs and to understand how the pore geometry affects the conductivity (n and m) of the rock a theoretical study was done. It was also an aim to examine the possibility for developing new S{sub w} - equations (or investigation an effective medium model) valid inhydrocarbon sandstone reservoirs. The results are presented in paper 1. A new equation for water saturation calculation in clean sandstone oil reservoirs is addressed in paper 2. A recommendation for best practice of water saturation calculation in non water wet formation is addressed in paper 3. Finally a new equation for water saturation calculation in thinly interbedded sandstone/mudstone reservoirs is presented in paper 4. The papers are titled: 1) Is the saturation exponent n a constant. 2) A New Model for Calculating Water Saturation In 3) Influence of wettability on water saturation modeling. 4) Water Saturation Calculations in Thinly Interbedded Sandstone/mudstone Reservoirs. A
Applications of the Peng-Robinson Equation of State Using Mathematica
Binous, Housam
2008-01-01
A single equation of state (EOS) such as the Peng-Robinson EOS can accurately describe both the liquid and vapor phase. We present several applications of this equation of state including adiabatic flash calculation, determination of the solubility of methanol in natural gas, and the calculation of high-pressure chemical equilibrium. The problems…
Derivation of continuous air monitor equations for DAC and DAC-h.
Justus, Alan L
2010-05-01
Equations are derived that provide the numerical algorithms necessary for the calculations of both concentration (such as #DAC) and exposure (such as #DAC-h) within continuous air monitors (CAMs) employing collection media. Both calculations utilize measured counts over certain CAM counting intervals. The relationship to similar, although oft misinterpreted, equations given in International Organization for Standardization Standard 11929-5:2005 is detailed.
X-ray calculations for a NLTE Ar plasma
Institute of Scientific and Technical Information of China (English)
WU Ze-qing; PANG Jin-qiao; HAN Guo-xing
2004-01-01
A model is developed to calculate emission spectrum of non-local thermodynamic equilibrium(NLTE) plasmas. The Collisional-Radiative model is adopted for non-LTE population calculations. Configuration-averaged rate coefficients that needed in the rate equations are obtained based on the first order perturbation theory. The Hatree-Fock-Slater self-consistent-field method is used to calculate electron wave functions. The present model is applied to the calculation of emissivity from a Ar plasma. The features of the spectra are in good agreement with those calculated by other theoretical models, but the data of the integrated emissivity differ by a factor 2～8.
Generalized estimating equations
Hardin, James W
2013-01-01
Generalized Estimating Equations, Second Edition updates the best-selling previous edition, which has been the standard text on the subject since it was published a decade ago. Combining theory and application, the text provides readers with a comprehensive discussion of GEE and related models. Numerous examples are employed throughout the text, along with the software code used to create, run, and evaluate the models being examined. Stata is used as the primary software for running and displaying modeling output; associated R code is also given to allow R users to replicat
Savvidy, G K
1998-01-01
We discuss the basic properties of the gonihedric string and the problem of its formulation in continuum. We propose a generalization of the Dirac equation and of the corresponding gamma matrices in order to describe the gonihedric string. The wave function and the Dirac matrices are infinite-dimensional. The spectrum of the theory consists of particles and antiparticles of increasing half-integer spin lying on quasilinear trajectories of different slope. Explicit formulas for the mass spectrum allow to compute the string tension and thus demonstrate the string character of the theory.
Dimensional Equations of Entropy
Sparavigna, Amelia Carolina
2015-01-01
Entropy is a quantity which is of great importance in physics and chemistry. The concept comes out of thermodynamics, proposed by Rudolf Clausius in his analysis of Carnot cycle and linked by Ludwig Boltzmann to the number of specific ways in which a physical system may be arranged. Any physics classroom, in its task of learning physics, has therefore to face this crucial concept. As we will show in this paper, the lectures can be enriched by discussing dimensional equations linked to the entropy of some physical systems.
Ordinary differential equations
Cox, William
1995-01-01
Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further
Partial differential equations
Sloan, D; Süli, E
2001-01-01
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in
Differential Equations as Actions
DEFF Research Database (Denmark)
Ronkko, Mauno; Ravn, Anders P.
1997-01-01
We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...... actions shall terminate. It is shown that the proposed differential action has a semantics which corresponds to a discrete approximation when the discrete step size goes to zero. The extension gives action systems the power to model real-time clocks and continuous evolutions within hybrid systems....
Program Transformation by Solving Equations
Institute of Scientific and Technical Information of China (English)
朱鸿
1991-01-01
Based on the theory of orthogonal program expansion[8-10],the paper proposes a method to transform programs by solving program equations.By the method,transformation goals are expressed in program equations,and achieved by solving these equations.Although such equations are usually too complicated to be solved directly,the orthogonal expansion of programs makes it possible to reduce such equations into systems of equations only containing simple constructors of programs.Then,the solutions of such equations can be derived by a system of solving and simplifying rules,and algebraic laws of programs.The paper discusses the methods to simplify and solve equations and gives some examples.
``Riemann equations'' in bidifferential calculus
Chvartatskyi, O.; Müller-Hoissen, F.; Stoilov, N.
2015-10-01
We consider equations that formally resemble a matrix Riemann (or Hopf) equation in the framework of bidifferential calculus. With different choices of a first-order bidifferential calculus, we obtain a variety of equations, including a semi-discrete and a fully discrete version of the matrix Riemann equation. A corresponding universal solution-generating method then either yields a (continuous or discrete) Cole-Hopf transformation, or leaves us with the problem of solving Riemann equations (hence an application of the hodograph method). If the bidifferential calculus extends to second order, solutions of a system of "Riemann equations" are also solutions of an equation that arises, on the universal level of bidifferential calculus, as an integrability condition. Depending on the choice of bidifferential calculus, the latter can represent a number of prominent integrable equations, like self-dual Yang-Mills, as well as matrix versions of the two-dimensional Toda lattice, Hirota's bilinear difference equation, (2+1)-dimensional Nonlinear Schrödinger (NLS), Kadomtsev-Petviashvili (KP) equation, and Davey-Stewartson equations. For all of them, a recent (non-isospectral) binary Darboux transformation result in bidifferential calculus applies, which can be specialized to generate solutions of the associated "Riemann equations." For the latter, we clarify the relation between these specialized binary Darboux transformations and the aforementioned solution-generating method. From (arbitrary size) matrix versions of the "Riemann equations" associated with an integrable equation, possessing a bidifferential calculus formulation, multi-soliton-type solutions of the latter can be generated. This includes "breaking" multi-soliton-type solutions of the self-dual Yang-Mills and the (2+1)-dimensional NLS equation, which are parametrized by solutions of Riemann equations.
Prolongation structures for supersymmetric equations
Roelofs, G.H.M.; Hijligenberg, van den N.W.
1990-01-01
The well known prolongation technique of Wahlquist and Estabrook (1975) for nonlinear evolution equations is generalized for supersymmetric equations and applied to the supersymmetric extension of the KdV equation of Manin-Radul. Using the theory of Kac-Moody Lie superalgebras, the explicit form of
Successfully Transitioning to Linear Equations
Colton, Connie; Smith, Wendy M.
2014-01-01
The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…
An Extented Wave Action Equation
Institute of Scientific and Technical Information of China (English)
左其华
2003-01-01
Based on the Navier-Stokes equation, an average wave energy equation and a generalized wave action conservation equation are presented in this paper. The turbulence effects on water particle velocity ui and wave surface elavation ξ as well as energy dissipation are included. Some simplified forms are also given.
Equation with the many fathers
DEFF Research Database (Denmark)
Kragh, Helge
1984-01-01
In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the us...
Solution of Finite Element Equations
DEFF Research Database (Denmark)
Krenk, Steen
An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...
Numerical Methods for Stochastic Partial Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Sharp, D.H.; Habib, S.; Mineev, M.B.
1999-07-08
This is the final report of a Laboratory Directed Research and Development (LDRD) project at the Los Alamos National laboratory (LANL). The objectives of this proposal were (1) the development of methods for understanding and control of spacetime discretization errors in nonlinear stochastic partial differential equations, and (2) the development of new and improved practical numerical methods for the solutions of these equations. The authors have succeeded in establishing two methods for error control: the functional Fokker-Planck equation for calculating the time discretization error and the transfer integral method for calculating the spatial discretization error. In addition they have developed a new second-order stochastic algorithm for multiplicative noise applicable to the case of colored noises, and which requires only a single random sequence generation per time step. All of these results have been verified via high-resolution numerical simulations and have been successfully applied to physical test cases. They have also made substantial progress on a longstanding problem in the dynamics of unstable fluid interfaces in porous media. This work has lead to highly accurate quasi-analytic solutions of idealized versions of this problem. These may be of use in benchmarking numerical solutions of the full stochastic PDEs that govern real-world problems.
Jupiter internal structure: the effect of different equations of state
Miguel, Yamila; Fayon, Lucile
2016-01-01
Heavy elements, even though its smaller constituent, are crucial to understand Jupiter formation history. Interior models are used to determine the amount of heavy elements in Jupiter interior, nevertheless this range is still subject to degeneracies due to uncertainties in the equations of state. Prior to Juno mission data arrival, we present Jupiter optimized calculations exploring the effect of different model parameters in the determination of Jupiter's core and heavy element's mass. We perform comparisons between equations of state published recently. The interior model of Jupiter is calculated from the equations of hydrostatic equilibrium, mass and energy conservation, and energy transport. The mass of the core and heavy elements is adjusted to match Jupiter's observational constrains radius and gravitational moments. We show that the determination of Jupiter interior structure is tied to the estimation of its gravitational moments and the accuracy of equations of state of hydrogen, helium and heavy ele...
Neyrinck, Marleen M; Vrielink, Hans
2015-02-01
It's important to work smoothly with your apheresis equipment when you are an apheresis nurse. Attention should be paid to your donor/patient and the product you're collecting. It gives additional value to your work when you are able to calculate the efficiency of your procedures. You must be capable to obtain an optimal product without putting your donor/patient at risk. Not only the total blood volume (TBV) of the donor/patient plays an important role, but also specific blood values influence the apheresis procedure. Therefore, not all donors/patients should be addressed in the same way. Calculation of TBV, extracorporeal volume, and total plasma volume is needed. Many issues determine your procedure time. By knowing the collection efficiency (CE) of your apheresis machine, you can calculate the number of blood volumes to be processed to obtain specific results. You can calculate whether you need one procedure to obtain specific results or more. It's not always needed to process 3× the TBV. In this way, it can be avoided that the donor/patient is needless long connected to the apheresis device. By calculating the CE of each device, you can also compare the various devices for quality control reasons, but also nurses/operators.
SINGULAR INTEGRAL EQUATIONS ALONG AN OPEN ARC WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER
Institute of Scientific and Technical Information of China (English)
Zhong Shouguo
2005-01-01
In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.
INVAP's Nuclear Calculation System
Directory of Open Access Journals (Sweden)
Ignacio Mochi
2011-01-01
Full Text Available Since its origins in 1976, INVAP has been on continuous development of the calculation system used for design and optimization of nuclear reactors. The calculation codes have been polished and enhanced with new capabilities as they were needed or useful for the new challenges that the market imposed. The actual state of the code packages enables INVAP to design nuclear installations with complex geometries using a set of easy-to-use input files that minimize user errors due to confusion or misinterpretation. A set of intuitive graphic postprocessors have also been developed providing a fast and complete visualization tool for the parameters obtained in the calculations. The capabilities and general characteristics of this deterministic software package are presented throughout the paper including several examples of its recent application.
Salgado, C A; Salgado, Carlos A.; Wiedemann, Urs Achim
2003-01-01
We calculate the probability (``quenching weight'') that a hard parton radiates an additional energy fraction due to scattering in spatially extended QCD matter. This study is based on an exact treatment of finite in-medium path length, it includes the case of a dynamically expanding medium, and it extends to the angular dependence of the medium-induced gluon radiation pattern. All calculations are done in the multiple soft scattering approximation (Baier-Dokshitzer-Mueller-Peign\\'e-Schiff--Zakharov ``BDMPS-Z''-formalism) and in the single hard scattering approximation (N=1 opacity approximation). By comparison, we establish a simple relation between transport coefficient, Debye screening mass and opacity, for which both approximations lead to comparable results. Together with this paper, a CPU-inexpensive numerical subroutine for calculating quenching weights is provided electronically. To illustrate its applications, we discuss the suppression of hadronic transverse momentum spectra in nucleus-nucleus colli...
OFTIFEL PERSONALIZED NUTRITIONAL CALCULATOR
Directory of Open Access Journals (Sweden)
Malte BETHKE
2016-11-01
Full Text Available A food calculator for elderly people was elaborated by Centiv GmbH, an active partner in the European FP7 OPTIFEL Project, based on the functional requirement specifications and the existing recommendations for daily allowances across Europe, data which were synthetized and used to give aims in amounts per portion. The OPTIFEL Personalised Nutritional Calculator is the only available online tool which allows to determine on a personalised level the required nutrients for elderly people (65+. It has been developed mainly to support nursing homes providing best possible (personalised nutrient enriched food to their patients. The European FP7 OPTIFEL project “Optimised Food Products for Elderly Populations” aims to develop innovative products based on vegetables and fruits for elderly populations to increase length of independence. The OPTIFEL Personalised Nutritional Calculator is recommended to be used by nursing homes.
Constitutive Equation of Superalloy In718 in Hammer Forging Process
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A constitutive equation reflecting the flow behavior ofSuperalloy In718 during the counter-blow hammer forging process was developed in terms of the relationship of flow stress and hot-deformation parameters, such as strain, strain rate, and deformation temperature. A new simplified approach for the complex multi-pass stress-strain curves has been attempted. The simulation curves calculated by constitutive equation are consistent with the experimental data.
Algorithm development for Maxwell's equations for computational electromagnetism
Goorjian, Peter M.
1990-01-01
A new algorithm has been developed for solving Maxwell's equations for the electromagnetic field. It solves the equations in the time domain with central, finite differences. The time advancement is performed implicitly, using an alternating direction implicit procedure. The space discretization is performed with finite volumes, using curvilinear coordinates with electromagnetic components along those directions. Sample calculations are presented of scattering from a metal pin, a square and a circle to demonstrate the capabilities of the new algorithm.
A Moment Equation Approach to a Muon Collider Cooling Lattice
Energy Technology Data Exchange (ETDEWEB)
Celata, C.M.; Sessler, A.M.; Lee, P.B.; Shadwick, B.A.; Wurtele, J.S.
1998-06-01
Equations are derived which describe the evolution of the second order moments of the beam distribution function in the ionization cooling section of a muon collider. Ionization energy loss, multiple scattering, and magnetic fields have been included, but forces are linearized. A computer code using the equations agrees well with tracking calculations. The code is extremely fast, and can be used for preliminary design, where such issues as beam halo, which must be explored using a tracking code, are not the focus.
Reduction of infinite dimensional equations
Directory of Open Access Journals (Sweden)
Zhongding Li
2006-02-01
Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.
A generalized advection dispersion equation
Indian Academy of Sciences (India)
Abdon Atangana
2014-02-01
This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of the operator are presented. The operator is used to generalize the advection dispersion equation. The generalized equation differs from the standard equation in four properties. The generalized equation is solved via the variational iteration technique. Some illustrative figures are presented.
Integral equations and their applications
Rahman, M
2007-01-01
For many years, the subject of functional equations has held a prominent place in the attention of mathematicians. In more recent years this attention has been directed to a particular kind of functional equation, an integral equation, wherein the unknown function occurs under the integral sign. The study of this kind of equation is sometimes referred to as the inversion of a definite integral. While scientists and engineers can already choose from a number of books on integral equations, this new book encompasses recent developments including some preliminary backgrounds of formulations of in
Discovering evolution equations with applications
McKibben, Mark
2011-01-01
Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversational approach, Discovering Evolution Equations with Applications: Volume 2-Stochastic Equations provides an introductory understanding of stochastic evolution equations. The text begins with hands-on introductions to the essentials of real and stochast
Ovarian and tubal cancer in Denmark
DEFF Research Database (Denmark)
Gottschau, Mathilde; Mellemkjaer, Lene; Hannibal, Charlotte G;
2016-01-01
INTRODUCTION: The Nordic countries are areas with a high-incidence of ovarian cancer; however, differences between the countries exist. MATERIAL AND METHODS: We used the Danish Cancer Registry to identify 11 264 cases of ovarian cancer and 363 cases of tubal cancer during 1993-2013. We calculated...
A Generalized Polynomial Form of the Objective Function in Flash Calculations
1992-05-01
Redlich - Kwong Equation of State , Applications to Gen- eral Physical Data Calculations," paper 15C...G.M., "A Modified Redlich - Kwong Equation of State , Applications to Gen- eral Physical Data Calculations," paper 15C, Proceedings, AIChE National Meeting...acceptance are Soave’s modifications of the Redlich - Kwong (1949) equation of state (SRKEOS) (Soave, 1972) and that presented by Peng and Robinson
The mechanical energy equation for total flow in open channels
Institute of Scientific and Technical Information of China (English)
刘士和; 范敏; 薛娇
2014-01-01
The mechanical energy equation is a fundamental equation of a 1-D mathematical model in Hydraulics and Engineering Fluid Mechanics. This equation for the total flow used to be deduced by extending the Bernoulli’s equation for the ideal fluid in the streamline to a stream tube, and then revised by considering the viscous effect and integrated on the cross section. This derivation is not rigorous and the effect of turbulence is not considered. In this paper, the energy equation for the total flow is derived by using the Navier-Stokes equations in Fluid Mechanics, the results are as follows:(1) A new energy equation for steady channel flows of in-compressible homogeneous liquid is obtained, which includes the variation of the turbulent kinetic energy along the channel, the for-mula for the mechanical energy loss of the total flow can be determined directly in the deduction process. (2) The theoretical solution of the velocity field for laminar flows in a rectangular open channel is obtained and the mechanical energy loss in the energy equa-tion is calculated. The variations of the coefficient of the mechanical energy loss against the Reynolds number and the width-depth ratio are obtained. (3) The turbulent flow in a rectangular open channel is simulated using 3-D Reynolds averaged equations closed by the Reynolds stress model (RSM), and the variations of the coefficient of the mechanical energy loss against the Reynolds number and the width-depth ratio are discussed.
On two-parameter equations of state and the limitations of a hard sphere Peng-Robinson equation
Harmens, A.; Jeremiah, Dawn E.
Simple two-parameter equations of state are exceptionally effective for calculations on systems of small, uncomplicated molecules. They are therefore extremely useful for vapour-liquid equilibrium calculations in cryogenic and light hydrocarbon process design. In a search for further improvement three two-parameter equations of state with a co-volume repulsion term and three with a hard sphere repulsion term have been investigated. Their characteristic constants at the critical point have been compared. The procedure for fitting the two parameters to empirical data in the subcritical region was analysed. A perturbed hard sphere equation with a Peng-Robinson attraction term was shown to be unsuitable for application over a wide range of p, T conditions. A similar equation with a Redlich-Kwong attraction term gives good service in the cryogenic range.
Solving the Bethe-Salpeter Equation in Euclidean Space
Dorkin, S M; Atti, C Ciofi degli; Kämpfer, B
2010-01-01
Different approaches to solve the spinor-spinor Bethe-Salpeter (BS) equation in Euclidean space are considered. It is argued that the complete set of Dirac matrices is the most appropriate basis to define the partial amplitudes and to solve numerically the resulting system of equations with realistic interaction kernels. Other representations can be obtained by performing proper unitary transformations. A generalization of the iteration method for finding the energy spectrum of the BS equation is discussed and examples of concrete calculations are presented. Comparison of relativistic calculations with available experimental data and with corresponding non relativistic results together with an analysis of the role of Lorentz boost effects and relativistic corrections are presented. A novel method related to the use of hyperspherical harmonics is considered for a representation of the vertex functions suitable for numerical calculations.
Solving the Bethe-Salpeter Equation in Euclidean Space
Dorkin, S. M.; Kaptari, L. P.; Ciofi degli Atti, C.; Kämpfer, B.
2011-03-01
Different approaches to solve the spinor-spinor Bethe-Salpeter (BS) equation in Euclidean space are considered. It is argued that the complete set of Dirac matrices is the most appropriate basis to define the partial amplitudes and to solve numerically the resulting system of equations with realistic interaction kernels. Other representations can be obtained by performing proper unitary transformations. A generalization of the iteration method for finding the energy spectrum of the BS equation is discussed and examples of concrete calculations are presented. Comparison of relativistic calculations with available experimental data and with corresponding non relativistic results together with an analysis of the role of Lorentz boost effects and relativistic corrections are presented. A novel method related to the use of hyperspherical harmonics is considered for a representation of the vertex functions suitable for numerical calculations.
Yehorchenko, Irina
2010-01-01
We study possible Lie and non-classical reductions of multidimensional wave equations and the special classes of possible reduced equations - their symmetries and equivalence classes. Such investigation allows to find many new conditional and hidden symmetries of the original equations.
Institute of Scientific and Technical Information of China (English)
黄虎; 丁平兴; 吕秀红
2001-01-01
The Hamiltonian formalism for surface waves and the mild-slope approximation were empolyed in handling the case of slowly varying three-dimensional currents and an uneven bottom, thus leading to an extended mild-slope equation. The bottom topography consists of two components: the slowly varying component whose horizontal length scale is longer than the surface wave length, and the fast varying component with the amplitude being smaller than that of the surface wave. The frequency of the fast varying depth component is, however, comparable to that of the surface waves. The extended mild- slope equation is more widely applicable and contains as special cases famous mild-slope equations below: the classical mild-slope equation of Berkhoff , Kirby' s mild-slope equation with current, and Dingemans' s mild-slope equation for rippled bed. The extended shallow water equations for ambient currents and rapidly varying topography are also obtained.
Scaling of differential equations
Langtangen, Hans Petter
2016-01-01
The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and exam...
$\\Lambda$ Scattering Equations
Gomez, Humberto
2016-01-01
The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter $\\Lambda$ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting $\\Lambda$ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the $\\Lambda$ algorithm.
Dirac equation on coordinate dependent noncommutative space-time
Kupriyanov, V G
2014-01-01
We consider the consistent deformation of the relativistic quantum mechanics introducing the noncommutativity of the space-time and preserving the Lorentz symmetry. The relativistic wave equation describing the spinning particle on coordinate dependent noncommutative space-time (noncommutative Dirac equation) is proposed. The fundamental properties of this equation, like the Lorentz covariance and the continuity equation for the probability density are verified. To this end using the properties of the star product we derive the corresponding probability current density and prove its conservation. The energy-momentum tensor for the free noncommutative spinor field is calculated. We solve the free noncommutative Dirac equation and show that the standard energy-momentum dispersion relation remains valid in the noncommutative case.
Gauge Poisson representations for birth/death master equations
Drummond, P D
2002-01-01
Poisson representation techniques provide a powerful method for mapping master equations for birth/death processes - found in many fields of physics, chemistry and biology - into more tractable stochastic differential equations. However, the usual expansion is not exact in the presence of boundary terms, which commonly occur when the differential equations are nonlinear. In this paper, a stochastic gauge technique is introduced that eliminates boundary terms, to give an exact representation as a weighted rate equation with stochastic terms. These methods provide novel techniques for calculating and understanding the effects of number correlations in systems that have a master equation description. As examples, correlations induced by strong mutations in genetics, and the astrophysical problem of molecule formation on microscopic grain surfaces are analyzed. Exact analytic results are obtained that can be compared with numerical simulations, demonstrating that stochastic gauge techniques can give exact results...
Localized standing waves in inhomogeneous Schrodinger equations
Marangell, R; Susanto, H
2010-01-01
A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a combination of self-focusing and self-defocusing nonlinearity, with the self-defocusing region localized in a finite interval, is investigated. Using numerical computations, the extension of linear eigenmodes of the corresponding linearized system into nonlinear states is established, particularly nonlinear continuations of the fundamental state and the first excited state. The (in)stability of the states is also numerically calculated, from which it is obtained that symmetric nonlinear solutions become unstable beyond a critical threshold norm. Instability of the symmetric states is then investigated analytically through the application of a topological argument. Determination of instability of positive symmetric states is reduced to simple geometric properties of the composite phas...
Coupling and reduction of the HAWC equations
DEFF Research Database (Denmark)
Nim, E.
2001-01-01
This report contains a description of a general method for coupling and reduction of the so-called HAWC equations, which constitute the basis equations of motion of the aeroelastic model HAWC used widely by research institutes and industrial companies formore than the ten years. The principal aim...... of the work has been to enable the modelling wind turbines with large displacements of the blades in order to predict phenomena caused by geometric non-linear effects. However, the method can also be applied tomodel the nacelle/shaft structure of a turbine more detailed than the present HAWC model....... In addition, the method enables the reduction of the number of degrees of freedom of the structure in order to increase the calculation efficiency and improve thecondition of the system....
Unpolarized coupled DGLAP evolution equation at small-
Indian Academy of Sciences (India)
Saurav Bhattacharjee; Ranjit Baishya; Jayanata Kumar Sarma
2013-01-01
In this paper, we have obtained the solution of the unpolarized coupled Dokshitzer–Gribove–Lipatov–Alterelli–Parisi (DGLAP) evolution equation in leading order at the small- limit. Here, we have used a Taylor series expansion, separation of functions and then the method of characteristics to solve the evolution equations. We have also calculated -evolution of singlet and gluon distribution functions and the results are compared with E665 and NNPDF data for singlet structure function and GRV1998 and MRST2004 gluon parametrizations. It is shown that our results are in good agreement with the parametrizations especially at small-x and high-2 region. From global parametrizations and our results, we have seen that the singlet and gluon distribution functions increase when 2 increases for fixed values of .
Optimal moving grids for time-dependent partial differential equations
Wathen, A. J.
1992-01-01
Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.
Patterson function and δ recycling: derivation of the phasing equations.
Rius, Jordi
2012-05-01
Two phasing equations based on the Fourier syntheses δ(P) = T(-1)[(E(2) - )exp(iφ)] and δ(M) = T(-1)[(E - )exp(iφ)] were recently described [Rius (2012). Acta Cryst. A 68, 77-81] (E is the quasi-normalized structure factor and is the average over all reflections). These equations were found by comparison with the direct methods origin-free modulus sum function and constitute the core of the `δ recycling' phasing procedure. The derivation of these phasing equations from the minimization of a residual (R(P)) between two differently calculated density functions (one of them including the positivity constraint) is shown.