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.
Calculation of evapotranspiration using the Penman-Monteith equation
Žugelj, Marko
2016-01-01
This thesis is presenting the most important facts in the process of evapotranspiration, with some definitions and Penman–Montetith equation, which is a standard equation for evapotranspiration calculation. In this work a calculation of reference evapotranspiration is presented, using Penman–Monteith equation, for Ljubljana-Bežigrad meteorological station. Several calculation procedures are presented, such as calculation using diffrent time steps of the data (hourly, daily, ten days, month...
Calculation of transonic flows using an extended integral equation method
Nixon, D.
1976-01-01
An extended integral equation method for transonic flows is developed. In the extended integral equation method velocities in the flow field are calculated in addition to values on the aerofoil surface, in contrast with the less accurate 'standard' integral equation method in which only surface velocities are calculated. The results obtained for aerofoils in subcritical flow and in supercritical flow when shock waves are present compare satisfactorily with the results of recent finite difference methods.
An integral equation solution for multistage turbomachinery design calculations
Mcfarland, Eric R.
1993-01-01
A method was developed to calculate flows in multistage turbomachinery. The method is an extension of quasi-three-dimensional blade-to-blade solution methods. Governing equations for steady compressible inviscid flow are linearized by introducing approximations. The linearized flow equations are solved using integral equation techniques. The flows through both stationary and rotating blade rows are determined in a single calculation. Multiple bodies can be modelled for each blade row, so that arbitrary blade counts can be analyzed. The method's benefits are its speed and versatility.
Recursive integral equations with positive kernel for lattice calculations
International Nuclear Information System (INIS)
A Kirkwood-Salzburg integral equation, with positive defined kernel, for the states of lattice models of statistical mechanics and quantum field theory is derived. The equation is defined in the thermodynamic limit, and its iterative solution is convergent. Moreover, positivity leads to an exact a priori bound on the iteration. The equation's relevance as a reliable algorithm for lattice calculations is therefore suggested, and it is illustrated with a simple application. It should provide a viable alternative to Monte Carlo methods for models of statistical mechanics and lattice gauge theories. 10 refs
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)
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.
Coupling algorithm for calculating sensitivities of Smoluchowski's coagulation equation
Man, Peter L W; Bailleul, Ismael F; Kraft, Markus
2009-01-01
In this paper, two new stochastic algorithms for calculating parametric derivatives of the solution to the Smoluchowski coagulation equation are presented. It is assumed that the coagulation kernel is dependent on these parameters. The new algorithms (called `Single' and `Double') work by coupling two Marcus-Lushnikov processes in such a way as to reduce the difference between their trajectories, thereby significantly reducing the variance of central difference estimators of the parametric derivatives. In the numerical results, the algorithms are shown have have a O(1/N) order of convergence as expected, where N is the initial number of particles. It was also found that the Single and Double algorithms provide much smaller variances. Furthermore, a method for establishing `efficiency' is considered, which takes into account the variances as well as CPU run times, and the `Double' is significantly more `efficient' compared to the `Independent' algorithm in most cases.
Master equation calculations of cluster formation in supersonic jets
International Nuclear Information System (INIS)
The kinetics of cluster formation in supersonic jets is examined by numerical integration of the master equation system. Some general characteristics of cluster kinetics could be formulated. Excellent agreement between experimental curves of p-cresol (H2O)0,1,2,3 formation as function of H2O pressure and the corresponding calculated curves were obtained assuming successive cluster formation. From the kinetic curves, and unambiguous assignment of cluster size was possible which agreed with mass-resolved REMPI measurements. The fit of the rate coefficients shows the formation of p-cresol (H2O)1 to be faster than p-cresol (H2O)2 and p-cresol (H2O)3. (orig.)
Calculating work in weakly driven quantum master equations: Backward and forward equations
Liu, Fei
2016-01-01
I present a technical report indicating that the two methods used for calculating characteristic functions for the work distribution in weakly driven quantum master equations are equivalent. One involves applying the notion of quantum jump trajectory [Phys. Rev. E 89, 042122 (2014), 10.1103/PhysRevE.89.042122], while the other is based on two energy measurements on the combined system and reservoir [Silaev et al., Phys. Rev. E 90, 022103 (2014), 10.1103/PhysRevE.90.022103]. These represent backward and forward methods, respectively, which adopt a very similar approach to that of the Kolmogorov backward and forward equations used in classical stochastic theory. The microscopic basis for the former method is also clarified. In addition, a previously unnoticed equality related to the heat is also revealed.
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 unsteady transonic flows using the integral equation method
Nixon, D.
1978-01-01
The basic integral equations for a harmonically oscillating airfoil in a transonic flow with shock waves are derived; the reduced frequency is assumed to be small. The problems associated with shock wave motion are treated using a strained coordinate system. The integral equation is linear and consists of both line integrals and surface integrals over the flow field which are evaluated by quadrature. This leads to a set of linear algebraic equations that can be solved directly. The shock motion is obtained explicitly by enforcing the condition that the flow is continuous except at a shock wave. Results obtained for both lifting and nonlifting oscillatory flows agree satisfactorily with other accurate results.
Prediction Equation for Calculating Fat Mass in Young Indian Adults
Sandhu; Gupta; Shenoy
2010-01-01
Purpose Accurate measurement or prediction of fat mass is useful in physiology, nutrition and clinical medicine. Most predictive equations currently used to assess percentage of body fat or fat mass, using simple anthropometric measurements were derived from people in western societies and they may not be appropriate for individuals with other genotypic and phenotypic characteristics. We developed equations to predict fat mass from anthropometric measurements in young Indian adul...
Prediction Equation for Calculating Fat Mass in Young Indian Adults
Directory of Open Access Journals (Sweden)
Sandhu
2010-06-01
Full Text Available Purpose Accurate measurement or prediction of fat mass is useful in physiology, nutrition and clinical medicine. Most predictive equations currently used to assess percentage of body fat or fat mass, using simple anthropometric measurements were derived from people in western societies and they may not be appropriate for individuals with other genotypic and phenotypic characteristics. We developed equations to predict fat mass from anthropometric measurements in young Indian adults. Methods Fat mass was measured in 60 females and 58 males, aged 20 to 29 yrs by using hydrostatic weighing and by simultaneous measurement of residual lung volume. Anthropometric measure included weight (kg, height (m and 4 skinfold thickness [STs (mm]. Sex specific linear regression model was developed with fat mass as the dependent variable and all anthropometric measures as independent variables. Results The prediction equation obtained for fat mass (kg for males was 8.46+0.32 (weight − 15.16 (height + 9.54 (log of sum of 4 STs (R2= 0. 53, SEE=3.42 kg and − 20.22 + 0.33 (weight + 3.44 (height + 7.66 (log of sum of 4 STs (R2=0.72, SEE=3.01kg for females. Conclusion A new prediction equation for the measurement of fat mass was derived and internally validated in young Indian adults using simple anthropometric measurements.
Solid body equations to calculate the trajectory of ramjet
Imai, Kenji
1982-01-01
Six-degree-of-freedom trajectory equations for a ranrjet propelled, gun launched projectile are formulated. An outline for FORTRAN computer program flow charts also appear in the report. Special emphasis is given to the effect of wind on trajectory errors.
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
43 CFR Appendix A to Part 418 - Calculation of Efficiency Equation
2010-10-01
... 43 Public Lands: Interior 1 2010-10-01 2010-10-01 false Calculation of Efficiency Equation A Appendix A to Part 418 Public Lands: Interior Regulations Relating to Public Lands BUREAU OF RECLAMATION.... 418, App. A Appendix A to Part 418—Calculation of Efficiency Equation ER18DE97.008 ER18DE97.009...
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.
Calculation of Effective Freezing Time in Lung Cancer Cryosurgery Based on Godunov Simulation
Т.G. Kotova; V.I. Kochenov; D.Y. Madai; А.V. Gurin; S.N. Tsybusov
2016-01-01
There have been presented the results of lung cancer cryosurgery simulation using numerical solutions of enthalpy equation according to Godunov method. For the cryodestruction improvement purposes we successfully calculated the effective freezing time taking into account the evolution of an ice ball covering the tumor area. Geometrical transformation parameters of an ice ball have been measured by calculating the temperature distribution and the interface position in biological tissu...
Calculation of Effective Freezing Time in Lung Cancer Cryosurgery Based on Godunov Simulation
Т.G. Kotova; V.I. Kochenov; S.N. Tsybusov; D.Y. Madai; А.V. Gurin
2016-01-01
There have been presented the results of lung cancer cryosurgery simulation using numerical solutions of enthalpy equation according to Godunov method. For the cryodestruction improvement purposes we successfully calculated the effective freezing time taking into account the evolution of an ice ball covering the tumor area. Geometrical transformation parameters of an ice ball have been measured by calculating the temperature distribution and the interface position in biological tissue. Mathem...
Numerical Calculation of the Flow Inside Pump Impellers Using 3D Euler Equations
SARIOĞLU, Kemal; Ayder, Erkan
1999-01-01
The flow pattern inside an impeller should be determined for maximum efficiency and performance. The effects of the design parameters on the pump performance can be determined using numerical calculations instead of empirical equations. Incompressible 3D time-dependent Euler equations, written in a conservative form, are used. An artificial pressure term is added to preserve the hyperbolic character of the equations. A finite-volume technique is used for space discretization. A fou...
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.
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.
Calculation of B/A for n-alkane liquids using the Tait equation
Hartmann; Lee; Balizer
2000-07-01
The B/A parameter of acoustic nonlinearity was calculated for a series of n-alkane liquids using the Tait PVT equation of state supplemented with specific heat data. The calculations of sound speed, sound speed derivatives, the two components of B/A, and the value of B/A itself were compared with experimental data taken from the literature and with earlier calculations using a different equation of state. In addition, a comparison of the results with Ballou's rule (linear relation of B/A and reciprocal sound speed) was made. It is concluded that B/A can be calculated from the Tait equation of state with about the same accuracy as direct measurements of sound speed versus pressure and temperature, though the the temperature derivatives of the sound speed are calculated with much lower accuracy than pressure derivatives. The calculations made using the Tait equation are about the same accuracy as calculations made using our equation of state. Also, Ballou's rule does not hold for these liquids. PMID:10923871
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.
Equation of state for technetium from X-ray diffraction and first-principle calculations
Mast, Daniel S.; Kim, Eunja; Siska, Emily M.; Poineau, Frederic; Czerwinski, Kenneth R.; Lavina, Barbara; Forster, Paul M.
2016-08-01
The ambient temperature equation of state (EoS) of technetium metal has been measured by X-ray diffraction. The metal was compressed using a diamond anvil cell and using a 4:1 methanol-ethanol pressure transmitting medium. The maximum pressure achieved, as determined from the gold pressureEquation of state for technetium from X-ray diffraction and first-principle calculations scale, was 67 GPa. The compression data shows that the HCP phase of technetium is stable up to 67 GPa. The compression curve of technetium was also calculated using first-principles total-energy calculations. Utilizing a number of fitting strategies to compare the experimental and theoretical data it is determined that the Vinet equation of state with an ambient isothermal bulk modulus of B0T=288 GPa and a first pressure derivative of B‧=5.9(2) best represent the compression behavior of technetium metal.
First-Principles Molecular Dynamics Calculations of the Equation of State for Tantalum
Directory of Open Access Journals (Sweden)
Shigeaki Ono
2009-10-01
Full Text Available The equation of state of tantalum (Ta has been investigated to 100 GPa and 3,000 K using the first-principles molecular dynamics method. A large volume dependence of the thermal pressure of Ta was revealed from the analysis of our data. A significant temperature dependence of the calculated effective Grüneisen parameters was confirmed at high pressures. This indicates that the conventional approach to analyze thermal properties using the Mie-Grüneisen approximation is likely to have a significant uncertainty in determining the equation of state for Ta, and that an intrinsic anharmonicity should be considered to analyze the equation of state.
Liu, Fei
2014-09-01
We present a characteristic function method to calculate the probability density functions of the inclusive work in adiabatic two-level quantum Markovian master equations. These systems are steered by some slowly varying parameters and the dissipations may depend on time. Our theory is based on the interpretation of the quantum jump for the master equations. In addition to the calculation, we also find that the fluctuation properties of the work can be described by the symmetry of the characteristic functions, which is exactly the same as in the case of isolated systems. A periodically driven two-level model is used to demonstrate the method. PMID:25314409
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.
On the Calculation of the Exact Number of Zeroes of a Set of Equations
Hoenders, B.J.; Slump, C.H.
1983-01-01
The number of simple zeroes common to a set of nonlinear equations is calculated exactly and analytically in terms of an integral taken over the boundary of the domain of interest. The integrand consists only of simple algebraic quantities containing the functions involved as well as their derivativ
Rath, Biswanath; Mallick, P.
2014-01-01
A new method for generating analytical expression of quantum Hamiltonian from non-linear differential equation with stationary energy level has been formulated.Further calculation of energy levels have been carried out analytically using and numerically using matrix diagonalisation method.
International Nuclear Information System (INIS)
Empirical rate equations are derived to estimate hydrogen generation based on chemical reactions, radiolysis of water and organic compounds, and corrosion processes. A comparison of the generation rates observed in the field with the rates calculated for twenty eight tanks shows agreement with in a factor of two to three
Calculation of Spin Observables for Proton-Neutron Elastic Scattering in the Bethe-Salpeter Equation
Kinpara, Susumu
2016-01-01
Bethe-Salpeter equation is applied to $p$-$n$ elastic scattering. The spin observables are calculated by the M matrix similar to $p$-$p$ case. The parameters of the meson-exchange model are used with the cut-off for the pion exchange interaction. Change of the M matrix indicates breaking of the charge independence in the nucleon-nucleon system.
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...... the problems of coupling of counterpropagating waves (Bragg gratings) and co-propagating waves (long-period gratings). In both cases the method applies for gratings with arbitrary dielectric modulation, including all kinds of chirp and apodization and possibly also imperfections in the dielectric modulation...
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.
Compliance with biopsy recommendations of a prostate cancer risk calculator
van Vugt, Heidi A.; Roobol, Monique J.; Busstra, Martijn; Kil, Paul; Oomens, Eric H.; de Jong, Igle J.; Bangma, Chris H.; Steyerberg, Ewout W.; Korfage, Ida
2012-01-01
OBJECTIVES To assess both urologist and patient compliance with a 'no biopsy' or 'biopsy' recommendation of the European Randomized study of Screening for Prostate Cancer (ERSPC) Risk Calculator (RC), as well as their reasons for non-compliance. To assess determinants of patient compliance. PATIENTS
Calculation of Effective Freezing Time in Lung Cancer Cryosurgery Based on Godunov Simulation
Directory of Open Access Journals (Sweden)
Т.G. Kotova
2016-03-01
Full Text Available There have been presented the results of lung cancer cryosurgery simulation using numerical solutions of enthalpy equation according to Godunov method. For the cryodestruction improvement purposes we successfully calculated the effective freezing time taking into account the evolution of an ice ball covering the tumor area. Geometrical transformation parameters of an ice ball have been measured by calculating the temperature distribution and the interface position in biological tissue. Mathematical cryosurgical procedures are described by heat transfer equations in solid and liquid phases. Numerical results for one-dimensional case were verified by comparing with exact solutions. In twodimensional modeling an effective cryotherapy time, which corresponds to freezing time of all tumor parts, was calculated as the area of forming ice balls covering all tumor region. The findings enable to set the effective time of a cryosurgical procedure in lung cancer. The knowledge of temperature distribution and interface position in biological tissue offers an opportunity to a cryosurgeon to finish the procedure within a certain time period to minimize the healthy tissue damage and destroy tumor cells to the maximum. Simulation application enables to schedule cryotherapy in lung cancer more effectively and to a good quality.
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...
International Nuclear Information System (INIS)
A method of solving the diffusion equation for the th ermal neutron flux in a heterogeneous medium is presented. Perturbation calculation is successfully applied for the cylindrical concentric system after testing this method for the spherical concentric geometry analytically solved by Czubek (1981). The method permits to calculate the t hermal neutron decay constant and the space distribution of the thermal neutron flux in a heterogeneous geom etry. The condition of the constant value of the neutron flux in the inner part of the system has to be m et. This method has an application in the measurement of the thermal neutron absorption cross section, presented by Czubek (1981). (author)
Exact Dirac equation calculation of ionization induced by ultrarelativistic heavy ions
Baltz, Anthony J.
1999-01-01
The time-dependent Dirac equation can be solved exactly for ionization induced by ultrarelativistic heavy ion collisions. Ionization calculations are carried out in such a framework for a number of representative ion-ion pairs. For each ion-ion pair, the computed cross section consists of two terms, a constant energy independent term and a term whose coefficient is ln(gamma). Scaled values of both terms are found to decrease with increasing Z of the nucleus that is ionized.
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 ${}^{\\rm 1}S_{\\rm 0}$.
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...
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.
Calculation of some solutions of the Bobylev-Krook-Wu and Tjon-Wu equations
Barnsley, M. F.; Turchetti, G.
1981-09-01
Two fully nonlinear Boltzmann equations for infinite spatially uniform gases consisting of a single species of particle are considered. The models are the one due to Bobylev, Krook and Wu and the one due to Tjon and Wu. These are shown to be related by the Abel transform and an existence uniqueness theorem is presented. Then a procedure for the numerical calculations of solutions - based upon the method of Barnsley and Cornille - is given and a device for speeding up its convergence is described. Finally, several numerical examples are discussed. Some enhancement is shown to occur, but not enough to be physically important.
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.
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.
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
International Nuclear Information System (INIS)
Purpose: To investigate the dosimetric impact of the heterogeneity dose calculation Acuros (Transpire Inc., Gig Harbor, WA), a grid-based Boltzmann equation solver (GBBS), for brachytherapy in a cohort of cervical cancer patients. Methods and Materials: The impact of heterogeneities was retrospectively assessed in treatment plans for 26 patients who had previously received 192Ir intracavitary brachytherapy for cervical cancer with computed tomography (CT)/magnetic resonance-compatible tandems and unshielded colpostats. The GBBS models sources, patient boundaries, applicators, and tissue heterogeneities. Multiple GBBS calculations were performed with and without solid model applicator, with and without overriding the patient contour to 1 g/cm3 muscle, and with and without overriding contrast materials to muscle or 2.25 g/cm3 bone. Impact of source and boundary modeling, applicator, tissue heterogeneities, and sensitivity of CT-to-material mapping of contrast were derived from the multiple calculations. American Association of Physicists in Medicine Task Group 43 (TG-43) guidelines and the GBBS were compared for the following clinical dosimetric parameters: Manchester points A and B, International Commission on Radiation Units and Measurements (ICRU) report 38 rectal and bladder points, three and nine o’clock, and D2cm3 to the bladder, rectum, and sigmoid. Results: Points A and B, D2 cm3 bladder, ICRU bladder, and three and nine o’clock were within 5% of TG-43 for all GBBS calculations. The source and boundary and applicator account for most of the differences between the GBBS and TG-43 guidelines. The D2cm3 rectum (n = 3), D2cm3 sigmoid (n = 1), and ICRU rectum (n = 6) had differences of >5% from TG-43 for the worst case incorrect mapping of contrast to bone. Clinical dosimetric parameters were within 5% of TG-43 when rectal and balloon contrast were mapped to bone and radiopaque packing was not overridden. Conclusions: The GBBS has minimal impact on clinical
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.
A mean field calculation of the equation of state of supernova matter
International Nuclear Information System (INIS)
The equation of state for hot dense matter occuring in stellar collapse is calculated using the Hartree-Fock approximation at finite temperature. The effective nucleon-nucleon interaction is a modified Skyrme force which gives a rather good value of the compression modulus in nuclear matter. Results are presented for the adiabat S=1 per baryon, with a fixed value of the electron fraction Ysub(e)=0.25, in the density range rho=0.02 to 0.07 baryons per fm3. We find that nuclei are still present in the medium. As a consequence the adiabatic index is slightly less than 4/3. We also discuss the presence of a transition, around half nuclear matter density, towards a phase made of bubbles
Transonic flow calculations using a flux vector splitting method for the Euler equations
Seaford, C. M.; Hassan, H. A.
1984-01-01
A study of the flux vector splitting method of Steger and Warming for the solution of the time dependent Euler equations in strong conservation law form for arbitrary two-dimensional geometries is presented. The procedure employed here differs from that of Buning and Steger in that it uses a different algorithm and employs implicit boundary conditions. Moreover, the method, as implemented here, does not contain any explicit smoothing or any adjustable parameters. Calculations were carried out for an NACA 0012 airfoil at various Mach numbers and angles of attack, and cylinders. Steady symmetric solutions were obtained for the full cylinder at a freestream Mach number of .5 without imposing a symmetry condition. In general, good agreement with other methods was obtained.
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.
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
International Nuclear Information System (INIS)
The numerical treatment of Orr-Sommerfeld equation which is the fundamental equation of linear hydrodynamic stability theory is described. Present calculation procedure is applied to the two-dimensional quasi-parallel flow for which linearized disturbance equation (Orr-Sommerfeld equation) contains one simple turning point and αR >> 1. The numerical procedure for this problem and one numerical example for Jeffery-Hamel flow (J-H III1) are presented. These treatment can be extended to the other velocity profiles by slight midifications. (author)
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.
A new three-parameter cubic equation of state for refrigeration engineering calculations
Energy Technology Data Exchange (ETDEWEB)
Zhang, H.-L.; Sato, H.; Watanabe, K. [Keio Univ., Yokohama (Japan). Dept. of Mechanical Engineering
1997-09-01
A new three-parameter cubic equation of state is proposed in which the repulsion pressure term of the semiempirical van der Waals equation has been modified based on the hard-sphere potential and a functional form similar to Redlich-Kwong attraction term is adopted for the attraction term. All three parameters are treated as functions of temperature. For the purpose of examining the applicability of the new equation, it was applied to describe the thermodynamic properties of difluoromethane (R-32) and pentafluoroethane (R-125). It has been found that the essential thermodynamic properties are represented by the new equation as accurately as a conventional far-complicated modified Benedict-Webb-Rubin equation in the working range of refrigeration equipment. The new cubic equation was also compared with the Peng-Robinson equation and the Carnahan-Starling-De Santis equation. (author)
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.
Egami, Yoshiyuki; Iwase, Shigeru; Tsukamoto, Shigeru; Ono, Tomoya; Hirose, Kikuji
2015-09-01
We develop a first-principles electron-transport simulator based on the Lippmann-Schwinger (LS) equation within the framework of the real-space finite-difference scheme. In our fully real-space-based LS (grid LS) method, the ratio expression technique for the scattering wave functions and the Green's function elements of the reference system is employed to avoid numerical collapse. Furthermore, we present analytical expressions and/or prominent calculation procedures for the retarded Green's function, which are utilized in the grid LS approach. In order to demonstrate the performance of the grid LS method, we simulate the electron-transport properties of the semiconductor-oxide interfaces sandwiched between semi-infinite jellium electrodes. The results confirm that the leakage current through the (001)Si-SiO_{2} model becomes much larger when the dangling-bond state is induced by a defect in the oxygen layer, while that through the (001)Ge-GeO_{2} model is insensitive to the dangling bond state. PMID:26465580
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.
International Nuclear Information System (INIS)
Purpose: To investigate the use of the linear Boltzmann transport equation as a dose calculation tool which can account for interface effects, while still having faster computation times than Monte Carlo methods. In particular, we introduce a forward scattering approximation, in hopes of improving calculation time without a significant hindrance to accuracy. Methods: Two coupled Boltzmann transport equations were constructed, one representing the fluence of photons within the medium, and the other, the fluence of electrons. We neglect the scattering term within the electron transport equation, resulting in an extreme forward scattering approximation to reduce computational complexity. These equations were then solved using a numerical technique for solving partial differential equations, known as a finite difference scheme, where the fluence at each discrete point in space is calculated based on the fluence at the previous point in the particle's path. Using this scheme, it is possible to develop a solution to the Boltzmann transport equations by beginning with boundary conditions and iterating across the entire medium. The fluence of electrons can then be used to find the dose at any point within the medium. Results: Comparisons with Monte Carlo simulations indicate that even simplistic techniques for solving the linear Boltzmann transport equation yield expected interface effects, which many popular dose calculation algorithms are not capable of predicting. Implementation of a forward scattering approximation does not appear to drastically reduce the accuracy of this algorithm. Conclusion: Optimized implementations of this algorithm have been shown to be very accurate when compared with Monte Carlo simulations, even in build up regions where many models fail. Use of a forward scattering approximation could potentially give a reasonably accurate dose distribution in a shorter amount of time for situations where a completely accurate dose distribution is not
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.
International Nuclear Information System (INIS)
The generalized quantum master equation provides a powerful tool to describe the dynamics in quantum impurity models driven away from equilibrium. Two complementary approaches, one based on Nakajima–Zwanzig–Mori time-convolution (TC) and the other on the Tokuyama–Mori time-convolutionless (TCL) formulations provide a starting point to describe the time-evolution of the reduced density matrix. A key in both approaches is to obtain the so called “memory kernel” or “generator,” going beyond second or fourth order perturbation techniques. While numerically converged techniques are available for the TC memory kernel, the canonical approach to obtain the TCL generator is based on inverting a super-operator in the full Hilbert space, which is difficult to perform and thus, nearly all applications of the TCL approach rely on a perturbative scheme of some sort. Here, the TCL generator is expressed using a reduced system propagator which can be obtained from system observables alone and requires the calculation of super-operators and their inverse in the reduced Hilbert space rather than the full one. This makes the formulation amenable to quantum impurity solvers or to diagrammatic techniques, such as the nonequilibrium Green’s function. We implement the TCL approach for the resonant level model driven away from equilibrium and compare the time scales for the decay of the generator with that of the memory kernel in the TC approach. Furthermore, the effects of temperature, source-drain bias, and gate potential on the TCL/TC generators are discussed
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...
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.
International Nuclear Information System (INIS)
In our country, in last congresses, Gomez et al carried out reactivity calculations based on the solution of the diffusion equation for an energy group using nodal methods in one dimension and the TPL approach (Lineal Perturbation Theory). Later on, Mugica extended the application to the case of multigroup so much so much in one as in two dimensions (X Y geometry) with excellent results. Presently work is carried out similar calculations but this time based on the solution of the neutron transport equation in X Y geometry using nodal methods and again the TPL approximation. The idea is to provide a calculation method that allows to obtain in quick form the reactivity solving the direct problem as well as the enclosed problem of the not perturbed problem. A test problem for the one that results are provided for the effective multiplication factor is described and its are offered some conclusions. (Author)
Institute of Scientific and Technical Information of China (English)
JingshanTong; GuanghuaGao
1995-01-01
In this paper,a molecular gaaregation function which represents the degree of molecular aggregation is derived based on statistical mechanic method.Then,a trucated virial equation is modified by the molecular aggregation theory.THe propsed extended equation of state gives good representation of the PVT properties of sturated vapors for some strong polar fluids including water,alcohols and carboxylic acid etc.
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.
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.
DEFF Research Database (Denmark)
Lam, Janni Uyen Hoa; Lynge, Elsebeth; Njor, Sisse Helle;
2015-01-01
BACKGROUND: The incidence rates of cervical cancer and the coverage in cervical cancer screening are usually reported by including in the denominator all women from the general population. However, after hysterectomy women are not at risk anymore of developing cervical cancer. Therefore, it makes...... sense to determine the indicators also for the true at-risk populations. We described the frequency of total hysterectomy in Denmark and its impact on the calculated incidence of cervical cancer and the screening coverage. MATERIAL AND METHODS: With data from five Danish population-based registries......, the incidence rate of cervical cancer and the screening coverage for women aged 23-64 years on 31 December 2010 were calculated with and without adjustments for hysterectomies undertaken for reasons other than cervical cancer. They were calculated as the number of cases divided by 1) the total number of woman...
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.
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...
Analytical equation for calculating the adiabatic temperature of the wet-bulb thermometer
Baskakov, A. P.; Rakov, O. A.
2013-03-01
A formula for calculating the adiabatic temperature of the wet-bulb thermometer has been obtained analytically without using the analogy between the heat and mass transfer processes. A comparison of the results of calculations with the use of this formula and formulas of other authors used in the technical literature has been made.
International Nuclear Information System (INIS)
Present article is devoted to application of Tate equation for calculation of thermal conductivity of solutions of sunflower oil and isomer hexane. The dependence of thermal conductivity of sunflower oil solution and isomer hexane on temperature was considered. The thermal conductivity of sunflower oil depending on mass concentration of isomer hexane at temperature ranges 290-410 K and pressure ranges 0.101-49.1 Mpa was studied.
Nguyen, Thanh Lam; Stanton, John F
2015-07-16
In the field of chemical kinetics, the solution of a two-dimensional master equation that depends explicitly on both total internal energy (E) and total angular momentum (J) is a challenging problem. In this work, a weak-E/fixed-J collisional model (i.e., weak-collisional internal energy relaxation/free-collisional angular momentum relaxation) is used along with the steady-state approach to solve the resulting (simplified) two-dimensional (E,J)-grained master equation. The corresponding solutions give thermal rate constants and product branching ratios as functions of both temperature and pressure. We also have developed a program that can be used to predict and analyze experimental chemical kinetics results. This expedient technique, when combined with highly accurate potential energy surfaces, is cable of providing results that may be meaningfully compared to experiments. The reaction of singlet oxygen with methane proceeding through vibrationally excited methanol is used as an illustrative example. PMID:25815602
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...
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.
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.
Boundary integral equation method calculations of surface regression effects in flame spreading
Altenkirch, R. A.; Rezayat, M.; Eichhorn, R.; Rizzo, F. J.
1982-01-01
A solid-phase conduction problem that is a modified version of one that has been treated previously in the literature and is applicable to flame spreading over a pyrolyzing fuel is solved using a boundary integral equation (BIE) method. Results are compared to surface temperature measurements that can be found in the literature. In addition, the heat conducted through the solid forward of the flame, the heat transfer responsible for sustaining the flame, is also computed in terms of the Peclet number based on a heated layer depth using the BIE method and approximate methods based on asymptotic expansions. Agreement between computed and experimental results is quite good as is agreement between the BIE and the approximate results.
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.
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.
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)
Karimi, F.; Davoody, A. H.; Knezevic, I.
2016-05-01
We introduce a method for calculating the dielectric function of nanostructures with an arbitrary band dispersion and Bloch wave functions. The linear response of a dissipative electronic system to an external electromagnetic field is calculated by a self-consistent-field approach within a Markovian master-equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations. The SCF-MMEF accurately accounts for several concurrent scattering mechanisms. The method captures interband electron-hole-pair generation, as well as the interband and intraband electron scattering with phonons and impurities. We employ the SCF-MMEF to calculate the dielectric function, complex conductivity, and loss function for supported graphene. From the loss-function maximum, we obtain plasmon dispersion and propagation length for different substrate types [nonpolar diamondlike carbon (DLC) and polar SiO2 and hBN], impurity densities, carrier densities, and temperatures. Plasmons on the two polar substrates are suppressed below the highest surface phonon energy, while the spectrum is broad on the nonpolar DLC. Plasmon propagation lengths are comparable on polar and nonpolar substrates and are on the order of tens of nanometers, considerably shorter than previously reported. They improve with fewer impurities, at lower temperatures, and at higher carrier densities.
de Urquijo, Jaime; Basurto, E.; Juarez, A. M.; Ness, Kevin; Robson, Robert; Brunger, Michael; White, Ron
2014-10-01
The drift velocity of electrons in mixtures of gaseous water with helium and argon are measured over the range of reduced electric fields from 0--300 Td using a pulsed-Townsend technique. Small admixtures of water to both helium and argon are found to produce negative differential conductivity (NDC), despite NDC being absent from the pure gases. Comparison of the measured drift velocities with those calculated from a multi-term solution of Boltzmann's equation provides a further discriminative assessment on the accuracy and completeness of electron water vapour cross-sections. Funding acknowledgements: ARC, Mexican govt (PAPIIT IN 111014).
Song, Linze; Shi, Qiang
2015-11-21
Based on recent findings in the hierarchical equations of motion (HEOM) for correlated initial state [Y. Tanimura, J. Chem. Phys. 141, 044114 (2014)], we propose a new stochastic method to obtain the initial conditions for the real time HEOM propagation, which can be used further to calculate the equilibrium correlation functions and symmetrized correlation functions. The new method is derived through stochastic unraveling of the imaginary time influence functional, where a set of stochastic imaginary time HEOM are obtained. The validity of the new method is demonstrated using numerical examples including the spin-Boson model, and the Holstein model with undamped harmonic oscillator modes. PMID:26590526
Energy Technology Data Exchange (ETDEWEB)
Song, Linze; Shi, Qiang, E-mail: qshi@iccas.ac.cn [Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190 (China)
2015-11-21
Based on recent findings in the hierarchical equations of motion (HEOM) for correlated initial state [Y. Tanimura, J. Chem. Phys. 141, 044114 (2014)], we propose a new stochastic method to obtain the initial conditions for the real time HEOM propagation, which can be used further to calculate the equilibrium correlation functions and symmetrized correlation functions. The new method is derived through stochastic unraveling of the imaginary time influence functional, where a set of stochastic imaginary time HEOM are obtained. The validity of the new method is demonstrated using numerical examples including the spin-Boson model, and the Holstein model with undamped harmonic oscillator modes.
First-Principles Equation of State Calculations of Warm Dense Nitrogen
Driver, K P
2016-01-01
Using path integral Monte Carlo (PIMC) and density functional molecular dynamics (DFT-MD) simulation methods, we compute a coherent equation of state (EOS) of nitrogen that spans the liquid, warm dense matter (WDM), and plasma regimes. Simulations cover a wide range of density-temperature space, $1.5-13.9$~g$~$cm$^{-3}$ and $10^3-10^9$~K. In the molecular dissociation regime, we extend the pressure-temperature phase diagram beyond previous studies, providing dissociation and Hugoniot curves in good agreement with experiments and previous DFT-MD work. Analysis of pair-correlation functions and the electronic density of states in the WDM regime reveals an evolving plasma structure and ionization process that is driven by temperature and pressure. Our Hugoniot curves display a sharp change in slope in the dissociation regime and feature two compression maxima as the K and L shells are ionized in the WDM regime, which have some significant differences from the predictions of plasma models.
3He(d,p)4He reaction calculation with three-body Faddeev equations
International Nuclear Information System (INIS)
In order to investigate the 3He-n-p system as a three-body problem, we have formulated 3He-n and 3H-p effective potentials using both a microscopic treatment and a phenomenological approach. In the microscopic treatment, potentials are generated by means of the resonating group method (RGM) based on the Minnesota nucleon-nucleon potential. These potentials are converted into separable form by means of the microscopic Pauli correct (MPC) method. The MPC potentials are properly formulated to avoid Pauli forbidden states. The phenomenological potentials are obtained by modifying parameters of the EST approximation to the Paris nucleon-nucleon potential, such that they fit the low-energy 3He-n, 3H-p, and 3He-p phase shifts. Therefore, they describe the 3He-n differential cross section, the polarization observables, and the energy levels of 4He. The 3He-n-p Faddeev equations are solved numerically. We reproduce correctly the ground state and the first excited state of 5Li. Furthermore, the Paris-type potential is used to investigate the 3He(d,p)4He reaction at a deuteron bombarding energy of 270 MeV, where the system is treated as a three-body problem. Results for the polarized and unpolarized differential cross sections demonstrate convergence of the Born series. (orig.)
Figueredo, Grazziela P.; Peer-Olaf Siebers; Owen, Markus R.; Jenna Reps; Uwe Aickelin
2014-01-01
There is great potential to be explored regarding the use of agent-based modelling and simulation as an alternative paradigm to investigate early-stage cancer interactions with the immune system. It does not suffer from some limitations of ordinary differential equation models, such as the lack of stochasticity, representation of individual behaviours rather than aggregates and individual memory. In this paper we investigate the potential contribution of agent-based modelling and simulation w...
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).
Calculated methods for table diagnosis of lung cancer metastases to regional lymph nodes
International Nuclear Information System (INIS)
The literary data and the author's material (132 patients with peripheral lung cancer and 112 patients with central lung cancer) are used to develop a technique for calculated table diagnosis of lung cancer metastases to regional lymph nodes. The results of table diagnostics are compared with therapeutic and computer diagnostics. The above technique improves the diagnostics of lung cancer metastases to regional lymph nodes by 20%. However, the results of table diagnostics of metastases are somewhat worse (2.8-4.4 %) than those of computer diagnosis. 5 refs.; 3 tabs
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.
International Nuclear Information System (INIS)
This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs
Energy Technology Data Exchange (ETDEWEB)
Johansson, Lisa
2003-07-01
Low-frequency, long-range sound propagation over a sea surface has been calculated using a wide-angel Cranck-Nicholson Parabolic Equation method. The model is developed to investigate noise from off-shore wind turbines. The calculations are made using normal meteorological conditions of the Baltic Sea. Special consideration has been made to a wind phenomenon called low level jet with strong winds on rather low altitude. The effects of water waves on sound propagation have been incorporated in the ground boundary condition using a boss model. This way of including roughness in sound propagation models is valid for water wave heights that are small compared to the wave length of the sound. Nevertheless, since only low frequency sound is considered, waves up to the mean wave height of the Baltic Sea can be included in this manner. The calculation model has been tested against benchmark cases and agrees well with measurements. The calculations show that channelling of sound occurs at downwind conditions and that the sound propagation tends towards cylindrical spreading. The effects of the water waves are found to be fairly small.
Tissue heterogeneity in IMRT dose calculation for lung cancer.
Pasciuti, Katia; Iaccarino, Giuseppe; Strigari, Lidia; Malatesta, Tiziana; Benassi, Marcello; Di Nallo, Anna Maria; Mirri, Alessandra; Pinzi, Valentina; Landoni, Valeria
2011-01-01
The aim of this study was to evaluate the differences in accuracy of dose calculation between 3 commonly used algorithms, the Pencil Beam algorithm (PB), the Anisotropic Analytical Algorithm (AAA), and the Collapsed Cone Convolution Superposition (CCCS) for intensity-modulated radiation therapy (IMRT). The 2D dose distributions obtained with the 3 algorithms were compared on each CT slice pixel by pixel, using the MATLAB code (The MathWorks, Natick, MA) and the agreement was assessed with the γ function. The effect of the differences on dose-volume histograms (DVHs), tumor control, and normal tissue complication probability (TCP and NTCP) were also evaluated, and its significance was quantified by using a nonparametric test. In general PB generates regions of over-dosage both in the lung and in the tumor area. These differences are not always in DVH of the lung, although the Wilcoxon test indicated significant differences in 2 of 4 patients. Disagreement in the lung region was also found when the Γ analysis was performed. The effect on TCP is less important than for NTCP because of the slope of the curve at the level of the dose of interest. The effect of dose calculation inaccuracy is patient-dependent and strongly related to beam geometry and to the localization of the tumor. When multiple intensity-modulated beams are used, the effect of the presence of the heterogeneity on dose distribution may not always be easily predictable. PMID:20970989
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)
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.
Lamah, C. A.; Harris, W. L.
1983-01-01
A novel analytical-numerical method for calculating unsteady small disturbance transonic flow over airfoils has been developed. The method uses an extended integral equation technique, based on both the velocity potential and the acceleration potential, to predict unsteady aerodynamic loading on airfoils oscillating in subcritical transonic free stream conditions. The formulation is an extension of the work of Sivaneri and Harris (1980) for steady, non-lifting flows and utilizes the linear theory of Landahl (1961) for decoupling of steady and unsteady components. The analytical-numerical procedure involves several intnegrating schemes and applies to general frequencies of oscillations. The technique is illustrated by computing the transonic flow about parabolic arc airfoils. Specific unsteady results for reduced frequencies based on semi-chord of 0.01, 0.1, 0.3, 0.4 and 0.6 are given. Comparison of results with those obtained by an ADI finite difference scheme is made.
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.
Goffin, Mark A.; Baker, Christopher M. J.; Buchan, Andrew G.; Pain, Christopher C.; Eaton, Matthew D.; Smith, Paul N.
2013-06-01
This article presents a method for goal-based anisotropic adaptive methods for the finite element method applied to the Boltzmann transport equation. The neutron multiplication factor, k, is used as the goal of the adaptive procedure. The anisotropic adaptive algorithm requires error measures for k with directional dependence. General error estimators are derived for any given functional of the flux and applied to k to acquire the driving force for the adaptive procedure. The error estimators require the solution of an appropriately formed dual equation. Forward and dual error indicators are calculated by weighting the Hessian of each solution with the dual and forward residual respectively. The Hessian is used as an approximation of the interpolation error in the solution which gives rise to the directional dependence. The two indicators are combined to form a single error metric that is used to adapt the finite element mesh. The residual is approximated using a novel technique arising from the sub-grid scale finite element discretisation. Two adaptive routes are demonstrated: (i) a single mesh is used to solve all energy groups, and (ii) a different mesh is used to solve each energy group. The second method aims to capture the benefit from representing the flux from each energy group on a specifically optimised mesh. The k goal-based adaptive method was applied to three examples which illustrate the superior accuracy in criticality problems that can be obtained.
Directory of Open Access Journals (Sweden)
Muhammad Saiedullah
2015-01-01
Full Text Available Background: Friedewald’s formula (FF is used worldwide to calculate low-density lipoprotein cholesterol (LDL-chol. But it has several shortcomings: overestimation at lower triglyceride (TG concentrations and underestimation at higher concentrations. In FF, TG to very low-density lipoprotein cholesterol (VLDL-chol ratio (TG/VLDL-chol is considered as constant, but practically it is not a fixed value. Recently, by analyzing lipid profiles in a large population, continuously adjustable values of TG/VLDL-chol were used to derive a novel method (NM for the calculation of LDL-chol. Objective: The aim of this study was to evaluate the performance of the novel method compared with direct measurement and regression equation (RE developed for Bangladeshi population. Materials and Methods: In this cross-sectional comparative study we used lipid profiles of 955 adult Bangladeshi subjects. Total cholesterol (TC, TG, HDL-chol and LDL-chol were measured by direct methods using automation. LDL-chol was also calculated by NM and RE. LDL-chol calculated by NM and RE were compared with measured LDL-chol by twotailed paired t test, Pearson’s correlation test, bias against measured LDL-chol by Bland-Altman test, accuracy within ±5% and ±12% of measured LDL-chol and by inter-rater agreements with measured LDL-chol at different cut-off values. Results: The mean values of LDL-chol were 110.7 ± 32.0 mg/dL for direct measurement, 111.9 ± 34.8 mg/dL for NM and 113.2 ± 31.7 mg/dL for RE. Mean values of calculated LDL-chol by both NM and RE differed from that of measured LDL-chol (p130 mg/dL were 0.816 vs 0.815, 0.637 vs 0.649 and 0.791 vs 0.791 for NM and RE respectively. Conclusion: This study reveals that NM and RE developed for Bangladeshi population have similar performance and can be used for the calculation of LDL-chol.
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. PMID:21895161
International Nuclear Information System (INIS)
Gabal Allouga area is located some 40 km due east from Abu Zenima town on the east coast of the Gulf of Suez, West-Central Sinai, Egypt. A network of exploratory tunnels totaling 670m in length and approximately 2x2 m in cross section, were excavated within a paleosol clayey bed. They host (Fe, Mn)-, Cu-, and U-mineralizations. Portions of the tunnels are naturally ventilated and others portions are non-ventilated and show ground water seepage through fractures. Model equations were developed for calculating the Rn-gas concentrations in the air of the tunnels under dry conditions where Rn-gas transport is mainly by air flow through porous media as well as for wet conditions where Rn-gas transport is mainly by ground water flow into the tunnels. Under dry conditions the model calculated Rn-gas concentrations(15.2-60.6 PCi/1) are consistent with measured values by active techniques (3.26-22.85 pCi/1) and by SSNTD techniques (19-69.1 pCi/1) when the Rn-emanation coefficient (alpha= 0.05-0.2), the emanating rock thickness (X=10 cm) and U-concentration averages 30 ppm. Under wet and non-ventilated conditions the model calculated Rn-gas concentrations (159-1248 pCi/1) are consistent with the measured values by active techniques (231-1348 pCi/1) and by SSNTD techniques (144-999pCi/1), when the Rn-emanation coefficient (alpha=0.1-0.25), the ground water flow (F=0.04-0.10 ml/s-1cm-2) and U-concertrations (100-250ppm)
International Nuclear Information System (INIS)
External linking scripts between Monte Carlo transport codes and burnup codes, and complete integration of burnup capability into Monte Carlo transport codes, have been or are currently being developed. Monte Carlo linked burnup methodologies may serve as an excellent benchmark for new deterministic burnup codes used for advanced systems; however, there are some instances where deterministic methodologies break down (i.e., heavily angularly biased systems containing exotic materials without proper group structure) and Monte Carlo burn up may serve as an actual design tool. Therefore, researchers are also developing these capabilities in order to examine complex, three-dimensional exotic material systems that do not contain benchmark data. Providing a reference scheme implies being able to associate statistical errors to any neutronic value of interest like k(eff), reaction rates, fluxes, etc. Usually in Monte Carlo, standard deviations are associated with a particular value by performing different independent and identical simulations (also referred to as 'cycles', 'batches', or 'replicas'), but this is only valid if the calculation itself is not biased. And, as will be shown in this paper, there is a bias in the methodology that consists of coupling transport and depletion codes because Bateman equations are not linear functions of the fluxes or of the reaction rates (those quantities being always measured with an uncertainty). Therefore, we have to quantify and correct this bias. This will be achieved by deriving an unbiased minimum variance estimator of a matrix exponential function of a normal mean. The result is then used to propose a reference scheme to solve Boltzmann/Bateman coupled equations, thanks to Monte Carlo transport codes. Numerical tests will be performed with an ad hoc Monte Carlo code on a very simple depletion case and will be compared to the theoretical results obtained with the reference scheme. Finally, the statistical error propagation
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.
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Epifanovsky, Evgeny [Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (United States); Department of Chemistry, University of California, Berkeley, California 94720 (United States); Q-Chem Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588 (United States); Klein, Kerstin; Gauss, Jürgen [Institut für Physikalische Chemie, Universität Mainz, D-55099 Mainz (Germany); Stopkowicz, Stella [Department of Chemistry, Centre for Theoretical and Computational Chemistry, University of Oslo, N-0315 Oslo (Norway); Krylov, Anna I. [Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (United States)
2015-08-14
We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results.
Epifanovsky, Evgeny; Klein, Kerstin; Stopkowicz, Stella; Gauss, Jürgen; Krylov, Anna I.
2015-08-01
We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results.
International Nuclear Information System (INIS)
We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results
Tetervin, Neal; Lin, Chia Chiao
1951-01-01
A general integral form of the boundary-layer equation, valid for either laminar or turbulent incompressible boundary-layer flow, is derived. By using the experimental finding that all velocity profiles of the turbulent boundary layer form essentially a single-parameter family, the general equation is changed to an equation for the space rate of change of the velocity-profile shape parameter. The lack of precise knowledge concerning the surface shear and the distribution of the shearing stress across turbulent boundary layers prevented the attainment of a reliable method for calculating the behavior of turbulent boundary layers.
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.
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 WWWW of Part 63 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR...
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.
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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.
Calculation of the equation of state of a dense hydrogen plasma by the Feynman path integral method
International Nuclear Information System (INIS)
A method is developed for calculating the equation of state of a system of quantum particles at a finite temperature, based on the Feynman formulation of quantum statistics. A general analytical expression is found for the virial estimator for the kinetic energy of a system with rigid boundaries at a finite pressure. An effective method is developed for eliminating the unphysical singularity in the electrostatic potential between a discretized Feynman path of an electron and a proton. It is shown that the 'refinement' of an expansion of a quantum-mechanical propagator by addition of high powers of time exacerbates, rather than eliminates, the divergence of a Feynman path integral. A brief summary of the current status of the problem is presented. The proposed new approaches are presented in relation to progress made in this field. Path integral Monte Carlo simulations are performed for nonideal hydrogen plasmas in which both indistinguishability and spin of electrons are taken into account under conditions preceding the formation of the electron shells of atoms. The electron permutation symmetry is represented in terms of Young operators. It is shown that, owing to the singularity of the Coulomb potential, quantum effects on the behavior of the electron component cannot be reduced to small corrections even if the system must be treated as a classical system according to the formal de Broglie criterion. Quantum-mechanical delocalization of electrons substantially weakens the repulsion between electrons as compared to protons. In relatively cold plasmas, many-body correlations lead to complex behavior of the potential of the average force between particles and give rise to repulsive forces acting between protons and electrons at distances of about 5 angstroms. Plasma pressure drops with decreasing plasma temperature as the electron shells of atoms begin to form, and the electron kinetic energy reaches a minimum at a temperature of about 31,000 K. The minimum point
A clinical study of lung cancer dose calculation accuracy with Monte Carlo simulation
International Nuclear Information System (INIS)
The accuracy of dose calculation is crucial to the quality of treatment planning and, consequently, to the dose delivered to patients undergoing radiation therapy. Current general calculation algorithms such as Pencil Beam Convolution (PBC) and Collapsed Cone Convolution (CCC) have shortcomings in regard to severe inhomogeneities, particularly in those regions where charged particle equilibrium does not hold. The aim of this study was to evaluate the accuracy of the PBC and CCC algorithms in lung cancer radiotherapy using Monte Carlo (MC) technology. Four treatment plans were designed using Oncentra Masterplan TPS for each patient. Two intensity-modulated radiation therapy (IMRT) plans were developed using the PBC and CCC algorithms, and two three-dimensional conformal therapy (3DCRT) plans were developed using the PBC and CCC algorithms. The DICOM-RT files of the treatment plans were exported to the Monte Carlo system to recalculate. The dose distributions of GTV, PTV and ipsilateral lung calculated by the TPS and MC were compared. For 3DCRT and IMRT plans, the mean dose differences for GTV between the CCC and MC increased with decreasing of the GTV volume. For IMRT, the mean dose differences were found to be higher than that of 3DCRT. The CCC algorithm overestimated the GTV mean dose by approximately 3% for IMRT. For 3DCRT plans, when the volume of the GTV was greater than 100 cm3, the mean doses calculated by CCC and MC almost have no difference. PBC shows large deviations from the MC algorithm. For the dose to the ipsilateral lung, the CCC algorithm overestimated the dose to the entire lung, and the PBC algorithm overestimated V20 but underestimated V5; the difference in V10 was not statistically significant. PBC substantially overestimates the dose to the tumour, but the CCC is similar to the MC simulation. It is recommended that the treatment plans for lung cancer be developed using an advanced dose calculation algorithm other than PBC. MC can accurately
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.
Brown, B.Alex; Schwenk, A.
2014-01-01
We use properties of doubly-magic nuclei and ab-initio calculations of low-density neutron matter to constrain Skyrme equations of state for neutron-rich conditions. All of these properties are consistent with a Skyrme functional form and a neutron-matter equation of state that depends on three parameters. With a reasonable range for the neutron-matter effective mass, the values of the two other Skyrme parameters are well constrained. This leads to predictions for other quantities. The neutro...
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)
International Nuclear Information System (INIS)
In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs
Cannizzaro, Frank E.; Von Lavante, E.; Melson, N. Duane
1988-01-01
A numerical method for solving the isenthalpic form of the Euler equations is developed. The method is based on the concept of flux vector splitting in its implicit form applied to a cell centered finite volume scheme. Approximate factorization is implemented in solving the implicit part of the governing equations. Time marching to a steady state solution requires short computational times due to the relative efficiency of the basic method. Computational times are further reduced by the implementation of multigrid. Results for several basic cases are shown.
Lee, Dong Hoon; Jung, Ha Bum; Park, Jae Won; Kim, Kyu Hyun; Kim, Jongchan; Lee, Seung Hwan; Chung, Byung Ha
2013-01-01
Purpose To access the predictive value of the European Randomized Screening of Prostate Cancer Risk Calculator (ERSPC-RC) and the Prostate Cancer Prevention Trial Risk Calculator (PCPT-RC) in the Korean population. Materials and Methods We retrospectively analyzed the data of 517 men who underwent transrectal ultrasound guided prostate biopsy between January 2008 and November 2010. Simple and multiple logistic regression analysis were performed to compare the result of prostate biopsy. Area u...
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.
Energy Technology Data Exchange (ETDEWEB)
Sutton, R.P.; Farshad, F.F.
1983-09-01
An evaluation of utilising the Peng-Robinson Equation of State to perform the PVT calculations required for pressure-gradient calculations in oil and gas-condensate wells is presented. The evaluation is made using a total of 50 well tests representing 30 different wellstream molar compositions. Twenty-five of the fluid systems are gas-condensates with liquid yields ranging from 5 to 194 bbls/MMcf. The remaining five compositions are from black-oil fluid systems with gas-oil ratios ranging from 481 to 2,026 scf/bbl. The compositional and well-test data are summarised in Tables 3 and 4. Multiphase flow pressure-gradient (MFPG) calculations were made using nine well-known correlations. PVT properties required by these correlations were derived using compositional and more traditional methods. The results of the calculations were compared with measured data to ascertain the suitability of the various methods for handling PVT calculations along with the overall general applicability of the MFPG correlations. This paper is not intended to provide an in-depth discussion of the various pressure-gradient calculation methods as the information is readily available from several gradient calculations and some general observations made as a result of the calculations.
Kilburn, K H; Warshaw, R H; Thornton, J C; Thornton, K.; Miller, A
1992-01-01
BACKGROUND: Published predicted values for total lung capacity and residual volume are often based on a small number of subjects and derive from different populations from predicted spirometric values. Equations from the only two large studies gave smaller predicted values for total lung capacity than the smaller studies. A large number of subjects have been studied from a population which has already provided predicted values for spirometry and transfer factor for carbon monoxide. METHODS: T...
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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.
Directory of Open Access Journals (Sweden)
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.
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Akasaka, Ryo [Faculty of Humanities, Kyushu Lutheran College, 3-12-16 Kurokami, Kumamoto 860-8520 (Japan)
2009-01-15
The critical point of the water + ammonia mixture was calculated directly from the Helmholtz free energy formulation. The calculation was performed according to the critical point criteria expressed in terms of the derivatives of the Helmholtz free energy with respect to mole numbers. Smooth critical locus linking between the critical points of pure water and ammonia was obtained. The critical locus showed a good agreement with the most reliable experimental data. Simple correlations for the critical temperature, pressure, and molar volume for a given composition were developed. The information obtained in this study is helpful for design and simulation of the cycles using the water + ammonia mixture as working fluid. (author)
Kang, Eunyoung; Park, Sue K; Lee, Jong Won; Kim, Zisun; Noh, Woo-Chul; Jung, Yongsik; Yang, Jung-Hyun; Jung, Sung Hoo; Kim, Sung-Won
2016-05-01
The widely used Western BRCA mutation prediction models underestimated the risk of having a BRCA mutation in Korean breast cancer patients. This study aimed to identify predictive factors for BRCA1/2 mutations and to develop a Korean BRCA risk calculator. The model was constructed by logistic regression model, and it was based on the Korean Hereditary Breast Cancer study, in which 1669 female patients were enrolled between May 2007 and December 2010. A separate data set of 402 patients, who were enrolled from Jan 2011 to August 2012, was used to test the performance of our model. In total, 264 (15.8%) and 67 (16.7%) BRCA mutation carriers were identified in the model and validation set, respectively. Multivariate analysis showed that age at breast cancer diagnosis, bilateral breast cancer, triple-negative breast cancer (TNBC) and the number of relatives with breast or ovarian cancer within third-degree relatives were independent predictors of the BRCA mutation among familial breast cancer patients. An age cancer, both breast and ovarian cancer and TNBC remained significant predictors in non-familial breast cancer cases. Our model was developed based on logistic regression models. The validation results showed no differences between the observed and expected carrier probabilities. This model will be a useful tool for providing genetic risk assessments in Korean populations. PMID:26763880
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.
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.
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.
Brown, B Alex
2013-01-01
We use properties of doubly-magic nuclei and ab-initio calculations of low-density neutron matter to constrain Skyrme equations of state for neutron-rich conditions. All of these properties are consistent with a Skyrme functional form and a neutron-matter equation of state that depends on three parameters. With a reasonable range for the neutron-matter effective mass, the values of the two other Skyrme parameters are well constrained. This leads to predictions for other quantities. The neutron skins for $^{208}$Pb and $^{48}$Ca are predicted to be 0.182(10) fm and 0.173(5) fm, respectively. Other results including the dipole polarizability are discussed.
Energy Technology Data Exchange (ETDEWEB)
Han Tao; Followill, David; Repchak, Roman; Molineu, Andrea; Howell, Rebecca; Salehpour, Mohammad [Department of Radiation Physics, University of Texas MD Anderson Cancer Center, Houston, Texas 77030 (United States); Mikell, Justin [Department of Radiation Physics, the University of Texas MD Anderson Cancer Center, Houston, Texas 77030 (United States); University of Texas Graduate School of Biomedical Sciences at Houston, Houston, Texas 77030 (United States); Mourtada, Firas [Department of Radiation Physics, the University of Texas MD Anderson Cancer Center, Houston, Texas 77030 (United States); Department of Radiation Oncology, Christiana Care Health System, Newark, Delaware 19713 (United States)
2013-05-15
Purpose: The novel deterministic radiation transport algorithm, Acuros XB (AXB), has shown great potential for accurate heterogeneous dose calculation. However, the clinical impact between AXB and other currently used algorithms still needs to be elucidated for translation between these algorithms. The purpose of this study was to investigate the impact of AXB for heterogeneous dose calculation in lung cancer for intensity-modulated radiation therapy (IMRT) and volumetric-modulated arc therapy (VMAT). Methods: The thorax phantom from the Radiological Physics Center (RPC) was used for this study. IMRT and VMAT plans were created for the phantom in the Eclipse 11.0 treatment planning system. Each plan was delivered to the phantom three times using a Varian Clinac iX linear accelerator to ensure reproducibility. Thermoluminescent dosimeters (TLDs) and Gafchromic EBT2 film were placed inside the phantom to measure delivered doses. The measurements were compared with dose calculations from AXB 11.0.21 and the anisotropic analytical algorithm (AAA) 11.0.21. Two dose reporting modes of AXB, dose-to-medium in medium (D{sub m,m}) and dose-to-water in medium (D{sub w,m}), were studied. Point doses, dose profiles, and gamma analysis were used to quantify the agreement between measurements and calculations from both AXB and AAA. The computation times for AAA and AXB were also evaluated. Results: For the RPC lung phantom, AAA and AXB dose predictions were found in good agreement to TLD and film measurements for both IMRT and VMAT plans. TLD dose predictions were within 0.4%-4.4% to AXB doses (both D{sub m,m} and D{sub w,m}); and within 2.5%-6.4% to AAA doses, respectively. For the film comparisons, the gamma indexes ({+-}3%/3 mm criteria) were 94%, 97%, and 98% for AAA, AXB{sub Dm,m}, and AXB{sub Dw,m}, respectively. The differences between AXB and AAA in dose-volume histogram mean doses were within 2% in the planning target volume, lung, heart, and within 5% in the spinal cord
Directory of Open Access Journals (Sweden)
Mitchell Schulte
2009-06-01
Full Text Available The citric acid cycle (CAC is the central pathway of energy transfer for many organisms, and understanding the origin of this pathway may provide insight into the origins of metabolism. In order to assess the thermodynamics of this key pathway for microorganisms that inhabit a wide variety of environments, especially those found in high temperature environments, we have calculated the properties and parameters for the revised Helgeson-Kirkham-Flowers equation of state for the major components of the CAC. While a significant amount of data is not available for many of the constituents of this fundamental pathway, methods exist that allow estimation of these missing data.
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.
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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
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.
International Nuclear Information System (INIS)
Volume property is the necessary thermodynamic property in the design and operation of the CO2 capture and storage system (CCS). Because of their simple structures, cubic equations of state (EOS) are preferable to be applied in predicting volumes for engineering applications. This paper evaluates the reliabilities of seven cubic EOS, including PR, PT, RK, SRK, MPR, MSRK and ISRK for predicting volumes of binary CO2 mixtures containing CH4, H2S, SO2, Ar and N2, based on the comparisons with the collected experimental data. Results show that for calculations on the volume properties of binary CO2 mixtures, PR and PT are generally superior to others for all of the studied mixtures. In addition, it was found that the binary interaction parameter has clear effects on the calculating accuracy of an EOS in the volume calculations of CO2 mixtures. In order to improve the accuracy, kij was calibrated for all of the EOS regarding the gas and liquid phases of all the studied binary CO2 mixtures, respectively.
Armour, E. A. G.; Plummer, M.
2016-08-01
In a previous paper (2010 Phys. Rev. A 82 042702; 2014 Phys. Rev. A 89 069901(E)), one of us (EAGA) calculated the resonant contribution to {Z}{eff}({k}0), the effective number of electrons available for annihilation by a positron with wave number k 0, in the scattering of a heavy positron by H2. The mass of the positron was increased just sufficiently for a bound state to occur. This calculation was carried out using the Kohn variational method. An alternative method is to use the close-coupled equations for the system under consideration. We compare our results with those obtained by Gribakin and Lee (2006 Phys. Rev. Lett. 97 193201). There is a resonant contribution to {Z}{eff}({k}0) from the vibrationally excited quasibound state which may be described by a Breit–Wigner resonance formula arising naturally from the close-coupling analysis if a certain additional assumption is made. There is also a separate resonant contribution to {Z}{eff}({k}0) from the open channel function influenced by the quasibound state, and a cross term. It is shown that the contribution from the quasibound state is very similar to the expression for the resonant contribution obtained by Gribakin and Lee. Comparison is made with other treatments, for example, the close-coupling calculation of Nishimura and Gianturco (2003 Phys. Rev. Lett. 90 183201).
International Nuclear Information System (INIS)
Isothermal-isobaric Monte Carlo calculations were used to obtain predictions of the elastic coefficients and derived engineering moduli and Poisson ratios for crystalline hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX). The elastic coefficients were computed using the strain fluctuation formula due to Rahman and Parrinello [J. Chem. Phys. 76, 2662 (1982)]. Calculations were performed as a function of temperature (218 K≤T≤333 K) and hydrostatic pressure (0 GPa≤p≤4 GPa). The predicted values of the moduli and Poisson ratios under ambient conditions are in accord with general expectations for molecular crystals and with a very recent, unpublished determination for RDX. The moduli exhibit a sensitive pressure dependence whereas the Poisson ratios are relatively independent of pressure. The temperature dependence of the moduli is comparable to the precision of the results. However, the crystal does exhibit thermal softening for most pressures. An additional product of the calculations is information about the pressure-volume-temperature (pVT) equation of state. We obtain near-quantitative agreement with experiment for the case of hydrostatic compression and reasonable, but not quantitative, correspondence for thermal expansion. The results indicate a significant dependence of the thermal expansion coefficients on hydrostatic pressure. (c) 2000 American Institute of Physics
A new equation for calculation of static loss of drilling fluid%一种新的钻井液静失水量方程
Institute of Scientific and Technical Information of China (English)
许晓琳; 乌效鸣; 杜晶
2013-01-01
It is found out that the viscosity of the remaining drilling fluid is higher than before the API loss test was taken. To explain this phenomenon, the paper presents a different opinion about the filtration mode used in the derivation of equation for calculation of static loss of drilling fluid, and derived a new equation based on a new fil-tration mode, which can explain the phenomenon. According to this new equation, twice of the result of 7.5 min test can replace that of the 30 min test in the API loss test.%实验室测试钻井液的 API 失水量结束后，仪器内剩余钻井液的粘度比测试前有所增大。为了解释这一现象，对原钻井液静失水量方程推导中所采用的渗滤模式提出了不同看法，以一种不同的渗滤模式为基础提出了新的钻井液静失水量方程，此方程可以解释这一现象。依照此方程，实验室测试API失水量时仍然可用7.5 min失水量的测试结果乘以2得到的数值代替30 min失水量的测试结果。
Equation of State of Solid Neon from Quantum Calculation%固氖高压物态方程的量子理论计算
Institute of Scientific and Technical Information of China (English)
武娜; 田春玲; 刘福生; 匡安农; 袁宏宽; 郑兴荣
2012-01-01
The interaction energy for fcc-neon-crystals at high pressure is calculated by Hartree-Fock method and the atomic cluster theory. The two- and three-body contributions to the static energy are also studied. Incorporating the influence of the zero-point vibration, the equations of state of fcc neon are calculated and compared with the available experimental 300 K isotherm up to the pressure of 208 GPa. It demonstrates that the calculated isotherm is in good agreement with measurements at pressures above 30 GPa. Compared with the recent predictions, the calculated results systematically improve the 300 K isotherm by 3%-5% between 100 and 210 GPa, and imply more static energyvolume relation at high pressure.%运用Hartree-Fock计算方法和原子团簇理论，研究了高压下面心立方晶体氖中的二体相互作用、三体相互作用对中心原子势能及冷能的贡献。结合零点振动能，计算得到了固氖在4～208GPa压强范围内的等温物态方程。结果表明，在较高压强区域内，等温压缩线与高压实验数据符合得非常好；在压强超过100GPa的区域内，计算得到的等温压缩线较目前已有的理论研究结果系统地改善并提高了3％～5％，精确地解释了固氖的高压实验数据。
Institute of Scientific and Technical Information of China (English)
刘晖; 王昱凯
2015-01-01
The accuracy of saturated steam and liquid volume calculations for R134a were compared, which was used by four general cubic equations of state:the SRK equation, the PR equation, the Tong Jingshan equation and the Su Zhijun equation.Calculations showed that in the range of -50 ~90 ℃, the Tong Jingshan equation had the least calculation error, average deviation of saturated gas volume and liquid volume calculation values and literature values were 1.63%and 4.12%, average deviation of the PR equation's calculation values and literature values were 1.90% and 4.76%, average deviation of the SRK equation had the largest error, it's calculation values and literature values were 3.35%and 18.64%, average deviation of the Su Zhijun equation was basically the same as the PR equation, it's calculation values and literature values were 2.00% and 5.21%.The results showed that for R134a, the calculation of Tong Jingshan equation was more accurate, and it was more suitable for engineering calculations for R134a's Thermodynamic properties.%比较了SRK方程， PR方程，童景山方程和苏志军方程4个通用立方型状态方程用于R134a饱和气、液的体积计算准确度。计算表明，在－50～90℃的范围内，童景山方程的计算偏差最小，饱和气与饱和液体积的计算值与文献值的平均偏差为1.63％和4.12％； PR方程的计算平均偏差为1.90％和4.76％； SRK方程平均偏差最大，为3.35％和18.64％；苏志军方程的计算偏差与PR方程基本相同，为2.00％和5.21％。结果表明，对于R134a来说，童景山方程的计算结果更加精确，更适合用于R134a热力性质的工程计算。
Directory of Open Access Journals (Sweden)
Peiman Haddad
2014-02-01
Conclusion: In this study, the mean testis dose of radiation was 3.77 Gy, similar to the dose calculated by the planning software (4.11 Gy. This dose could be significantly harmful for spermatogenesis, though low doses of scattered radiation to the testis in fractionated radiotherapy might be followed with better recovery. Based on above findings, careful attention to testicular dose in radiotherapy of rectal cancer for the males desiring continued fertility seems to be required.
International Nuclear Information System (INIS)
The ill-posedness degree for the controllability of the one-dimensional heat equation by a Dirichlet boundary control is the purpose of this work. This problem is severely (or exponentially) ill-posed. We intend to shed more light on this assertion and the underlying mathematics. We start by discussing the framework liable to fit an efficient numerical implementation without introducing further complications into the theoretical analysis. Afterward we expose the Fourier calculations that transform the ill-posedness issue to the one related to linear algebra. This consists of investigating the singular values of some infinite structured matrices that are obtained as sums of Cauchy matrices. Utilising the Gershgorin–Hadamard theorem and the Collatz–Wielandt formula, we are able to provide the lower and upper bounds for the largest singular value of these matrices. After checking whether they are also solutions of some symmetric Lyapunov (or Sylvester) equations with a very low displacement rank, we use an estimate that improves Penzl's former result to bound the ratio's smaller/largest singular values of these matrices. Accordingly, the controllability problem is confirmed to be severely ill-posed. The bounds proved here will be supported by computations made using Matlab procedures. At last, the well-known explicit inverse of Cauchy-type matrices allows us to provide a formal exponential series representation of the Dirichlet control in a long horizon controllability. That series has to be checked afterward to discover whether it is convergent or not and to find out if the desired state can be reached. Here again, some examples ran within Matlab will be discussed and commented upon
Dekker, N.; Hermens, R.P.M.G.; Elwyn, G.; Weijden, G.D.E.M. van der; Nagengast, F.M.; Duijvendijk, P. van; Salemink, S.; Adang, E.M.M.; Krieken, J.H.J.M. van; Ligtenberg, M.J.L.; Hoogerbrugge-van der Linden, N.
2010-01-01
BACKGROUND: Individuals with multiple relatives with colorectal cancer (CRC) and/or a relative with early-onset CRC have an increased risk of developing CRC. They are eligible for preventive measures, such as surveillance by regular colonoscopy and/or genetic counselling. Currently, most at-risk ind
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".
Wilson, Nick; Selak, Vanessa; Blakely, Tony; Leung, William; Clarke, Philip; Jackson, Rod
2016-03-11
Based on new systematic reviews of the evidence, the US Preventive Services Task Force has drafted updated guidelines on the use of low-dose aspirin for the primary prevention of both cardiovascular disease (CVD) and cancer. The Task Force generally recommends consideration of aspirin in adults aged 50-69 years with 10-year CVD risk of at least 10%, in who absolute health gain (reduction of CVD and cancer) is estimated to exceed absolute health loss (increase in bleeds). With the ongoing decline in CVD, current risk calculators for New Zealand are probably outdated, so it is difficult to be precise about what proportion of the population is in this risk category (roughly equivalent to 5-year CVD risk ≥5%). Nevertheless, we suspect that most smokers aged 50-69 years, and some non-smokers, would probably meet the new threshold for taking low-dose aspirin. The country therefore needs updated guidelines and risk calculators that are ideally informed by estimates of absolute net health gain (in quality-adjusted life-years (QALYs) per person) and cost-effectiveness. Other improvements to risk calculators include: epidemiological rigour (eg, by addressing competing mortality); providing enhanced graphical display of risk to enhance risk communication; and possibly capturing the issues of medication disutility and comparison with lifestyle changes. PMID:27005878
Energy Technology Data Exchange (ETDEWEB)
Hu, Chih-Chung [National Taiwan Univ. Hospital and College of Medicine, Taipei (China). Division of Radiation Oncology; Yuanpei Univ., Hsinchu (China). Dept. of Radiological Technology; Huang, Wen-Tao [Yuanpei Univ., Hsinchu (China). Dept. of Radiological Technology; Tsai, Chiao-Ling; Chao, Hsiao-Ling; Huang, Guo-Ming; Wang, Chun-Wei [National Taiwan Univ. Hospital and College of Medicine, Taipei (China). Division of Radiation Oncology; Wu, Jian-Kuen [National Taiwan Univ. Hospital and College of Medicine, Taipei (China). Division of Radiation Oncology; National Taiwan Normal Univ., Taipei (China). Inst. of Electro-Optical Science and Technology; Wu, Chien-Jang [National Taiwan Normal Univ., Taipei (China). Inst. of Electro-Optical Science and Technology; Cheng, Jason Chia-Hsien [National Taiwan Univ. Hospital and College of Medicine, Taipei (China). Division of Radiation Oncology; National Taiwan Univ. Taipei (China). Graduate Inst. of Oncology; National Taiwan Univ. Taipei (China). Graduate Inst. of Clinical Medicine; National Taiwan Univ. Taipei (China). Graduate Inst. of Biomedical Electronics and Bioinformatics
2011-10-15
On-line cone-beam computed tomography (CBCT) may be used to reconstruct the dose for geometric changes of patients and tumors during radiotherapy course. This study is to establish a practical method to modify the CBCT for accurate dose calculation in head and neck cancer. Fan-beam CT (FBCT) and Elekta's CBCT were used to acquire images. The CT numbers for different materials on CBCT were mathematically modified to match them with FBCT. Three phantoms were scanned by FBCT and CBCT for image uniformity, spatial resolution, and CT numbers, and to compare the dose distribution from orthogonal beams. A Rando phantom was scanned and planned with intensity-modulated radiation therapy (IMRT). Finally, two nasopharyngeal cancer patients treated with IMRT had their CBCT image sets calculated for dose comparison. With 360 acquisition of CBCT and high-resolution reconstruction, the uniformity of CT number distribution was improved and the otherwise large variations for background and high-density materials were reduced significantly. The dose difference between FBCT and CBCT was < 2% in phantoms. In the Rando phantom and the patients, the dose-volume histograms were similar. The corresponding isodose curves covering {>=} 90% of prescribed dose on FBCT and CBCT were close to each other (within 2 mm). Most dosimetric differences were from the setup errors related to the interval changes in body shape and tumor response. The specific CBCT acquisition, reconstruction, and CT number modification can generate accurate dose calculation for the potential use in adaptive radiotherapy.
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.
A clinical study of lung cancer dose calculation accuracy with Monte Carlo simulation
Zhao, Yanqun; Qi, Guohai; Yin, Gang; Wang, Xianliang; Wang, Pei; Li, Jian; Xiao, Mingyong; Li, Jie; Kang, Shengwei; Liao, Xiongfei
2014-01-01
Background The accuracy of dose calculation is crucial to the quality of treatment planning and, consequently, to the dose delivered to patients undergoing radiation therapy. Current general calculation algorithms such as Pencil Beam Convolution (PBC) and Collapsed Cone Convolution (CCC) have shortcomings in regard to severe inhomogeneities, particularly in those regions where charged particle equilibrium does not hold. The aim of this study was to evaluate the accuracy of the PBC and CCC alg...
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
Directory of Open Access Journals (Sweden)
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
Gleim, Tobias
2006-01-01
There exists a Klein-Gordon-like equation for a spin-1/2 particle in an electromagnetic field with 2-spinors as wave functions that is a direct consequence of the corresponding Dirac equation. Thus, it reproduces the same binding energies for an electron in a hydrogen atom as the Dirac equation. There is also a square-root equation for 2-spinors which can give the same binding energies up to the forth order of the fine structure constant, inclusively, what will be shown by means of a comparis...
International Nuclear Information System (INIS)
There was a problem with using MU verification programs for the reasons that there were errors of MU when using MU verification programs based on Pencil Beam Convolution (PBC) Algorithm with radiation treatment plans around lung using Analytical Anisotropic Algorithm (AAA). On this study, we studied the methods that can verify the calculated treatment plans using AAA. Using Eclipse treatment planning system (Version 8.9, Varian, USA), for each 57 fields of 7 cases of Lung Stereotactic Body Radiation Therapy (SBRT), we have calculated using PBC and AAA with dose calculation algorithm. By developing MU of established plans, we compared and analyzed with MU of manual calculation programs. We have analyzed relationship between errors and 4 variables such as field size, lung path distance of radiation, Tumor path distance of radiation, effective depth that can affect on errors created from PBC algorithm and AAA using commonly used programs. Errors of PBC algorithm have showned 0.2±1.0% and errors of AAA have showned 3.5±2.8%. Moreover, as a result of analyzing 4 variables that can affect on errors, relationship in errors between lung path distance and MU, connection coefficient 0.648 (P=0.000) has been increased and we could calculate MU correction factor that is A.E=L.P 0.00903+0.02048 and as a result of replying for manual calculation program, errors of 3.5±2.8% before the application has been decreased within 0.4±2.0%. On this study, we have learned that errors from manual calculation program have been increased as lung path distance of radiation increases and we could verified MU of AAA with a simple method that is called MU correction factor.
International Nuclear Information System (INIS)
Regional contraction work (RCW) of left ventricle (LV) was evaluated from cardiac perfusion images of ECG-gated single photon emission computed tomography (ECG-SPECT). The mechanical work was computed as a product of force and displaced distance. Force was determined from Laplace's law under a rectangle pressure. Deformation of wireframe representing LV was calculated from equations of continuity for two-dimensional fluids. Experiments were performed with homemade life-sized cardiac models. Total contraction work (TCW) and stroke work (SW) were 524.0 ± 166.1 mJ/beat and 709.8 ± 169.5 mJ/beat, respectively, in normal subjects (n = 23). Moderate correlation was seen between TCW and SW (y = −43.4 + 0.779 x, r = 0.815). The regional contraction amplitude (RCA), synchronous contraction index and RCW were 35.4 ± 3.5%, 95.4 ± 3.1% and 5.58 ± 0.97 mJ cm−2/beat in normal subjects, whereas those in patients with decreased ejection raction (EF) ≤ 30% (n = 6) were 19.6 ± 7.7%, 64.4 ± 32.2% and 2.58 ± 0.82 mJ cm−2/beat (p < 0.0001, Student's t-test). There was a poor correlation between RCW and RCA (y = 1.648 ± 0.116 x, r = 0.501) in normal subjects, suggesting that it might not be suitable to use RCA as an alternative to evaluate RCW. (paper)
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.
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.
International Nuclear Information System (INIS)
This study describes initial testing and evaluation of a vertical-field open Magnetic Resonance Imaging (MRI) scanner for the purpose of simulation in radiation therapy for prostate cancer. We have evaluated the clinical workflow of using open MRI as a sole modality for simulation and planning. Relevant results related to MRI alignment (vs. CT) reference dataset with Cone-Beam CT (CBCT) for daily localization are presented. Ten patients participated in an IRB approved study utilizing MRI along with CT simulation with the intent of evaluating the MRI-simulation process. Differences in prostate gland volume, seminal vesicles, and penile bulb were assessed with MRI and compared to CT. To evaluate dose calculation accuracy, bulk-density-assignments were mapped onto respective MRI datasets and treated IMRT plans were re-calculated. For image localization purposes, 400 CBCTs were re-evaluated with MRI as the reference dataset and daily shifts compared against CBCT-to-CT registration. Planning margins based on MRI/CBCT shifts were computed using the van Herk formalism. Significant organ contour differences were noted between MRI and CT. Prostate volumes were on average 39.7% (p = 0.002) larger on CT than MRI. No significant difference was found in seminal vesicle volumes (p = 0.454). Penile bulb volumes were 61.1% higher on CT, without statistical significance (p = 0.074). MRI-based dose calculations with assigned bulk densities produced agreement within 1% with heterogeneity corrected CT calculations. The differences in shift positions for the cohort between CBCT-to-CT registration and CBCT-to-MRI registration are −0.15 ± 0.25 cm (anterior-posterior), 0.05 ± 0.19 cm (superior-inferior), and −0.01 ± 0.14 cm (left-right). This study confirms the potential of using an open-field MRI scanner as primary imaging modality for prostate cancer treatment planning simulation, dose calculations and daily image localization
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.
Directory of Open Access Journals (Sweden)
Bassem Elshahat
2015-09-01
Full Text Available Purpose: Boron neutron capture therapy (BNCT is a promising technique for the treatment of malignant disease targeting organs of the human body. Monte Carlo simulations were carried out to calculate optimum design parameters of an accelerator based beam shaping assembly (BSA for BNCT of brain cancer setup.Methods: Epithermal beam of neutrons were obtained through moderation of fast neutrons from 3H(p,n reaction in a high density polyethylene moderator and a graphite reflector. The dimensions of the moderator and the reflector were optimized through optimization of epithermal / fast neutron intensity ratio as a function of geometric parameters of the setup. Results: The results of our calculation showed the capability of our setup to treat the tumor within 4 cm of the head surface. The calculated peak therapeutic ratio for the setup was found to be 2.15. Conclusion: With further improvement in the polyethylene moderator design and brain phantom irradiation arrangement, the setup capabilities can be improved to reach further deep-seated tumor.
Devpura, S.; Siddiqui, M. S.; Chen, D.; Liu, D.; Li, H.; Kumar, S.; Gordon, J.; Ajlouni, M.; Movsas, B.; Chetty, I. J.
2014-03-01
The purpose of this study was to systematically evaluate dose distributions computed with 5 different dose algorithms for patients with lung cancers treated using stereotactic ablative body radiotherapy (SABR). Treatment plans for 133 lung cancer patients, initially computed with a 1D-pencil beam (equivalent-path-length, EPL-1D) algorithm, were recalculated with 4 other algorithms commissioned for treatment planning, including 3-D pencil-beam (EPL-3D), anisotropic analytical algorithm (AAA), collapsed cone convolution superposition (CCC), and Monte Carlo (MC). The plan prescription dose was 48 Gy in 4 fractions normalized to the 95% isodose line. Tumors were classified according to location: peripheral tumors surrounded by lung (lung-island, N=39), peripheral tumors attached to the rib-cage or chest wall (lung-wall, N=44), and centrally-located tumors (lung-central, N=50). Relative to the EPL-1D algorithm, PTV D95 and mean dose values computed with the other 4 algorithms were lowest for "lung-island" tumors with smallest field sizes (3-5 cm). On the other hand, the smallest differences were noted for lung-central tumors treated with largest field widths (7-10 cm). Amongst all locations, dose distribution differences were most strongly correlated with tumor size for lung-island tumors. For most cases, convolution/superposition and MC algorithms were in good agreement. Mean lung dose (MLD) values computed with the EPL-1D algorithm were highly correlated with that of the other algorithms (correlation coefficient =0.99). The MLD values were found to be ~10% lower for small lung-island tumors with the model-based (conv/superposition and MC) vs. the correction-based (pencil-beam) algorithms with the model-based algorithms predicting greater low dose spread within the lungs. This study suggests that pencil beam algorithms should be avoided for lung SABR planning. For the most challenging cases, small tumors surrounded entirely by lung tissue (lung-island type), a Monte
Anti-cancer properties of green Tea Probed viaquantum mechanics calculations
Directory of Open Access Journals (Sweden)
Azin Chitsazan
2015-03-01
Full Text Available 10.13005/ojc/310147Tea, from the plant camellia sinensis, is consumed in different parts of the world as green, black or oolong tea. Among all of these, however, the most significant effects on human health have been observed with the consumption of green tea. Green tea contains polyphenols, which include flavanols, flavandiols, flavonoids, and phenolic acids. Most of the green tea polyphenols (GTPs are flavonols, commonly known as catechins. There are four kinds of catechins mainly find in green tea: epicatechin, epigallocatechin, epicatechin-3-gallate, and EGCG. Green tea catechins have demonstrated significant antioxidant, anticarcinogenic, anti-inflammatory, thermogenic, probiotic, and antimicrobial properties in numerous human, animal, and in vitro studies. In the present study, four type catechins of green tea were studied. For each catechin ab initio method was employed for calculations and related parameters were computed.
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.
Steyerl, A.; Kaufman, C.; Müller, G.; Malik, S. S.; Desai, A. M.; Golub, R.
2014-05-01
Pendlebury etal . [Phys. Rev. A 70, 032102 (2004), 10.1103/PhysRevA.70.032102] were the first to investigate the role of geometric phases in searches for an electric dipole moment (EDM) of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in general fields and in bounded geometries. We solve the Schrödinger equation directly for cylindrical trap geometry and obtain a full description of EDM-relevant spin behavior in general fields, including the short-time transients and vertical spin oscillation in the entire range of particle velocities. We apply this method to general macroscopic fields and to the field of a microscopic magnetic dipole.
Fahy, G. M.
1980-01-01
Slowly frozen cells are said to be subject to solution effects injury. An understanding of the mechanism of solution effects injury depends upon an understanding of the compositional changes brought about in the extracellular solution during the freezing process. To facilitate analysis of the mechanisms of freezing injury during slow cooling, empirical equations have been developed which permit a description of these changes in composition for the NaCl-dimethylsulfoxide-water ternary system a...
Steyerl, A.; Kaufman, C.; Müller, G.; Malik, S. S.; Desai, A. M.; Golub, R.
2014-01-01
Pendlebury $\\textit{et al.}$ [Phys. Rev. A $\\textbf{70}$, 032102 (2004)] were the first to investigate the role of geometric phases in searches for an electric dipole moment (EDM) of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in gene...
Energy Technology Data Exchange (ETDEWEB)
Schopohl, N.
1980-11-01
On the basis of Gorkov's formulation of superconductivity theory, generalized Eilenberger equations are derived which apply to rotating superfluid /sup 3/He in the presence of a magnetic field h and finite superflow v. In analyogy to conventional type II superconductors, the possibility of vortex solutions in discussed. An implicit equation determining the upper critical angular velocity ..cap omega../sub c/2 as a function of temperature T, magnetic field h, and superflow v parallel to the rotation axis is-inferred from the linearized Eilenberger equations. In contrast to the case of slowly rotating /sup 3/He-A, the solution of the eigenvalue problem determining the order parameter ..delta.. near the the upper critical angular velocity admits no coreless vortex no coreless solutions. The space-dependent amplitude of the order parameter is analogous to Abrikosov's vortex array solution, while the spin-orbit part is given either by a polar-state type or an Anderson-Brinkman-Morel (ABM)-state-type eigensolution. Among the possible eigensolutions the polar-state type yields for vanishing superflow v the highest critical rotation frequency. For finite superflow v parallel to the rotation axis, however, the ABM-state-type solution is stabilized in comparison to the polar state for Vertical BarvVertical Bar> or approx. =0.2..pi..(Tc/sub c/0/T/sub F/)v/sub f/ at zero temperature.
International Nuclear Information System (INIS)
Cardiac procedures are among the most common procedures in interventional radiology (IR), and can lead to high medical and occupational exposures, as in most cases are procedures complex and long lasting. In this work, conversion coefficients (CC) for the risk of cancer, normalized by kerma area product (KAP) to the patient, cardiologist and nurse were calculated using Monte Carlo simulation. The patient and the cardiologist were represented by anthropomorphic simulators MESH, and the nurse by anthropomorphic phantom FASH. Simulators were incorporated into the code of Monte Carlo MCNPX. Two scenarios were created: in the first (1), lead curtain and protective equipment suspended were not included, and in the second (2) these devices were inserted. The radiographic parameters employed in Monte Carlo simulations were: tube voltage of 60 kVp and 120 kVp; filtration of the beam and 3,5 mmAl beam area of 10 x 10 cm2. The average values of CCs to eight projections (in 10-4 / Gy.cm2 were 1,2 for the patient, 2,6E-03 (scenario 1) and 4,9E-04 (scenario 2) for cardiologist and 5,2E-04 (scenario 1) and 4,0E-04 (Scenario 2) to the nurse. The results show a significant reduction in CCs for professionals, when the lead curtain and protective equipment suspended are employed. The evaluation method used in this work can provide important information on the risk of cancer patient and professional, and thus improve the protection of workers in cardiac procedures of RI
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)
王双进; 李凌云; 张建
2011-01-01
An amendment to the original Master equation was put forward, and a mechanism for node increases was introduced. The modified Master equation was of discreteness, which was more accurate, more efficient to calculate the evolution law of degree distribution of real complex network. The analysis formula of degree distribution of model BA and its calculation by the modified Master equation were discussed. From this. the logarithmic figure of degree distribution of model BA was gotlen. Then a compassion was made between the discrete Master equation and mean - field theory, and logarithmic figure was gotten, that of degree distribution of model BA wich two kinds calculative theory in the same coordinate system.%Master方程是计算无标度网络度分布演化规律的一种常用方法.提出了对原始的Master方程进行修正,加入了节点增长机制,修正后的Master方程具有离散性,能够更精确、更有效的计算真实复杂网络的度分布演化规律.用修正的Master方程分析BA模型度分布的解析武并计算,由此得到BA模型度分布对数图.把离散性的Master方程与连续性的平均场理论进行对比分析,并在同一坐标系下分别做出用两种理论计算的BA模型度分布的对数图.
Institute of Scientific and Technical Information of China (English)
王双进; 李凌云; 李佳
2011-01-01
An amendment to the original Master equation and add a mechanism for node increases is be put for ward. The modified Master equation is of discreteness, which is more accurate, more efficient to calculate the evo lution law of degree distribution of real complex network. The analysis formula of degree distribution of model BA and its calculation by the modified Master equation is discussed. From this we get the logarithmic figure of degree distribution of model BA. Then we make a compassion between the discrete Master equation and mean-field theory, and get logarithmic figure of degree distribution of model BA with two kinds calculative theory in the same coor dinate system.%提出了对原始的Master方程进行修正,加入了节点增长机制,修正后的Master方程具有离散性,能够更精确、更有效地计算真实复杂网络的度分布演化规律.用修正的Master方程分析BA模型度分布的解析式并计算,由此得出BA模型度分布对数图.把离散性的Master方程与连续性的平均场理论进行对比分析,并在同一坐标系下分别作出用2种理论计算的BA模型度分布的对数图.
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)
International Nuclear Information System (INIS)
The results of a previous study giving fecal and urinary excretion curves of five radioelements (cesium 137, cobalt 60, cerium 144, strontium 90, and plutonium 239) after radioactive aerosol inhalation by a man were interpreted. It is tried to draw conclusions on the validity of the theoretical parameters needed for calculating the load and the dose in man
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)
International Nuclear Information System (INIS)
Reviewed is the effect of heat flux of different system parameters on critical density in order to give an initial view on the value of several parameters. A thorough analysis of different equations is carried out to calculate burnout is steam-water flows in uniformly heated tubes, annular, and rectangular channels and rod bundles. Effect of heat flux density distribution and flux twisting on burnout and storage determination according to burnout are commended
DEFF Research Database (Denmark)
Ottosson, Wiviann; Sibolt, Patrik; Larsen, Christina;
2015-01-01
Background and purpose: Studies indicate that Deep-Inspiration Breath-Hold (DIBH) is advantageous over Free-Breathing (FB) for locally advanced lung cancer radiotherapy. However, these studies were based on simplified dose calculation algorithms, potentially critical due to the heterogeneous nature...... of the lung region. Using detailed Monte-Carlo (MC) calculations, a comparative study of DIBH vs. FB was therefore designed. Material and methods: Eighteen locally advanced lung cancer patients underwent FB and DIBH CT imaging and treatment planning with the Anisotropic-Analytical-Algorithm (AAA......) for intensity-modulated-radio therapy or volumetric-modulated-arc-therapy using 66 Gy in 33 fractions. All plans were re-calculated with MC. Results: Relative to FB, the total lung volume increased 86.8% in DIBH, while the gross tumor volume decreased 14.8%. MC revealed equally under- and over...
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.
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
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.
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...
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.
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.
Zhang, L; Weng, M -H
2016-01-01
The matrix element of the weak transition {\\Lambda}_b\\rightarrow{\\Lambda}_c can be expressed in terms of six form factors. {\\Lambda}_Q(Q = b;c) can be regarded as composed of a heavy quark Q(Q = b;c) and a diquark which is made up of the remaining two light quarks. In this picture, we express these six form factors in terms of Bethe-Salpeter wave functions to second order in the 1/m_Q expansion. With the kernel containing both the scalar confinement and the one-gluon-exchange terms we calculate the form factors and the decay widths of the semileptonic decay {\\Lambda}_b\\rightarrow{\\Lambda}_clv as well as nonleptonic decays {\\Lambda}_b\\rightarrow{\\Lambda}_cP(V) numerically. We also add QCD corrections since they are comparable with 1/m_Q corrections.
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.
Piron, R; Blenski, T
2011-02-01
The numerical code VAAQP (variational average atom in quantum plasmas), which is based on a fully variational model of equilibrium dense plasmas, is applied to equation-of-state calculations for aluminum, iron, copper, and lead in the warm-dense-matter regime. VAAQP does not impose the neutrality of the Wigner-Seitz ion sphere; it provides the average-atom structure and the mean ionization self-consistently from the solution of the variational equations. The formula used for the electronic pressure is simple and does not require any numerical differentiation. In this paper, the virial theorem is derived in both nonrelativistic and relativistic versions of the model. This theorem allows one to express the electron pressure as a combination of the electron kinetic and interaction energies. It is shown that the model fulfills automatically the virial theorem in the case of local-density approximations to the exchange-correlation free-energy. Applications of the model to the equation-of-state and Hugoniot shock adiabat of aluminum, iron, copper, and lead in the warm-dense-matter regime are presented. Comparisons with other approaches, including the inferno model, and with available experimental data are given. This work allows one to understand the thermodynamic consistency issues in the existing average-atom models. Starting from the case of aluminum, a comparative study of the thermodynamic consistency of the models is proposed. A preliminary study of the validity domain of the inferno model is also included. PMID:21405914
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.
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.
Adibi, Atoosa; Mortazavi, Mojgan; Shayganfar, Azin; Kamal, Sima; Azad, Roya; Aalinezhad, Marzieh
2016-01-01
It is essential to ascertain the state of health and renal function of potential kidney donors before organ removal. In this regard, one of the primary steps is to estimate the donor's glomerular filtration rate (GFR). For this purpose, the modification of diet in renal disease (MDRD) and the Cockcroft-Gault (CG) formulas has been used. However, these two formulas produce different results and finding new techniques with greater accuracy is required. Measuring the renal volume from computed tomography (CT) scan may be a valuable index to assess the renal function. This study was conducted to investigate the correlation between renal volume and the GFR values in potential living kidney donors referred to the multislice imaging center at Alzahra Hospital during 2014. The study comprised 66 subjects whose GFR was calculated using the two aforementioned formulas. Their kidney volumes were measured by using 64-slice CT angiography and the correlation between renal volume and GFR values were analyzed using the Statistical Package for the Social Science software. There was no correlation between the volume of the left and right kidneys and the MDRD-based estimates of GFR (P = 0.772, r = 0.036, P = 0.251, r = 0.143, respectively). A direct linear correlation was found between the volume of the left and right kidneys and the CG-based GFR values (P = 0.001, r = 0.397, P kidney volume derived from multislice CT scan can help predict the GFR value in kidney donors with normal renal function. The limitations of our study include the small sample size and the medium resolution of 64-slice multislice scanners. Further studies with larger sample size and using higher resolution scanners are warranted to determine the accuracy of this method in potential kidney donors. PMID:27424682
Institute of Scientific and Technical Information of China (English)
无
2004-01-01
At the beginning of 16th century, mathematicians found it easy to solve equations of the first degree(linear equations, involving x) and of the second degree(quadratic equatiorts, involving x2). Equations of the third degree(cubic equations, involving x3)defeated them.
Calculation of Single Scattering Parameters in Vector Radiative Transfer Equation%辐射传输方程中的单次散射参数计算
Institute of Scientific and Technical Information of China (English)
王海华; 孙贤明; 刘万强; 申晋; 刘伟
2011-01-01
Based on Mie theory, the single scattering characteristics of a cluster of polydisperse spherical aerosols are calculated. The size distribution of particles is Gamma distribution and effective radii are 5.56, 7, 11 μm,respectively. The average extinction coefficients, average scattering coefficients, single scattering albedos,asymmetry parameters and elements of single scattering phase matrix in the spectral range of 0.4 ～ 100 μm are analyzed. The numerical results show that the single scattering properties of aerosols are seldom affected by particle effective radius in visual light waveband, but greater at higher waveband. The single scattering albedo approximately equals 1 at visual light waveband and the characteristics of single scattering albedo are opposite to the imagery part of refraction index. The polarization ratios of single scattering phase matrix are more sensitive to particle size than phase functions.%根据米氏(Mie)理论,计算了多分散球形气溶胶粒子的单次散射特性.粒子的尺寸分布为伽马分布,有效半径分别为5.56.7和11 μm,分析了0.4-100 μm光谱范围内气溶胶粒子的平均消光系数、平均散射系数、单次散射反照率、不对称因子以及相矩阵与粒子的尺寸参数以及折射率的关系.结果表明,在可见光波段,粒子的有效半径对粒子的散射特性影响较小,在更长的波段上其影响较大;单次散射反照率在可见光范围内近似为1,随波长的变化和水滴折射率虚部随波长的变化曲线正好相反,这说明影响其大小的主要因素为粒子的折射率,即虚部越大则反照率越小;且极化率对粒子的尺寸比相函数更敏感.
International Nuclear Information System (INIS)
To investigate the effect of computed tomography (CT) using hepatic arterial phase (HAP) and portal venous phase (PVP) contrast on dose calculation of stereotactic body radiation therapy (SBRT) for liver cancer. Twenty-one patients with liver cancer were studied. HAP, PVP and non-enhanced CTs were performed on subjects scanned in identical positions under active breathing control (ABC). SBRT plans were generated using seven-field three-dimensional conformal radiotherapy (7 F-3D-CRT), seven-field intensity-modulated radiotherapy (7 F-IMRT) and single-arc volumetric modulated arc therapy (VMAT) based on the PVP CT. Plans were copied to the HAP and non-enhanced CTs. Radiation doses calculated from the three phases of CTs were compared with respect to the planning target volume (PTV) and the organs at risk (OAR) using the Friedman test and the Wilcoxon signed ranks test. SBRT plans calculated from either PVP or HAP CT, including 3D-CRT, IMRT and VMAT plans, demonstrated significantly lower (p <0.05) minimum absorbed doses covering 98%, 95%, 50% and 2% of PTV (D98%, D95%, D50% and D2%) than those calculated from non-enhanced CT. The mean differences between PVP or HAP CT and non-enhanced CT were less than 2% and 1% respectively. All mean dose differences between the three phases of CTs for OARs were less than 2%. Our data indicate that though the differences in dose calculation between contrast phases are not clinically relevant, dose underestimation (IE, delivery of higher-than-intended doses) resulting from CT using PVP contrast is larger than that resulting from CT using HAP contrast when compared against doses based upon non-contrast CT in SBRT treatment of liver cancer using VMAT, IMRT or 3D-CRT
Institute of Scientific and Technical Information of China (English)
刘艳梅
2015-01-01
Smoothness in order to optimize the differential equations of calculating process, put forward a kind of Laplace transform and the wavelet matching calculate the smoothness of ordinary differential equation solution method and Laplace transform method is used to convert ordinary differential equation (group) to the algebraic equation (group) of complex variable, by some algebraic operation and Laplace transform table, get initial smoothness solution of ordinary differential equations, the arbitrary function expansion ChengXiaoBo basis function, through the fast discrete wavelet transform technology, shape the smoothness of approximate solution of ordinary differential equations, in the process of operation, in wavelet levels, as well as the independent variable interval, using multilayer adaptive method, adaptive and interval section to solve the problems of the long time, ensure in each time period to achieve the required accuracy and smoothness of solution to solve and improve efficiency and accuracy. The result of numerical experiment shows that the proposed method for solving ordinary differential equations of smooth solution accuracy and timeliness is better than the traditional state long time propulsion method.%为了优化常微分方程光滑性解的求取过程，提出一种拉普拉斯变换以及小波匹配的常微分方程光滑性解求取方法，采用拉普拉斯变换方法将常微分方程（组）转换成复变数的代数方程（组），通过一些代数运算和拉普拉斯变换表，获取常微分方程的初始光滑性解，将任意函数展开成小波基函数，通过快速离散小波转换技术，塑造常微分方程的近似光滑性解，在运算过程中，在小波展开层次以及自变量区间，使用多层自适应以及多区间自适应方法，对长时间问题进行分段求解，保证在每个时间段上达到所要求的数值精度，提高光滑性解求解的效率和精度。数值实验结果说
Farhi, Asaf
2016-01-01
An exact calculation of the local electric field ${\\bf E}({\\bf r})$ is described for the case of a time dependent point electric dipole ${\\bf p}e^{-i\\omega t}$ in the top layer of an $\\epsilon_2$, $\\epsilon_1$, $\\epsilon_2$ three parallel slabs composite structure, where the $\\epsilon_1$ layer has a finite thickness $2d$ but the $\\epsilon_2$ layers are infinitely thick. For this purpose we first calculate all the eigenstates of the full Maxwell equations for the case where $\\mu=1$ everywhere in the system. The eigenvalues appear as special, non-physical values of $\\epsilon_1$ when $\\epsilon_2$ is given. These eigenstates are then used to develop an exact expansion for the physical values of ${\\bf E}({\\bf r})$ in the system characterized by physical values of $\\epsilon_1(\\omega)$ and $\\epsilon_2(\\omega)$. Results are compared with those of a previous calculation of the local field of a time dependent point charge in the quasi-static regime. Numerical results are shown for the local electric field in practicall...
Oroji, Amin; Omar, Mohd; Yarahmadian, Shantia
2016-10-21
In this paper, a new mathematical model is proposed for studying the population dynamics of breast cancer cells treated by radiotherapy by using a system of stochastic differential equations. The novelty of the model is essentially in capturing the concept of the cell cycle in the modeling to be able to evaluate the tumor lifespan. According to the cell cycle, each cell belongs to one of three subpopulations G, S, or M, representing gap, synthesis and mitosis subpopulations. Cells in the M subpopulation are highly radio-sensitive, whereas cells in the S subpopulation are highly radio-resistant. Therefore, in the process of radiotherapy, cell death rates of different subpopulations are not equal. In addition, since flow cytometry is unable to detect apoptotic cells accurately, the small changes in cell death rate in each subpopulation during treatment are considered. Subsequently, the proposed model is calibrated using experimental data from previous experiments involving the MCF-7 breast cancer cell line. Consequently, the proposed model is able to predict tumor lifespan based on the number of initial carcinoma cells. The results show the effectiveness of the radiation under the condition of stability, which describes the decreasing trend of the tumor cells population. PMID:27457094
The new pooled cohort equations risk calculator
DEFF Research Database (Denmark)
Preiss, David; Kristensen, Søren L
2015-01-01
In the National Cholesterol Education Program Adult Treatment Panel III guidelines published in 2001, estimation of cardiovascular risk was recommended based on the Framingham score for 10-year risk of myocardial infarction and the Canadian Cardiovascular Society currently recommends the Framingh...
Calculation of wing-body junction flow using Gao-Yong turbulence equations%使用Gao-Yong湍流方程计算翼体角偶流动
Institute of Scientific and Technical Information of China (English)
高歌; 江立军; 高琳
2012-01-01
The derivation of Gao-Yong turbulence equations was based on a partial statistical average scheme proposed in the past by the first author in an attempt to capture the drift flow, a first-order statistical moment of turbulent fluctuations. Continuity and momentum equations of turbulent fluctuations were obtained as a result of this valuable first statistical information. Orthotropic turbulence and momentum transfer chain were formulated in the modeling of correlation terms, eventually, led to a complete set of equations of turbu- lent flow with no empirical coefficients and wall functions. Numerical simulations in the past preliminarily veri- fied the adaptability of Gao-Yong equations to a wide range of complex benchmark turbulent flows. In order to further application of these equations to engineering flows, the Gao-Yong turbulence equations were implemen- ted into OpenFOAM and applied to the calculation of wing-body junction flow. The wing-body junction flow in- volves very complex feathers, such as a 3-D separation and a horseshoe vortex. The results of numerical simu- lation of this flow compared to experimental data show that all these main characteristics have been captured, both qualitatively and quantitatively.%Gao—Yong湍流方程基于侧偏统计平均方法保留了湍流脉动量的一阶统计信息，并引入加权漂移速度对称性及正交各向异性，导出漂移流连续方程、动量方程和机械能方程，最后依据湍流物理的唯象论，使用动量传输链概念模化封闭了整个方程组．大量算例验证了此方程对广泛范围的复杂湍流问题的适定性．为了进一步的工程应用，将其加入开源计算流体力学软件OpenFOAM（OpenFieldOperationandManipulation）中，并就翼体角偶流动进行了数值模拟．翼体角偶流动具有三维分离、马蹄涡等十分复杂的流动特征，通过与实验测量结果的对比研究表明，Gao—Yong湍流方程不论在定性还是定
Directory of Open Access Journals (Sweden)
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
Energy Technology Data Exchange (ETDEWEB)
Zhang, J; Zhang, W; Lu, J [Cancer Hospital of Shantou University Medical College, Shantou, Guangdong (China)
2015-06-15
Purpose: To investigate the accuracy and feasibility of dose calculations using kilovoltage cone beam computed tomography in cervical cancer radiotherapy using a correction algorithm. Methods: The Hounsfield units (HU) and electron density (HU-density) curve was obtained for both planning CT (pCT) and kilovoltage cone beam CT (CBCT) using a CIRS-062 calibration phantom. The pCT and kV-CBCT images have different HU values, and if the HU-density curve of CBCT was directly used to calculate dose in CBCT images may have a deviation on dose distribution. It is necessary to normalize the different HU values between pCT and CBCT. A HU correction algorithm was used for CBCT images (cCBCT). Fifteen intensity-modulated radiation therapy (IMRT) plans of cervical cancer were chosen, and the plans were transferred to the pCT and cCBCT data sets without any changes for dose calculations. Phantom and patient studies were carried out. The dose differences and dose distributions were compared between cCBCT plan and pCT plan. Results: The HU number of CBCT was measured by several times, and the maximum change was less than 2%. To compare with pCT, the CBCT and cCBCT has a discrepancy, the dose differences in CBCT and cCBCT images were 2.48%±0.65% (range: 1.3%∼3.8%) and 0.48%±0.21% (range: 0.1%∼0.82%) for phantom study, respectively. For dose calculation in patient images, the dose differences were 2.25%±0.43% (range: 1.4%∼3.4%) and 0.63%±0.35% (range: 0.13%∼0.97%), respectively. And for the dose distributions, the passing rate of cCBCT was higher than the CBCTs. Conclusion: The CBCT image for dose calculation is feasible in cervical cancer radiotherapy, and the correction algorithm offers acceptable accuracy. It will become a useful tool for adaptive radiation therapy.
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
Directory of Open Access Journals (Sweden)
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.
Energy Technology Data Exchange (ETDEWEB)
Kido, Kentaro, E-mail: kido.kentaro@jaea.go.jp [Nuclear Safety Research Center, Japan Atomic Energy Agency, 2-4 Shirane, Shirakata, Tokai-mura, Naka-gun, Ibaraki 319-1195 (Japan); Kasahara, Kento [Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510 (Japan); Yokogawa, Daisuke [Department of Chemistry, Graduate School of Science, Nagoya University, Chikusa, Nagoya 464-8602 (Japan); Institute of Transformative Bio-Molecules (WPI-ITbM), Nagoya University, Chikusa, Nagoya 464-8062 (Japan); Sato, Hirofumi [Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510 (Japan); Elements Strategy Institute for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520 (Japan)
2015-07-07
In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein–Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple S{sub N}2 reaction (Cl{sup −} + CH{sub 3}Cl → ClCH{sub 3} + Cl{sup −}) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.
Ai, Jinqin; Xie, Tianwu; Sun, Wenjuan; Liu, Qian
2014-04-01
Red bone marrow (RBM) is an important dose-limiting tissue that has high radiosensitivity but is difficult to identify on clinical medical images. In this study, we investigated dose distribution in RBM for prostate cancer radiotherapy. Four suborgans were identified in the skeleton of the visible Chinese human phantom: cortical bone (CB), trabecular bone (TB), RBM, and yellow bone marrow (YBM). Dose distributions in the phantom were evaluated by the Monte Carlo method. When the left os coxae was taken as the organ-at-risk (OAR), the difference in absorbed dose between RBM and each CB and TB was up to 20%, but was much less (≤3.1%) between RBM and YBM. When the left os coxae and entire bone were both taken as OARs, RBM dose also increased with increasing planning target volume size. The results indicate the validity of using dose to homogeneous bone marrow mixture for estimating dose to RBM when RBM is not available in computational phantoms. In addition, the human skeletal system developed in this study provides a model for considering RBM dose in radiotherapy planning.
International Nuclear Information System (INIS)
Red bone marrow (RBM) is an important dose-limiting tissue that has high radiosensitivity but is difficult to identify on clinical medical images. In this study, we investigated dose distribution in RBM for prostate cancer radiotherapy. Four suborgans were identified in the skeleton of the visible Chinese human phantom: cortical bone (CB), trabecular bone (TB), RBM, and yellow bone marrow (YBM). Dose distributions in the phantom were evaluated by the Monte Carlo method. When the left os coxae was taken as the organ-at-risk (OAR), the difference in absorbed dose between RBM and each CB and TB was up to 20%, but was much less (≤3.1%) between RBM and YBM. When the left os coxae and entire bone were both taken as OARs, RBM dose also increased with increasing planning target volume size. The results indicate the validity of using dose to homogeneous bone marrow mixture for estimating dose to RBM when RBM is not available in computational phantoms. In addition, the human skeletal system developed in this study provides a model for considering RBM dose in radiotherapy planning. (paper)
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.
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)
... Blood tests (which look for chemicals such as tumor markers) Bone marrow biopsy (for lymphoma or leukemia) Chest ... the case with skin cancers , as well as cancers of the lung, breast, and colon. If the tumor has spread ...
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 ...
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.
Uncertainty of empirical correlation equations
Feistel, R.; Lovell-Smith, J. W.; Saunders, P.; Seitz, S.
2016-08-01
The International Association for the Properties of Water and Steam (IAPWS) has published a set of empirical reference equations of state, forming the basis of the 2010 Thermodynamic Equation of Seawater (TEOS-10), from which all thermodynamic properties of seawater, ice, and humid air can be derived in a thermodynamically consistent manner. For each of the equations of state, the parameters have been found by simultaneously fitting equations for a range of different derived quantities using large sets of measurements of these quantities. In some cases, uncertainties in these fitted equations have been assigned based on the uncertainties of the measurement results. However, because uncertainties in the parameter values have not been determined, it is not possible to estimate the uncertainty in many of the useful quantities that can be calculated using the parameters. In this paper we demonstrate how the method of generalised least squares (GLS), in which the covariance of the input data is propagated into the values calculated by the fitted equation, and in particular into the covariance matrix of the fitted parameters, can be applied to one of the TEOS-10 equations of state, namely IAPWS-95 for fluid pure water. Using the calculated parameter covariance matrix, we provide some preliminary estimates of the uncertainties in derived quantities, namely the second and third virial coefficients for water. We recommend further investigation of the GLS method for use as a standard method for calculating and propagating the uncertainties of values computed from empirical equations.
Viljamaa, Panu; Jacobs, J. Richard; Chris; JamesHyman; Halma, Matthew; EricNolan; Coxon, Paul
2014-07-01
In reply to a Physics World infographic (part of which is given above) about a study showing that Euler's equation was deemed most beautiful by a group of mathematicians who had been hooked up to a functional magnetic-resonance image (fMRI) machine while viewing mathematical expressions (14 May, http://ow.ly/xHUFi).
Directory of Open Access Journals (Sweden)
Kaveh Shirani Tak Abi
2015-05-01
Full Text Available Introduction Intensity-Modulated Radiotherapy (IMRT is becoming an increasingly routine treatment method. IMRT can be delivered by use of conventional Multileaf Collimators (MLCs and/or physical compensators. One of the most important factors in selecting an appropriate IMRT technique is integral dose. Integral dose is equal to the mean energy deposited in the total irradiated volume of the patient. The aim of the present study was to calculate and compare the integral dose in normal and target organs in two different procedures of IMRT: Step-and-Shoot (SAS and compensator-based IMRT. Materials and Methods In this comparative study, five patients with prostate cancer were selected. Module Integrated Radiotherapy System was applied, using three energy ranges. In both treatment planning methods, the integral dose dramatically decreased by increasing energy. Results Comparison of two treatment methods showed that on average, the integral dose of body in SAS radiation therapy was about 1.62% lower than that reported in compensator-based IMRT. In planning target volume, rectum, bladder, and left and right femoral heads, the integral doses for SAS method were 1.01%, 1.02%, 1.11%, 1.47%, and 1.40% lower than compensator-based IMRT, respectively. Conclusion Considering the treatment conditions, the definition of dose volume constraints for healthy tissues, and the equal volume of organs in both treatment methods, SAS radiation therapy by providing a lower integral dose seems to be more advantageous and efficient for prostate cancer treatment, compared to compensator-based IMRT.
de la Peña-López, Roberto; Remolina-Bonilla, Yuly Andrea
2016-09-01
Cancer is a group of diseases which represents a significant public health problem in Mexico and worldwide. In Mexico neoplasms are the second leading cause of death. An increased morbidity and mortality are expected in the next decades. Several preventable risk factors for cancer development have been identified, the most relevant including tobacco use, which accounts for 30% of the cancer cases; and obesity, associated to another 30%. These factors, in turn, are related to sedentarism, alcohol abuse and imbalanced diets. Some agents are well knokn to cause cancer such as ionizing radiation, viruses such as the papilloma virus (HPV) and hepatitis virus (B and C), and more recently environmental pollution exposure and red meat consumption have been pointed out as carcinogens by the International Agency for Research in Cancer (IARC). The scientific evidence currently available is insufficient to consider milk either as a risk factor or protective factor against different types of cancer. PMID:27603890
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)
Electronic representation of wave equation
Veigend, Petr; Kunovský, Jiří; Kocina, Filip; Nečasová, Gabriela; Šátek, Václav; Valenta, Václav
2016-06-01
The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.
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)
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.
International Nuclear Information System (INIS)
Current practice is to perform a completion axillary lymph node dissection (ALND) for breast cancer patients with tumor-involved sentinel lymph nodes (SLNs), although fewer than half will have non-sentinel node (NSLN) metastasis. Our goal was to develop new models to quantify the risk of NSLN metastasis in SLN-positive patients and to compare predictive capabilities to another widely used model. We constructed three models to predict NSLN status: recursive partitioning with receiver operating characteristic curves (RP-ROC), boosted Classification and Regression Trees (CART), and multivariate logistic regression (MLR) informed by CART. Data were compiled from a multicenter Northern California and Oregon database of 784 patients who prospectively underwent SLN biopsy and completion ALND. We compared the predictive abilities of our best model and the Memorial Sloan-Kettering Breast Cancer Nomogram (Nomogram) in our dataset and an independent dataset from Northwestern University. 285 patients had positive SLNs, of which 213 had known angiolymphatic invasion status and 171 had complete pathologic data including hormone receptor status. 264 (93%) patients had limited SLN disease (micrometastasis, 70%, or isolated tumor cells, 23%). 101 (35%) of all SLN-positive patients had tumor-involved NSLNs. Three variables (tumor size, angiolymphatic invasion, and SLN metastasis size) predicted risk in all our models. RP-ROC and boosted CART stratified patients into four risk levels. MLR informed by CART was most accurate. Using two composite predictors calculated from three variables, MLR informed by CART was more accurate than the Nomogram computed using eight predictors. In our dataset, area under ROC curve (AUC) was 0.83/0.85 for MLR (n = 213/n = 171) and 0.77 for Nomogram (n = 171). When applied to an independent dataset (n = 77), AUC was 0.74 for our model and 0.62 for Nomogram. The composite predictors in our model were the product of angiolymphatic invasion and size of SLN
Directory of Open Access Journals (Sweden)
Johnson Denise L
2008-03-01
Full Text Available Abstract Background Current practice is to perform a completion axillary lymph node dissection (ALND for breast cancer patients with tumor-involved sentinel lymph nodes (SLNs, although fewer than half will have non-sentinel node (NSLN metastasis. Our goal was to develop new models to quantify the risk of NSLN metastasis in SLN-positive patients and to compare predictive capabilities to another widely used model. Methods We constructed three models to predict NSLN status: recursive partitioning with receiver operating characteristic curves (RP-ROC, boosted Classification and Regression Trees (CART, and multivariate logistic regression (MLR informed by CART. Data were compiled from a multicenter Northern California and Oregon database of 784 patients who prospectively underwent SLN biopsy and completion ALND. We compared the predictive abilities of our best model and the Memorial Sloan-Kettering Breast Cancer Nomogram (Nomogram in our dataset and an independent dataset from Northwestern University. Results 285 patients had positive SLNs, of which 213 had known angiolymphatic invasion status and 171 had complete pathologic data including hormone receptor status. 264 (93% patients had limited SLN disease (micrometastasis, 70%, or isolated tumor cells, 23%. 101 (35% of all SLN-positive patients had tumor-involved NSLNs. Three variables (tumor size, angiolymphatic invasion, and SLN metastasis size predicted risk in all our models. RP-ROC and boosted CART stratified patients into four risk levels. MLR informed by CART was most accurate. Using two composite predictors calculated from three variables, MLR informed by CART was more accurate than the Nomogram computed using eight predictors. In our dataset, area under ROC curve (AUC was 0.83/0.85 for MLR (n = 213/n = 171 and 0.77 for Nomogram (n = 171. When applied to an independent dataset (n = 77, AUC was 0.74 for our model and 0.62 for Nomogram. The composite predictors in our model were the product of
Non RG logarithms via RG equations
Malyshev, Dmitry
2004-01-01
We compute complete leading logarithms in $\\Phi^4$ theory with the help of Connes and Kreimer RG equations. These equations are defined in the Lie algebra dual to the Hopf algebra of graphs. The results are compared with calculations in parquet approximation. An interpretation of the new RG equations is discussed.
Kilgour, Robert D; Cardiff, Katrina; Rosenthall, Leonard; Lucar, Enriqueta; Trutschnigg, Barbara; Vigano, Antonio
2016-01-01
Measurements of body composition using dual-energy X-ray absorptiometry (DXA) and single abdominal images from computed tomography (CT) in advanced cancer patients (ACP) have important diagnostic and prognostic value. The question arises as to whether CT scans can serve as surrogates for DXA in terms of whole-body fat-free mass (FFM), whole-body fat mass (FM), and appendicular skeletal muscle (ASM) mass. Predictive equations to estimate body composition for ACP from CT images have been proposed (Mourtzakis et al. 2008; Appl. Physiol. Nutr. Metabol. 33(5): 997-1006); however, these equations have yet to be validated in an independent cohort of ACP. Thus, this study evaluated the accuracy of these equations in estimating FFM, FM, and ASM mass using CT images at the level of the third lumbar vertebrae and compared these values with DXA measurements. FFM, FM, and ASM mass were estimated from the prediction equations proposed by Mourtzakis and colleagues (2008) using single abdominal CT images from 43 ACP and were compared with whole-body DXA scans using Spearman correlations and Bland-Altman analyses. Despite a moderate to high correlation between the actual (DXA) and predicted (CT) values for FM (rho = 0.93; p ≤ 0.001), FFM (rho = 0.78; p ≤ 0.001), and ASM mass (rho = 0.70; p ≤ 0.001), Bland-Altman analyses revealed large range-of-agreement differences between the 2 methods (29.39 kg for FFM, 15.47 kg for FM, and 3.99 kg for ASM mass). Based on the magnitude of these differences, we concluded that prediction equations using single abdominal CT images have poor accuracy, cannot be considered as surrogates for DXA, and may have limited clinical utility. PMID:26695688
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)
Relativistic shell model calculations
Furnstahl, R. J.
1986-06-01
Shell model calculations are discussed in the context of a relativistic model of nuclear structure based on renormalizable quantum field theories of mesons and baryons (quantum hadrodynamics). The relativistic Hartree approximation to the full field theory, with parameters determined from bulk properties of nuclear matter, predicts a shell structure in finite nuclei. Particle-hole excitations in finite nuclei are described in an RPA calculation based on this QHD ground state. The particle-hole interaction is prescribed by the Hartree ground state, with no additional parameters. Meson retardation is neglected in deriving the RPA equations, but it is found to have negligible effects on low-lying states. The full Dirac matrix structure is maintained throughout the calculation; no nonrelativistic reductions are made. Despite sensitive cancellations in the ground state calculation, reasonable excitation spectra are obtained for light nuclei. The effects of including charged mesons, problems with heavy nuclei, and prospects for improved and extended calculations are discussed.
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.
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
Calculation of two Belyi pairs
Dremov, V. A.
2008-01-01
We calculate two Belyi pairs using the properties of Mulase-Penkava differential. Details are provided including accurate construction of coordinates, variables and equations. The calculation is a part of the work which results in a catalogue arXiv:0710.2658
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
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.
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.
DEFF Research Database (Denmark)
Petersen, Kurt Erling
1986-01-01
approaches have been introduced in some cases for the calculation of the reliability of structures or components. A new computer program has been developed based upon numerical integration in several variables. In systems reliability Monte Carlo simulation programs are used especially in analysis of very...... complex systems. In order to increase the applicability of the programs variance reduction techniques can be applied to speed up the calculation process. Variance reduction techniques have been studied and procedures for implementation of importance sampling are suggested....
International Nuclear Information System (INIS)
In 1977, Dave Young published an equation-of-state (EOS) for lithium. This EOS was used by Lew Glenn in his AFTON calculations of the HYLIFE inertial-fusion-reactor hydrodynamics. In this paper, I summarize Young's development of the EOS and demonstrate a computer program (MATHSY) that plots isotherms, isentropes and constant energy lines on a P-V diagram
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.
KUCHIDA, Keigo; Kono, S.; KONISHI, Kazuyuki; Van, Vleck LD; SUZUKI, Mitsuyoshi; Miyoshi, Syunzou; 口田, 圭吾; 小西, 一之; 鈴木, 三義; 三好, 俊三
2000-01-01
Crude fat content of longissimus (ribeye) muscle of beef cattle was predicted from a ratio of fat area (RFA) to area of ribeye muscle calculated from computer image analysis (CIA). Cross sections of 64 ribeyes taken from the 6-7(th) rib from cattle at experiment station A and cross sections of 94 ribeyes taken from the 6-7(th) rib from cattle at Experiment Station B were used in this study. Slices (1 to 1.5 cm in thickness) of just the Longissimus dorsi were homogenized and sampled for chemic...
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.
Quadratic field equations on the brane
International Nuclear Information System (INIS)
It is shown that four-dimensional vacuum Einstein solutions simply embedded in five dimensions obey the Gauss-Bonnet-Einstein field equations: Gab+ αGBab + δ55abαexp[-2χ/√α]GB4 = 0 and the Pauli-Einstein equations Gab - 3αPab/5 = 0, and the Bach-Einstein equations Bab = 0. General equations are calculated for which these and similar results follow. It is briefly argued that such field equations could be significant on large distance scales.
Institute of Scientific and Technical Information of China (English)
洪迎春; 谷波; 韩华
2011-01-01
Based on the Martin-Hou equation of state,a fast calculation model for R410a thermodynamic and transport properties,covering superheat region（pressure：4—4 355 kPa,superheating of 0—100 K）,was presented due to no need of iteration.This method can not only achieve the accuracy,but guarantee the calculation stability and high calculation speed of thermophysical and transport properties of R410a,and it is also convenient in cases of simulation of refrigeration system.The source data was calculated from REFPROP 7.The total mean relative error and maximum relative error for all fast calculation models are less than 1.24% and 14.30%,respectively.The comparison result shows that the calculation speed of the fast calculation model is two to four orders faster than those of REFPROP 7.%在Martin-Hou方程的基础上,提出了R410a制冷剂在过热区（压力4~4 355 kPa,过热度0~100 K）的热力学性能参数和传输特性参数的计算模型,以REFPROP 7的数据源作为原始数据,在过热区范围内对R410a制冷剂的热力学性能参数进行拟合,并将该模型的计算结果与REF-PROP 7数据源进行对比.结果表明,所提出的显式计算模型的平均误差小于1.24%,最大误差小于14.30%,计算速度比REFPROP 7提高了2~4个数量级.
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.
Institute of Scientific and Technical Information of China (English)
张学义; 谭红梅; 肖汝诚; 柴生波
2014-01-01
The main cable was treated as springs in considering its constraint on the tower .The for-mula of the longitudinal constraint stiffness of springs was derived by variational method based on cat-enary equation ,and a finite element model was established for verification .The results show that the tower stiffness formula based on catenary has higher accuracy ;the cable spring stiffness is mainly re-lated to the unit length weight of the bridge as well as the horizontal and vertical components of the main cable in the overhead of the mid-tower ,while the unstressed length of the main cable is deter-mined .%以悬链线方程为基础，将主缆对桥塔的约束等效为弹簧，通过变分方法推导了主缆对多塔悬索桥中塔纵向弹簧约束刚度的表达式，并建立有限元模型对公式进行验证。研究结果表明：基于悬链线的中塔刚度公式比已有文献具有更高的精度，在主缆无应力长度确定的情况下，主缆弹簧刚度主要与荷载集度、主缆在塔顶的水平及竖向分力有关。
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.
A New Route to the Majorana Equation
Directory of Open Access Journals (Sweden)
Eckart Marsch
2013-09-01
Full Text Available In this paper, we suggest an alternative strategy to derive the complex two-component Majorana equation with a mass term and elucidate the related Lorentz transformation. The Majorana equation is established completely on its own, rather than derived from the chiral Dirac equation. Thereby, use is made of the complex conjugation operator and Pauli spin matrices only. The eigenfunctions of the two-component complex Majorana equation are also calculated. The associated quantum fields are found to describe particles and antiparticles, which have opposite mean helicities and are not their own antiparticles, but correspond to two independent degrees of freedom. The four-component real Dirac equation in its Majorana representation is shown to be the natural outcome of the two-component complex Majorana equation. Both types of equations come in two forms, which correspond to the irreducible left- and right-chiral representations of the Lorentz group.
Recent calculational work at Department of Reactor Physics CTH
International Nuclear Information System (INIS)
Short presentations are given on various ANISN calculations, on studies of the Xe reactivity effect, on some Monte Carlo calculations, and on benchmark calculations of eigenvalues to the Boltzmann transport equation. (author)
Calculations of turbulent separated flows
Zhu, J.; Shih, T. H.
1993-01-01
A numerical study of incompressible turbulent separated flows is carried out by using two-equation turbulence models of the K-epsilon type. On the basis of realizability analysis, a new formulation of the eddy-viscosity is proposed which ensures the positiveness of turbulent normal stresses - a realizability condition that most existing two-equation turbulence models are unable to satisfy. The present model is applied to calculate two backward-facing step flows. Calculations with the standard K-epsilon model and a recently developed RNG-based K-epsilon model are also made for comparison. The calculations are performed with a finite-volume method. A second-order accurate differencing scheme and sufficiently fine grids are used to ensure the numerical accuracy of solutions. The calculated results are compared with the experimental data for both mean and turbulent quantities. The comparison shows that the present model performs quite well for separated flows.
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Pennington, A; Selvaraj, R; Kirkpatrick, S; Oliveira, S [21st Century Oncology, Deerfield Beach, FL (United States); Leventouri, T [Florida Atlantic University, Boca Raton, FL (United States)
2014-06-01
Purpose: The latest publications indicate that the Ray Tracing algorithm significantly overestimates the dose delivered as compared to the Monte Carlo (MC) algorithm. The purpose of this study is to quantify this overestimation and to identify significant correlations between the RT and MC calculated dose distributions. Methods: Preliminary results are based on 50 preexisting RT algorithm dose optimization and calculation treatment plans prepared on the Multiplan treatment planning system (Accuray Inc., Sunnyvale, CA). The analysis will be expanded to include 100 plans. These plans are recalculated using the MC algorithm, with high resolution and 1% uncertainty. The geometry and number of beams for a given plan, as well as the number of monitor units, is constant for the calculations for both algorithms and normalized differences are compared. Results: MC calculated doses were significantly smaller than RT doses. The D95 of the PTV was 27% lower for the MC calculation. The GTV and PTV mean coverage were 13 and 39% less for MC calculation. The first parameter of conformality, as defined as the ratio of the Prescription Isodose Volume to the PTV Volume was on average 1.18 for RT and 0.62 for MC. Maximum doses delivered to OARs was reduced in the MC plans. The doses for 1000 and 1500 cc of total lung minus PTV, respectively were reduced by 39% and 53% for the MC plans. The correlation of the ratio of air in PTV to the PTV with the difference in PTV coverage had a coefficient of −0.54. Conclusion: The preliminary results confirm that the RT algorithm significantly overestimates the dosages delivered confirming previous analyses. Finally, subdividing the data into different size regimes increased the correlation for the smaller size PTVs indicating the MC algorithm improvement verses the RT algorithm is dependent upon the size of the PTV.
Difference equations by differential equation methods
Hydon, Peter E
2014-01-01
Most well-known solution techniques for differential equations exploit symmetry in some form. Systematic methods have been developed for finding and using symmetries, first integrals and conservation laws of a given differential equation. Here the author explains how to extend these powerful methods to difference equations, greatly increasing the range of solvable problems. Beginning with an introduction to elementary solution methods, the book gives readers a clear explanation of exact techniques for ordinary and partial difference equations. The informal presentation is suitable for anyone who is familiar with standard differential equation methods. No prior knowledge of difference equations or symmetry is assumed. The author uses worked examples to help readers grasp new concepts easily. There are 120 exercises of varying difficulty and suggestions for further reading. The book goes to the cutting edge of research; its many new ideas and methods make it a valuable reference for researchers in the field.
Alternative to the Kohn-Sham equations: The Pauli potential differential equation
Levämäki, H.; Nagy, Á.; Kokko, K.; Vitos, L.
2015-12-01
A recently developed theoretical framework of performing self-consistent orbital-free (OF) density functional theory (DFT) calculations at Kohn-Sham DFT level accuracy is tested in practice. The framework is valid for spherically symmetric systems. Numerical results for the Beryllium atom are presented and compared to accurate Kohn-Sham data. These calculations make use of a differential equation that we have developed for the so called Pauli potential, a key quantity in OF-DFT. The Pauli potential differential equation and the OF Euler equation form a system of two coupled differential equations, which have to be solved simultaneously within the DFT self-consistent loop.
Hydraulic calculation of pressure pipes
Mikhalev, M. A.
2012-01-01
In the present time there is only one classic method for hydraulic calculation of pressure pipes. In it fluid flow velocity and pipeline diameter are considered as given values.The paper proposes a procedure for physical modeling and hydraulic calculation of pressure pipes, based on the theory of similarity. Methods for obtaining similarity criteria from combinations of similarity numbers were discussed. Similarity numbers and criteria and criteria equations were defined.
Random diophantine equations, I
Brüdern, Jörg; Dietmann, Rainer
2012-01-01
We consider additive diophantine equations of degree $k$ in $s$ variables and establish that whenever $s\\ge 3k+2$ then almost all such equations satisfy the Hasse principle. The equations that are soluble form a set of positive density, and among the soluble ones almost all equations admit a small solution. Our bound for the smallest solution is nearly best possible.
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.
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...
International Nuclear Information System (INIS)
Risk and reliability analysis is increasingly being used in evaluations of plant safety and plant reliability. The analysis can be performed either during the design process or during the operation time, with the purpose to improve the safety or the reliability. Due to plant complexity and safety and availability requirements, sophisticated tools, which are flexible and efficient, are needed. Such tools have been developed in the last 20 years and they have to be continuously refined to meet the growing requirements. Two different areas of application were analysed. In structural reliability probabilistic approaches have been introduced in some cases for the calculation of the reliability of structures or components. A new computer program has been developed based upon numerical integration in several variables. In systems reliability Monte Carlo simulation programs are used especially in analysis of very complex systems. In order to increase the applicability of the programs variance reduction techniques can be applied to speed up the calculation process. Variance reduction techniques have been studied and procedures for implementation of importance sampling are suggested. (author)
Thermohydraulic calculation of WWER-type NPP
International Nuclear Information System (INIS)
Technique of thermohydraulic calculation of the WWER-type NPP in unsteady processes is described. Effective algorithm for solving hydrodynamics equations without regard for acoustic effects permitting to use enough large time integration step is given. Calculation of two-dimensional temperature fields in fuel element is considered. Method for calculating a pressurizer, steam generators and pumps is described as well
International Nuclear Information System (INIS)
This book is a clear, practical, and balanced view of toxicology and risk management. The introduction argues the case for risks assessment and outlines the benefits and problems associated with chemical exposure. The first part of the book covers the basic science and the sources of human exposure to chemicals. Absorption, distribution, metabolism, and excretion are covered in some detail. The subsequent chapter gives a lively discussion of toxicity studies and then describes slow and fast poisons. The author gives the arguments for as well as against animal testing. There is much public bewilderment caused by reports of cancer-causing pesticides in apple juice and poisons emanating from nearby hazardous waste sites. The author believes that too much has been written in an attempt to expose governmental and corporate ignorance, negligence, and corruption. This book is less of a polemic, and more of a clear, unbiased clarification of the scientific basis for our concerns and uncertainties. It should serve to refocus the debate
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.
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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.
BMN correlators by loop equations
International Nuclear Information System (INIS)
In the BMN approach to N=4 SYM a large class of correlators of interest are expressible in terms of expectation values of traces of words in a zero-dimensional gaussian complex matrix model. We develop a loop-equation based, analytic strategy for evaluating such expectation values to any order in the genus expansion. We reproduce the expectation values which were needed for the calculation of the one-loop, genus one correction to the anomalous dimension of BMN-operators and which were earlier obtained by combinatorial means. Furthermore, we present the expectation values needed for the calculation of the one-loop, genus two correction. (author)
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.)
Institute of Scientific and Technical Information of China (English)
洪迎春; 谷波; 韩华
2011-01-01
在Martin-Hou方程的基础上,提出了R410a制冷剂在饱和线的热力学性能参数和传输特性参数的显式快速计算模型.该模型不存在迭代,在保证较高计算精度的同时,可以保证模型的计算速度和稳定性.以热力学性能参数计算软件REFPROP 7的数据源作为原始数据,在饱和线（139.00~343.32 K）范围内,对R410a制冷剂的性能参数进行拟合,并将该模型的计算结果与REFPROP 7数据源进行对比.结果表明：所有快速计算模型的总平均误差均小于1.174%,最大误差小于13.218%;其计算速度比REFPROP 7提高了2~4个数量级.%Based on the Martin-Hou equation of state,a fast calculation model for R410a thermodynamic and transport properties,covering saturation curve（139.00—343.32 K）,was presented due to no need of iteration.This method can not only achieve the accuracy,but guarantee the calculation stability and high calculation speed of thermophysical and transport properties of R410a.The source data was calculated from REFPROP 7.The total mean relative error and maximum relative error for all fast calculation models are less than 1.174% and 13.218%,respectively.The comparison result shows that the calculation speed of the fast calculation model is two to four orders faster than those of REFPROP 7.
Delay Equation for Charged Brown Particle
Vlasov, Alexander A.
2001-01-01
In previous work (physics/0004026) was shown, with the help of numerical calculations, that the effective Brown temperature for charged particle is lower than that for particle without charge. Here we derive this result without numerical calculations, integrating the delay equation analytically, as for zero, so for nonzero viscosity.
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.
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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Get Tested for Colon Cancer: Here's How
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Spreadsheet Templates for Chemical Equilibrium Calculations.
Joshi, Bhairav D.
1993-01-01
Describes two general spreadsheet templates to carry out all types of one-equation chemical equilibrium calculations encountered by students in undergraduate chemistry courses. Algorithms, templates, macros, and representative examples are presented to illustrate the approach. (PR)
Directory of Open Access Journals (Sweden)
Grodzki Tomasz
2011-03-01
Full Text Available Abstract Background Lung cancer diagnosis in tissue material with commonly used histological techniques is sometimes inconvenient and in a number of cases leads to ambiguous conclusions. Frequently advanced immunostaining techniques have to be employed, yet they are both time consuming and limited. In this study a proteomic approach is presented which may help provide unambiguous pathologic diagnosis of tissue material. Methods Lung tissue material found to be pathologically changed was prepared to isolate proteome with fast and non selective procedure. Isolated peptides and proteins in ranging from 3.5 to 20 kDa were analysed directly using high resolution mass spectrometer (MALDI-TOF/TOF with sinapic acid as a matrix. Recorded complex spectra of a single run were then analyzed with multivariate statistical analysis algorithms (principle component analysis, classification methods. In the applied protocol we focused on obtaining the spectra richest in protein signals constituting a pattern of change within the sample containing detailed information about its protein composition. Advanced statistical methods were to indicate differences between examined groups. Results Obtained results indicate changes in proteome profiles of changed tissues in comparison to physiologically unchanged material (control group which were reflected in the result of principle component analysis (PCA. Points representing spectra of control group were located in different areas of multidimensional space and were less diffused in comparison to cancer tissues. Three different classification algorithms showed recognition capability of 100% regarding classification of examined material into an appropriate group. Conclusion The application of the presented protocol and method enabled finding pathological changes in tissue material regardless of localization and size of abnormalities in the sample volume. Proteomic profile as a complex, rich in signals spectrum of proteins
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.
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.
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.
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.
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
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
Reducible functional differential equations
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S. M. Shah
1985-01-01
Full Text Available This is the first part of a survey on analytic solutions of functional differential equations (FDE. Some classes of FDE that can be reduced to ordinary differential equations are considered since they often provide an insight into the structure of analytic solutions to equations with more general argument deviations. Reducible FDE also find important applications in the study of stability of differential-difference equations and arise in a number of biological models.
New unified evolution equation
Lim, Jyh-Liong; Li, Hsiang-nan
1998-01-01
We propose a new unified evolution equation for parton distribution functions appropriate for both large and small Bjorken variables $x$, which is an improved version of the Ciafaloni-Catani-Fiorani-Marchesini equation. In this new equation the cancellation of soft divergences between virtual and real gluon emissions is explicit without introducing infrared cutoffs, next-to-leading contributions to the Sudakov resummation can be included systematically. It is shown that the new equation reduc...
Diophantine equations and identities
Directory of Open Access Journals (Sweden)
Malvina Baica
1985-01-01
Full Text Available The general diophantine equations of the second and third degree are far from being totally solved. The equations considered in this paper are i x2−my2=±1 ii x3+my3+m2z3−3mxyz=1iii Some fifth degree diopantine equations
Test of Information Theory on the Boltzmann Equation
Hyeon-Deuk, Kim; Hayakawa, Hisao
2002-01-01
We examine information theory using the steady-state Boltzmann equation. In a nonequilibrium steady-state system under steady heat conduction, the thermodynamic quantities from information theory are calculated and compared with those from the steady-state Boltzmann equation. We have found that information theory is inconsistent with the steady-state Boltzmann equation.
Test of Information Theory on the Boltzmann Equation
Kim, Hyeon-Deuk; Hayakawa, Hisao
2003-01-01
We examine information theory using the steady-state Boltzmann equation. In a nonequilibrium steady-state system under steady heat conduction, the thermodynamic quantities from information theory are calculated and compared with those from the steady-state Boltzmann equation. We have found that information theory is inconsistent with the steady-state Boltzmann equation.
Energy Technology Data Exchange (ETDEWEB)
Pedicini, Piernicola, E-mail: ppiern@libero.it [Service of Medical Physics, I.R.C.C.S. Regional Cancer Hospital C.R.O.B, Rionero in Vulture (Italy); Strigari, Lidia [Laboratory of Medical Physics and Expert Systems, Regina Elena National Cancer Institute, Rome (Italy); Benassi, Marcello [Service of Medical Physics, Scientific Institute of Tumours of Romagna I.R.S.T., Meldola (Italy); Caivano, Rocchina [Service of Medical Physics, I.R.C.C.S. Regional Cancer Hospital C.R.O.B, Rionero in Vulture (Italy); Fiorentino, Alba [U.O. of Radiotherapy, I.R.C.C.S. Regional Cancer Hospital C.R.O.B., Rionero in Vulture (Italy); Nappi, Antonio [U.O. of Nuclear Medicine, I.R.C.C.S. Regional Cancer Hospital C.R.O.B., Rionero in Vulture (Italy); Salvatore, Marco [U.O. of Nuclear Medicine, I.R.C.C.S. SDN Foundation, Naples (Italy); Storto, Giovanni [U.O. of Nuclear Medicine, I.R.C.C.S. Regional Cancer Hospital C.R.O.B., Rionero in Vulture (Italy)
2014-04-01
To increase the efficacy of radiotherapy for non–small cell lung cancer (NSCLC), many schemes of dose fractionation were assessed by a new “toxicity index” (I), which allows one to choose the fractionation schedules that produce less toxic treatments. Thirty-two patients affected by non resectable NSCLC were treated by standard 3-dimensional conformal radiotherapy (3DCRT) with a strategy of limited treated volume. Computed tomography datasets were employed to re plan by simultaneous integrated boost intensity-modulated radiotherapy (IMRT). The dose distributions from plans were used to test various schemes of dose fractionation, in 3DCRT as well as in IMRT, by transforming the dose-volume histogram (DVH) into a biological equivalent DVH (BDVH) and by varying the overall treatment time. The BDVHs were obtained through the toxicity index, which was defined for each of the organs at risk (OAR) by a linear quadratic model keeping an equivalent radiobiological effect on the target volume. The less toxic fractionation consisted in a severe/moderate hyper fractionation for the volume including the primary tumor and lymph nodes, followed by a hypofractionation for the reduced volume of the primary tumor. The 3DCRT and IMRT resulted, respectively, in 4.7% and 4.3% of dose sparing for the spinal cord, without significant changes for the combined-lungs toxicity (p < 0.001). Schedules with reduced overall treatment time (accelerated fractionations) led to a 12.5% dose sparing for the spinal cord (7.5% in IMRT), 8.3% dose sparing for V{sub 20} in the combined lungs (5.5% in IMRT), and also significant dose sparing for all the other OARs (p < 0.001). The toxicity index allows to choose fractionation schedules with reduced toxicity for all the OARs and equivalent radiobiological effect for the tumor in 3DCRT, as well as in IMRT, treatments of NSCLC.
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.
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.
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. PMID:27586766
Roosta, Sara; Hashemianzadeh, Seyed Majid; Ketabi, Sepideh
2016-10-01
Encapsulation of cisplatin anticancer drug into the single walled (10, 0) carbon nanotube and (10, 0) boron-nitride nanotube was investigated by quantum mechanical calculations and Monte Carlo Simulation in aqueous solution. Solvation free energies and complexation free energies of the cisplatin@ carbon nanotube and cisplatin@ boron-nitride nanotube complexes was determined as well as radial distribution functions of entitled compounds. Solvation free energies of cisplatin@ carbon nanotube and cisplatin@ boron-nitride nanotube were -4.128kcalmol(-1) and -2457.124kcalmol(-1) respectively. The results showed that cisplatin@ boron-nitride nanotube was more soluble species in water. In addition electrostatic contribution of the interaction of boron- nitride nanotube complex and solvent was -281.937kcalmol(-1) which really more than Van der Waals and so the electrostatic interactions play a distinctive role in the solvation free energies of boron- nitride nanotube compounds. On the other hand electrostatic part of the interaction of carbon nanotube complex and solvent were almost the same as Van der Waals contribution. Complexation free energies were also computed to study the stability of related structures and the free energies were negative (-374.082 and -245.766kcalmol(-1)) which confirmed encapsulation of drug into abovementioned nanotubes. However, boron-nitride nanotubes were more appropriate for encapsulation due to their larger solubility in aqueous solution. PMID:27287103
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.
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.
Equilibrium calculations for helical axis stellarators
International Nuclear Information System (INIS)
An average method based on a vacuum flux coordinate system is presented. This average method permits the study of helical axis stellarators with toroidally dominated shifts. An ordering is introduced, and to lowest order the toroidally averaged equilibrium equations are reduced to a Grad-Shafranov equation. Also, to lowest order, a Poisson-type equation is obtained for the toroidally varying corrections to the equilibium. By including these corrections, systems that are toroidally dominated, but with significant helical distortion to the equilibrium, may be studied. Numerical solutions of the average method equations are shown to agree well with three-dimensional calculations
Lanczos's equation to replace Dirac's equation ?
Gsponer, A; Gsponer, Andre; Hurni, Jean-Pierre
1994-01-01
Lanczos's quaternionic interpretation of Dirac's equation provides a unified description for all elementary particles of spin 0, 1/2, 1, and 3/2. The Lagrangian formulation given by Einstein and Mayer in 1933 predicts two main classes of solutions. (1) Point like partons which come in two families, quarks and leptons. The correct fractional or integral electric and baryonic charges, and zero mass for the neutrino and the u-quark, are set by eigenvalue equations. The electro-weak interaction of the partons is the same as with the Standard model, with the same two free parameters: e and sin^2 theta. There is no need for a Higgs symmetry breaking mechanism. (2) Extended hadrons for which there is no simple eigenvalue equation for the mass. The strong interaction is essentially non-local. The pion mass and pion-nucleon coupling constant determine to first order the nucleon size, mass and anomalous magnetic moment.
International Nuclear Information System (INIS)
We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A0(t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field
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...
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.
Elliptic partial differential equations
Volpert, Vitaly
If we had to formulate in one sentence what this book is about it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Mathematical anaylsis of reaction-diffusion equations will be based on the theory of Fredholm operators presented in the first volume. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equ...
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.
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.
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.
Solving Ordinary Differential Equations
Krogh, F. T.
1987-01-01
Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.
Fundamental Equation of Economics
Wayne, James J.
2013-01-01
Recent experience of the great recession of 2008 has renewed one of the oldest debates in economics: whether economics could ever become a scientific discipline like physics. This paper proves that economics is truly a branch of physics by establishing for the first time a fundamental equation of economics (FEOE), which is similar to many fundamental equations governing other subfields of physics, for example, Maxwell’s Equations for electromagnetism. From recently established physics laws of...
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.
Configuration space Faddeev calculations
International Nuclear Information System (INIS)
The detailed study of few-body systems provides one of the most effective means for studying nuclear physics at subnucleon distance scales. For few-body systems the model equations can be solved numerically with errors less than the experimental uncertainties. We have used such systems to investigate the size of relativistic effects, the role of meson-exchange currents, and the importance of quark degrees of freedom in the nucleus. Complete calculations for momentum-dependent potentials have been performed, and the properties of the three-body bound state for these potentials have been studied. Few-body calculations of the electromagnetic form factors of the deuteron and pion have been carried out using a front-form formulation of relativistic quantum mechanics. The decomposition of the operators transforming convariantly under the Poincare group into kinematical and dynamical parts has been studies. New ways for constructing interactions between particles, as well as interactions which lead to the production of particles, have been constructed in the context of a relativistic quantum mechanics. To compute scattering amplitudes in a nonperturbative way, classes of operators have been generated out of which the phase operator may be constructed. Finally, we have worked out procedures for computing Clebsch-Gordan and Racah coefficients on a computer, as well as giving procedures for dealing with the multiplicity problem
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 ...
Zhalij, Alexander
2002-01-01
We classify (1+3)-dimensional Pauli equations for a spin-1/2 particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the eleven classes of vector-potentials of the electro-magnetic field A(t,x) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is...
International Nuclear Information System (INIS)
A new evolution equation is proposed for the gluon density relevant (GLR) for the region of small xB. It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists of taking shadowing effects more comprehensively into account by including multi gluon correlations, and allowing for an arbitrary initial gluon distribution in a hadron. We solve the new equation for fixed αs. It is found that the effects of multi gluon correlations on the deep-inelastic structure function are small. (author) 15 refs, 5 figs, 2 tabs
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...
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.)
Non-perturbative background field calculations
Stephens, C. R.
1988-01-01
New methods are developed for calculating one loop functional determinants in quantum field theory. Instead of relying on a calculation of all the eigenvalues of the small fluctuation equation, these techniques exploit the ability of the proper time formalism to reformulate an infinite dimensional field theoretic problem into a finite dimensional covariant quantum mechanical analog, thereby allowing powerful tools such as the method of Jacobi fields to be used advantageously in a field theory setting. More generally the methods developed herein should be extremely valuable when calculating quantum processes in non-constant background fields, offering a utilitarian alternative to the two standard methods of calculation—perturbation theory in the background field or taking the background field into account exactly. The formalism developed also allows for the approximate calculation of covariances of partial differential equations from a knowledge of the solutions of a homogeneous ordinary differential equation.
Landoni, V; Borzì, G R; Strolin, S; Bruzzaniti, V; Soriani, A; D'Alessio, D; Ambesi, F; Di Grazia, A M; Strigari, L
2015-06-01
The purpose of this study is to evaluate the differences between dose distributions calculated with the pencil beam (PB) and X-ray voxel Monte Carlo (MC) algorithms for patients with lung cancer using intensity-modulated radiotherapy (IMRT) or HybridArc techniques. The 2 algorithms were compared in terms of dose-volume histograms, under normal and deep inspiration breath hold, and in terms of the tumor control probability (TCP). The dependence of the differences in tumor volume and location was investigated. Dosimetric validation was performed using Gafchromic EBT3 (International Specialty Products, ISP, Wayne, NJ). Forty-five Computed Tomography (CT) data sets were used for this study; 40 Gy at 8 Gy/fraction was prescribed with 5 noncoplanar 6-MV IMRT beams or 3 to 4 dynamic conformal arcs with 3 to 5 IMRT beams distributed per arc. The plans were first calculated with PB and then recalculated with MC. The difference between the mean tumor doses was approximately 10% ± 4%; these differences were even larger under deep inspiration breath hold. Differences between the mean tumor dose correlated with tumor volume and path length of the beams. The TCP values changed from 99.87% ± 0.24% to 96.78% ± 4.81% for both PB- and MC-calculated plans (P = .009). When a fraction of hypoxic cells was considered, the mean TCP values changed from 76.01% ± 5.83% to 34.78% ± 18.06% for the differently calculated plans (P < .0001). When the plans were renormalized to the same mean dose at the tumor, the mean TCP for oxic cells was 99.05% ± 1.59% and for hypoxic cells was 60.20% ± 9.53%. This study confirms that the MC algorithm adequately accounts for inhomogeneities. The inclusion of the MC in the process of IMRT optimization could represent a further step in the complex problem of determining the optimal treatment plan. PMID:25223324
Calculation of plasma characteristics of the sun
Institute of Scientific and Technical Information of China (English)
Muhammad Abbas Bari; Zhong Jia-Yong; Chen Miu; Zhao Jing; Zhang Jie
2006-01-01
The ionization level and free electron density of most abundant elements (C, N, O, Mg, Al, Si, S, and Fe) in the sun are calculated from the centre of the sun to the surface of the photosphere. The model and computations are made under the assumption of local thermodynamic equilibrium (LTE). The Saha equation has been used to calculate the ionization level of elements and the electron density. Temperature values for calculations along the solar radius are taken from referebces.
Some Calculations for Cold Fusion Superheavy Elements
X. H. Zhong; Li, L.; Ning, P. Z.
2004-01-01
The Q value and optimal exciting energy of the hypothetical superheavy nuclei in cold fusion reaction are calculated with relativistic mean field model and semiemperical shell model mass equation(SSME) and the validity of the two models is tested. The fusion barriers are also calculated with two different models and reasonable results are obtained. The calculations can give useful references for the experiments in the superheavy nuclei synthesized in cold fusion reactions.
Wetterich, C
2016-01-01
We propose a gauge invariant flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations, corresponding to a particular gauge fixing. The freedom in the precise choice of the macroscopic field can be exploited in order to keep the flow equation simple.
Zahari, N. M.; Sapar, S. H.; Mohd Atan, K. A.
2013-04-01
This paper discusses an integral solution (a, b, c) of the Diophantine equations x3n+y3n = 2z2n for n ≥ 2 and it is found that the integral solution of these equation are of the form a = b = t2, c = t3 for any integers t.
Some classical Diophantine equations
Directory of Open Access Journals (Sweden)
Nikita Bokarev
2014-09-01
Full Text Available An attempt to find common solutions complete some Diophantine equations of the second degree with three variables, traced some patterns, suggest a common approach, which being elementary, however, lead to a solution of such equations. Using arithmetic functions allowed to write down the solutions in a single formula with no restrictions on the parameters used.
Ramirez, Erandy; Liddle, Andrew
2004-01-01
We generalize the flow equations approach to inflationary model building to the Randall–Sundrum Type II braneworld scenario. As the flow equations are quite insensitive to the expansion dynamics, we find results similar to, though not identical to, those found in the standard cosmology.
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-
Linear Equations: Equivalence = Success
Baratta, Wendy
2011-01-01
The ability to solve linear equations sets students up for success in many areas of mathematics and other disciplines requiring formula manipulations. There are many reasons why solving linear equations is a challenging skill for students to master. One major barrier for students is the inability to interpret the equals sign as anything other than…
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.
The relativistic Pauli equation
Delphenich, David
2012-01-01
After discussing the way that C2 and the algebra of complex 2x2 matrices can be used for the representation of both non-relativistic rotations and Lorentz transformations, we show that Dirac bispinors can be more advantageously represented as 2x2 complex matrices. One can then give the Dirac equation a form for such matrix-valued wave functions that no longer necessitates the introduction of gamma matrices or a choice for their representation. The minimally-coupled Dirac equation for a charged spinning particle in an external electromagnetic field then implies a second order equation in the matrix-valued wave functions that is of Klein-Gordon type and represents the relativistic analogue of the Pauli equation. We conclude by presenting the Lagrangian form for the relativistic Pauli equation.
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...
Landau levels from the Bethe Ansatz equations
Hoshi, K.; Hatsugai, Y.
2000-01-01
The Bethe ansatz (BA) equations for the two-dimensional Bloch electrons in a uniform magnetic field are treated in the weak-field limit. We have calculated energies near the lower boundary of the energy spectrum up to the first nontrivial order. It corresponds to calculating a finite size correction for the excitation energies of the BA solvable lattice models and gives the Landau levels in the present problem.
Landau Levels from the Bethe Ansatz Equations
Hoshi, K.; Hatsugai, Y.
1999-01-01
The Bethe ansatz (BA) equations for the two-dimensional Bloch electrons in a uniform magnetic field are treated in the weak field limit. We have calculated energies near the lower boundary of the energy spectrum up to the first nontrivial order. It corresponds to calculating a finite size correction for the excitation energies of the BA solvable lattice models and gives the Landau levels in the present problem.
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.
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…
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...
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
Path Integral Methods for Stochastic Differential Equations
Chow, Carson C.; Buice, Michael A.
2015-01-01
Stochastic differential equations (SDEs) have multiple applications in mathematical neuroscience and are notoriously difficult. Here, we give a self-contained pedagogical review of perturbative field theoretic and path integral methods to calculate moments of the probability density function of SDEs. The methods can be extended to high dimensional systems such as networks of coupled neurons and even deterministic systems with quenched disorder.
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,
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.
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
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
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.
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.
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.
Modern introduction to differential equations
Ricardo, Henry J
2009-01-01
A Modern Introduction to Differential Equations, Second Edition, provides an introduction to the basic concepts of differential equations. The book begins by introducing the basic concepts of differential equations, focusing on the analytical, graphical, and numerical aspects of first-order equations, including slope fields and phase lines. The discussions then cover methods of solving second-order homogeneous and nonhomogeneous linear equations with constant coefficients; systems of linear differential equations; the Laplace transform and its applications to the solution of differential equat
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.
A Comparison of IRT Equating and Beta 4 Equating.
Kim, Dong-In; Brennan, Robert; Kolen, Michael
Four equating methods were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional mean squared error (CMSE) difference, and the equipercentile equating property. The four methods were: (1) three parameter logistic (3PL) model true score equating; (2) 3PL observed score equating; (3) beta 4 true…
On-Site was developed to provide modelers and model reviewers with prepackaged tools ("calculators") for performing site assessment calculations. The philosophy behind OnSite is that the convenience of the prepackaged calculators helps provide consistency for simple calculations,...
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.
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...
Diophantine Equations and Computation
Davis, Martin
Unless otherwise stated, we’ll work with the natural numbers: N = \\{0,1,2,3, dots\\}. Consider a Diophantine equation F(a1,a2,...,an,x1,x2,...,xm) = 0 with parameters a1,a2,...,an and unknowns x1,x2,...,xm For such a given equation, it is usual to ask: For which values of the parameters does the equation have a solution in the unknowns? In other words, find the set: \\{ mid exists x_1,ldots,x_m [F(a_1,ldots,x_1,ldots)=0] \\} Inverting this, we think of the equation F = 0 furnishing a definition of this set, and we distinguish three classes: a set is called Diophantine if it has such a definition in which F is a polynomial with integer coefficients. We write \\cal D for the class of Diophantine sets.
Nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
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.
Nonlinear differential equations
International Nuclear Information System (INIS)
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics
Garkavenko A. S.
2011-01-01
The rate equations of the exciton laser in the system of interacting excitons have been obtained and the inverted population conditions and generation have been derived. The possibility of creating radically new gamma-ray laser has been shown.
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.
Tsintsadze, Nodar L.; Tsintsadze, Levan N.
2008-01-01
A general derivation of the charging equation of a dust grain is presented, and indicated where and when it can be used. A problem of linear fluctuations of charges on the surface of the dust grain is discussed.
Adek Tasri
2010-01-01
Problem statement: Pressure and velocity decoupling have been source of problem in solving Navier-Stokes and continuity equation particularly in complex collocated grid. The problem of pressure velocity decoupling is usually reduced by using momentum interpolation to calculate mass flux at face of control volume. Equation of momentum interpolation was derived by assumption that the face of cell is equidistant from two neighbor cell centers and face of cell is collinear with two neighbor cell ...
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.
SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER
Collier, D.M.; Meeks, L.A.; Palmer, J.P.
1960-05-10
A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.
Hedin Equations for Superconductors
Linscheid, A.; Essenberger, F.
2015-01-01
We generalize Hedin equations to a system of superconducting electrons coupled with a system of phonons. The electrons are described by an electronic Pauli Hamiltonian which includes the Coulomb interaction among electrons and an external vector and scalar potential. We derive the continuity equation in the presence of the superconducting condensate and point out how to cast vertex corrections in the form of a non-local effective interaction that can be used to describe both fluctuations of s...
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.
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.
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.
Functional Equations and Fourier Analysis
Yang, Dilian
2010-01-01
By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson equation, and the d'Alembert long equation, on compact groups.
Sensitivity of rocky planet structures to the equation of state
International Nuclear Information System (INIS)
Structures were calculated for Mercury, Venus, Earth, the Moon, and Mars, using a core-mantle model and adjusting the core radius to reproduce the observed mass and diameter of each body. Structures were calculated using Fe and basalt equations of state of different degrees of sophistication for the core and mantle. The choice of equation of state had a significant effect on the inferred structure. For each structure, the moment of inertia ratio was calculated and compared with observed values. Linear Grueneisen equations of state fitted to limited portions of shock data reproduced the observed moments of inertia significantly better than did more detailed equations of state incorporating phase transitions, presumably reflecting the actual compositions of the bodies. The linear Grueneisen equations of state and corresponding structures seem however to be a reasonable starting point for comparative simulations of large-scale astrophysical impacts.
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.
Integral equations and computation problems
International Nuclear Information System (INIS)
Volterra's Integral Equations and Fredholm's Integral Equations of the second kind are discussed. Computational problems are found in the derivations and the computations. The theorem of the solution of the Fredholm's Integral Equation is discussed in detail. (author)
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.
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.
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.
Unified derivation of evolution equations
Li, Hsiang-nan
1998-01-01
We derive the evolution equations of parton distribution functions appropriate in different kinematic regions in a unified and simple way using the resummation technique. They include the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation for large momentum transfer $Q$, the Balitskii-Fadin-Kuraev-Lipatov equation for a small Bjorken variable $x$, and the Ciafaloni-Catani-Fiorani-Marchesini equation which embodies the above two equations. The relation among these equations is explored, and p...
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.
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.
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.
Quadratic Diophantine equations
Andreescu, Titu
2015-01-01
This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.
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...
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.
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.
Magnetic Positioning Equations Theory and Applications
Esh, Mordechay
2012-01-01
In the study of Magnetic Positioning Equations, it is possible to calculate and create analytical expressions for the intensity of magnetic fields when the coordinates x, y and z are known; identifying the inverse expressions is more difficult. This book is designed to explore the discovery of how to get the coordinates of analytical expressions x, y and z when the intensity of the magnetic fields are known. The discovery also deals with the problem of how to analyze, define and design any type of transmitter along with its positioning equation(s).Presents new simple mathematical solution expr
Drukker, Nadav
1999-01-01
We derive a new form of loop equations for light-like Wilson loops. In bosonic theories those loop equations close only for straight light-like Wilson lines. In the case of N=1 in ten dimensions they close for any light-like Wilson loop. Upon dimensional reduction to N=4 SYM in four dimensions, these loops become exactly the chiral loops which can be evaluated semiclassically, in the strong coupling limit, by a minimal surface in anti de-Sitter space. We show that the AdS calculation satisfie...
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.
Amorim, R G G; Silva, Edilberto O
2015-01-01
Symplectic unitary representations for the Poincar\\'{e} group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space is constructed. The state of a quantum mechanics system is described by a quasi-probability amplitude that is in association with the Wigner function. As a result, the Klein-Gordon and Dirac equations are derived in phase space. As an application, we study the Dirac equation with electromagnetic interaction in phase space.
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.
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
The relativistic Pauli equation
Delphenich, David
2012-01-01
After discussing the way that C2 and the algebra of complex 2x2 matrices can be used for the representation of both non-relativistic rotations and Lorentz transformations, we show that Dirac bispinors can be more advantageously represented as 2x2 complex matrices. One can then give the Dirac equation a form for such matrix-valued wave functions that no longer necessitates the introduction of gamma matrices or a choice for their representation. The minimally-coupled Dirac equation for a charge...
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....
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.
Cira, Octavian; Smarandache, Florentin
2016-01-01
In this book a multitude of Diophantine equations and their partial or complete solutions are presented. How should we solve, for example, the equation {\\eta}({\\pi}(x)) = {\\pi}({\\eta}(x)), where {\\eta} is the Smarandache function and {\\pi} is Riemann function of counting the number of primes up to x, in the set of natural numbers? If an analytical method is not available, an idea would be to recall the empirical search for solutions. We establish a domain of searching for the solutions and th...
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
Markley, F. Landis
1995-01-01
Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation. This method is not iterative, and requires only four transcendental function evaluations: a square root, a cube root, and two trigonometric functions. The maximum relative error of the algorithm is less than one part in 10(exp 18), exceeding the capability of double-precision computer arithmetic. Roundoff errors in double-precision implementation of the algorithm are addressed, and procedures to avoid them are developed.
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
Cancer Statistics: Endometrial Cancer
... a third party. HPF: Did You Know? Endometrial Cancer Endometrial Cancer - Did you know that endometrial cancer ... mfhs0vbvWi8?rel=0 SEER Stat Fact Sheets: Endometrial Cancer Expand All Collapse All Lifetime risk estimates are ...
On difference Riccati equations and second order linear difference equations
Ishizaki, Katsuya
2011-01-01
In this paper, we treat difference Riccati equations and second order linear difference equations in the complex plane. We give surveys of basic properties of these equations which are analogues in the differential case. We are concerned with the growth and value distributions of transcendental meromorphic solutions of these equations. Some examples are given.
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.
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...
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.
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.
Modelling by Differential Equations
Chaachoua, Hamid; Saglam, Ayse
2006-01-01
This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations. By analysing the problems posed by scientists in the seventeenth century, we note that physics is very important for the emergence of this theory. Taking into account this analysis, we show the…
Do Differential Equations Swing?
Maruszewski, Richard F., Jr.
2006-01-01
One of the units of in a standard differential equations course is a discussion of the oscillatory motion of a spring and the associated material on forcing functions and resonance. During the presentation on practical resonance, the instructor may tell students that it is similar to when they take their siblings to the playground and help them on…
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…
Kasari, Hikoya; Yamaguchi, Yoshio
2001-01-01
Contrary to the conventional belief, it was shown that the Breit equation has the eigenvalues for bound states of two oppositely charged Dirac particles interacting through the (static) Coulomb potential. All eigenvalues reduced to those of the Sch\\"odinger case in the non-relativistic limit.
Chi, Do Minh
1999-01-01
We research the natural causality of the Universe. We find that the equation of causality provides very good results on physics. That is our first endeavour and success in describing a quantitative expression of the law of causality. Hence, our theoretical point suggests ideas to build other laws including the law of the Universe's evolution.
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.
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 0solar panels, electrochemical phenomena and the description of anomalous complex processes.
Calculus & ordinary differential equations
Pearson, David
1995-01-01
Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.
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
Dual Diagonalization of Reactive Transport Equations
Yeh, G.; Tsai, C.
2013-12-01
One solves a system of species transport equations in the primitive approach to reactive transport modeling. This approach is not able to decouple equilibrium reaction rates from species concentrations. This problem has been overcome with the approach to diagonalizing the reaction matrix since mid 1990's, which yields the same number of transport equations for reaction-extents. In the diagonalization approach, first, a subset of reaction- extent transport equations is solved for concentrations of components and kinetic-variables. Then, the component, kinetic-variable, and mass action equations are solved for all species concentrations. Finally, the equilibrium reaction rates are posterior computed. The difficulty in this approach is that the solution of species concentrations in the second step is a stiff problem when the concentrations of master species are small compared to those of equilibrium species. To overcome the problem of stiffness, we propose a dual diagonalization approach. Here, a second diagonalization is performed on the decomposed unit matrix to yield species concentrations, each as a linear function of reaction extents. In this dual diagonalization approach, four steps are needed to complete the modeling. First, component and kinetic-variable transport equations are solved for the concentrations of components (a subset of reaction-extents) and kinetic-variables (another subset of reaction-extents). Second, the set of mass action equations written in terms of reaction extents are solved for equilibrium-variables (yet another subset of reaction-extents). Third, species concentrations are posterior obtained by solving the set of linear equations defining reaction-extents. Fourth, equilibrium rates are posterior calculated with transport equations for equilibrium-variables. Several example problems will be used to demonstrate the efficiency of this approach. Keywords: Reactive Transport, Reaction-Extent, Component, Kinetic-Variable, Equilibrium
Distillation Calculations with a Programmable Calculator.
Walker, Charles A.; Halpern, Bret L.
1983-01-01
Describes a three-step approach for teaching multicomponent distillation to undergraduates, emphasizing patterns of distribution as an aid to understanding the separation processes. Indicates that the second step can be carried out by programmable calculators. (A more complete set of programs for additional calculations is available from the…
Resources - cancer ... The following organizations are good resources for information on cancer : American Cancer Society -- www.cancer.org Cancer Care -- www.cancercare.org National Cancer Institute -- www.cancer.gov
... What Is Cancer? Cancer Statistics Cancer Disparities Cancer Statistics Cancer has a major impact on society in ... success of efforts to control and manage cancer. Statistics at a Glance: The Burden of Cancer in ...
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.
Anticipated backward stochastic differential equations
Peng, Shige; Yang, Zhe
2009-01-01
In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and stochastic differential delay equations.
恶性肿瘤患者体表面积计算方法的比较%Comparison of methods for calculating human body surface area in cancer patients
Institute of Scientific and Technical Information of China (English)
李小优; 吴剑秋; 汤唯艳; 张琰; 刘宇飞; 冯继锋
2012-01-01
Objective To extend the method for calculating human body surface area in cancer patients with different BMI ranges. Methods The actual body weight and the height of cancer patients were measured at admission, the second day and before chemotherapy to get the average value. The subjects were divided into magensuchl group, normal quality group, overweight group and obesity group according to BMI( ≤18. 6kg/m2, 18.6-23.9kg/m2, 24-27.9kg/m2 and ≥28kg/m2). Ideal body weight, ideal surface area and actual surface area were formulated and analyzed. Results The actual body surface area and ideal body surface area were 1.590m2 and 1. 584 m2 in normal quality group (P >0.05). The actual body surface area and ideal body surface area were 1.523m2 and 1.641m2,1.724m2 and 1. 590m2, 1. 813m2 and 1.570m2 in magersucht group, overweight group and obesity group( P < 0. 05). Conclusion There are significant differences between actual body surface area and ideal body surface area of patients according to BMI classification. The ideal body surface area based on ideal body weight could get more precise drug dose and avoid otiose therapeutic risk.%目的 探讨不同体重指数(BMI)的恶性肿瘤患者体表面积的计算方法.方法 对227例恶性肿瘤患者在住院当天、第2天和化疗前各测量1次空腹时的身高和实际体重,计算其平均值.按照不同BMI值(≤18.6kg/m2、18.6～23.9kg/m2、24～27.9kg/m2和≥28kg/m2)将患者分为消瘦组(17例)、正常体重组(107例)、超重组(82例)和肥胖组(21例)；计算各组患者的实际和理想体表面积,比较两者间差异.结果 正常体重组患者的实际和理想体表面积分别为1.590m2和1.584m2,差异无统计学意义(P＞0.05)；消瘦组患者的实际和理想体表面积分别为1.523m2和1.641m2(P＜0.05)；超重组患者的实际和理想体表面积分别为1.724m2和1.590m2(P＜0.05)；肥胖组患者的实际和理想体表面积分别为1.813m2和1.570m2(P＜0.05).结论
Exact Solution to Terzaghi's Consolidation Equation
Di Francesco, Romolo
2011-01-01
The application of the consolidation equation is based on Taylor's approximate solution alone. The existence of the exact solution emerged from the analysis of the logical structure of d'Alambert's, Fourier' and Laplace's differential equations. This led to a nonlinear equation - based on the properties of elastic waves and elastic functions - which is able to simulate excess pore pressure transmission in the soil. The research is completed with the application of the solution obtained, thereby discovering that consolidation decay times may be calculated both through the construction of dissipation curves and through he analytical research of the time value satisfying the condition Delta u(z,t100) = 0. Finally, decay times match the approximate solution eliminating in fact the introduction of Taylor's additional parameters.
A New Kinetic Equation for Compton Scattering
Rybicki, G B
2003-01-01
A kinetic equation for Compton scattering is given that differs from the Kompaneets equation in several significant ways. By using an inverse differential operator this equation allows treatment of problems for which the radiation field varies rapidly on the scale of the width of the Compton kernel. This inverse operator method describes, among other effects, the thermal Doppler broadening of spectral lines and continuum edges, and automatically incorporates the process of Compton heating/cooling. It is well adapted for inclusion into a numerical iterative solution of radiative transfer problems. The equivalent kernel of the new method is shown to be a positive function and with reasonable accuracy near the intitial frequency, unlike the Kompaneets kernel, which is singular and not wholly positive. It is shown that iterates of the inverse operator kernel can be easily calculated numerically, and a simple summation formula over these iterates is derived that can be efficiently used to compute Comptonized spect...
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...
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.
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
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.
Argosy 4 - A programme for lattice calculations
International Nuclear Information System (INIS)
This report contains a detailed description of the methods of calculation used in the Argosy 4 computer programme, and of the input requirements and printed results produced by the programme. An outline of the physics of the Argosy method is given. Section 2 describes the lattice calculation, including the burn up calculation, section 3 describes the control rod calculation and section 4 the reflector calculation. In these sections the detailed equations solved by the programme are given. In section 5 input requirements are given, and in section 6 the printed output obtained from an Argosy calculation is described. In section 7 are noted the principal differences between Argosy 4 and earlier versions of the Argosy programme
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 calculators. Three…
6 Common Cancers - Prostate Cancer
... PSA tests. Read More "6 Common Cancers" Articles Lung Cancer / Breast Cancer / Prostate Cancer / Colorectal Cancer / Skin Cancer / Gynecologic Cancers Spring 2007 Issue: Volume 2 Number 2 Page 10 MedlinePlus | Subscribe | Magazine Information | Contact Us | Viewers & ...
6 Common Cancers - Colorectal Cancer
... certain people. Read More "6 Common Cancers" Articles Lung Cancer / Breast Cancer / Prostate Cancer / Colorectal Cancer / Skin Cancer / Gynecologic Cancers Spring 2007 Issue: Volume 2 Number 2 Page 11 MedlinePlus | Subscribe | Magazine Information | Contact Us | Viewers & ...
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
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
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.
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.
Institute of Scientific and Technical Information of China (English)
张富利; 王军良; 盛洪国; 郑明民
2011-01-01
Objective: To compare the dosimetric differences between intensity modulated radiotherapy (IMRT) plans for non-small cell lung cancer using pencil beam convolution (PBC) and anisotropic analytical algorithm (AAA) methods.Materials and Methods: For a cohort of 7 patients, IMRT plans were designed using PBC and AAA calculation methods, respectively.In the planning process, identical planning objectives and dose constraints were set.Plans were compared according to dose-volume histogram (DVH) analysis in terms of PTV homogeneity and conformity indices (HI and CI) as well as OARs dose and volume parameters.Results: On average, no statistically significant differences between PBC and AAA plans were observed except Dmean and VI0 of lung.Conclusions: Both PBC and AAA algorithms provide similar dose computation accuracy for NSCLC,but the latter is less affected by the variation of respiratory phase and suggested as a priority choice.%目的:分析、比较笔形束卷积算法(PBC)和各向异性解析算法(AAA)在非小细胞肺癌(NSCLC)调强放疗计划设计中的剂量学差异.方法:随机选择7例NSCLC患者,采用Eclipse version 7.3.10计划系统提供的PBC算法和AAA算法对每例NSCLC进行IMRT的计划设计,比较靶区及危及器官的剂量分布、DVH等指标.结果:两种算法获得治疗计划的靶区剂量均匀性和适形度均无明显差别,食管、心脏、脊髓等危及器官的受量也基本相同.结论:对于NSCLC,剂量计算应采用受呼吸时相影响更小的AAA算法.
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, ...
Multiscale Decomposition for Vlasov-Poisson Equations
Fedorova, A N; Fedorova, Antonina N.; Zeitlin, Michael G.
2002-01-01
We consider the applications of a numerical-analytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of Vlasov-Poisson/Maxwell equations. We calculate the exact fast convergent representations for solutions in high-localized wavelet-like bases functions, which correspond to underlying hidden (coherent) nonlinear eigenmodes. This helps to control stability/unstability scenario of evolution in parameter space on pure algebraical level.
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.
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.
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
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.
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
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. PMID:26577856
FINITE PROXIMATE METHOD FOR CONVECTION-DIFFUSION EQUATION
Institute of Scientific and Technical Information of China (English)
ZHAO Ming-deng; LI Tai-ru; HUAI Wen-xin; LI Liang-liang
2008-01-01
A finite proximate method was presented to solve the convection-diffusion equation in curvilinear grids. The method has characteristics of automatic upwind effect and the good stability. It was verified through exact solution and other calculation results of two-dimensional dam-break flow in a frictionless, horizontal channel. The calculation results are in good agreement with the exact solution and other calculation results, which show that the finite proximate method can be applied to solve the convection-diffusion equation directly not only in the rectangular grids, but also in the curvilinear grids.
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.)
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...
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.
Telegrapher's equation for light derived from the transport equation
Hoenders, Bernhard J.; Graaff, R.
2005-01-01
Shortcomings of diffusion theory when applied to turbid media such as biological tissue makes the development of more accurate equations desirable. Several authors developed telegrapher's equations in the well known P-1 approximation. The method used in this paper is different: it is based on the asymptotic evaluation of the solutions of the equation of radiative transport with respect to place and time for all values of the albedo. Various coefficients for the telegrapher's equations were de...
Converting fractional differential equations into partial differential equations
He Ji-Huan; Li Zheng-Biao
2012-01-01
A transform is suggested in this paper to convert fractional differential equations with the modified Riemann-Liouville derivative into partial differential equations, and it is concluded that the fractional order in fractional differential equations is equivalent to the fractal dimension.
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.
On the calculation of soft phase space integral
Zhu, Hua
2014-01-01
The recent discovery of the Higgs boson at the LHC attracts much attention to the precise calculation of its production cross section in quantum chromodynamics. In this work, we discuss the calculation of soft triple-emission phase space integral, which is an essential ingredient in the recently calculated soft-virtual corrections to Higgs boson production at next-to-next-to-next-to-leading order. The main techniques used this calculation are method of differential equation for Feynman integr...
Personal Finance Calculations.
Argo, Mark
1982-01-01
Contains explanations and examples of mathematical calculations for a secondary level course on personal finance. How to calculate total monetary cost of an item, monthly payments, different types of interest, annual percentage rates, and unit pricing is explained. (RM)
What is the probability that radiation caused a particular cancer
International Nuclear Information System (INIS)
Courts, lawyers, health physicists, physicians, and others are searching for a credible answer to the question posed in the title of this paper. The cases in which the question arises frequently stem from an individual that has cancer and they, or their next-of-kin, are convinced that a past radiation exposure - usually small - is responsible for causing it. An arithmetic expression of this problem is simple: the probability of causation by the radiation dose in question is equal to the risk of cancer from the radiation dose divided by the risk of cancer from all causes. The application of risk factors to this equation is not so simple. It must involve careful evaluation of the reliability of and variations in risk coefficients for development of cancer due to radiation exposure, other carcinogenic agents, and natural causes for the particular individual. Examination of our knowledge of these various factors indicates that a large range in the answers can result due to the variability and imprecision of the data. Nevertheless, the attempts to calculate and the probability that radiation caused the cancer is extremely useful to provide a gross perspective on the probability of causation. It will likely rule in or out a significant number of cases despite the limitations in our understandings of the etiology of cancer and the risks from various factors. For the remaining cases, a thoughtful and educated judgment based on selected data and circumstances of the case will also be needed before the expert can develop and support his opinion
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
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....
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.
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
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
Lopez, Cesar
2014-01-01
MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Differential Equations introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving an introduct
Cancer - vulva; Cancer - perineum; Cancer - vulvar; Genital warts - vulvar cancer; HPV - vulvar cancer ... cells. Other types of cancers found on the vulva are: Adenocarcinoma Basal cell carcinoma Melanoma Sarcoma Vulvar ...
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 ...
Threlfall, John
2002-01-01
Suggests that strategy choice is a misleading characterization of efficient mental calculation and that teaching mental calculation methods as a whole is not conducive to flexibility. Proposes an alternative in which calculation is thought of as an interaction between noticing and knowledge. Presents an associated teaching approach to promote…
Conservational PDF Equations of Turbulence
Shih, Tsan-Hsing; Liu, Nan-Suey
2010-01-01
Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application
On Certain Dual Integral Equations
Directory of Open Access Journals (Sweden)
R. S. Pathak
1974-01-01
Full Text Available Dual integral equations involving H-Functions have been solved by using the theory of Mellin transforms. The proof is analogous to that of Busbridge on solutions of dual integral equations involving Bessel functions.
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.
Equation of state of warm condensed matter
Energy Technology Data Exchange (ETDEWEB)
Barbee, T.W., III; Young, D.A.; Rogers, F.J.
1998-03-01
Recent advances in computational condensed matter theory have yielded accurate calculations of properties of materials. These calculations have, for the most part, focused on the low temperature (T=0) limit. An accurate determination of the equation of state (EOS) at finite temperature also requires knowledge of the behavior of the electron and ion thermal pressure as a function of T. Current approaches often interpolate between calculated T=0 results and approximations valid in the high T limit. Plasma physics-based approaches are accurate in the high temperature limit, but lose accuracy below T{approximately}T{sub Fermi}. We seek to ``connect up`` these two regimes by using ab initio finite temperature methods (including linear-response[1] based phonon calculations) to derive an equation of state of condensed matter for T{<=}T{sub Fermi}. We will present theoretical results for the principal Hugoniot of shocked materials, including carbon and aluminum, up to pressures P>100 GPa and temperatures T>10{sup 4}K, and compare our results with available experimental data.
Kepler's Differential Equations
Holder, Martin
2011-01-01
Although the differential calculus was invented by Newton, Kepler established his famous laws 70 years earlier by using the same idea, namely to find a path in a nonuniform field of force by small steps. It is generally not known that Kepler demonstrated the elliptic orbit to be composed of intelligeable differential pieces, in modern language, to result from a differential equation. Kepler was first to attribute planetary orbits to a force from the sun, rather than giving them a predetermined geometric shape. Even though neither the force was known nor its relation to motion, he could determine the differential equations of motion from observation. This is one of the most important achievements in the history of physics. In contrast to Newton's Principia and Galilei's Dialogo Kepler's text is not easy to read, for various reasons. Therefore, in the present article, his results -- most of them well known -- are first presented in modern language. Then, in order to justify the claim, the full text of some rele...
International Nuclear Information System (INIS)
This monograph treats most of the usual material to be found in texts on the Dirac equation such as the basic formalism of quantum mechanics, representations of Dirac matrices, covariant realization of the Dirac equation, interpretation of negative energies, Foldy-Wouthuysen transformation, Klein's paradox, spherically symmetric interactions and a treatment of the relativistic hydrogen atom, etc., and also provides excellent additional treatments of a variety of other relevant topics. The monograph contains an extensive treatment of the Lorentz and Poincare groups and their representations. The author discusses in depth Lie algebaic and projective representations, covering groups, and Mackey's theory and Wigner's realization of induced representations. A careful classification of external fields with respect to their behavior under Poincare transformations is supplemented by a basic account of self-adjointness and spectral properties of Dirac operators. A state-of-the-art treatment of relativistic scattering theory based on a time-dependent approach originally due to Enss is presented. An excellent introduction to quantum electrodynamics in external fields is provided. Various appendices containing further details, notes on each chapter commenting on the history involved and referring to original research papers and further developments in the literature, and a bibliography covering all relevant monographs and over 500 articles on the subject, complete this text. This book should satisfy the needs of a wide audience, ranging from graduate students in theoretical physics and mathematics to researchers interested in mathematical physics
Growth Equation with Conservation Law
Lauritsen, Kent Baekgaard
1995-01-01
A growth equation with a generalized conservation law characterized by an integral kernel is introduced. The equation contains the Kardar-Parisi-Zhang, Sun-Guo-Grant, and Molecular-Beam Epitaxy growth equations as special cases and allows for a unified investigation of growth equations. From a dynamic renormalization-group analysis critical exponents and universality classes are determined for growth models with a conservation law.
``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.
Understanding Cancer Prognosis
Full Text Available ... Renal Cell) Cancer Leukemia Lung Cancer Lymphoma Pancreatic Cancer Prostate Cancer Skin Cancer Thyroid Cancer Uterine Cancer All ... Cancer Biology Cancer Genomics Causes of Cancer Diagnosis Prevention Screening & Early Detection Treatment Cancer & Public Health Cancer ...
... Cancer? Breast Cancer Colon/Rectum Cancer Lung Cancer Prostate Cancer Skin Cancer Show All Cancer Types News and Features Cancer Glossary ACS Bookstore Cancer Information Cancer Basics Cancer Prevention & Detection Signs & Symptoms of Cancer Treatments & Side Effects ...
... Renal Cell) Cancer Leukemia Lung Cancer Lymphoma Pancreatic Cancer Prostate Cancer Skin Cancer Thyroid Cancer Uterine Cancer All ... Cancer Treatment Prostate Cancer Prevention Genetics of Prostate Cancer Prostate Cancer Screening Research Prostate Cancer Treatment (PDQ®)–Patient ...
Hyperbolic Methods for Einstein's Equations
Reula Oscar
1998-01-01
I review evolutionary aspects of general relativity, in particular those related to the hyperbolic character of the field equations and to the applications or consequences that this property entails. I look at several approaches to obtaining symmetric hyperbolic systems of equations out of Einstein's equations by either removing some gauge freedoms from them, or by considering certain linear combinations of a subset of them.
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.
Solving Nonlinear Coupled Differential Equations
Mitchell, L.; David, J.
1986-01-01
Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.
The Schroedinger equation and spin
International Nuclear Information System (INIS)
Galilei invariance of the Schroedinger equation requires linearization of the operator by the introduction of anticommuting matrices as coefficients of the linear form. In an external field this leads directly to the Pauli equation, the non-relativistic limit of Dirac's equation. An overview of the complete argument that defines spin as a non-relativistic concept is presented. 9 refs
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...
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....
Chaliasos, Evangelos
2006-01-01
As we know, from the Einstein equations the vanishing of the four-divergence of the energy-momentum tensor follows. This is the case because the four-divergence of the Einstein tensor vanishes identically. Inversely, we find that from the vanishing of the four-divergence of the energy-momentum tensor not only the Einstein equations follow. Besides, the so-named anti-Einstein equations follow. These equations must be considered as complementary to the Einstein equations. And while from the Ein...
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.
Equation with the many fathers
DEFF Research Database (Denmark)
Kragh, Helge
1984-01-01
of the usual Schrödinger equation. In most of the early versions the Klein-Gordon equation was connected with the general theory of relativity. Klein and some other physicists attempted to express quantum mechanics within a five-dimensional unified theory, embracing general relativity as well......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...
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
Generalized Klein-Kramers equations
Fa, Kwok Sau
2012-12-01
A generalized Klein-Kramers equation for a particle interacting with an external field is proposed. The equation generalizes the fractional Klein-Kramers equation introduced by Barkai and Silbey [J. Phys. Chem. B 104, 3866 (2000), 10.1021/jp993491m]. Besides, the generalized Klein-Kramers equation can also recover the integro-differential Klein-Kramers equation for continuous-time random walk; this means that it can describe the subdiffusive and superdiffusive regimes in the long-time limit. Moreover, analytic solutions for first two moments both in velocity and displacement (for force-free case) are obtained, and their dynamic behaviors are investigated.
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.
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.)
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...
Cardona, Carlos
2016-01-01
Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a $\\mathbb{C}P^2$ space. We show that for the simplest integrand, namely the ${\\rm n-gon}$, our proposal indeed reproduces the expected result. By using the recently formulated $\\Lambda-$algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.
$\\Lambda$ 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.
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.
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.
Alain Cornet; Martine De Mazière; Christian Hermans; Alexis Merlaud
2012-01-01
Direct Sun light absorption by trace gases can be used to quantify them and investigate atmospheric chemistry. In such experiments, the main optical apparatus is often a grating or a Fourier transform spectrometer. A solar tracker based on motorized rotating mirrors is also needed to direct the light along the spectrometer axis, correcting for the apparent rotation of the Sun. Calculating the Sun azimuth and altitude for a given time and location can be achieved with high accuracy but differe...
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...
Institute of Scientific and Technical Information of China (English)
曾凤伟; 李建芳; 谢良骏; 张峰; 彭小林; 吴春兴; 程木华
2014-01-01
Objective To compare the applications of renal dynamic imaging with 99m Tc-DTPA ( Gates′met-hod), abbreviated MDRD (aMDRD) equation and CKD-EPI equation in renal function assessment in the patients with chronic kidney disease ( CKD) .Methods A total of 159 adult patients with CKD were included .The glomerular filtra-tion rate (GFR) obtained by Gates′method, aMDRD equation and CKD-EPI equation against 99mTc-DTPA dual plasma clearance ( rGFR) with Pearson correlational analyses and Bland -Altman method were performed .Results A statistical-ly significant correlation was found between rGFR and Gates′method (r=0.900, P0.05).Conclusion All three methods underestimate the rGFR, the new CDK-EPI equa-tion performs no better than aMDRD equation .Both equations can′t provide as much accuracy as Gates′method.%目的：比较99m Tc-DTPA肾动态显像（ Gates′法）、简化MDRD方程及CKD-EPI方程评价慢性肾脏病（ CKD）患者肾小球滤过率（ GFR）的价值。方法选择CKD成人患者159例，以双血浆法测定的GFR（ rGFR）作为参照，应用Pearson相关分析及Bland-Altman分析比较Gates′法、简化MDRD方程及CKD-EPI方程估算的GFR（eGFR）的相关性、一致性及准确性。结果 Gates′法估测的eGFR与rGFR呈正相关（r＝0.900，P＜0.001），高于简化MDRD方程（r＝0.816，P＜0.001）及CKD-EPI方程（r＝0.825，P＜0.001）。3种方法都低估了rGFR值，但是Gates′法的偏差最小[-3.4 mL/（min·1.73 m2）]、精确度最高[11.8 mL/（min·1.73 m2）]、±30％的准确性最高（71.7％）。除了CKD1～2期，Gates′法±30％的准确性均高于简化MDRD方程及CKD-EPI方程（ P＜0.05）。简化MDRD方程与CKD-EPI方程准确性比较差异无统计学意义（P＞0.05）。结论3种方法均低估了rGFR。 CKD-EPI方程并不优于简化MDRD方程。 Gates′法的准确性高于其他两种方程。
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.
Atanassov, Atanas Marinov
2010-01-01
Different possible sources are discussed for enhancement of the calculation time when solving ordinary differential equations systems to forecast space objects' motion. This paper presents an approach for building an integrator of ordinary differential equations systems for simultaneous solving of motion equations of multiple objects. A parallelization of calculation on the base of threads is offered. A method for synchronization is presented. The technological advance and the invasion of mul...
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
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,...
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
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.
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.
Some comments on `Equation for the second virial coefficient`
Umirzakov, I. H.
2013-01-01
The second viral coefficient calculated using the equation suggested in the paper of Kaplun A.B., Meshalkin A.B. Equation for the second virial coefficient published in High temperature high pressure, 1999, Volume 31, pages 253-258 is compared with experimental data for helium, hydrogen, neon, argon, krypton, xenon, carbon dioxide, water, ammonia, methane, ethylene. It is shown the formula cannot describe the temperature dependence of the experimental data on the second virial coefficient for...
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.
Equation of state for detonation product gases
International Nuclear Information System (INIS)
Based on the empirical linear relationship between detonation velocity and loading density, an approximate description for the Chapman-Jouguet (CJ) state for detonation product gases has been presented. Assuming that the Grüneisen parameter is a function only of volume, we obtained the Grüneisen parameter along CJ states. Thermodynamic identity between the Grüneisen parameter and another non-dimensional material parameter R used in the Rice-Walsh type equation of state introduced by Wu and Jing can be used to derive the enthalpy-pressure-volume equation of state for detonation gases. Behavior of this parameter R as a function of pressure is calculated and revealed that their change with pressure is very gradual and seems to approach a finite value with decreasing pressure. Release isentropes from CJ states of several initial density detonation of PETN is shown.