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.
Difference equations in massive higher order calculations
International Nuclear Information System (INIS)
Bierenbaum, I.; Bluemlein, J.; Klein, S.; Schneider, C.
2007-07-01
The calculation of massive 2-loop operator matrix elements, required for the higher order Wilson coefficients for heavy flavor production in deeply inelastic scattering, leads to new types of multiple infinite sums over harmonic sums and related functions, which depend on the Mellin parameter N. We report on the solution of these sums through higher order difference equations using the summation package Sigma. (orig.)
The new pooled cohort equations risk calculator
DEFF Research Database (Denmark)
Preiss, David; Kristensen, Søren L
2015-01-01
disease and any measure of social deprivation. An early criticism of the Pooled Cohort Equations Risk Calculator has been its alleged overestimation of ASCVD risk which, if confirmed in the general population, is likely to result in statin therapy being prescribed to many individuals at lower risk than...
Standardization of equations for radiochemical calculations
International Nuclear Information System (INIS)
Danahy, R.J.; Dugan, T.A.; Tomlinson, F.K.; Jones, H.W.
1994-01-01
In mid 1993, the Fernald Environmental Restoration Management Corporation (FERMCO), with USEPA approval implemented a project quality assurance plan containing performance-based specifications for radiochemical sample analyses conducted in support of the Fernald site remediation activities. FERMCO's initial approach to acquiring performance-based radioanalytical services was to provide limited guidance regarding equations for computation of the quantities required in each analysis report. It became evident that there was a significant divergence of opinion on how to compute some very basic radiochemical quantities. The use of a standardized set of equations was needed in order to ensure comparability of data from different laboratories. In a remediation project of this magnitude, use of multiple laboratories is a virtual necessity. Consequently comparability of data becomes an extremely important issue. A critical issue in the Remedial Investigation/Feasibility Study (RI/FS) phase of the dean up project is to avoid the occurrence of excessive false positive sample results. Such results could lead to unnecessary clean up and significant additional cost. This paper describes the specific formulas FERMCO is currently using to define such quantities as net sample count rate, sample radionuclide concentration, radiometric tracer and gravimetric carrier recovery. Equations have also been produced to define the uncertainty in each of the above quantities. Equations for the Total Propagated Uncertainty (TPU) and for a sample-specific Minimum Detectable Concentration (MDC) have also been specified. Generalized equations have been reformulated to address the specific conditions which apply to the analysis of FERMCO samples. In particular, FERMCO requires results which have been corrected for the radioactivity in the blank while in other instances, sample results without blank correction are required
Programmable calculator programs to solve softwood volume and value equations.
Janet K. Ayer. Sachet
1982-01-01
This paper presents product value and product volume equations as programs for handheld calculators. These tree equations are for inland Douglas-fir, young-growth Douglas-fir, western white pine, ponderosa pine, and western larch. Operating instructions and an example are included.
Equation for calculation of nitrogen solubility in iron alloys
International Nuclear Information System (INIS)
Pomarin, Yu.M.; Grigorenko, G.M.
1989-01-01
Equation for calculating nitrogen solubility in multicomponent iron melts in a wide range of partial pressures (1-1600 kPa), of doping component concentrations and temperatures (1773-2373 K) is proposed. Comparative analysis of experimental and calculated values of nitrogen solubility has demonstrated a principle possibility of applying the equation proposed for evaluating absorption ability to nitrogen of industrial nitrogen containing steels and ferroalloys subjected to melting or remelting in plasma or other melting devices
Recursive integral equations with positive kernel for lattice calculations
International Nuclear Information System (INIS)
Illuminati, F.; Isopi, M.
1990-11-01
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
Changes of the calculation equation for σMUF
International Nuclear Information System (INIS)
Yoshida, Hideki; Niiyama, Toshitaka; Sonobe, Kentaro
2002-01-01
The error variance (σ MUF 2 ) of the material accountancy for the material balance is used for evaluating the MUF of the conventional material accountancy and the near real time material accountancy (NRTA). The σ MUF 2 calculated by the error propagation using the material accounting data and the measurement error. The error propagation equation of σ MUF 2 written on the text of 'The statistical concepts and technique for IAEA safeguards (IAEA/SG/SCT5)'. There are some assumptions in order to simplify the equation. These assumptions are available in the assessment of the facility design. However when the σ MUF 2 of the actual MUF is calculated, it is necessary to drop some assumptions and modify the adapted equation. Furthermore, because the material balance is more frequently taken for NRTA, the inventory of all times cannot be always re-measured at each time. To be solved the matter, the error propagation equation has to be modified. For a reprocessing plant which has material in solution, the equation has been improved to obtain more exact equation. In this paper we present the changes of the error propagation for σ MUF 2 and explain the features. (author)
Opacity calculations and Saha's equation for high Z elements
International Nuclear Information System (INIS)
Godwal, B.K.; Sikka, S.K.
1977-01-01
Opacity calculations are needed for energy transport by radiation for high Z element plasmas as these have been suggested as temper materials in laser, electron beam and heavy ion fusion schemes. The pressure ionised modified form of Saha's ionisation equation has been used to obtain the free electron density, populations of various ionic species and the populations of various energy states for a given ion. Results are presented for two typical elements; tungsten and uranium. The ionisation potential have been evaluated using the Bohr's formula with suitable effective screened charges for ions. The results show that for uranium, even at a temperature of 10 kev, the K shell is intact. The reliability of the Saha's equation solution has been checked by comparing the equation of state (total pressure vs total energy curve) with that given by the Thomas-Fermi-Dirac equation of state. The agreement between the two is good from temperature upwards of 0.2 kev. (author)
Parametric equations for calculation of macroscopic cross sections
International Nuclear Information System (INIS)
Botelho, Mario Hugo; Carvalho, Fernando
2015-01-01
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)
Differential equations with applications in cancer diseases.
Ilea, M; Turnea, M; Rotariu, M
2013-01-01
Mathematical modeling is a process by which a real world problem is described by a mathematical formulation. The cancer modeling is a highly challenging problem at the frontier of applied mathematics. A variety of modeling strategies have been developed, each focusing on one or more aspects of cancer. The vast majority of mathematical models in cancer diseases biology are formulated in terms of differential equations. We propose an original mathematical model with small parameter for the interactions between these two cancer cell sub-populations and the mathematical model of a vascular tumor. We work on the assumption that, the quiescent cells' nutrient consumption is long. One the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. MATLAB simulations obtained for transition rate from the quiescent cells' nutrient consumption is long, we show a similar asymptotic behavior for two solutions of the perturbed problem. In this system, the small parameter is an asymptotic variable, different from the independent variable. The graphical output for a mathematical model of a vascular tumor shows the differences in the evolution of the tumor populations of proliferating, quiescent and necrotic cells. The nutrient concentration decreases sharply through the viable rim and tends to a constant level in the core due to the nearly complete necrosis in this region. Many mathematical models can be quantitatively characterized by ordinary differential equations or partial differential equations. The use of MATLAB in this article illustrates the important role of informatics in research in mathematical modeling. The study of avascular tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.
Automatic calculation of supersymmetric renormalization group equations and loop corrections
Staub, Florian
2011-03-01
SARAH is a Mathematica package for studying supersymmetric models. It calculates for a given model the masses, tadpole equations and all vertices at tree-level. This information can be used by SARAH to write model files for CalcHep/ CompHep or FeynArts/ FormCalc. In addition, the second version of SARAH can derive the renormalization group equations for the gauge couplings, parameters of the superpotential and soft-breaking parameters at one- and two-loop level. Furthermore, it calculates the one-loop self-energies and the one-loop corrections to the tadpoles. SARAH can handle all N=1 SUSY models whose gauge sector is a direct product of SU(N) and U(1) gauge groups. The particle content of the model can be an arbitrary number of chiral superfields transforming as any irreducible representation with respect to the gauge groups. To implement a new model, the user has just to define the gauge sector, the particle, the superpotential and the field rotations to mass eigenstates. Program summaryProgram title: SARAH Catalogue identifier: AEIB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 97 577 No. of bytes in distributed program, including test data, etc.: 2 009 769 Distribution format: tar.gz Programming language: Mathematica Computer: All systems that Mathematica is available for Operating system: All systems that Mathematica is available for Classification: 11.1, 11.6 Nature of problem: A supersymmetric model is usually characterized by the particle content, the gauge sector and the superpotential. It is a time consuming process to obtain all necessary information for phenomenological studies from these basic ingredients. Solution method: SARAH calculates the complete Lagrangian for a given model whose
Calculation of similarity solutions of partial differential equations
International Nuclear Information System (INIS)
Dresner, L.
1980-08-01
When a partial differential equation in two independent variables is invariant to a group G of stretching transformations, it has similarity solutions that can be found by solving an ordinary differential equation. Under broad conditions, this ordinary differential equation is also invariant to another stretching group G', related to G. The invariance of the ordinary differential equation to G' can be used to simplify its solution, particularly if it is of second order. Then a method of Lie's can be used to reduce it to a first-order equation, the study of which is greatly facilitated by analysis of its direction field. The method developed here is applied to three examples: Blasius's equation for boundary layer flow over a flat plate and two nonlinear diffusion equations, cc/sub t/ = c/sub zz/ and c/sub t/ = (cc/sub z/)/sub z/
Equations for calculating interfacial drag and shear from void fraction correlations
International Nuclear Information System (INIS)
Putney, J.M.
1988-12-01
Equations are developed for calculating interfacial drag and shear coefficients for dispersed vapour flows from void fraction correlations. The equations have a sound physical basis and lead to physically correct coefficients in all flow situations. (author)
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
Optimum biasing of integral equations in Monte Carlo calculations
International Nuclear Information System (INIS)
Hoogenboom, J.E.
1979-01-01
In solving integral equations and estimating average values with the Monte Carlo method, biasing functions may be used to reduce the variancee of the estimates. A simple derivation was used to prove the existence of a zero-variance collision estimator if a specific biasing function and survival probability are applied. This optimum biasing function is the same as that used for the well known zero-variance last-event estimator
Biased calculations: Numeric anchors influence answers to math equations
Directory of Open Access Journals (Sweden)
Andrew R. Smith
2011-02-01
Full Text Available People must often perform calculations in order to produce a numeric estimate (e.g., a grocery-store shopper estimating the total price of his or her shopping cart contents. The current studies were designed to test whether estimates based on calculations are influenced by comparisons with irrelevant anchors. Previous research has demonstrated that estimates across a wide range of contexts assimilate toward anchors, but none has examined estimates based on calculations. In two studies, we had participants compare the answers to math problems with anchors. In both studies, participants' estimates assimilated toward the anchor values. This effect was moderated by time limit such that the anchoring effects were larger when the participants' ability to engage in calculations was limited by a restrictive time limit.
Elementary exact calculations of degree growth and entropy for discrete equations.
Halburd, R G
2017-05-01
Second-order discrete equations are studied over the field of rational functions [Formula: see text], where z is a variable not appearing in the equation. The exact degree of each iterate as a function of z can be calculated easily using the standard calculations that arise in singularity confinement analysis, even when the singularities are not confined. This produces elementary yet rigorous entropy calculations.
Directory of Open Access Journals (Sweden)
Thomas Gomez
2018-04-01
Full Text Available Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods. Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numerical complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. This technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.
Numerical calculation of the cross section by the solution of the wave equation
International Nuclear Information System (INIS)
Drewko, J.
1982-01-01
A numerical method of solving of the wave equation is described for chosen vibrational eigenfunctions. A prepared program calculates the total cross sections for the resonant vibrational excitation for diatomic molecules on the basis of introduced molecular data. (author)
The transition equation of the state intensities for exciton model and the calculation program
International Nuclear Information System (INIS)
Yu Xian; Zheng Jiwen; Liu Guoxing; Chen Keliang
1995-01-01
An equation set of the exciton model is given and calculation program is developed. The process of approaching to equilibrium state has been investigated with the program for 12 C + 64 Ni reaction at energy 72 MeV
Fast and accurate calculation of dilute quantum gas using Uehling–Uhlenbeck model equation
Energy Technology Data Exchange (ETDEWEB)
Yano, Ryosuke, E-mail: ryosuke.yano@tokiorisk.co.jp
2017-02-01
The Uehling–Uhlenbeck (U–U) model equation is studied for the fast and accurate calculation of a dilute quantum gas. In particular, the direct simulation Monte Carlo (DSMC) method is used to solve the U–U model equation. DSMC analysis based on the U–U model equation is expected to enable the thermalization to be accurately obtained using a small number of sample particles and the dilute quantum gas dynamics to be calculated in a practical time. Finally, the applicability of DSMC analysis based on the U–U model equation to the fast and accurate calculation of a dilute quantum gas is confirmed by calculating the viscosity coefficient of a Bose gas on the basis of the Green–Kubo expression and the shock layer of a dilute Bose gas around a cylinder.
Calculation of 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.
A deterministic partial differential equation model for dose calculation in electron radiotherapy.
Duclous, R; Dubroca, B; Frank, M
2010-07-07
High-energy ionizing radiation is a prominent modality for the treatment of many cancers. The approaches to electron dose calculation can be categorized into semi-empirical models (e.g. Fermi-Eyges, convolution-superposition) and probabilistic methods (e.g.Monte Carlo). A third approach to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. We derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on Berthon et al (2007 J. Sci. Comput. 31 347-89) that exactly preserves the key properties of the analytical solution on the discrete level. We discuss several test cases taken from the medical physics literature. A test case with an academic Henyey-Greenstein scattering kernel is considered. We compare our model to a benchmark discrete ordinate solution. A simplified model of electron interactions with tissue is employed to compute the dose of an electron beam in a water phantom, and a case of irradiation of the vertebral column. Here our model is compared to the PENELOPE Monte Carlo code. In the academic example, the fluences computed with the new model and a benchmark result differ by less than 1%. The depths at half maximum differ by less than 0.6%. In the two comparisons with Monte Carlo, our model gives qualitatively reasonable dose distributions. Due to the crude interaction model, these so far do not have the accuracy needed in clinical practice. However, the new model has a computational cost that is less than one-tenth of the cost of a Monte Carlo simulation. In addition, simulations can be set up in a similar way as a Monte Carlo simulation. If more detailed effects such as coupled electron-photon transport, bremsstrahlung
A deterministic partial differential equation model for dose calculation in electron radiotherapy
Duclous, R.; Dubroca, B.; Frank, M.
2010-07-01
High-energy ionizing radiation is a prominent modality for the treatment of many cancers. The approaches to electron dose calculation can be categorized into semi-empirical models (e.g. Fermi-Eyges, convolution-superposition) and probabilistic methods (e.g. Monte Carlo). A third approach to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. We derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on Berthon et al (2007 J. Sci. Comput. 31 347-89) that exactly preserves the key properties of the analytical solution on the discrete level. We discuss several test cases taken from the medical physics literature. A test case with an academic Henyey-Greenstein scattering kernel is considered. We compare our model to a benchmark discrete ordinate solution. A simplified model of electron interactions with tissue is employed to compute the dose of an electron beam in a water phantom, and a case of irradiation of the vertebral column. Here our model is compared to the PENELOPE Monte Carlo code. In the academic example, the fluences computed with the new model and a benchmark result differ by less than 1%. The depths at half maximum differ by less than 0.6%. In the two comparisons with Monte Carlo, our model gives qualitatively reasonable dose distributions. Due to the crude interaction model, these so far do not have the accuracy needed in clinical practice. However, the new model has a computational cost that is less than one-tenth of the cost of a Monte Carlo simulation. In addition, simulations can be set up in a similar way as a Monte Carlo simulation. If more detailed effects such as coupled electron-photon transport, bremsstrahlung
Directory of Open Access Journals (Sweden)
Pedro L. Valencia
2017-04-01
Full Text Available We provide initial rate data from enzymatic reaction experiments and tis processing to estimate the kinetic parameters from the substrate uncompetitive inhibition equation using the median method published by Eisenthal and Cornish-Bowden (Cornish-Bowden and Eisenthal, 1974; Eisenthal and Cornish-Bowden, 1974. The method was denominated the direct linear plot and consists in the calculation of the median from a dataset of kinetic parameters Vmax and Km from the Michaelis–Menten equation. In this opportunity we present the procedure to applicate the direct linear plot to the substrate uncompetitive inhibition equation; a three-parameter equation. The median method is characterized for its robustness and its insensibility to outlier. The calculations are presented in an Excel datasheet and a computational algorithm was developed in the free software Python. The kinetic parameters of the substrate uncompetitive inhibition equation Vmax, Km and Ks were calculated using three experimental points from the dataset formed by 13 experimental points. All the 286 combinations were calculated. The dataset of kinetic parameters resulting from this combinatorial was used to calculate the median which corresponds to the statistic estimator of the real kinetic parameters. A comparative statistical analyses between the median method and the least squares was published in Valencia et al. [3].
Energy Technology Data Exchange (ETDEWEB)
Surdoval, Wayne A. [National Energy Technology Lab. (NETL), Pittsburgh, PA, (United States); Berry, David A. [National Energy Technology Lab. (NETL), Morgantown, WV (United States); Shultz, Travis R. [National Energy Technology Lab. (NETL), Morgantown, WV (United States)
2018-03-09
A set of equations are presented for calculating atomic principal spectral lines and fine-structure energy splits for single and multi-electron atoms. Calculated results are presented and compared to the National Institute of Science and Technology database demonstrating very good accuracy. The equations do not require fitted parameters. The only experimental parameter required is the Ionization energy for the electron of interest. The equations have comparable accuracy and broader applicability than the single electron Dirac equation. Three Appendices discuss the origin of the new equations and present calculated results. New insights into the special relativistic nature of the Dirac equation and its relationship to the new equations are presented.
Equation-of-motion coupled cluster method for high spin double electron attachment calculations
Energy Technology Data Exchange (ETDEWEB)
Musiał, Monika, E-mail: musial@ich.us.edu.pl; Lupa, Łukasz; Kucharski, Stanisław A. [Institute of Chemistry, University of Silesia, Szkolna 9, 40-006 Katowice (Poland)
2014-03-21
The new formulation of the equation-of-motion (EOM) coupled cluster (CC) approach applicable to the calculations of the double electron attachment (DEA) states for the high spin components is proposed. The new EOM equations are derived for the high spin triplet and quintet states. In both cases the new equations are easier to solve but the substantial simplification is observed in the case of quintets. Out of 21 diagrammatic terms contributing to the standard DEA-EOM-CCSDT equations for the R{sub 2} and R{sub 3} amplitudes only four terms survive contributing to the R{sub 3} part. The implemented method has been applied to the calculations of the excited states (singlets, triplets, and quintets) energies of the carbon and silicon atoms and potential energy curves for selected states of the Na{sub 2} (triplets) and B{sub 2} (quintets) molecules.
Hardouin, Charlotte; Minchenko, Andrei; Ovchinnikov, Alexey
2015-01-01
The main motivation of our work is to create an efficient algorithm that decides hypertranscendence of solutions of linear differential equations, via the parameterized differential and Galois theories. To achieve this, we expand the representation theory of linear differential algebraic groups and develop new algorithms that calculate unipotent radicals of parameterized differential Galois groups for differential equations whose coefficients are rational functions. P. Berman and M.F. Singer ...
International Nuclear Information System (INIS)
Mamikonyan, S.V.; Berezkin, V.V.; Lyubimova, S.V.; Svetajlo, Yu.N.; Shchekin, K.I.
1978-01-01
A method to derive multiple regression equations for X-ray radiometric analysis is described. Te method is realized in the form of the REGRA program in an algorithmic language. The subprograms included in the program are describe. In analyzing cement for Mg, Al, Si, Ca and Fe contents as an example, the obtainment of working equations in the course of calculations by the program is shown to simpliy the realization of computing devices in instruments for X-ray radiometric analysis
Making sense of cancer risk calculators on the web.
Levy, Andrea Gurmankin; Sonnad, Seema S; Kurichi, Jibby E; Sherman, Melani; Armstrong, Katrina
2008-03-01
Cancer risk calculators on the internet have the potential to provide users with valuable information about their individual cancer risk. However, the lack of oversight of these sites raises concerns about low quality and inconsistent information. These concerns led us to evaluate internet cancer risk calculators. After a systematic search to find all cancer risk calculators on the internet, we reviewed the content of each site for information that users should seek to evaluate the quality of a website. We then examined the consistency of the breast cancer risk calculators by having 27 women complete 10 of the breast cancer risk calculators for themselves. We also completed the breast cancer risk calculators for a hypothetical high- and low-risk woman, and compared the output to Surveillance Epidemiology and End Results estimates for the average same-age and same-race woman. Nineteen sites were found, 13 of which calculate breast cancer risk. Most sites do not provide the information users need to evaluate the legitimacy of a website. The breast cancer calculator sites vary in the risk factors they assess to calculate breast cancer risk, how they operationalize each risk factor and in the risk estimate they provide for the same individual. Internet cancer risk calculators have the potential to provide a public health benefit by educating individuals about their risks and potentially encouraging preventive health behaviors. However, our evaluation of internet calculators revealed several problems that call into question the accuracy of the information that they provide. This may lead the users of these sites to make inappropriate medical decisions on the basis of misinformation.
International Nuclear Information System (INIS)
Wang Huaiyu; Long Yao; Chen Nanxian
2006-01-01
In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin quantum number S. The Chebyshev equation is transformed from an ordinary differential equation obtained when we dealt with Heisenberg model, in order to calculate all three components of magnetization, by many-body Green's function under random phase approximation. The Chebyshev functions with argument being greater than 1 are discussed. This paper shows that the Chebyshev polynomials with their argument being greater than 1 have their physical application.
Ishizaki, Akihito; Tanimura, Yoshitaka
2008-05-01
Based on the influence functional formalism, we have derived a nonperturbative equation of motion for a reduced system coupled to a harmonic bath with colored noise in which the system-bath coupling operator does not necessarily commute with the system Hamiltonian. The resultant expression coincides with the time-convolutionless quantum master equation derived from the second-order perturbative approximation, which is also equivalent to a generalized Redfield equation. This agreement occurs because, in the nonperturbative case, the relaxation operators arise from the higher-order system-bath interaction that can be incorporated into the reduced density matrix as the influence operator; while the second-order interaction remains as a relaxation operator in the equation of motion. While the equation describes the exact dynamics of the density matrix beyond weak system-bath interactions, it does not have the capability to calculate nonlinear response functions appropriately. This is because the equation cannot describe memory effects which straddle the external system interactions due to the reduced description of the bath. To illustrate this point, we have calculated the third-order two-dimensional (2D) spectra for a two-level system from the present approach and the hierarchically coupled equations approach that can handle quantal system-bath coherence thanks to its hierarchical formalism. The numerical demonstration clearly indicates the lack of the system-bath correlation in the present formalism as fast dephasing profiles of the 2D spectra.
Sohn, J. L.; Heinrich, J. C.
1990-01-01
The calculation of pressures when the penalty-function approximation is used in finite-element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least-squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.
Simple renormalization group method for calculating geometrical and other equations of states
International Nuclear Information System (INIS)
Tsallis, C.; Schwaccheim, G.; Coniglio, A.
1984-01-01
A real space renormalization group procedure to calculate geometrical and thermal equations of states for the entire range of values of the external parameters is described. Its use is as simple as a Mean Field Approximation; however, it yields non trivial results and can be systematically improved. Such a procedure is illustrated by calculating, for all bond concentrations, the site mass density for the complete and the backbone percolating infinite clusters in square lattice: the results are quite satisfactory. (Author) [pt
Analytical calculation of an invariant curve for Chew-Low equations
International Nuclear Information System (INIS)
Gerdt, V.P.
1978-01-01
The local structure of the one-parameter set of invariant curves for Chew-Low equations having the form of the convergent series is considered. Coefficients of this series βsub(i)(C) are polynomials in set parameter C. The transition to the general solution of Chew-Low equations is carried out by replacing the parameter C by arbitrary even, real, meromorphic function C(w) with the property C(w+1)=-C(w). The procedure for calculation of coefficients βsub(i)(C), which is based on the solution of nonlinear functional eqtions, following from Chew-Low equations, is developed. First twelve coefficients βsub(i)(C) are calculated analytically by computer, using program system SCHOONSCHIP
Empirical rate equation model and rate calculations of hydrogen generation for Hanford tank waste
International Nuclear Information System (INIS)
HU, T.A.
1999-01-01
Empirical rate equations are derived to estimate hydrogen generation based on chemical reactions, radiolysis of water and organic compounds, and corrosion processes. A comparison of the generation rates observed in the field with the rates calculated for twenty eight tanks shows agreement within a factor of two to three
Variational Calculation for the Equation of State of Hot Asymmetric Nuclear Matter
International Nuclear Information System (INIS)
Togashi, Hajime; Kanzawa, Hiroaki; Takano, Masatoshi
2010-01-01
We calculate the equation of state (EOS) of asymmetric nuclear matter at finite temperatures with the cluster variational method based on the realistic nuclear Hamiltonian composed of the AV18 and UIX nuclear potentials. The free energy is calculated with an extension of the variational method proposed by Schmidt and Pandharipande. The obtained thermodynamic quantities such as entropy, internal energy, pressure and chemical potential derived from the free energy are reasonable. It is also found that the present variational calculation is self-consistent. These thermodynamic quantities are essential ingredients in our project for constructing a new nuclear EOS applicable to supernova simulations.
Calculation of crystalline lens power in chickens with a customized version of Bennett's equation.
Iribarren, Rafael; Rozema, Jos J; Schaeffel, Frank; Morgan, Ian G
2014-03-01
This paper customizes Bennett's equation for calculating lens power in chicken eyes from refraction, keratometry and biometry. Previously published data on refraction, corneal power, anterior chamber depth, lens thickness, lens radii of curvature, axial length and eye power in chickens aged 10-90 days were used to estimate Gullstrand's lens power and Bennett's lens power for chicken eyes, and to calculate the lens equivalent refractive index. Bennett's A and B constants for the front and back surface powers of the lens were calculated for data measured from day 10 to 90 at 10 day intervals, and mean customized constants were calculated. The mean customized constants for Bennett's equation for chicks were A=0.574±0.023 and B=0.379±0.021. As found previously, lens power decreases with age in chicks, while corneal power decreases and axial length increases. The lens equivalent refractive index decreases with age from 10 to 90 days after hatching. Bennett's equation can be used to calculate lens power in chicken eyes for studies on animal myopia, using standard biometry. Copyright © 2014 Elsevier B.V. All rights reserved.
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.
Li, Changping; Park, Ki-Hong; Alouini, Mohamed-Slim
2014-01-01
In this report, we propose a fast numerical solution for the steady state radiative transfer equation in order to calculate the path loss due to light absorption and scattering in various type of underwater channels. In the proposed scheme, we apply a direct non-uniform method to discretize the angular space and an upwind type finite difference method to discretize the spatial space. A Gauss-Seidel iterative method is then applied to solve the fully discretized system of linear equations. The accuracy and efficiency of the proposed scheme is validated by Monte Carlo simulations.
International Nuclear Information System (INIS)
Belov, V.E.; Rodygin, L.V.; Fil'chenko, S.E.; Yunakovskii, A.D.
1988-01-01
A method is described for calculating the electrodynamic characteristics of periodically corrugated waveguide systems. This method is based on representing the field as the solution of the Helmholtz vector equation in the form of a simple layer potential, transformed with the use of the Floquet conditions. Systems of compound integral equations based on a weighted vector function of the simple layer potential are derived for waveguides with azimuthally symmetric and helical corrugations. A numerical realization of the Fourier method is cited for seeking the dispersion relation of azimuthally symmetric waves of a circular corrugated waveguide
A nodal collocation method for the calculation of the lambda modes of the P L equations
International Nuclear Information System (INIS)
Capilla, M.; Talavera, C.F.; Ginestar, D.; Verdu, G.
2005-01-01
P L equations are classical approximations to the neutron transport equation admitting a diffusive form. Using this property, a nodal collocation method is developed for the P L approximations, which is based on the expansion of the flux in terms of orthonormal Legendre polynomials. This method approximates the differential lambda modes problem by an algebraic eigenvalue problem from which the fundamental and the subcritical modes of the system can be calculated. To test the performance of this method, two problems have been considered, a homogeneous slab, which admits an analytical solution, and a seven-region slab corresponding to a more realistic problem
A four-equation friction model for water hammer calculation in quasi-rigid pipelines
International Nuclear Information System (INIS)
Ghodhbani, Abdelaziz; Haj Taïeb, Ezzeddine
2017-01-01
Friction coupling affects water hammer evolution in pipelines according to the initial flow regime. Unsteady friction models are only validated with uncoupled formulation. On the other hand, coupled models such as four-equation model, provide more accurate prediction of water hammer since fluid-structure interaction (FSI) is taken into account, but they are limited to steady-state friction formulation. This paper deals with the creation of the “four-equation friction model” which is based on the incorporation of the unsteady head loss given by an unsteady friction model into the four-equation model. For transient laminar flow cases, the Zielke model is considered. The proposed model is applied to a quasi-rigid pipe with axial moving valve, and then calculated by the method of characteristics (MOC). Damping and shape of the numerical solution are in good agreement with experimental data. Thus, the proposed model can be incorporated into a new computer code. - Highlights: • Both Zielke model and four-equation model are insufficient to predict water hammer. • The four-equation friction model proposed is obtained by incorporating the unsteady head loss in the four-equation model. • The solution obtained by the proposed model is in good agreement with experimental data. • The wave-speed adjustment scheme is more efficient than interpolations schemes.
The two-wave X-ray field calculated by means of integral-equation methods
International Nuclear Information System (INIS)
Bremer, J.
1984-01-01
The problem of calculating the two-wave X-ray field on the basis of the Takagi-Taupin equations is discussed for the general case of curved lattice planes. A two-dimensional integral equation which incorporates the nature of the incoming radiation, the form of the crystal/vacuum boundary, and the curvature of the structure, is deduced. Analytical solutions for the symmetrical Laue case with incoming plane waves are obtained directly for perfect crystals by means of iteration. The same method permits a simple derivation of the narrow-wave Laue and Bragg cases. Modulated wave fronts are discussed, and it is shown that a cut-off in the width of an incoming plane wave leads to lateral oscillations which are superimposed on the Pendelloesung fringes. Bragg and Laue shadow fields are obtained. The influence of a non-zero kernel is discussed and a numerical procedure for calculating wave amplitudes in curved crystals is presented. (Auth.)
Calculation of the power factor using the neutron diffusion hybrid equation
International Nuclear Information System (INIS)
Costa da Silva, Adilson; Carvalho da Silva, Fernando; Senra Martinez, Aquilino
2013-01-01
Highlights: ► A neutron diffusion hybrid equation with an external neutron source was used. ► Nodal expansion method to obtain the neutron flux was used. ► Nuclear power factors in each fuel element in the reactor core were calculated. ► The results obtained were very accurate. -- Abstract: In this paper, we used a neutron diffusion hybrid equation with an external neutron source to calculate nuclear power factors in each fuel element in the reactor core. We used the nodal expansion method to obtain the neutron flux for a given control rods bank position. The results were compared with results obtained for eigenvalue problem near criticality condition and fixed source problem during the start-up of the reactor, where external neutron sources are extremely important for the stabilization of external neutron detectors.
Correction of the calculation of beam loading based in the RF power diffusion equation
International Nuclear Information System (INIS)
Silva, R. da.
1980-01-01
It is described an empirical correction based upon experimental datas of others authors in ORELA, GELINA and SLAC accelerators, to the calculation of the energy loss due to the beam loading effect as stated by the RF power diffusion equation theory an accelerating structure. It is obtained a dependence of this correction with the electron pulse full width half maximum, but independent of the electron energy. (author) [pt
Calculation of Rayleigh type sums for zeros of the equation arising in spectral problem
Kostin, A. B.; Sherstyukov, V. B.
2017-12-01
For zeros of the equation (arising in the oblique derivative problem) μ J n ‧ ( μ ) cos α + i n J n ( μ ) sin α = 0 , μ ∈ ℂ , with parameters n ∈ ℤ, α ∈ [-π/2, π/2] and the Bessel function Jn (μ) special summation relationships are proved. The obtained results are consistent with the theory of well-known Rayleigh sums calculating by zeros of the Bessel function.
CSIR Research Space (South Africa)
Kirton, A
2010-08-01
Full Text Available for calculating the variance and prediction intervals for biomass estimates obtained from allometric equations A KIRTON B SCHOLES S ARCHIBALD CSIR Ecosystem Processes and Dynamics, Natural Resources and the Environment P.O. BOX 395, Pretoria, 0001, South... intervals (confidence intervals for predicted values) for allometric estimates can be obtained using an example of estimating tree biomass from stem diameter. It explains how to deal with relationships which are in the power function form - a common form...
Fast Near-Field Calculation for Volume Integral Equations for Layered Media
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Meincke, Peter; Breinbjerg, Olav
2005-01-01
. Afterwards, the scattered electric field can be easily computed at a regular rectangular grid on any horizontal plane us-ing a 2-dimensional FFT. This approach provides significant speedup in the near-field calculation in comparison to a straightforward numerical evaluation of the ra-diation integral since......An efficient technique based on the Fast Fourier Transform (FFT) for calculating near-field scattering by dielectric objects in layered media is presented. A higher or-der method of moments technique is employed to solve the volume integral equation for the unknown induced volume current density...
International Nuclear Information System (INIS)
Ma, Ting; Zhang, Zhongjie
2014-01-01
Irregular surface topography has revolutionized how seismic traveltime is calculated and the data are processed. There are two main schemes for dealing with an irregular surface in the seismic first-arrival traveltime calculation: (1) expanding the model and (2) flattening the surface irregularities. In the first scheme, a notional infill medium is added above the surface to expand the physical space into a regular space, as required by the eikonal equation solver. Here, we evaluate the chosen propagation velocity in the infill medium through ray path tracking with the eikonal equation-solved traveltime field, and observe that the ray paths will be physically unrealistic for some values of this propagation velocity. The choice of a suitable propagation velocity in the infill medium is crucial for seismic processing of irregular topography. Our model expansion criterion for dealing with surface topography in the calculation of traveltime and ray paths using the eikonal equation highlights the importance of both the propagation velocity of the infill physical medium and the topography gradient. (paper)
Abstract of programs for nuclear reactor calculation and kinetic equations solution
International Nuclear Information System (INIS)
Marakazov, A.A.
1977-01-01
The collection includes about 50 annotations of programmes,developed in the Kurchatov Atomic Energy Institute in 1971-1976. The programmes are intended for calculating the neutron flux, for solving systems of multigroup equations in P 3 approximation, for calculating the reactor cell, for analysing the system stability, breeding ratio etc. The programme annotations are compiled according to the following diagram: 1.Programme title. 2.Computer type. 3.Physical problem. 4.Solution method. 5.Calculation limitations. 6.Characteristic computer time. 7.Programme characteristic features. 8.Bound programmes. 9.Programme state. 10.Literature allusions in the programme. 11.Required memory resourses. 12.Programming language. 13.Operation system. 14.Names of authors and place of programme adjusting
Isothermal Multiphase Flash Calculations with the PC-SAFT Equation of State
International Nuclear Information System (INIS)
Justo-Garcia, Daimler N.; Garcia-Sanchez, Fernando; Romero-Martinez, Ascencion
2008-01-01
A computational approach for isothermal multiphase flash calculations with the PC-SAFT (Perturbed-Chain Statistical Associating Fluid Theory) equation of state is presented. In the framework of the study of fluid phase equilibria of multicomponent systems, the general multiphase problem is the single most important calculation which consists of finding the correct number and types of phases and their corresponding equilibrium compositions such that the Gibbs energy of the system is a minimum. For solving this problem, the system Gibbs energy was minimized using a rigorous method for thermodynamic stability analysis to find the most stable state of the system. The efficiency and reliability of the approach to predict and calculate complex phase equilibria are illustrated by solving three typical problems encountered in the petroleum industry
Mar, Javier; Sainz-Ezkerra, María; Moler-Cuiral, Jose Antonio
2008-01-01
Neurological diseases now make up 6.3% of the global burden of disease mainly because they cause disability. To assess disability, prevalence estimates are needed. The objective of this study is to apply a method based on differential equations to calculate the prevalence of stroke-related disability. On the basis of a flow diagram, a set of differential equations for each age group was constructed. The linear system was solved analytically and numerically. The parameters of the system were obtained from the literature. The model was validated and calibrated by comparison with previous results. The stroke prevalence rate per 100,000 men was 828, and the rate for stroke-related disability was 331. The rates steadily rose with age, but the group between the ages of 65 and 74 years had the highest total number of individuals. Differential equations are useful to represent the natural history of neurological diseases and to make possible the calculation of the prevalence for the various states of disability. In our experience, when compared with the results obtained by Markov models, the benefit of the continuous use of time outweighs the mathematical requirements of our model. (c) 2008 S. Karger AG, Basel.
A Study on the Consistency of Discretization Equation in Unsteady Heat Transfer Calculations
Directory of Open Access Journals (Sweden)
Wenhua Zhang
2013-01-01
Full Text Available The previous studies on the consistency of discretization equation mainly focused on the finite difference method, but the issue of consistency still remains with several problems far from totally solved in the actual numerical computation. For instance, the consistency problem is involved in the numerical case where the boundary variables are solved explicitly while the variables away from the boundary are solved implicitly. And when the coefficient of discretization equation of nonlinear numerical case is the function of variables, calculating the coefficient explicitly and the variables implicitly might also give rise to consistency problem. Thus the present paper mainly researches the consistency problems involved in the explicit treatment of the second and third boundary conditions and that of thermal conductivity which is the function of temperature. The numerical results indicate that the consistency problem should be paid more attention and not be neglected in the practical computation.
A reduction method for phase equilibrium calculations with cubic equations of state
Directory of Open Access Journals (Sweden)
D. V. Nichita
2006-09-01
Full Text Available In this work we propose a new reduction method for phase equilibrium calculations using a general form of cubic equations of state (CEOS. The energy term in the CEOS is a quadratic form, which is diagonalized by applying a linear transformation. The number of the reduction parameters is related to the rank of the matrix C with elements (1-Cij, where Cij denotes the binary interaction parameters (BIPs. The dimensionality of the problem depends only on the number of reduction parameters, and is independent of the number of components in the mixture.
Interaction and collective effects in classical-equations-of-motion calculations
International Nuclear Information System (INIS)
Bodmer, A.R.
1981-01-01
We discuss results obtained with the classical-equations-of-motion (CEOM) approach, with particular reference to interaction (potential energy) and collective effects in central collisions of equal mass nuclei. The essence of the CEOM approach is the classical calculation of all A = A/sub P/ + A/sub T/ trajectories using a 2-body potential V between all pairs of nucleons; V = V/sub short/ + V/sub long/ has a short range repulsion and a longer range attractive tail. In contrast to hydrodynamics, the CEOM approach is microscopic and includes transparency and nonequilibrium effects
Directory of Open Access Journals (Sweden)
Masuda Kazuhiko
2016-01-01
Full Text Available Backscattering properties of ice crystal models (Voronoi aggregates (VA, hexagonal columns (COL, and six-branched bullet rosettes (BR6 are calculated by using geometrical-opticsintegral-equation (GOIE method. Characteristics of depolarization ratio (δ and lidar ratio (L of the crystal models are examined. δ (L values are 0.2~0.3 (4~50, 0.3~0.4 (10~25, and 0.5~0.6 (50~100 for COL, BR6, and VA, respectively, at wavelength λ=0.532 μm. It is found that small deformation of COL model could produce significant changes in δ and L.
International Nuclear Information System (INIS)
Wills, John M.; Mattsson, Ann E.
2012-01-01
Brooks, Johansson, and Skriver, using the LMTO-ASA method and considerable insight, were able to explain many of the ground state properties of the actinides. In the many years since this work was done, electronic structure calculations of increasing sophistication have been applied to actinide elements and compounds, attempting to quantify the applicability of DFT to actinides and actinide compounds and to try to incorporate other methodologies (i.e. DMFT) into DFT calculations. Through these calculations, the limits of both available density functionals and ad hoc methodologies are starting to become clear. However, it has also become clear that approximations used to incorporate relativity are not adequate to provide rigorous tests of the underlying equations of DFT, not to mention ad hoc additions. In this talk, we describe the result of full-potential LMTO calculations for the elemental actinides, comparing results obtained with a full Dirac basis with those obtained from scalar-relativistic bases, with and without variational spin-orbit. This comparison shows that the scalar relativistic treatment of actinides does not have sufficient accuracy to provide a rigorous test of theory and that variational spin-orbit introduces uncontrolled errors in the results of electronic structure calculations on actinide elements.
Rock, N. M. S.; Duffy, T. R.
REGRES allows a range of regression equations to be calculated for paired sets of data values in which both variables are subject to error (i.e. neither is the "independent" variable). Nonparametric regressions, based on medians of all possible pairwise slopes and intercepts, are treated in detail. Estimated slopes and intercepts are output, along with confidence limits, Spearman and Kendall rank correlation coefficients. Outliers can be rejected with user-determined stringency. Parametric regressions can be calculated for any value of λ (the ratio of the variances of the random errors for y and x)—including: (1) major axis ( λ = 1); (2) reduced major axis ( λ = variance of y/variance of x); (3) Y on Xλ = infinity; or (4) X on Y ( λ = 0) solutions. Pearson linear correlation coefficients also are output. REGRES provides an alternative to conventional isochron assessment techniques where bivariate normal errors cannot be assumed, or weighting methods are inappropriate.
International Nuclear Information System (INIS)
Matthes, W.K.
1998-01-01
The 'adjoint transport equation in its integro-differential form' is derived for the radiation damage produced by atoms injected into solids. We reduce it to the one-dimensional form and prepare it for a numerical solution by: --discretizing the continuous variables energy, space and direction, --replacing the partial differential quotients by finite differences and --evaluating the collision integral by a double sum. By a proper manipulation of this double sum the adjoint transport equation turns into a (very large) set of linear equations with tridiagonal matrix which can be solved by a special (simple and fast) algorithm. The solution of this set of linear equations contains complete information on a specified damage type (e.g. the energy deposited in a volume V) in terms of the function D(i,E,c,x) which gives the damage produced by all particles generated in a cascade initiated by a particle of type i starting at x with energy E in direction c. It is essential to remark that one calculation gives the damage function D for the complete ranges of the variables {i,E,c and x} (for numerical reasons of course on grid-points in the {E,c,x}-space). This is most useful to applications where a general source-distribution S(i,E,c,x) of particles is given by the experimental setup (e.g. beam-window and and target in proton accelerator work. The beam-protons along their path through the window--or target material generate recoil atoms by elastic collisions or nuclear reactions. These recoil atoms form the particle source S). The total damage produced then is eventually given by: D = (Σ)i ∫ ∫ ∫ S(i, E, c, x)*D(i, E, c, x)*dE*dc*dx A Fortran-77 program running on a PC-486 was written for the overall procedure and applied to some problems
Calculational and experimental approaches to the equation of state of irradiated fuel
International Nuclear Information System (INIS)
Bober, M.; Breitung, W.; Karow, H.U.; Schumacher, G.
1977-07-01
The oxygen potential is an important parameter for the estimation of the vapor pressure of mixed oxide fuel and fission products. Dissolved fission products can have great influence on this potential in hypostoichiometric fuel. Therefore an attempt was made to calculate oxygen potentials of uranium-plutonium mixed oxides which contain fission products using models based on the equilibrium of oxygen defects. Vapor pressures have been calculated applying these data. The results of the calculation with various models differ especially at high temperatures above 4,000 K. Experimental work has been done to determine the vapor pressure of oxide fuel material at temperatures between 3,000 K and 5,000 K using laser beam heating. A measuring technique and a detailed evaluation model of laser evaporation measurements have been developed. The evaluation model describes the complex phenomena occurring during surface evaporation of liquid oxide fuel. Vapor pressure measurements with UO 2 have been carried out in the temperature region up to 4,500 K. With thermodynamic calculations the required equilibrium vapor pressures (EOS) can be derived from the vapor pressures measured. The caloric equation-of-state of the liquid-vapor equilibrium of the fuel up to temperatures of 5,000 K has been considered theoretically. (orig.) [de
Microscopic equation of state calculations: 1. Nuclear matter. 2. Liquid helium 3
International Nuclear Information System (INIS)
Heyer, J.P.
1989-01-01
A new method for calculating the equation of state of extended Fermi systems is proposed and applied to nuclear matter and liquid 3 He. New techniques are developed for summing up the particle-particle (pp) and particle-hole (ph) ring diagrams to all orders in the calculation of the ground state shift ΔE 0 for many-body systems. Analytic expressions for ΔE pp P 0 , the contribution from all of the pp ring diagrams to ΔE 0 , and ΔE ph 0 , the corresponding contribution from all of the ph ring diagrams, have been obtained. It has been shown that the pp ring diagram sum may be written as an integral over frequency, involving the particle-particle Green's function. A similar integral expression is derived for the ph ring diagram sum. Two methods are developed for carrying out the frequency integrations, namely the multipole and transition amplitude methods. These methods have been tested on an exactly-solvable many-fermion model, a modified Lipkin model, and compared. The author has studied the instability of nuclear matter at both zero and finite temperature within the pp ring diagram framework. He has found using the Gogny D1 effective nucleon-nucleon interaction, complex eigenvalues of an RPA-type secular equation are obtained in a well-defined temperature-density region. When complex eigenvalues occur, the thermodynamic potential becomes complex. The possible connection between the occurrence of complex eigenvalues and liquid-gas phase separation is discussed. The pp ring diagrams are also found to lower the compression modulus of nuclear matter. Lastly, the pp ring diagram method is applied to the calculation of the ground state energy of normal and spin-polarized liquid 3 He. We have found a binding energy per particle (BE/A) of 1.45 degree K and 1.79 degree K for the normal and spin-polarized systems, respectively
Use of the Boltzmann equation for calculating the scattering law in gas mixtures
International Nuclear Information System (INIS)
Eder, O.J.; Lackner, T.
1989-01-01
A new approach is presented for the calculation of the dynamical incoherent structure factor S s (q, ω) for a dilute binary gas mixture. The starting point is the linearized one-dimensional Boltzmann equation for a mixture of particles interacting via a quasi-Maxwell potential (V(r) ≅ 1/r ν , ν=4). It is shown how - in the Fourier-Laplace space (q, ω) - the solution of the Boltzman equation can be expressed as an infinite continued fraction. The well known hydrodynamic limit (q→0) and the free gas limit (q→∞) are correctly reproduced as the appropriate limits of the continued fraction. A brief comparison between S s (q, ω) for two interaction potentials (quasi-Maxwell potential, ν=4, and hard core potential, ν=∞) is presented, and it is found that, after scaling the variables to the respective diffusion coefficients, only little dependence on the potential remains. Furthermore, for a one-component system in three dimensions results are summarized for the dynamical incoherent and coherent structure factor. (orig.) [de
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.
Efficient implementation of core-excitation Bethe-Salpeter equation calculations
Gilmore, K.; Vinson, John; Shirley, E. L.; Prendergast, D.; Pemmaraju, C. D.; Kas, J. J.; Vila, F. D.; Rehr, J. J.
2015-12-01
We present an efficient implementation of the Bethe-Salpeter equation (BSE) method for obtaining core-level spectra including X-ray absorption (XAS), X-ray emission (XES), and both resonant and non-resonant inelastic X-ray scattering spectra (N/RIXS). Calculations are based on density functional theory (DFT) electronic structures generated either by ABINIT or QuantumESPRESSO, both plane-wave basis, pseudopotential codes. This electronic structure is improved through the inclusion of a GW self energy. The projector augmented wave technique is used to evaluate transition matrix elements between core-level and band states. Final two-particle scattering states are obtained with the NIST core-level BSE solver (NBSE). We have previously reported this implementation, which we refer to as OCEAN (Obtaining Core Excitations from Ab initio electronic structure and NBSE) (Vinson et al., 2011). Here, we present additional efficiencies that enable us to evaluate spectra for systems ten times larger than previously possible; containing up to a few thousand electrons. These improvements include the implementation of optimal basis functions that reduce the cost of the initial DFT calculations, more complete parallelization of the screening calculation and of the action of the BSE Hamiltonian, and various memory reductions. Scaling is demonstrated on supercells of SrTiO3 and example spectra for the organic light emitting molecule Tris-(8-hydroxyquinoline)aluminum (Alq3) are presented. The ability to perform large-scale spectral calculations is particularly advantageous for investigating dilute or non-periodic systems such as doped materials, amorphous systems, or complex nano-structures.
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
Srivastava, R. C.; Coen, J. L.
1992-01-01
The traditional explicit growth equation has been widely used to calculate the growth and evaporation of hydrometeors by the diffusion of water vapor. This paper reexamines the assumptions underlying the traditional equation and shows that large errors (10-30 percent in some cases) result if it is used carelessly. More accurate explicit equations are derived by approximating the saturation vapor-density difference as a quadratic rather than a linear function of the temperature difference between the particle and ambient air. These new equations, which reduce the error to less than a few percent, merit inclusion in a broad range of atmospheric models.
International Nuclear Information System (INIS)
Fujimura, Kaoru
1980-11-01
The numerical treatment of Orr-Sommerfeld equation which is the fundamental equation of linear hydrodynamic stability theory is described. Present calculation procedure is applied to the two-dimensional quasi-parallel flow for which linearized disturbance equation (Orr-Sommerfeld equation) contains one simple turning point and αR >> 1. The numerical procedure for this problem and one numerical example for Jeffery-Hamel flow (J-H III 1 ) are presented. These treatment can be extended to the other velocity profiles by slight midifications. (author)
International Nuclear Information System (INIS)
Mozolevski, I.E.
2001-01-01
We consider the splitting of the straight-ahead Boltzmann transport equation in the Boltzmann-Fokker-Planck equation, decomposing the differential cross-section into a singular part, corresponding to small energy transfer events, and in a regular one, which corresponds to large energy transfer. The convergence of implantation profile, nuclear and electronic energy depositions, calculated from the Boltzmann-Fokker-Planck equation, to the respective exact distributions, calculated from Monte-Carlo method, was exanimate in a large-energy interval for various values of splitting parameter and for different ion-target mass relations. It is shown that for the universal potential there exists an optimal value of splitting parameter, for which range and deposited energy distributions, calculated from the Boltzmann-Fokker-Planck equation, accurately approximate the exact distributions and which minimizes the computational expenses
Calculation of coherent synchrotron radiation in toroidal waveguides by paraxial wave equation
Directory of Open Access Journals (Sweden)
D. R. Gillingham
2007-05-01
Full Text Available A new technique for the simulation of coherent synchrotron radiation (CSR and space-charge fields from a single electron bunch in straight or toroidal rectangular waveguide sections has been developed. It is based on the integration of the paraxial approximation to the wave equations, using the perturbation technique where the bending radius is large compared to the dimension of the waveguide. We have implemented an unconditionally stable integration method in the time domain with transparent boundary conditions that allows the use of a minimally sized computational domain about the bunch. This technique explicitly enforces the causality condition so that no portion of the fields can propagate faster than the speed of light, can be used with arbitrary three-dimensional charge distributions, and contains corrections for finite energy. We have also developed a method for the calculation of the transverse forces within the bunch including space-charge. This method has been developed for incorporation with a particle-in-cell code so that we may self-consistently model CSR and space-charge in combinations of bending sections with a fully dynamic electron bunch in an efficient manner. In this paper we describe the model and methods for calculation of the fields in detail and compare results to theory wherever possible.
Kidon, Lyran; Wilner, Eli Y.; Rabani, Eran
2015-12-01
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.
Appelo, C.A.J.; Parkhurst, David L.; Post, V.E.A.
2014-01-01
Calculating the solubility of gases and minerals at the high pressures of carbon capture and storage in geological reservoirs requires an accurate description of the molar volumes of aqueous species and the fugacity coefficients of gases. Existing methods for calculating the molar volumes of aqueous species are limited to a specific concentration matrix (often seawater), have been fit for a limited temperature (below 60 °C) or pressure range, apply only at infinite dilution, or are defined for salts instead of individual ions. A more general and reliable calculation of apparent molar volumes of single ions is presented, based on a modified Redlich–Rosenfeld equation. The modifications consist of (1) using the Born equation to calculate the temperature dependence of the intrinsic volumes, following Helgeson–Kirkham–Flowers (HKF), but with Bradley and Pitzer’s expression for the dielectric permittivity of water, (2) using the pressure dependence of the extended Debye–Hückel equation to constrain the limiting slope of the molar volume with ionic strength, and (3) adopting the convention that the proton has zero volume at all ionic strengths, temperatures and pressures. The modifications substantially reduce the number of fitting parameters, while maintaining or even extending the range of temperature and pressure over which molar volumes can be accurately estimated. The coefficients in the HKF-modified-Redlich–Rosenfeld equation were fitted by least-squares on measured solution densities.The limiting volume and attraction factor in the Van der Waals equation of state can be estimated with the Peng–Robinson approach from the critical temperature, pressure, and acentric factor of a gas. The Van der Waals equation can then be used to determine the fugacity coefficients for pure gases and gases in a mixture, and the solubility of the gas can be calculated from the fugacity, the molar volume in aqueous solution, and the equilibrium constant. The
Appelo, C. A. J.; Parkhurst, D. L.; Post, V. E. A.
2014-01-01
Calculating the solubility of gases and minerals at the high pressures of carbon capture and storage in geological reservoirs requires an accurate description of the molar volumes of aqueous species and the fugacity coefficients of gases. Existing methods for calculating the molar volumes of aqueous species are limited to a specific concentration matrix (often seawater), have been fit for a limited temperature (below 60 °C) or pressure range, apply only at infinite dilution, or are defined for salts instead of individual ions. A more general and reliable calculation of apparent molar volumes of single ions is presented, based on a modified Redlich-Rosenfeld equation. The modifications consist of (1) using the Born equation to calculate the temperature dependence of the intrinsic volumes, following Helgeson-Kirkham-Flowers (HKF), but with Bradley and Pitzer’s expression for the dielectric permittivity of water, (2) using the pressure dependence of the extended Debye-Hückel equation to constrain the limiting slope of the molar volume with ionic strength, and (3) adopting the convention that the proton has zero volume at all ionic strengths, temperatures and pressures. The modifications substantially reduce the number of fitting parameters, while maintaining or even extending the range of temperature and pressure over which molar volumes can be accurately estimated. The coefficients in the HKF-modified-Redlich-Rosenfeld equation were fitted by least-squares on measured solution densities. The limiting volume and attraction factor in the Van der Waals equation of state can be estimated with the Peng-Robinson approach from the critical temperature, pressure, and acentric factor of a gas. The Van der Waals equation can then be used to determine the fugacity coefficients for pure gases and gases in a mixture, and the solubility of the gas can be calculated from the fugacity, the molar volume in aqueous solution, and the equilibrium constant. The coefficients for the
3-D resistive MHD calculations for tokamak plasmas: beyond the simple reduced set of equations
International Nuclear Information System (INIS)
Carreras, B.A.; Garcia, L.; Hender, T.C.; Hicks, H.R.; Holmes, J.A.; Lynch, V.E.; Masden, B.F.
1983-01-01
Numerical studies of the resistive stability of tokamak plasmas in cylindrical geometry have been performed using: (1) the full set of resistive Magnetohydrodynamic (MHD) equations and (2) an extended version of the reduced set of resistive MHD equations including diamagnetic and electron temperature effects. In particular, the nonlinear interaction of tearing modes of many helicities has been investigated. The numerical results confirm many of the features uncovered previously using the simple reduced equations. (author)
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)
Benoist, P.
1990-06-01
The migration area, which relates the buckling to the multiplication factor, can be calculated by means of the Deniz formula. This formula involves the direct and adjoint angular fluxes. It is shown in this note that it is possible, using the integral form of the transport equation, to establish an equivalent formula in which only angle-integrated quantities appear. This formulation is more suitable for the calculation by the collision probably method [fr
International Nuclear Information System (INIS)
Edery, D.
1983-11-01
The reduced system of the non linear resistive MHD equations is used in the 2-D one helicity approximation in the numerical computations of stationary tearing modes. The critical magnetic Raynolds number S (S=tausub(r)/tausub(H) where tausub(R) and tausub(H) are respectively the characteristic resistive and hydro magnetic times) and the corresponding linear solution are computed as a starting approximation for the full non linear equations. These equations are then treated numerically by an iterative procedure which is shown to be rapidly convergent. A numerical application is given in the last part of this paper
International Nuclear Information System (INIS)
Gilles, D.
2005-01-01
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)
International Nuclear Information System (INIS)
Filippov, A.V.; Shirkov, G.D.; Consoli, F.; Gammino, S.; Ciavola, G.; Celona, L.; Barbarino, S.
2008-01-01
The investigation of the widespread model for the calculation of ion charge-state distributions (CSD) in electron cyclotron-resonance ion source based on the set of balance equations is given. The modification of this model that allows one to describe the confinement and accumulation processes of highly charged ions in ECR plasma for gas mixing case more precisely is discussed. The new approach for the time confinement calculation (ions and electrons) based on the theory of Pastukhov is offered, viz. - calculation of confinement times during two step minimization of special type functionals. The results obtained by this approach have been compared with available experimental data
International Nuclear Information System (INIS)
Azmy, Y. Y.
2004-01-01
An approach is developed for solving the neutron diffusion equation on combinatorial geometry computational cells, that is computational cells composed by combinatorial operations involving simple-shaped component cells. The only constraint on the component cells from which the combinatorial cells are assembled is that they possess a legitimate discretization of the underlying diffusion equation. We use the Finite Difference (FD) approximation of the x, y-geometry diffusion equation in this work. Performing the same combinatorial operations involved in composing the combinatorial cell on these discrete-variable equations yields equations that employ new discrete variables defined only on the combinatorial cell's volume and faces. The only approximation involved in this process, beyond the truncation error committed in discretizing the diffusion equation over each component cell, is a consistent-order Legendre series expansion. Preliminary results for simple configurations establish the accuracy of the solution to the combinatorial geometry solution compared to straight FD as the system dimensions decrease. Furthermore numerical results validate the consistent Legendre-series expansion order by illustrating the second order accuracy of the combinatorial geometry solution, the same as standard FD. Nevertheless the magnitude of the error for the new approach is larger than FD's since it incorporates the additional truncated series approximation. (authors)
International Nuclear Information System (INIS)
Valle G, E. del; Mugica R, C.A.
2005-01-01
In our country, in last congresses, Gomez et al carried out reactivity calculations based on the solution of the diffusion equation for an energy group using nodal methods in one dimension and the TPL approach (Lineal Perturbation Theory). Later on, Mugica extended the application to the case of multigroup so much so much in one as in two dimensions (X Y geometry) with excellent results. Presently work is carried out similar calculations but this time based on the solution of the neutron transport equation in X Y geometry using nodal methods and again the TPL approximation. The idea is to provide a calculation method that allows to obtain in quick form the reactivity solving the direct problem as well as the enclosed problem of the not perturbed problem. A test problem for the one that results are provided for the effective multiplication factor is described and its are offered some conclusions. (Author)
Energy Technology Data Exchange (ETDEWEB)
Bore, C; Dandeu, Y; Saint-Amand, Ch [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1965-07-01
MUDE is a nuclear code written in FORTRAN II for IBM 7090-7094. It resolves a system of difference equations approximating to the one-dimensional multigroup neutron scattering problem. More precisely, this code makes it possible to: 1. Calculate the critical condition of a reactor (k{sub eff}, critical radius, critical composition) and the corresponding fluxes; 2. Calculate the associated fluxes and various subsidiary results; 3. Carry out perturbation calculations; 4. Study the propagation of fluxes at a distance; 5. Estimate the relative contributions of the cross sections (macroscopic or microscopic); 6. Study the changes with time of the composition of the reactor. (authors) [French] MUDE est un code nucleaire ecrit en FORTRAN II pour IBM 7090-7094. Il resout un systeme d'equations aux differences approchant le probleme de diffusion neutronique multigroupe a une dimension. Plus precisement ce code permet de: 1. Calculer la condition critique d'un reacteur (k{sub eff}, rayon critique, composition critique) et les flux correspondants; 2. Calculer les flux adjoints et divers resultats connexes; 3. Effectuer des calculs de perturbation; 4. Etudier la propagation des flux a longue distance; 5. Ponderer des sections efficaces (macroscopiques ou microscopiques); 6. Etudier l'evolution de la composition du reacteur au cours du temps. (auteurs)
Hippisley-Cox, Julia; Coupland, Carol
2017-01-01
Objective: To develop and externally validate risk prediction equations to estimate absolute and conditional survival in patients with colorectal cancer. \\ud \\ud Design: Cohort study.\\ud \\ud Setting: General practices in England providing data for the QResearch database linked to the national cancer registry.\\ud \\ud Participants: 44 145 patients aged 15-99 with colorectal cancer from 947 practices to derive the equations. The equations were validated in 15 214 patients with colorectal cancer ...
International Nuclear Information System (INIS)
Yasa, F.; Anli, F.; Guengoer, S.
2007-01-01
We present analytical calculations of spherically symmetric radioactive transfer and neutron transport using a hypothesis of P1 and T1 low order polynomial approximation for diffusion coefficient D. Transport equation in spherical geometry is considered as the pseudo slab equation. The validity of polynomial expansionion in transport theory is investigated through a comparison with classic diffusion theory. It is found that for causes when the fluctuation of the scattering cross section dominates, the quantitative difference between the polynomial approximation and diffusion results was physically acceptable in general
International Nuclear Information System (INIS)
Bodmer, A.R.
1978-01-01
The study of high energy heavy ion reactions includes the three principle a priori approaches used for central collisions, namely, hydrodynamics, cascade--Boltzman equation, and the classical equations of motion. While no clearly justified central or near central collisions are found, the classical equations of motion are used to illustrate some general features of these reactions. It is expected that the hot nuclear matter produced in such collisions is a dense, viscous, and thermally conductive fluid with important nonequilibrium and nonclassical features, rapidity, distribution, noncentral collisions, potential dependent effects for a given two-body scattering, and c.m. cross sections for a central collision with given parameters are among the properties considered. 12 references
Bound states of quarks calculated with stochastic integration of the Bethe-Salpeter equation
International Nuclear Information System (INIS)
Salomon, M.
1992-07-01
We have computed the masses, wave functions and sea quark content of mesons in their ground state by integrating the Bethe-Salpeter equation with a stochastic algorithm. This method allows the inclusion of a large set of diagrams. Inspection of the kernel of the equation shows that q-q-bar pairs with similar constituent masses in a singlet spin state exhibit a high bound state which is not present in other pairs. The pion, kaon and eta belongs to this category. 19 refs., 2 figs., 2 tabs
A modified SOR method for the Poisson equation in unsteady free-surface flow calculations.
Botta, E.F.F.; Ellenbroek, Marcellinus Hermannus Maria
1985-01-01
Convergence difficulties that sometimes occur if the successive overrelaxation (SOR) method is applied to the Poisson equation on a region with irregular free boundaries are analyzed. It is shown that these difficulties are related to the treatment of the free boundaries and caused by the appearance
New equations to calculate 3D joint centres in the lower extremities
DEFF Research Database (Denmark)
Sandau, Martin; Heimbürger, Rikke V; Villa, Chiara
2015-01-01
Biomechanical movement analysis in 3D requires estimation of joint centres in the lower extremities and this estimation is based on extrapolation from markers placed on anatomical landmarks. The purpose of the present study was to quantify the accuracy of three established set of equations and pr...
Extension of a GIS procedure for calculating the RUSLE equation LS factor
Zhang, H.; Yang, Q.; Li, R.; Liu, Q.; Moore, D.; He, P.; Ritsema, C.J.; Geissen, V.
2013-01-01
The Universal Soil Loss Equation (USLE) and revised USLE (RUSLE) are often used to estimate soil erosion at regional landscape scales, however a major limitation is the difficulty in extracting the LS factor. The geographic information system-based (GIS-based) methods which have been developed for
New equations to calculate temperature correction factors for PO2 in human blood.
Inaba, H; Ohwada, T; Sato, J; Mizuguchi, T; Hirasawa, H
1986-01-01
Effects of hemoglobin concentration (Hb), pH, and body temperature (T) on the relationships between delta log PO2/delta T and PO2 were studied by means of a mathematical model using a Newton-Raphson iteration method. The functions between delta log PO2/delta T and PO2 were affected by the above three factors. New equations considering the effects of Hb, pH, and T were proposed by modifying the equation reported by Severinghaus: delta log PO2/delta T = (L +(U-L)/(A(vPO237)B + 1))(10(-2) where U = 3.15-0.45(7.4-pH37) L = 0.68-0.09(7.4-pH37) A = 5.86(exp10(0.074(T)-0.294(7.4-pH37)-11))((Hb)0.913) B = 6.33(exp10(-0.0051(T)))((Hb)-0.113) + 0.24(7.4-pH37) and vPO237 is virtual PO237 which may exist when PO237 is corrected to standard conditions (pH = 7.4, BE = 0) by the following equations: vPO237 = PO237(exp10(fB(7.4-pH37)-0.0013(BE))) fB = (PO237/26.6)0.08-1.52 where fB is the Bohr factor. The above equations provided values of delta log PO2/delta T which fit closely to those obtained by the complex iteration method with maximum differences of less than 1.3 X 10(-3) at T = 27, indicating that maximum % errors for PO2 at T (PO2T) are less than 3.0% at T = 27 and that our equations can be applied over a wide range of Hb, pH37 and T.
International Nuclear Information System (INIS)
Song, T.; Ma, Q.; Sun, X.W.; Liu, Z.J.; Fu, Z.J.; Wei, X.P.; Wang, T.; Tian, J.H.
2016-01-01
The phase transition, electronic band structure, and equation of state (EOS) of cubic TcN are investigated by first-principles pseudopotential method based on density-functional theory. The calculated enthalpies show that TcN has a transformation between zincblende and rocksalt phases and the pressure determined by the relative enthalpy is 32 GPa. The calculated band structure indicates the metallic feature and it might make cubic TcN a better candidate for hard materials. Particular attention is paid to the predictions of volume, bulk modulus and its pressure derivative which play a central role in the formulation of approximate EOSs using the quasi-harmonic Debye model. - Highlights: • The phase transition pressure and electronic band structure for cubic TcN are determined. • Particular attention is paid to investigate the equation of state parameters for cubic TcN. • The thermodynamic properties up to 80 GPa and 3000 K are successfully predicted.
International Nuclear Information System (INIS)
Bento, Dercio Lopes
2006-01-01
PUREX is one of the purification process for irradiated nuclear fuel. In the flowchart the program uses various uranium and plutonium extraction phases by using organic solvent contained in the aqueous phase obtained in the dissolution of the fuel element. A posterior extraction U and Pu are changed to the aqueous phase. So it is fundamental to know the distribution coefficient (dS), at the temperature (tc), of the substances among the two immiscible phases, for better calculation the suitable flowchart. A mathematical model was elaborated based on experimental data, for the calculation of the dS and applied to a referential band of substance concentrations in the aqueous phase (xS) and organic (yS). By using the program Excel, we personalized the empirical equations calculated by the root mean square. The relative deviation, among the calculated values and the experimental ones are the standards
Motornenko, A.; Bravina, L.; Gorenstein, M. I.; Magner, A. G.; Zabrodin, E.
2018-03-01
Properties of equilibrated nucleon system are studied within the ultra-relativistic quantum molecular dynamics (UrQMD) transport model. The UrQMD calculations are done within a finite box with periodic boundary conditions. The system achieves thermal equilibrium due to nucleon-nucleon elastic scattering. For the UrQMD-equilibrium state, nucleon energy spectra, equation of state, particle number fluctuations, and shear viscosity η are calculated. The UrQMD results are compared with both, statistical mechanics and Chapman-Enskog kinetic theory, for a classical system of nucleons with hard-core repulsion.
International Nuclear Information System (INIS)
Lee, J. H.; Park, I. S.; Ahmad, D.; Kim, D.; Kim, Y. C.; Ko, R. K.; Jeong, D. Y.
2012-01-01
The macroscopic magnetic behaviors of a type-II superconductor, such as the field- or the temperature-dependent magnetization, have been described by using critical state models. However, because the models are time-independent, the magnetic relaxation in a type-II superconductor cannot be described by them, and the time dependence of the magnetization can affect the field or the temperature-dependent magnetization curve described by the models. In order to avoid the time independence of critical state models, we try the numerical calculation used by Qin et al., who mainly calculated the temperature dependence of the ac susceptibility χ(T). Their calculation showed that the frequency-dependent χ(T) could be obtained by using the flux-creep equation. We calculated the field-dependent magnetization and magnetic relaxation by using a numerical method. The calculated field-dependent magnetization M(H) curves shows the shapes of a typical type-II superconductor. The calculated magnetic relaxation do not show a logarithmic decay of the magnetization, but the addition of a surface barrier to the relaxation calculation caused a clear logarithmic decay of the magnetization, producing a crossover at a mid-time. This means that the logarithmic magnetic relaxation is caused by not only flux creep but also a combination of flux creep and a surface barrier.
Energy Technology Data Exchange (ETDEWEB)
Dufour, J M [CEA Limeil Valenton, 94 - Villeneuve-Saint-Georges (France)
1969-05-01
The aim of this report is to find, with a fair accuracy, a proper value {lambda}{sub mn}(c) for the spheroidal differential equation: d/dz[(1-z{sup 2})du/dz]+[ {lambda} - c{sup 2}z{sup 2} - m{sup 2}/(1-z{sup 2})]u = 0 obtained by the separation of the three variables of the wave equation: {delta}{sup 2}u + k{sup 2}u = 0 with rotational elongated or flattened ellipsoidal coordinates. The program drawn up calculates {lambda}{sub mn}(c) for any values of (mnc) chosen in the zones 0 {<=} | m | {<=} 10, a whole number; |m| {<=} n {<=} 20, n a whole number; 0 {<=} |c | {<=} 30; previous work has covered a smaller field of values. The function to be solved by the approximation method of the Newton-Raphson type, and the initial value, are chosen so as to converge towards the required solution. (author) [French] L'objet de ce rapport est de rechercher avec une tres bonne approximation, une valeur propre {lambda}{sub mn}(c) de l'equation differentielle spheroidale: d/dz[(1-z{sup 2})du/dz]+[ {lambda} - c{sup 2}z{sup 2} - m{sup 2}/1-z{sup 2}]u = 0 obtenue par separation des 3 variables de l'equation des ondes: {delta}{sup 2}u + k{sup 2}u = 0 en coordonnees des ellipsoides de revolution allonges ou aplatis. Le programme etabli calcule {lambda}{sub mn}(c) quel que soit le jeu (mnc) choisi dans le domaine 0 {<=} | m | {<=} 10 entier; |m| {<=} n {<=} 20, n entier; 0 {<=} |c | {<=} 30; alors que les etudes precedentes portaient sur un domaine plus restreint. La fonction a resoudre par la methode d'approximation du type NEWTON-RAPHSON et la valeur initiale, sont choisies de facon a converger vers la solution desiree. (auteur)
Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation
International Nuclear Information System (INIS)
Cherny, A.Yu.; Brand, J.
2004-01-01
A method is proposed for a self-consistent evaluation of the coupling constant in the Gross-Pitaevskii equation without involving a pseudopotential replacement. A renormalization of the coupling constant occurs due to medium effects and the trapping potential, e.g., in quasi-1D or quasi-2D systems. It is shown that a simplified version of the Hartree-Fock-Bogoliubov approximation leads to a variational problem for both the condensate and a two-body wave function describing the behavior of a pair of bosons in the Bose-Einstein condensate. The resulting coupled equations are free of unphysical divergences. Particular cases of this scheme that admit analytical estimations are considered and compared to the literature. In addition to the well-known cases of low-dimensional trapping, crossover regimes can be studied. The values of the kinetic, interaction, external, and release energies in low dimensions are also evaluated and contributions due to short-range correlations are found to be substantial
International Nuclear Information System (INIS)
Konter, A.W.A.; Kusters, G.M.A.
1981-01-01
Several constitutive equations are used to analyse the structural behaviour of a simply supported beam and circular plate loaded at its center, both tested at 1100 0 F. The time-independent plastic behaviour has been analysed with the isotropic and kinematic hardening model as well as with the ORNL 10th cycle model and the fraction model of Besseling. The time-dependent creep behaviour has been analysed using the isotropic hardening rules and the ORNL auxiliary hardening rules. No interaction of the creep and plastic behaviour was taken into account. Especially for cyclic loading conditions, large differences occur in the predictions of the inelastic behaviour. Good agreement between theory and prediction can be obtained with models which accurately account for the ratio of kinematic and saturating isotropic hardening of the used material. (orig./HP)
Li, Changping; Park, Kihong; Alouini, Mohamed-Slim
2015-01-01
In this letter, we propose a fast numerical solution for the steady state radiative transfer equation based on the approach in [1] in order to calculate the optical path loss of light propagation suffering from attenuation due to the absorption and scattering in various water types. We apply an optimal non-uniform method to discretize the angular space and an upwind type finite difference method to discretize the spatial space. A Gauss-Seidel iterative method is then applied to solve the fully discretized system of linear equations. Finally, we extend the resulting radiance in 2-dimensional to 3-dimensional by the azimuthal symmetric assumption to compute the received optical power under the given receiver aperture and field of view. The accuracy and efficiency of the proposed scheme are validated by uniform RTE solver and Monte Carlo simulations.
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.
International Nuclear Information System (INIS)
Soysal, A.O.; Semlyen, A.
1994-01-01
A general methodology is presented for the state equation approximation of a multiple input-output linear system from transfer matrix data. A complex transformation matrix, obtained by eigen analysis at a fixed frequency, is used for diagonalization of the transfer matrix over the whole frequency range. A scalar estimation procedure is applied for identification of the modal transfer functions. The state equations in the original coordinates are obtained by inverse transformation. An iterative Gauss-Newton refinement process is used to reduce the overall error of the approximation. The developed methodology is applied to the phase domain modeling of untransposed transmission lines. The approach makes it possible to perform EMTP calculations directly in the phase domain. This results in conceptual simplification and savings in computation time since modal transformations are not needed in the sequences of the transient analysis. The presented procedure is compared with the conventional modal approach in terms of accuracy and computation time
International Nuclear Information System (INIS)
Rowland, D R
2006-01-01
Introductory courses covering modern physics sometimes introduce some elementary ideas from general relativity, though the idea of a geodesic is generally limited to shortest Euclidean length on a curved surface of two spatial dimensions rather than extremal aging in spacetime. It is shown that Epstein charts provide a simple geometric picture of geodesics in one space and one time dimension and that for a hypothetical uniform gravitational field, geodesics are straight lines on a planar diagram. This means that the properties of geodesics in a uniform field can be calculated with only a knowledge of elementary geometry and trigonometry, thus making the calculation of some basic results of general relativity accessible to students even in an algebra-based survey course on physics
Multi-Center Electronic Structure Calculations for Plasma Equation of State
Energy Technology Data Exchange (ETDEWEB)
Wilson, B G; Johnson, D D; Alam, A
2010-12-14
We report on an approach for computing electronic structure utilizing solid-state multi-center scattering techniques, but generalized to finite temperatures to model plasmas. This approach has the advantage of handling mixtures at a fundamental level without the imposition of ad hoc continuum lowering models, and incorporates bonding and charge exchange, as well as multi-center effects in the calculation of the continuum density of states.
Microscopic classical equations of motion calculations of high-energy heavy-ion collisions
International Nuclear Information System (INIS)
Panos, C.N.
1979-01-01
Classical microscopic nonrelativistic calculations are made for collisions between equal-mass-nuclei projectile and target with A/sub P/ = A/sub T/ = 20 for laboratory energies E/sub L/ = 117, 400, and 800 MeV/A/sub P/ and also between nuclei with A/sub P/ = A/sub T/ = 40 for E/sub L/ = 400 MeV/A/sub P/. For a given initial configuration of the projectile and target nucleons the trajectories of all nucleons are calculated classically with two-body forces between all pairs of nucleons. The implementation of the CEOM calculations is discussed in detail. More limited relativistic calculations for single initial configurations are also made. The configurations representing the initial nuclei are chosen to have a reasonable radius and kinetic energy; however, they do not saturate with the two-body potentials used. The trajectory information is analyzed to give a large number of position and momentum dependent quantities such as densities, rapidity distributions, inclusive double differential cross sections, etc. The results show that a central collision (b = 0) proceeds in three stages, an initial transparent stage, a strongly interacting stage where the dissipation is large, and finally an expansion stage for which there is considerable dissipation. Appreciable potential energy effects were found for b = 0; however, the final distributions were very similar for the scattering equivalent potentials. For lower energies (E/sub L/ approx. = 100 MeV) there is some evidence of fusion into large fragments. The thermal models for b = 0 are tested. Noncentral collisions show typical nonequilibrium and transparency features. The multiplicity distribution is obtained for A/sub P/ = A/sub T/ = 20 and E/sub L/ = 800 MeV. A comparison of the impact parameter-integrated inclusive double differential cross sections is made with the experimental data for A/sub P/ = A/sub T/ = 20, E/sub L/ = 800 MeV and shows fair agreement
Plummer, Niel; 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)
International Nuclear Information System (INIS)
Kolahdooz, M.; Abotalebi, A.; Sheikh Aleslam, F.
2011-01-01
The goal of this article is calculation of the electric field at the end of loaded path in solid-state track detectors. For the calculation, Laplace-Equation has been solved numerically. By solving the equation, upon considering a specific potential at the boundary of the region, in addition to calculating the electric field at the end of path, the parameters which are affecting the electric field have also been investigated.
International Nuclear Information System (INIS)
Leont'ev, K.L.
1981-01-01
Known theoretical and empirical formulae are considered for the difference in specific heats at constant pressure and volume. On the basis of the Grunaiser law on the ratio of specific heat to thermal expansion and on the basis of the correlation proposed by the author, between this ratio and average velocity of elastic waves obtained in a new expression for the difference in specific heats and determined are conditions at which empiric Nernst-Lindeman equation can be considered to be strict. Results of calculations for metals with fcc lattice are presented
International Nuclear Information System (INIS)
Walsh, L.M.
1988-01-01
A new treatment is given to the problem studied in the previous work 'Conveccao Natural em um Circuito Termico a Sodio' (1981) by the same author. It consists of another method of the solution of the energy equation. It was obtained some stability in the numerical calculation independent of the value of the step; it was also obtained a considerable reduction in the machine time. A new program is being elaborated for testing the time reduction as compared to the previous one. (author) [pt
International Nuclear Information System (INIS)
Moeller, K.
1978-01-01
A system of three particles is considered which interacts by rank-1 separable potential. For the Faddeev equation kernel of this system a method is proposed for calculating the eigenvalues on the nonphysical sheet of the three-particle cms-energy. From the consideration of the analytical structure of the eigenvalues in the energy plane it follows that the analytical continuations of the eigenvalues from the physical to the nonphysical region are different above and below the three-particle threshold. In this paper the continuation below the threshold is discussed. (author)
International Nuclear Information System (INIS)
Girometti, Rossano; Signor, Marco Andrea; Pancot, Martina; Cereser, Lorenzo; Zuiani, Chiara
2016-01-01
Purpose: To investigate the agreement between Roach equations (RE) and multiparametric magnetic resonance imaging (mpMRI) in assessing the T-stage of prostate cancer (PCa). Materials and methods: Seventy-three patients with biopsy-proven PCa and previous RE assessment prospectively underwent mpMRI on a 3.0T magnet before external beam radiation therapy (EBRT). Using Cohen’s kappa statistic, we assessed the agreement between RE and mpMRI in defining the T-stage (≥T3 vs.T ≤ 2) and risk category according to the National comprehensive cancer network criteria (≤intermediate vs. ≥high). We also calculated sensitivity and specificity for ≥T3 stage in an additional group of thirty-seven patients with post-prostatectomy histological examination (mpMRI validation group). Results: The agreement between RE and mpMRI in assessing the T stage and risk category was moderate (k = 0.53 and 0.56, respectively). mpMRI changed the T stage and risk category in 21.9% (95%C.I. 13.4–33-4) and 20.5% (95%C.I. 12.3–31.9), respectively, prevalently downstaging PCa compared to RE. Sensitivity and specificity for ≥T3 stage in the mpMRI validation group were 81.8% (95%C.I. 65.1–91.9) and 88.5% (72.8–96.1). Conclusion: RE and mpMRI show moderate agreement only in assessing the T-stage of PCa, translating into an mpMRI-induced change in risk assessment in about one fifth of patients. As supported by high sensitivity/specificity for ≥T3 stage in the validation group, the discrepancy we found is in favour of mpMRI as a tool to stage PCa before ERBT.
Energy Technology Data Exchange (ETDEWEB)
Girometti, Rossano, E-mail: rgirometti@sirm.org [Institute of Diagnostic Radiology, Department of Medical and Biological Sciences, University of Udine, Azienda Ospedaliero-Universitaria Santa Maria della Misericordia − via Colugna, 50–33100, Udine (Italy); Signor, Marco Andrea, E-mail: marco.signor@asuiud.sanita.fvg.it [Department of Oncological Radiation Therapy, Azienda Ospedaliero-Universitaria Santa Maria della Misericordia, Piazzale S. M. della Misericordia, 15–33100, Udine (Italy); Pancot, Martina, E-mail: martypancot@libero.it [Institute of Diagnostic Radiology, Department of Medical and Biological Sciences, University of Udine, Azienda Ospedaliero-Universitaria Santa Maria della Misericordia − via Colugna, 50–33100, Udine (Italy); Cereser, Lorenzo, E-mail: lcereser@sirm.org [Institute of Diagnostic Radiology, Department of Medical and Biological Sciences, University of Udine, Azienda Ospedaliero-Universitaria Santa Maria della Misericordia − via Colugna, 50–33100, Udine (Italy); Zuiani, Chiara, E-mail: chiara.zuiani@uniud.it [Institute of Diagnostic Radiology, Department of Medical and Biological Sciences, University of Udine, Azienda Ospedaliero-Universitaria Santa Maria della Misericordia − via Colugna, 50–33100, Udine (Italy)
2016-12-15
Purpose: To investigate the agreement between Roach equations (RE) and multiparametric magnetic resonance imaging (mpMRI) in assessing the T-stage of prostate cancer (PCa). Materials and methods: Seventy-three patients with biopsy-proven PCa and previous RE assessment prospectively underwent mpMRI on a 3.0T magnet before external beam radiation therapy (EBRT). Using Cohen’s kappa statistic, we assessed the agreement between RE and mpMRI in defining the T-stage (≥T3 vs.T ≤ 2) and risk category according to the National comprehensive cancer network criteria (≤intermediate vs. ≥high). We also calculated sensitivity and specificity for ≥T3 stage in an additional group of thirty-seven patients with post-prostatectomy histological examination (mpMRI validation group). Results: The agreement between RE and mpMRI in assessing the T stage and risk category was moderate (k = 0.53 and 0.56, respectively). mpMRI changed the T stage and risk category in 21.9% (95%C.I. 13.4–33-4) and 20.5% (95%C.I. 12.3–31.9), respectively, prevalently downstaging PCa compared to RE. Sensitivity and specificity for ≥T3 stage in the mpMRI validation group were 81.8% (95%C.I. 65.1–91.9) and 88.5% (72.8–96.1). Conclusion: RE and mpMRI show moderate agreement only in assessing the T-stage of PCa, translating into an mpMRI-induced change in risk assessment in about one fifth of patients. As supported by high sensitivity/specificity for ≥T3 stage in the validation group, the discrepancy we found is in favour of mpMRI as a tool to stage PCa before ERBT.
3He(d,p)4He reaction calculation with three-body Faddeev equations
International Nuclear Information System (INIS)
Oryu, S.; Uzu, E.; Sunahara, H.; Yamada, T.; Tabaru, G.; Hino, T.
1998-01-01
In order to investigate the 3 He-n-p system as a three-body problem, we have formulated 3 He-n and 3 H-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 3 He-n, 3 H-p, and 3 He-p phase shifts. Therefore, they describe the 3 He-n differential cross section, the polarization observables, and the energy levels of 4 He. The 3 He-n-p Faddeev equations are solved numerically. We reproduce correctly the ground state and the first excited state of 5 Li. Furthermore, the Paris-type potential is used to investigate the 3 He(d,p) 4 He 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.)
Calculation and experimental estimation of the equation of state of irradiated fuel
Energy Technology Data Exchange (ETDEWEB)
Bober, M; Breitung, W; Karow, H U; Schumacher, G [Gesellschaft fuer Kernforschung mbH, INR Kernforschungszentrum, Karlsruhe (Germany)
1977-07-01
The gas pressure development in an irradiated mixed oxide fuel is mainly influenced by fission gases and volatile fission products in the temperature range below the melting point and by the fuel material itself and the less volatile fission products in the temperature region above 4000 K. Besides the temperature the important factors for the vapor pressure are the oxygen potential of the fuel and the concentration of fission products in the fuel. As demonstrated previously the oxygen potential influences strongly the pressure of vapor species above (U Pu)O{sub 2}. The pressure of the species U, UO, UO{sub 2}, Pu, PuO, PuO{sub 2} varies over a range of more than five orders of magnitude by variation of the oxygen potential at 2000 K. Similar effects were observed with oxides of the fission products. Fission products dissolved in mixed oxide fuel on the other hand can influence significantly the oxygen potential of the irradiated mixed oxide. In the first paragraph of the paper an attempt is made to calculate oxygen potentials of mixed oxides containing dissolved fission products. The model used is based on the equilibrium of oxygen defects in the mixed oxide. The chemical state and distribution of fission products is a further behavior that should be considered in calculation of the local and overall pressures and behavior of the fuel. Fission products were transported during the irradiation time and collect at different positions within the fuel pin. This process can produce high local concentrations of fission products, thus enabling elements with low overall concentrations to reach their saturation pressure. The distribution of fission products and their behavior in irradiated mixed oxide fuel is described in the second paragraph. The third paragraph deals with the calculation of vapor pressures that has been conducted using a model described for uranium-plutonium mixed oxides. This model is based on the law of mass action and provides vapor pressures as a
International Nuclear Information System (INIS)
Reynolds, J. M.; Lopez-Bruna, D.
2009-01-01
This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs
LINPACK, Subroutine Library for Linear Equation System Solution and Matrix Calculation
International Nuclear Information System (INIS)
Dongarra, J.J.
1979-01-01
1 - Description of problem or function: LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE: General, GB: General band, PO: Positive definite, PP: Positive definite packed, PB: Positive definite band, SI: Symmetric indefinite, SP: Symmetric indefinite packed, HI: Hermitian indefinite, HP: Hermitian indefinite packed, TR: Triangular, GT: General tridiagonal, PT: Positive definite tridiagonal, CH: Cholesky decomposition, QR: Orthogonal-triangular decomposition, SV: Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA: Factor, CO: Factor and estimate condition, SL: Solve, DI: Determinant and/or inverse and/or inertia, DC: Decompose, UD: Update, DD: Down-date, EX Exchange. The following chart shows all the LINPACK subroutines. The initial 'S' in the names may be replaced by D, C or Z and the initial 'C' in the complex-only names may be replaced by a Z. SGE: FA, CO, SL, DI; SGB: FA, CO, SL, DI; SPO: FA, CO, SL, DI; SPP: FA, CO, SL, DI; SPB: FA, CO, SL, DI; SSI: FA, CO, SL, DI; SSP: FA, CO, SL, DI; CHI: FA, CO, SL, DI; CHP: FA, CO, SL, DI; STR
Directory of Open Access Journals (Sweden)
A. Mashentseva
2013-05-01
Full Text Available One of the most urgent and extremely social problems in environmental safeties area in Kazakhstan is providing the population of all regions of the country with quality drinking water. Development of filter elements based on nuclear track-etch membranes may be considered as one of best solutions this problem. The values of bulk etch rate and activation energy were calculated in view the effect of temperature, alkaline solution concentration as well as stirring effect. The semi-empirical equation of the bulk etch rate for PET track membranes was calculated. As a result of theoretical and experimental studies a semi-empirical equation of the bulk etch rate VB=3.4∙1012∙C2.07∙exp(-0.825/kT for 12 microns PET film, irradiated by ions 84Kr15+ (energy of 1.75 MeV/nucleon at the heavy ion accelerator DC-60 in Astana branch of the INP NNC RK, was obtained.
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.
Directory of Open Access Journals (Sweden)
Nikita A. Moiseev
2017-01-01
other, and in case if one of them is significant, the other will almost certainly show the same significance. On the other hand, if the sample variance-covariance matrix tends to be diagonal and the number of observations tends to infinity, the proposed numerical method will return corrections close to the simple correction. In the case when the number of observations is much greater than the number of potential predictors, then the Shehata and White corrections give approximately the same corrections with the proposed numerical method. However, in much more common cases, when the number of observations is comparable to the number of potential predictors, the existing methods demonstrate significant inaccuracies. When the number of potential predictors is greater than the available number of observations, it seems impossible to calculate the true p-values. Therefore, it is recommended not to consider such datasets when constructing regression models, since only the fulfillment of the above condition ensures calculation of unbiased p-value corrections. The proposed method is easy to program and can be integrated into any statistical software package.
SU-E-T-22: A Deterministic Solver of the Boltzmann-Fokker-Planck Equation for Dose Calculation
Energy Technology Data Exchange (ETDEWEB)
Hong, X; Gao, H [Shanghai Jiao Tong University, Shanghai, Shanghai (China); Paganetti, H [Massachusetts General Hospital, Boston, MA (United States)
2015-06-15
Purpose: The Boltzmann-Fokker-Planck equation (BFPE) accurately models the migration of photons/charged particles in tissues. While the Monte Carlo (MC) method is popular for solving BFPE in a statistical manner, we aim to develop a deterministic BFPE solver based on various state-of-art numerical acceleration techniques for rapid and accurate dose calculation. Methods: Our BFPE solver is based on the structured grid that is maximally parallelizable, with the discretization in energy, angle and space, and its cross section coefficients are derived or directly imported from the Geant4 database. The physical processes that are taken into account are Compton scattering, photoelectric effect, pair production for photons, and elastic scattering, ionization and bremsstrahlung for charged particles.While the spatial discretization is based on the diamond scheme, the angular discretization synergizes finite element method (FEM) and spherical harmonics (SH). Thus, SH is used to globally expand the scattering kernel and FFM is used to locally discretize the angular sphere. As a Result, this hybrid method (FEM-SH) is both accurate in dealing with forward-peaking scattering via FEM, and efficient for multi-energy-group computation via SH. In addition, FEM-SH enables the analytical integration in energy variable of delta scattering kernel for elastic scattering with reduced truncation error from the numerical integration based on the classic SH-based multi-energy-group method. Results: The accuracy of the proposed BFPE solver was benchmarked against Geant4 for photon dose calculation. In particular, FEM-SH had improved accuracy compared to FEM, while both were within 2% of the results obtained with Geant4. Conclusion: A deterministic solver of the Boltzmann-Fokker-Planck equation is developed for dose calculation, and benchmarked against Geant4. Xiang Hong and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang
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.
DEFF Research Database (Denmark)
Lam, Janni Uyen Hoa; Lynge, Elsebeth; Njor, Sisse Helle
2015-01-01
sense to determine the indicators also for the true at-risk populations. We described the frequency of total hysterectomy in Denmark and its impact on the calculated incidence of cervical cancer and the screening coverage. MATERIAL AND METHODS: With data from five Danish population-based registries......% (adjusted). In Denmark, hysterectomies do not have a large overall impact on the calculated cancer incidence and screening coverage. Nevertheless, at ≥ 65 years adjusted rates would increase by almost 20% compared to unadjusted rates. This suggests that calculating disease risks per organ-years may have......, the incidence rate of cervical cancer and the screening coverage for women aged 23-64 years on 31 December 2010 were calculated with and without adjustments for hysterectomies undertaken for reasons other than cervical cancer. They were calculated as the number of cases divided by 1) the total number of woman...
Gaik Tay, Kim; Cheong, Tau Han; Foong Lee, Ming; Kek, Sie Long; Abdul-Kahar, Rosmila
2017-08-01
In the previous work on Euler’s spreadsheet calculator for solving an ordinary differential equation, the Visual Basic for Application (VBA) programming was used, however, a graphical user interface was not developed to capture users input. This weakness may make users confuse on the input and output since those input and output are displayed in the same worksheet. Besides, the existing Euler’s spreadsheet calculator is not interactive as there is no prompt message if there is a mistake in inputting the parameters. On top of that, there are no users’ instructions to guide users to input the derivative function. Hence, in this paper, we improved previous limitations by developing a user-friendly and interactive graphical user interface. This improvement is aimed to capture users’ input with users’ instructions and interactive prompt error messages by using VBA programming. This Euler’s graphical user interface spreadsheet calculator is not acted as a black box as users can click on any cells in the worksheet to see the formula used to implement the numerical scheme. In this way, it could enhance self-learning and life-long learning in implementing the numerical scheme in a spreadsheet and later in any programming language.
Quadratic-linear pattern in cancer fractional radiotherapy. Equations for a computering program
International Nuclear Information System (INIS)
Burgos, D.; Bullejos, J.; Garcia Puche, J.L.; Pedraza, V.
1990-01-01
Knowledge of equivalence between different tratment schemes with the same iso-effect is the essential thing in clinical cancer radiotherapy. For this purpose it is very useful the group of ideas derived from quadratic-linear pattern (Q-L) proposed in order to analyze cell survival curve to radiation. Iso-effect definition caused by several irradiation rules is done by extrapolated tolerance dose (ETD). Because equations for ETD are complex, a computering program have been carried out. In this paper, iso-effect equations for well defined therapeutic situations and flow diagram proposed for resolution, have been studied. (Author)
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.
International Nuclear Information System (INIS)
Djouder, M.; Kermoun, F.; Mitiche, M. D.; Lamrous, O.
2016-01-01
Dust particles observed in universe as well as in laboratory and technological plasma devices are still under investigation. At low temperature, these particles are strongly negatively charged and are able to form a 2D or 3D coulomb crystal. In this work, our aim was to check the ideal gas law validity for a 2D single-layer dust crystal recently reported in the literature. For this purpose, we have simulated, using the molecular dynamics method, its thermodynamic properties for different values of dust particles number and confinement parameters. The obtained results have allowed us to invalidate the ideal gas behaviour and to propose an effective equation of state which assumes a near zero dust temperature. Furthermore, the value of the calculated sound velocity was found to be in a good agreement with experimental data published elsewhere
Wang, Shan-Shan; Zhang, Yu-Qi; Chen, Shu-Bao; Huang, Guo-Ying; Zhang, Hong-Yan; Zhang, Zhi-Fang; Wu, Lan-Ping; Hong, Wen-Jing; Shen, Rong; Liu, Yi-Qing; Zhu, Jun-Xue
2017-06-01
Clinical decision making in children with congenital and acquired heart disease relies on measurements of cardiac structures using two-dimensional echocardiography. We aimed to establish z-score regression equations for right heart structures in healthy Chinese Han children. Two-dimensional and M-mode echocardiography was performed in 515 patients. We measured the dimensions of the pulmonary valve annulus (PVA), main pulmonary artery (MPA), left pulmonary artery (LPA), right pulmonary artery (RPA), right ventricular outflow tract at end-diastole (RVOTd) and at end-systole (RVOTs), tricuspid valve annulus (TVA), right ventricular inflow tract at end-diastole (RVIDd) and at end-systole (RVIDs), and right atrium (RA). Regression analyses were conducted to relate the measurements of right heart structures to 4body surface area (BSA). Right ventricular outflow-tract fractional shortening (RVOTFS) was also calculated. Several models were used, and the best model was chosen to establish a z-score calculator. PVA, MPA, LPA, RPA, RVOTd, RVOTs, TVA, RVIDd, RVIDs, and RA (R 2 = 0.786, 0.705, 0.728, 0.701, 0.706, 0.824, 0.804, 0.663, 0.626, and 0.793, respectively) had a cubic polynomial relationship with BSA; specifically, measurement (M) = β0 + β1 × BSA + β2 × BSA 2 + β3 × BSA. 3 RVOTFS (0.28 ± 0.02) fell within a narrow range (0.12-0.51). Our results provide reference values for z scores and regression equations for right heart structures in Han Chinese children. These data may help interpreting the routine clinical measurement of right heart structures in children with congenital or acquired heart disease. © 2016 Wiley Periodicals, Inc. J Clin Ultrasound 45:293-303, 2017. © 2017 Wiley Periodicals, Inc.
Kaplan, David J.; Boorjian, Stephen A.; Ruth, Karen; Egleston, Brian L.; Chen, David Y.T.; Viterbo, Rosalia; Uzzo, Robert G.; Buyyounouski, Mark K.; Raysor, Susan; Giri, Veda N.
2009-01-01
Introduction Clinical factors in addition to PSA have been evaluated to improve risk assessment for prostate cancer. The Prostate Cancer Prevention Trial (PCPT) risk calculator provides an assessment of prostate cancer risk based on age, PSA, race, prior biopsy, and family history. This study evaluated the risk calculator in a screening cohort of young, racially diverse, high-risk men with a low baseline PSA enrolled in the Prostate Cancer Risk Assessment Program. Patients and Methods Eligibility for PRAP include men ages 35-69 who are African-American, have a family history of prostate cancer, or have a known BRCA1/2 mutation. PCPT risk scores were determined for PRAP participants, and were compared to observed prostate cancer rates. Results 624 participants were evaluated, including 382 (61.2%) African-American men and 375 (60%) men with a family history of prostate cancer. Median age was 49.0 years (range 34.0-69.0), and median PSA was 0.9 (range 0.1-27.2). PCPT risk score correlated with prostate cancer diagnosis, as the median baseline risk score in patients diagnosed with prostate cancer was 31.3%, versus 14.2% in patients not diagnosed with prostate cancer (p<0.0001). The PCPT calculator similarly stratified the risk of diagnosis of Gleason score ≥7 disease, as the median risk score was 36.2% in patients diagnosed with Gleason ≥7 prostate cancer versus 15.2% in all other participants (p<0.0001). Conclusion PCPT risk calculator score was found to stratify prostate cancer risk in a cohort of young, primarily African-American men with a low baseline PSA. These results support further evaluation of this predictive tool for prostate cancer risk assessment in high-risk men. PMID:19709072
Kuś, Tomasz; Krylov, Anna I
2011-08-28
The charge-stabilization method is applied to double ionization potential equation-of-motion (EOM-DIP) calculations to stabilize unstable dianion reference functions. The auto-ionizing character of the dianionic reference states spoils the numeric performance of EOM-DIP limiting applications of this method. We demonstrate that reliable excitation energies can be computed by EOM-DIP using a stabilized resonance wave function instead of the lowest energy solution corresponding to the neutral + free electron(s) state of the system. The details of charge-stabilization procedure are discussed and illustrated by examples. The choice of optimal stabilizing Coulomb potential, which is strong enough to stabilize the dianion reference, yet, minimally perturbs the target states of the neutral, is the crux of the approach. Two algorithms of choosing optimal parameters of the stabilization potential are presented. One is based on the orbital energies, and another--on the basis set dependence of the total Hartree-Fock energy of the reference. Our benchmark calculations of the singlet-triplet energy gaps in several diradicals show a remarkable improvement of the EOM-DIP accuracy in problematic cases. Overall, the excitation energies in diradicals computed using the stabilized EOM-DIP are within 0.2 eV from the reference EOM spin-flip values. © 2011 American Institute of Physics
International Nuclear Information System (INIS)
Abdel-Monem, A.A.; Soliman, S.F.H.; Abd El-Kader, F.H.; El-Naggar, A.M.; Eissa, H.M.; Abd El-Hafez, A.A.
2001-01-01
Gabal Allouga area is located some 40 km due east from Abu Zenima town on the east coast of the Gulf of Suez, West-Central Sinai, Egypt. A network of exploratory tunnels totaling 670m in length and approximately 2x2 m in cross section, were excavated within a paleosol clayey bed. They host (Fe, Mn)-, Cu-, and U-mineralizations. Portions of the tunnels are naturally ventilated and others portions are non-ventilated and show ground water seepage through fractures. Model equations were developed for calculating the Rn-gas concentrations in the air of the tunnels under dry conditions where Rn-gas transport is mainly by air flow through porous media as well as for wet conditions where Rn-gas transport is mainly by ground water flow into the tunnels. Under dry conditions the model calculated Rn-gas concentrations(15.2-60.6 PCi/1) are consistent with measured values by active techniques (3.26-22.85 pCi/1) and by SSNTD techniques (19-69.1 pCi/1) when the Rn-emanation coefficient (alpha= 0.05-0.2), the emanating rock thickness (X=10 cm) and U-concentration averages 30 ppm. Under wet and non-ventilated conditions the model calculated Rn-gas concentrations (159-1248 pCi/1) are consistent with the measured values by active techniques (231-1348 pCi/1) and by SSNTD techniques (144-999pCi/1), when the Rn-emanation coefficient (alpha=0.1-0.25), the ground water flow (F=0.04-0.10 ml/s -1 cm -2 ) and U-concertrations (100-250ppm)
International Nuclear Information System (INIS)
Dumonteil, E.; Diop, C.M.
2011-01-01
External linking scripts between Monte Carlo transport codes and burnup codes, and complete integration of burnup capability into Monte Carlo transport codes, have been or are currently being developed. Monte Carlo linked burnup methodologies may serve as an excellent benchmark for new deterministic burnup codes used for advanced systems; however, there are some instances where deterministic methodologies break down (i.e., heavily angularly biased systems containing exotic materials without proper group structure) and Monte Carlo burn up may serve as an actual design tool. Therefore, researchers are also developing these capabilities in order to examine complex, three-dimensional exotic material systems that do not contain benchmark data. Providing a reference scheme implies being able to associate statistical errors to any neutronic value of interest like k(eff), reaction rates, fluxes, etc. Usually in Monte Carlo, standard deviations are associated with a particular value by performing different independent and identical simulations (also referred to as 'cycles', 'batches', or 'replicas'), but this is only valid if the calculation itself is not biased. And, as will be shown in this paper, there is a bias in the methodology that consists of coupling transport and depletion codes because Bateman equations are not linear functions of the fluxes or of the reaction rates (those quantities being always measured with an uncertainty). Therefore, we have to quantify and correct this bias. This will be achieved by deriving an unbiased minimum variance estimator of a matrix exponential function of a normal mean. The result is then used to propose a reference scheme to solve Boltzmann/Bateman coupled equations, thanks to Monte Carlo transport codes. Numerical tests will be performed with an ad hoc Monte Carlo code on a very simple depletion case and will be compared to the theoretical results obtained with the reference scheme. Finally, the statistical error propagation
Directory of Open Access Journals (Sweden)
V. M. Ovsianko
2012-01-01
Full Text Available The paper reveals a brand-new direction in simulation of frame and continual structures while calculating static and dynamic loads and stability. An electronic model has been synthesized for an investigated object and then it has been analyzed not with the help of specialized analog computing techniques but by means of high-performance software package for electronic circuit calculation using a personal computer.The given paper contains exact algebraic equations corresponding to differential equations for lateral bending calculation of frame structures without and with due account of viscoelastic material properties in compliance with the Kelvin model.The exact algebraic equation for a beam on elastic supports (or elastic Winkler foundation has been derived for quartic differential equation.The paper presents a number of exact algebraic equations which are equivalent to differential equations for transverse-longitudinal bending calculation of frame structures without and with due account of viscoelastic material properties when lateral and longitudinal loads are applied in the form of impulses with any periods of their duration and any interchangeability.
Energy Technology Data Exchange (ETDEWEB)
Davidenko, V. D., E-mail: Davidenko-VD@nrcki.ru; Zinchenko, A. S., E-mail: zin-sn@mail.ru; Harchenko, I. K. [National Research Centre Kurchatov Institute (Russian Federation)
2016-12-15
Integral equations for the shape functions in the adiabatic, quasi-static, and improved quasi-static approximations are presented. The approach to solving these equations by the Monte Carlo method is described.
Energy Technology Data Exchange (ETDEWEB)
Epifanovsky, Evgeny [Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (United States); Department of Chemistry, University of California, Berkeley, California 94720 (United States); Q-Chem Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588 (United States); Klein, Kerstin; Gauss, Jürgen [Institut für Physikalische Chemie, Universität Mainz, D-55099 Mainz (Germany); Stopkowicz, Stella [Department of Chemistry, Centre for Theoretical and Computational Chemistry, University of Oslo, N-0315 Oslo (Norway); Krylov, Anna I. [Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (United States)
2015-08-14
We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results.
International Nuclear Information System (INIS)
Tanaka, Midori; Tanimura, Yoshitaka
2010-01-01
Multiple displaced oscillators coupled to an Ohmic heat bath are used to describe electron transfer (ET) in a dissipative environment. By performing a canonical transformation, the model is reduced to a multilevel system coupled to a heat bath with the Brownian spectral distribution. A reduced hierarchy equations of motion approach is introduced for numerically rigorous simulation of the dynamics of the three-level system with various oscillator configurations, for different nonadiabatic coupling strengths and damping rates, and at different temperatures. The time evolution of the reduced density matrix elements illustrates the interplay of coherences between the electronic and vibrational states. The ET reaction rates, defined as a flux-flux correlation function, are calculated using the linear response of the system to an external perturbation as a function of activation energy. The results exhibit an asymmetric inverted parabolic profile in a small activation regime due to the presence of the intermediate state between the reactant and product states and a slowly decaying profile in a large activation energy regime, which arises from the quantum coherent transitions.
International Nuclear Information System (INIS)
McFee, D.G.; Mueller, K.H.; Lielmezs, J.
1982-01-01
By means of the available experimental gas compressibility data, the predictive accuracy of the Benedict-Webb-Rubin, Starling and Lee-Kesler equations was tested over wide temperature and pressure ranges for the following commonly used industrial gases: CH 4 , C 2 H 6 , C 3 H 8 , CO 2 , Ar, He, H 2 and N 2 . The root mean square (RMS) percent errors calculated over the T-P range investigated for all compounds, showed a degree of superiority and ease of use of the Lee-Kesler equation over the Benedict-Webb-Rubin and Starling equations. In order to treat quantal fluids H 2 and He, the Benedict-Webb-Rubin equation was modified by making constant B 0 temperature dependent, while the Starling and Lee-Kesler equations were rewritten through inclusion of quantum effect corrected pseudo-critical state parameters. (orig.)
Park, Jae Young; Yoon, Sungroh; Park, Man Sik; Choi, Hoon; Bae, Jae Hyun; Moon, Du Geon; Hong, Sung Kyu; Lee, Sang Eun; Park, Chanwang; Byun, Seok-Soo
2017-01-01
We developed the Korean Prostate Cancer Risk Calculator for High-Grade Prostate Cancer (KPCRC-HG) that predicts the probability of prostate cancer (PC) of Gleason score 7 or higher at the initial prostate biopsy in a Korean cohort (http://acl.snu.ac.kr/PCRC/RISC/). In addition, KPCRC-HG was validated and compared with internet-based Western risk calculators in a validation cohort. Using a logistic regression model, KPCRC-HG was developed based on the data from 602 previously unscreened Korean men who underwent initial prostate biopsies. Using 2,313 cases in a validation cohort, KPCRC-HG was compared with the European Randomized Study of Screening for PC Risk Calculator for high-grade cancer (ERSPCRC-HG) and the Prostate Cancer Prevention Trial Risk Calculator 2.0 for high-grade cancer (PCPTRC-HG). The predictive accuracy was assessed using the area under the receiver operating characteristic curve (AUC) and calibration plots. PC was detected in 172 (28.6%) men, 120 (19.9%) of whom had PC of Gleason score 7 or higher. Independent predictors included prostate-specific antigen levels, digital rectal examination findings, transrectal ultrasound findings, and prostate volume. The AUC of the KPCRC-HG (0.84) was higher than that of the PCPTRC-HG (0.79, pexternal validation. Calibration plots also revealed better performance of KPCRC-HG and ERSPCRC-HG than that of PCPTRC-HG on external validation. At a cut-off of 5% for KPCRC-HG, 253 of the 2,313 men (11%) would not have been biopsied, and 14 of the 614 PC cases with Gleason score 7 or higher (2%) would not have been diagnosed. KPCRC-HG is the first web-based high-grade prostate cancer prediction model in Korea. It had higher predictive accuracy than PCPTRC-HG in a Korean population and showed similar performance with ERSPCRC-HG in a Korean population. This prediction model could help avoid unnecessary biopsy and reduce overdiagnosis and overtreatment in clinical settings.
Energy Technology Data Exchange (ETDEWEB)
Hu, Hanshi; Bhaskaran-Nair, Kiran; Apra, Edoardo; Govind, Niranjan; Kowalski, Karol
2014-10-02
In this paper we discuss the application of novel parallel implementation of the coupled cluster (CC) and equation-of-motion coupled cluster methods (EOMCC) in calculations of excitation energies of triplet states in beta-carotene. Calculated excitation energies are compared with experimental data, where available. We also provide a detailed description of the new parallel algorithms for iterative CC and EOMCC models involving single and doubles excitations.
Integration of second cancer risk calculations in a radiotherapy treatment planning system
International Nuclear Information System (INIS)
Hartmann, M; Schneider, U
2014-01-01
Second cancer risk in patients, in particular in children, who were treated with radiotherapy is an important side effect. It should be minimized by selecting an appropriate treatment plan for the patient. The objectives of this study were to integrate a risk model for radiation induced cancer into a treatment planning system which allows to judge different treatment plans with regard to second cancer induction and to quantify the potential reduction in predicted risk. A model for radiation induced cancer including fractionation effects which is valid for doses in the radiotherapy range was integrated into a treatment planning system. From the three-dimensional (3D) dose distribution the 3D-risk equivalent dose (RED) was calculated on an organ specific basis. In addition to RED further risk coefficients like OED (organ equivalent dose), EAR (excess absolute risk) and LAR (lifetime attributable risk) are computed. A risk model for radiation induced cancer was successfully integrated in a treatment planning system. Several risk coefficients can be viewed and used to obtain critical situations were a plan can be optimised. Risk-volume-histograms and organ specific risks were calculated for different treatment plans and were used in combination with NTCP estimates for plan evaluation. It is concluded that the integration of second cancer risk estimates in a commercial treatment planning system is feasible. It can be used in addition to NTCP modelling for optimising treatment plans which result in the lowest possible second cancer risk for a patient.
International Nuclear Information System (INIS)
Shiino, Masatoshi; Yamana, Michiko
2004-01-01
We study the statistical mechanical aspects of stochastic analog neural network models for associative memory with correlation type learning. We take three approaches to derive the set of the order parameter equations for investigating statistical properties of retrieval states: the self-consistent signal-to-noise analysis (SCSNA), the Thouless-Anderson-Palmer (TAP) equation, and the replica symmetric calculation. On the basis of the cavity method the SCSNA can be generalized to deal with stochastic networks. We establish the close connection between the TAP equation and the SCSNA to elucidate the relationship between the Onsager reaction term of the TAP equation and the output proportional term of the SCSNA that appear in the expressions for the local fields
Quiney, H. M.; Glushkov, V. N.; Wilson, S.; Sabin,; Brandas, E
2001-01-01
A comparison is made of the accuracy achieved in finite difference and finite basis set approximations to the Dirac equation for the ground state of the hydrogen molecular ion. The finite basis set calculations are carried out using a distributed basis set of Gaussian functions the exponents and
Xiao, Guizhen; Xie, Qiuyou; He, Yanbin; Wang, Ziwen; Chen, Yan; Jiang, Mengliu; Ni, Xiaoxiao; Wang, Qinxian; Murong, Min; Guo, Yequn; Qiu, Xiaowen; Yu, Ronghao
2017-10-01
Accurately predicting the basal metabolic rate (BMR) of patients in a vegetative state (VS) or minimally conscious state (MCS) is critical to proper nutritional therapy, but commonly used equations have not been shown to be accurate. Therefore, we compared the BMR measured by indirect calorimetry (IC) to BMR values estimated using common predictive equations in VS and MCS patients. Body composition variables were measured using the bioelectric impedance analysis (BIA) technique. BMR was measured by IC in 82 patients (64 men and 18 women) with VS or MCS. Patients were classified by body mass index as underweight (BMR was estimated for each group using the Harris-Benedict (H-B), Schofield, or Cunningham equations and compared to the measured BMR using Bland-Altman analyses. For the underweight group, there was a significant difference between the measured BMR values and the estimated BMR values calculated using the H-B, Schofield, and Cunningham equations (p BMR values estimated using the H-B and Cunningham equations were different significantly from the measured BMR (p BMR in the normal-weight group. The Schofield equation showed the best concordance (only 41.5%) with the BMR values measured by IC. None of the commonly used equations to estimate BMR were suitable for the VS or MCS populations. Indirect calorimetry is the preferred way to avoid either over or underestimate of BMR values. Copyright © 2016. Published by Elsevier Ltd.
Ferenczy, György G
2013-04-05
The application of the local basis equation (Ferenczy and Adams, J. Chem. Phys. 2009, 130, 134108) in mixed quantum mechanics/molecular mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) methods is investigated. This equation is suitable to derive local basis nonorthogonal orbitals that minimize the energy of the system and it exhibits good convergence properties in a self-consistent field solution. These features make the equation appropriate to be used in mixed QM/MM and QM/QM methods to optimize orbitals in the field of frozen localized orbitals connecting the subsystems. Calculations performed for several properties in divers systems show that the method is robust with various choices of the frozen orbitals and frontier atom properties. With appropriate basis set assignment, it gives results equivalent with those of a related approach [G. G. Ferenczy previous paper in this issue] using the Huzinaga equation. Thus, the local basis equation can be used in mixed QM/MM methods with small size quantum subsystems to calculate properties in good agreement with reference Hartree-Fock-Roothaan results. It is shown that bond charges are not necessary when the local basis equation is applied, although they are required for the self-consistent field solution of the Huzinaga equation based method. Conversely, the deformation of the wave-function near to the boundary is observed without bond charges and this has a significant effect on deprotonation energies but a less pronounced effect when the total charge of the system is conserved. The local basis equation can also be used to define a two layer quantum system with nonorthogonal localized orbitals surrounding the central delocalized quantum subsystem. Copyright © 2013 Wiley Periodicals, Inc.
Chen, Rui; Xie, Liping; Xue, Wei; Ye, Zhangqun; Ma, Lulin; Gao, Xu; Ren, Shancheng; Wang, Fubo; Zhao, Lin; Xu, Chuanliang; Sun, Yinghao
2016-09-01
Substantial differences exist in the relationship of prostate cancer (PCa) detection rate and prostate-specific antigen (PSA) level between Western and Asian populations. Classic Western risk calculators, European Randomized Study for Screening of Prostate Cancer Risk Calculator, and Prostate Cancer Prevention Trial Risk Calculator, were shown to be not applicable in Asian populations. We aimed to develop and validate a risk calculator for predicting the probability of PCa and high-grade PCa (defined as Gleason Score sum 7 or higher) at initial prostate biopsy in Chinese men. Urology outpatients who underwent initial prostate biopsy according to the inclusion criteria were included. The multivariate logistic regression-based Chinese Prostate Cancer Consortium Risk Calculator (CPCC-RC) was constructed with cases from 2 hospitals in Shanghai. Discriminative ability, calibration and decision curve analysis were externally validated in 3 CPCC member hospitals. Of the 1,835 patients involved, PCa was identified in 338/924 (36.6%) and 294/911 (32.3%) men in the development and validation cohort, respectively. Multivariate logistic regression analyses showed that 5 predictors (age, logPSA, logPV, free PSA ratio, and digital rectal examination) were associated with PCa (Model 1) or high-grade PCa (Model 2), respectively. The area under the curve of Model 1 and Model 2 was 0.801 (95% CI: 0.771-0.831) and 0.826 (95% CI: 0.796-0.857), respectively. Both models illustrated good calibration and substantial improvement in decision curve analyses than any single predictors at all threshold probabilities. Higher predicting accuracy, better calibration, and greater clinical benefit were achieved by CPCC-RC, compared with European Randomized Study for Screening of Prostate Cancer Risk Calculator and Prostate Cancer Prevention Trial Risk Calculator in predicting PCa. CPCC-RC performed well in discrimination and calibration and decision curve analysis in external validation compared
Prediction of prostate cancer in unscreened men: external validation of a risk calculator.
van Vugt, Heidi A; Roobol, Monique J; Kranse, Ries; Määttänen, Liisa; Finne, Patrik; Hugosson, Jonas; Bangma, Chris H; Schröder, Fritz H; Steyerberg, Ewout W
2011-04-01
Prediction models need external validation to assess their value beyond the setting where the model was derived from. To assess the external validity of the European Randomized study of Screening for Prostate Cancer (ERSPC) risk calculator (www.prostatecancer-riskcalculator.com) for the probability of having a positive prostate biopsy (P(posb)). The ERSPC risk calculator was based on data of the initial screening round of the ERSPC section Rotterdam and validated in 1825 and 531 men biopsied at the initial screening round in the Finnish and Swedish sections of the ERSPC respectively. P(posb) was calculated using serum prostate specific antigen (PSA), outcome of digital rectal examination (DRE), transrectal ultrasound and ultrasound assessed prostate volume. The external validity was assessed for the presence of cancer at biopsy by calibration (agreement between observed and predicted outcomes), discrimination (separation of those with and without cancer), and decision curves (for clinical usefulness). Prostate cancer was detected in 469 men (26%) of the Finnish cohort and in 124 men (23%) of the Swedish cohort. Systematic miscalibration was present in both cohorts (mean predicted probability 34% versus 26% observed, and 29% versus 23% observed, both pscreened men, but overestimated the risk of a positive biopsy. Further research is necessary to assess the performance and applicability of the ERSPC risk calculator when a clinical setting is considered rather than a screening setting. Copyright © 2010 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Reynolds, J. M.; Lopez-Bruna, D.
2009-01-01
This report is the third of a series [Informes Tecnicos Ciemat 1165 y 1172] devoted to the development of a new numerical code to solve the guiding center equation for electrons and ions in toroidal plasmas. Two calculation meshes corresponding to axisymmetric tokamaks are now prepared and the kinetic equation is expanded so the standard terms of neoclassical theory --fi rst order terms in the Larmor radius expansion-- can be identified, restricting the calculations correspondingly. Using model density and temperature profiles for the plasma, several convergence test are performed depending on the calculation meshes and the expansions of the distribution function; then the results are compared with the theory [Hinton and Hazeltine, Rev. Mod. Phys. (1976)]. (Author) 18 refs
International Nuclear Information System (INIS)
Lampin, E.; Cristiano, F.; Lamrani, Y.; Colombeau, B.
2004-01-01
We present simulations of B TED based on a complete calculation of the extended defect growth/shrinkage during annealing. The Si self-interstitial supersaturation calculated at the extended defect depth is coupled to the set of equations for the B kick-out diffusion through a generation/recombination term in the diffusion equation of the Si self-interstitials. The simulations are compared to the measurements performed on a Si wafer containing several B marker layers, where the amount of TED varies from one peak to the other. The good agreement obtained on this experiment is very promising for the application of these calculations to the case of ultra-shallow B + implants
DEFF Research Database (Denmark)
Lübeck Christiansen, Rasmus; Jensen, Henrik R.; Brink, Carsten
2017-01-01
Background: Current state of the art radiotherapy planning of prostate cancer utilises magnetic resonance (MR) for soft tissue delineation and computed tomography (CT) to provide an electron density map for dose calculation. This dual scan workflow is prone to setup and registration error....... This study evaluates the feasibility of an MR-only workflow and the validity of dose calculation from an MR derived pseudo CT. Material and methods: Thirty prostate cancer patients were CT and MR scanned. Clinical treatment plans were generated on CT using a single 18 MV arc volumetric modulated arc therapy...... was successfully delivered to one patient, including manually performed daily IGRT. Conclusions: Median gamma pass rates were high for pseudo CT and proved superior to uniform density. Local differences in dose calculations were concluded not to have clinical relevance. Feasibility of the MR-only workflow...
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)
Reynolds, J. M.; Lopez-Bruna, D.
2009-01-01
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)
Ali, R.M.; England, A.; McEntee, M.F.; Hogg, P.
2015-01-01
Purpose: To propose a method for evaluating the effective lifetime risk of radiation-induced cancer from screening mammography and to present initial data for the UK National Breast Screening Programme. Material and methods: The imaging was undertaken using a Hologic Selenia full field digital mammographic unit. The proposed method utilises an ATOM phantom containing thermoluminescent dosimeters and a perspex-polyethylene breast phantom to measure organ doses during a standard four view screening mammogram. Effective dose was calculated and effective risk was modelled for a range of client ages. The total lifetime effective risk was then calculated for the UK national screening programme. Calculation of effective risk includes the radiation dose to examined and contralateral breasts in addition to other body organs; this is an advantage over the mean glandular dose. Results: The contralateral breast, thyroid, thymus, brain, lung, salivary glands, and bone marrow all receive more than 1 μGy radiation dose during screening mammography. A major difference exists for total effective lifetime risk of radiation-induced cancer between clients with average and high breast cancer risk. Differences are attributed to the commencement age of screening and time interval between screens. Conclusion: This study proposes a method to evaluate effective lifetime risk of radiation-induced cancer from screening mammography in order to compare different mammography screening programmes. - Highlights: • We proposed a method for the calculation of radiation-induced cancer from screening mammography. • We measured the radiation absorbed dose of different organs during screening mammography. • There are major differences between mammography screening programme categories with regard to radiation effective risk.
International Nuclear Information System (INIS)
Brizzi, R.; Fabre de la Ripelle, M.; Lassaut, M.
1999-01-01
The binding energies and root mean square radii obtained from the Integro-Differential Equation Approach (IDEA) and from the Weight Function Approximation (WFA) of the IDEA for an even number of bosons and for 12 C, 16 O and 40 Ca are compared to those recently obtained by the Variational Monte Carlo, Fermi Hypernetted Chain and Coupled Cluster expansion method with model potentials. The IDEA provides numbers very similar to those obtained by other methods although it takes only two-body correlations into account. The analytical expression of the wave function for the WFA is given for bosons in ground state when the interaction pair is outside the potential range. Due to its simple structure, the equations of the IDEA can easily be extended to realistic interaction for nuclei like it has already been done for the tri-nucleon and the 4 He. (authors)
International Nuclear Information System (INIS)
Fadel, Ana M.; Chebel, G.M.; Valdivieso, C.M.; Degrossi, Osvaldo J.; Cabrejas, R.; Cabrejas, M.L.
2006-01-01
The optimum dose for the differentiated thyroid cancer treatment is a motive of controversy. There exist two ways of deciding the dose to administer: the empirical method (fixed doses) and dosimetric calculation method. The use of fixed doses has demonstrated safety and effectiveness. Nevertheless there are cases in which the use of several small doses not resolves the metastases illness of the patients. Using the Benua-Leeper method for dosimetric calculation we have evaluated the maximum dose treatment that could be administered to 20 patients who showed persistent disease after several treatments with 131 I. (author) [es
International Nuclear Information System (INIS)
JORGENSON, ROY E.; WARNE, LARRY K.
2001-01-01
One of the tasks performed routinely by the Electromagnetics and Plasma Physics Analysis Department at Sandia National Laboratories is analyzing the effects of direct-strike lightning on Faraday cages that protect sensitive items. The Faraday cages analyzed thus far have many features in common. This report is an attempt to collect equations and other information that have been routinely used in the past in order to facilitate future analysis
International Nuclear Information System (INIS)
Schopohl, N.
1980-01-01
On the basis of Gorkov's formulation of superconductivity theory, generalized Eilenberger equations are derived which apply to rotating superfluid 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 Ω/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 3 He-A, the solution of the eigenvalue problem determining the order parameter Δ 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. =0.2π(Tc/sub c/0/T/sub F/)v/sub f/ at zero temperature
International Nuclear Information System (INIS)
Charlton, L.A.; Carreras, B.A.; Holmes, J.A.; Lynch, V.E.
1988-01-01
The linear stability and nonlinear evolution of the resistive m = 1 mode in tokamaks is studied using a full set of resistive magnetohydrodynamic (MHD) equations in toroidal geometry. The modification of the linear and nonlinear properties of the mode by a combination of strong toroidal effects and low resistivity is the focus of this work. Linearly there is a transition from resistive kink to resistive tearing behavior as the aspect ratio and resistivity are reduced, and there is a corresponding modification of the nonlinear behavior, including a slowing of the island growth and development of a Rutherford regime, as the tearing regime is approached. In order to study the sensitivity of the stability and evolution to assumptions concerning the equation of state, two sets of full nonlinear resistive MHD equations (a pressure convection set and an incompressible set) are used. Both sets give more stable nonlinear behavior as the aspect ratio is reduced. The pressure convection set shows a transition from a Kadomtsev reconnection at large aspect ratio to a saturation at small aspect ratio. The incompressible set yields Kadomtsev reconnection for all aspect ratios, but with a significant lengthening of the reconnection time and development of a Rutherford regime at an aspect ratio approaching the transition from a resistive kink mode to a tearing mode. The pressure convection set gives an incomplete reconnection similar to that sometimes seen experimentally. The pressure convection set is, however, strictly justified only at high beta
Energy Technology Data Exchange (ETDEWEB)
Myint, P. C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Hao, Y. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Firoozabadi, A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-03-27
Thermodynamic property calculations of mixtures containing carbon dioxide (CO_{2}) and water, including brines, are essential in theoretical models of many natural and industrial processes. The properties of greatest practical interest are density, solubility, and enthalpy. Many models for density and solubility calculations have been presented in the literature, but there exists only one study, by Spycher and Pruess, that has compared theoretical molar enthalpy predictions with experimental data [1]. In this report, we recommend two different models for enthalpy calculations: the CPA equation of state by Li and Firoozabadi [2], and the CO_{2} activity coefficient model by Duan and Sun [3]. We show that the CPA equation of state, which has been demonstrated to provide good agreement with density and solubility data, also accurately calculates molar enthalpies of pure CO_{2}, pure water, and both CO_{2}-rich and aqueous (H_{2}O-rich) mixtures of the two species. It is applicable to a wider range of conditions than the Spycher and Pruess model. In aqueous sodium chloride (NaCl) mixtures, we show that Duan and Sun’s model yields accurate results for the partial molar enthalpy of CO_{2}. It can be combined with another model for the brine enthalpy to calculate the molar enthalpy of H_{2}O-CO_{2}-NaCl mixtures. We conclude by explaining how the CPA equation of state may be modified to further improve agreement with experiments. This generalized CPA is the basis of our future work on this topic.
Bhatnagar, Shashank; Alemu, Lmenew
2018-02-01
In this work we calculate the mass spectra of charmonium for 1 P ,…,4 P states of 0++ and 1++, for 1 S ,…,5 S states of 0-+, and for 1 S ,…,4 D states of 1- along with the two-photon decay widths of the ground and first excited states of 0++ quarkonia for the process O++→γ γ in the framework of a QCD-motivated Bethe-Salpeter equation (BSE). In this 4 ×4 BSE framework, the coupled Salpeter equations are first shown to decouple for the confining part of the interaction (under the heavy-quark approximation) and are analytically solved, and later the one-gluon-exchange interaction is perturbatively incorporated, leading to mass spectral equations for various quarkonia. The analytic forms of wave functions obtained are used for the calculation of the two-photon decay widths of χc 0. Our results are in reasonable agreement with data (where available) and other models.
International Nuclear Information System (INIS)
Reis Filho, P.E.G. dos
1982-01-01
A new synthesis method to substitute for the classical method of finite diferences for XYZ geometry (geometry of critical experiments in fast reactors), is developed. The new method allows a fine energy group division, that is, finer than the 6 groups division used in calculations of power core specification. (E.G.) [pt
Turgumbayeva, R. Kh; Abdikarimov, M. N.; Sagintayeva, S. S.
2018-05-01
Results of studying an aerosol of the dioxide of sulfur and pentoxide of phosphorus released into the atmosphere by the chemical company for processing of phosphorit are presented. Influence of the direction and speed of wind on sulfur dioxide distribution and pentoxide of phosphorus in a ground layer of the atmosphere is studied, and the points of the direction of wind leading to pollution of the atmosphere of the nearby city are allocated. The statistical analysis of environmental pollution is carried out by the method of the correlation and regression analysis. The equations of dependence of the amount of the sulfur dioxide and pentoxide of phosphorus, released into the atmosphere, on the volume, released by the enterprise of production, are defined. The obtained results are recommended for control, regulation and management of the environment.
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.
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
2014-12-16
The accuracy of dose calculation is crucial to the quality of treatment planning and, consequently, to the dose delivered to patients undergoing radiation therapy. Current general calculation algorithms such as Pencil Beam Convolution (PBC) and Collapsed Cone Convolution (CCC) have shortcomings in regard to severe inhomogeneities, particularly in those regions where charged particle equilibrium does not hold. The aim of this study was to evaluate the accuracy of the PBC and CCC algorithms in lung cancer radiotherapy using Monte Carlo (MC) technology. Four treatment plans were designed using Oncentra Masterplan TPS for each patient. Two intensity-modulated radiation therapy (IMRT) plans were developed using the PBC and CCC algorithms, and two three-dimensional conformal therapy (3DCRT) plans were developed using the PBC and CCC algorithms. The DICOM-RT files of the treatment plans were exported to the Monte Carlo system to recalculate. The dose distributions of GTV, PTV and ipsilateral lung calculated by the TPS and MC were compared. For 3DCRT and IMRT plans, the mean dose differences for GTV between the CCC and MC increased with decreasing of the GTV volume. For IMRT, the mean dose differences were found to be higher than that of 3DCRT. The CCC algorithm overestimated the GTV mean dose by approximately 3% for IMRT. For 3DCRT plans, when the volume of the GTV was greater than 100 cm(3), the mean doses calculated by CCC and MC almost have no difference. PBC shows large deviations from the MC algorithm. For the dose to the ipsilateral lung, the CCC algorithm overestimated the dose to the entire lung, and the PBC algorithm overestimated V20 but underestimated V5; the difference in V10 was not statistically significant. PBC substantially overestimates the dose to the tumour, but the CCC is similar to the MC simulation. It is recommended that the treatment plans for lung cancer be developed using an advanced dose calculation algorithm other than PBC. MC can accurately
Lung Dose Calculation With SPECT/CT for {sup 90}Yittrium Radioembolization of Liver Cancer
Energy Technology Data Exchange (ETDEWEB)
Yu, Naichang, E-mail: yun@ccf.org [Department of Radiation Oncology, Cleveland Clinic, Cleveland, OH (United States); Srinivas, Shaym M.; DiFilippo, Frank P.; Shrikanthan, Sankaran [Department of Nuclear Medicine, Cleveland Clinic, Cleveland, OH (United States); Levitin, Abraham; McLennan, Gordon; Spain, James [Department of Interventional Radiology, Cleveland Clinic, Cleveland, OH (United States); Xia, Ping; Wilkinson, Allan [Department of Radiation Oncology, Cleveland Clinic, Cleveland, OH (United States)
2013-03-01
Purpose: To propose a new method to estimate lung mean dose (LMD) using technetium-99m labeled macroaggregated albumin ({sup 99m}Tc-MAA) single photon emission CT (SPECT)/CT for {sup 90}Yttrium radioembolization of liver tumors and to compare the LMD estimated using SPECT/CT with clinical estimates of LMD using planar gamma scintigraphy (PS). Methods and Materials: Images of 71 patients who had SPECT/CT and PS images of {sup 99m}Tc-MAA acquired before TheraSphere radioembolization of liver cancer were analyzed retrospectively. LMD was calculated from the PS-based lung shunt assuming a lung mass of 1 kg and 50 Gy per GBq of injected activity shunted to the lung. For the SPECT/CT-based estimate, the LMD was calculated with the activity concentration and lung volume derived from SPECT/CT. The effect of attenuation correction and the patient's breathing on the calculated LMD was studied with the SPECT/CT. With these effects correctly taken into account in a more rigorous fashion, we compared the LMD calculated with SPECT/CT with the LMD calculated with PS. Results: The mean dose to the central region of the lung leads to a more accurate estimate of LMD. Inclusion of the lung region around the diaphragm in the calculation leads to an overestimate of LMD due to the misregistration of the liver activity to the lung from the patient's breathing. LMD calculated based on PS is a poor predictor of the actual LMD. For the subpopulation with large lung shunt, the mean overestimation from the PS method for the lung shunt was 170%. Conclusions: A new method of calculating the LMD for TheraSphere and SIR-Spheres radioembolization of liver cancer based on {sup 99m}Tc-MAA SPECT/CT is presented. The new method provides a more accurate estimate of radiation risk to the lungs. For patients with a large lung shunt calculated from PS, a recalculation of LMD based on SPECT/CT is recommended.
Lung Dose Calculation With SPECT/CT for 90Yittrium Radioembolization of Liver Cancer
International Nuclear Information System (INIS)
Yu, Naichang; Srinivas, Shaym M.; DiFilippo, Frank P.; Shrikanthan, Sankaran; Levitin, Abraham; McLennan, Gordon; Spain, James; Xia, Ping; Wilkinson, Allan
2013-01-01
Purpose: To propose a new method to estimate lung mean dose (LMD) using technetium-99m labeled macroaggregated albumin ( 99m Tc-MAA) single photon emission CT (SPECT)/CT for 90 Yttrium radioembolization of liver tumors and to compare the LMD estimated using SPECT/CT with clinical estimates of LMD using planar gamma scintigraphy (PS). Methods and Materials: Images of 71 patients who had SPECT/CT and PS images of 99m Tc-MAA acquired before TheraSphere radioembolization of liver cancer were analyzed retrospectively. LMD was calculated from the PS-based lung shunt assuming a lung mass of 1 kg and 50 Gy per GBq of injected activity shunted to the lung. For the SPECT/CT-based estimate, the LMD was calculated with the activity concentration and lung volume derived from SPECT/CT. The effect of attenuation correction and the patient's breathing on the calculated LMD was studied with the SPECT/CT. With these effects correctly taken into account in a more rigorous fashion, we compared the LMD calculated with SPECT/CT with the LMD calculated with PS. Results: The mean dose to the central region of the lung leads to a more accurate estimate of LMD. Inclusion of the lung region around the diaphragm in the calculation leads to an overestimate of LMD due to the misregistration of the liver activity to the lung from the patient's breathing. LMD calculated based on PS is a poor predictor of the actual LMD. For the subpopulation with large lung shunt, the mean overestimation from the PS method for the lung shunt was 170%. Conclusions: A new method of calculating the LMD for TheraSphere and SIR-Spheres radioembolization of liver cancer based on 99m Tc-MAA SPECT/CT is presented. The new method provides a more accurate estimate of radiation risk to the lungs. For patients with a large lung shunt calculated from PS, a recalculation of LMD based on SPECT/CT is recommended
Lung dose calculation with SPECT/CT for ⁹⁰Yittrium radioembolization of liver cancer.
Yu, Naichang; Srinivas, Shaym M; Difilippo, Frank P; Shrikanthan, Sankaran; Levitin, Abraham; McLennan, Gordon; Spain, James; Xia, Ping; Wilkinson, Allan
2013-03-01
To propose a new method to estimate lung mean dose (LMD) using technetium-99m labeled macroaggregated albumin ((99m)Tc-MAA) single photon emission CT (SPECT)/CT for (90)Yttrium radioembolization of liver tumors and to compare the LMD estimated using SPECT/CT with clinical estimates of LMD using planar gamma scintigraphy (PS). Images of 71 patients who had SPECT/CT and PS images of (99m)Tc-MAA acquired before TheraSphere radioembolization of liver cancer were analyzed retrospectively. LMD was calculated from the PS-based lung shunt assuming a lung mass of 1 kg and 50 Gy per GBq of injected activity shunted to the lung. For the SPECT/CT-based estimate, the LMD was calculated with the activity concentration and lung volume derived from SPECT/CT. The effect of attenuation correction and the patient's breathing on the calculated LMD was studied with the SPECT/CT. With these effects correctly taken into account in a more rigorous fashion, we compared the LMD calculated with SPECT/CT with the LMD calculated with PS. The mean dose to the central region of the lung leads to a more accurate estimate of LMD. Inclusion of the lung region around the diaphragm in the calculation leads to an overestimate of LMD due to the misregistration of the liver activity to the lung from the patient's breathing. LMD calculated based on PS is a poor predictor of the actual LMD. For the subpopulation with large lung shunt, the mean overestimation from the PS method for the lung shunt was 170%. A new method of calculating the LMD for TheraSphere and SIR-Spheres radioembolization of liver cancer based on (99m)Tc-MAA SPECT/CT is presented. The new method provides a more accurate estimate of radiation risk to the lungs. For patients with a large lung shunt calculated from PS, a recalculation of LMD based on SPECT/CT is recommended. Copyright © 2013 Elsevier Inc. All rights reserved.
Ferenczy, György G
2013-04-05
Mixed quantum mechanics/quantum mechanics (QM/QM) and quantum mechanics/molecular mechanics (QM/MM) methods make computations feasible for extended chemical systems by separating them into subsystems that are treated at different level of sophistication. In many applications, the subsystems are covalently bound and the use of frozen localized orbitals at the boundary is a possible way to separate the subsystems and to ensure a sensible description of the electronic structure near to the boundary. A complication in these methods is that orthogonality between optimized and frozen orbitals has to be warranted and this is usually achieved by an explicit orthogonalization of the basis set to the frozen orbitals. An alternative to this approach is proposed by calculating the wave-function from the Huzinaga equation that guaranties orthogonality to the frozen orbitals without basis set orthogonalization. The theoretical background and the practical aspects of the application of the Huzinaga equation in mixed methods are discussed. Forces have been derived to perform geometry optimization with wave-functions from the Huzinaga equation. Various properties have been calculated by applying the Huzinaga equation for the central QM subsystem, representing the environment by point charges and using frozen strictly localized orbitals to connect the subsystems. It is shown that a two to three bond separation of the chemical or physical event from the frozen bonds allows a very good reproduction (typically around 1 kcal/mol) of standard Hartree-Fock-Roothaan results. The proposed scheme provides an appropriate framework for mixed QM/QM and QM/MM methods. Copyright © 2012 Wiley Periodicals, Inc.
International Nuclear Information System (INIS)
Tit, N.; Halley, J.W.
1992-01-01
Traditional methods of calculating the electronic structure of defects in semiconductors rely on matrix-diagonalization methods which use the unperturbed crystalline wave functions as a basis. Equation-of-motion (EOM) methods, on the other hand, give excellent results with strong disorder and many defects and make no use of the basis of unperturbed wave functions, but require self-averaging properties of the wave functions which appear superficially to make them unsuitable for study of local properties. We show here that EOM methods are better than traditional methods for calculating the electronic structure of essentially any finite-range impurity potential. The reason is basically that the numerical cost of the traditional Green's-function methods grows approximately as R 7 o/Iper sitet/P, where R is the range of the potential, whereas the cost of the EOM methods per site is independent of the range of the potential. Our detailed calculations on a model of an oxygen vacancy in rutile TiO 2 show that a crossover occurs very soon, so that equation-of-motion methods are better than the traditional ones in the case of potentials of realistic range
Han, Song; Zhang, Wei; Zhang, Jie
2017-09-01
A fast sweeping method (FSM) determines the first arrival traveltimes of seismic waves by sweeping the velocity model in different directions meanwhile applying a local solver. It is an efficient way to numerically solve Hamilton-Jacobi equations for traveltime calculations. In this study, we develop an improved FSM to calculate the first arrival traveltimes of quasi-P (qP) waves in 2-D tilted transversely isotropic (TTI) media. A local solver utilizes the coupled slowness surface of qP and quasi-SV (qSV) waves to form a quartic equation, and solve it numerically to obtain possible traveltimes of qP-wave. The proposed quartic solver utilizes Fermat's principle to limit the range of the possible solution, then uses the bisection procedure to efficiently determine the real roots. With causality enforced during sweepings, our FSM converges fast in a few iterations, and the exact number depending on the complexity of the velocity model. To improve the accuracy, we employ high-order finite difference schemes and derive the second-order formulae. There is no weak anisotropy assumption, and no approximation is made to the complex slowness surface of qP-wave. In comparison to the traveltimes calculated by a horizontal slowness shooting method, the validity and accuracy of our FSM is demonstrated.
Noori, Nazanin; Wald, Ron; Sharma Parpia, Arti; Goldstein, Marc B
2018-01-01
Accurate assessment of total body water (TBW) is essential for the evaluation of dialysis adequacy (Kt/V urea ). The Watson formula, which is recommended for the calculation of TBW, was derived in healthy volunteers thereby leading to potentially inaccurate TBW estimates in maintenance hemodialysis recipients. Bioimpedance spectroscopy (BIS) may be a robust alternative for the measurement of TBW in hemodialysis recipients. The primary objective of this study was to evaluate the accuracy of Watson formula-derived TBW estimates as compared with TBW measured with BIS. Second, we aimed to identify the anthropometric characteristics that are most likely to generate inaccuracy when using the Watson formula to calculate TBW. Finally, we derived novel anthropometric equations for the more accurate estimation of TBW. This was a cross-sectional study of prevalent in-center HD patients at St Michael's Hospital. One hundred eighty-four hemodialysis patients (109 men and 75 women) were evaluated in this study. Anthropometric measurements including weight, height, waist circumference, midarm circumference, and 4-site skinfold (biceps, triceps, subscapular, and suprailiac) thickness were measured; fat mass was measured using the formula by Durnin and Womersley. We measured TBW by BIS using the Body Composition Monitor (Fresenius Medical Care, Bad Homburg, Germany). We used the Bland-Altman method to calculate the difference between the TBW derived from the Watson method and the BIS. To derive new equations for TBW estimation, Pearson's correlation coefficients between BIS-TBW (the reference test) and other variables were examined. We used the least squares regression analysis to develop parsimonious equations to predict TBW. TBW values based on the Watson method had a high correlation with BIS-TBW (correlation coefficients = 0.87 and P Watson formula overestimated TBW by 5.1 (4.5-5.8) liters and 3.8 (3.0-4.5) liters, in men and women, respectively. Higher fat mass and waist
International Nuclear Information System (INIS)
Reva, T.D.; Semenov, A.M.
1984-01-01
Statistically significant estimations of the second, third and fourth group integrals of sodium and potassium vapors were obtained in the framework of the initial atom method on the basis of semiempirical equation of state derived by the authors. Possibility is duscussed of estimating dimer, trimer and tetramer concentrations from these data with account of unideality of vapors. High rate of convergence of density and pressure group expansion is demonstrated. Virial coefficients were calculated. It is shown that virial expansions of thermodynamic functions diverge at elevated densities of the gases under study. The estimations of senior virial coefficients of sodium and potassium vapors available in literature were proved to be faulty
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.
Green, David L.; Berry, Lee A.; Simpson, Adam B.; Younkin, Timothy R.
2018-04-01
We present the KINETIC-J code, a computational kernel for evaluating the linearized Vlasov equation with application to calculating the kinetic plasma response (current) to an applied time harmonic wave electric field. This code addresses the need for a configuration space evaluation of the plasma current to enable kinetic full-wave solvers for waves in hot plasmas to move beyond the limitations of the traditional Fourier spectral methods. We benchmark the kernel via comparison with the standard k →-space forms of the hot plasma conductivity tensor.
CT-based dose calculations and in vivo dosimetry for lung cancer treatment
International Nuclear Information System (INIS)
Essers, M.; Lanson, J.H.; Leunens, G.; Schnabel, T.; Mijnheer, B.J.
1995-01-01
Reliable CT-based dose calculations and dosimetric quality control are essential for the introduction of new conformal techniques for the treatment of lung cancer. The first aim of this study was therefore to check the accuracy of dose calculations based on CT-densities, using a simple inhomogeneity correction model, for lung cancer patients irradiated with an AP-PA treatment technique. Second, the use of diodes for absolute exit dose measurements and an Electronic Portal Imaging Device (EPID) for relative transmission dose verification was investigated for 22 and 12 patients, respectively. The measured dose values were compared with calculations performed using our 3-dimensional treatment planning system, using CT-densities or assuming the patient to be water-equivalent. Using water-equivalent calculations, the actual exit dose value under lung was, on average, underestimated by 30%, with an overall spread of 10% (1 SD). Using inhomogeneity corrections, the exit dose was, on average, overestimated by 4%, with an overall spread of 6% (1 SD). Only 2% of the average deviation was due to the inhomogeneity correction model. An uncertainty in exit dose calculation of 2.5% (1 SD) could be explained by organ motion, resulting from the ventilatory or cardiac cycle. The most important reason for the large overall spread was, however, the uncertainty involved in performing point measurements: about 4% (1 SD). This difference resulted from the systematic and random deviation in patient set-up and therefore in diode position with respect to patient anatomy. Transmission and exit dose values agreed with an average difference of 1.1%. Transmission dose profiles also showed good agreement with calculated exit dose profiles. Our study shows that, for this treatment technique, the dose in the thorax region is quite accurately predicted using CT-based dose calculations, even if a simple inhomogeneity correction model is used. Point detectors such as diodes are not suitable for exit
International Nuclear Information System (INIS)
Chen, Qianghua; Zhang, Mengce; Liu, Shuaijie; He, Yongxi; Luo, Huifu; Luo, Jun; Lv, Weiwei
2016-01-01
At present the formulae proposed by G Boensch and E Potulski in 1998 (Boensch and Potulski 1998 Metrologia 35 133–9) are mostly used to calculate the air refractive index. However, the humidity correction equation in the formulae is derived by using the light source of a Cd lamp whose light frequency stability is poor and at a narrow temperature range, around 20 °C. So it is no longer suitable in present optical precision measurements. To solve this problem, we propose a refractive index measurement system based on phase step interferometer with three frequency stabilized lasers (532 nm, 633 nm, 780 nm), corrected coefficients of the humidity are measured and a corresponding revised humidity correction equation is acquired. Meanwhile, the application temperature range is extended from 14.6 °C to 25.0 °C. The experiment comparison results at the temperature of 22.2–23.2 °C show the accuracy by the presented equation is better than that of Boensch and Potulski. (paper)
International Nuclear Information System (INIS)
Watanabe, Nami; Sugai Yukio; Komatani, Akio; Yamaguchi, Koichi; Takahashi, Kazuei
1999-01-01
This study was designed to investigate the empirical tubular extraction rate (TER) of the normal renal function in childhood and then propose a new equation to obtain TER theoretically. The empirical TER was calculated using Russell's method for determination of single-sample plasma clearance and 99m Tc-MAG 3 in 40 patients with renal disease younger than 10 years of age who were classified as having normal renal function using diagnostic criteria defined by the Paediatric Task Group of EANM. First, we investigated the relationships of the empirical value of absolute TER to age, body weight, body surface area (BSA) and distribution volume. Next we investigated the relationships of the empirical value of BSA corrected TER to age, body weight, BSA and distribution volume. Linear relationship was indicated between the absolute TER and each body dimensional factors, especially regarding to BSA, its correlation coefficient was 0.90 (p value). The BSA-corrected TER showed a logarithmic relationship with BSA, but linear regression did not show any significant correlation. Therefore, it was thought that the normal value of TER could be calculated theoretically using the body surface area, and here we proposed the following linear regression equation; Theoretical TER (ml/min/1.73 m 2 )=(-39.8+257.2 x BSA)/BSA/1.73. The theoretical TER could be one of the reference values of the renal function in the period of the renal maturation. (author)
Directory of Open Access Journals (Sweden)
Nelson H. T. Lemes
2010-01-01
Full Text Available Analytical solutions of a cubic equation with real coefficients are established using the Cardano method. The method is first applied to simple third order equation. Calculation of volume in the van der Waals equation of state is afterwards established. These results are exemplified to calculate the volumes below and above critical temperatures. Analytical and numerical values for the compressibility factor are presented as a function of the pressure. As a final example, coexistence volumes in the liquid-vapor equilibrium are calculated. The Cardano approach is very simple to apply, requiring only elementary operations, indicating an attractive method to be used in teaching elementary thermodynamics.
International Nuclear Information System (INIS)
Thalhofer, J. L.; Marques L, J.; Da Silva, A. X.; Dos Reis J, J. P.; Da Silva J, W. F. R.; Arruda C, S. C.; Monteiro de S, E.; Santos B, D. V.
2017-10-01
Actually, lung cancer is one of the most lethal types, due to the disease in the majority of the cases asymptomatic in the early stages, being the detection of the pathology in advanced stage, with tumor considerable volume. Dosimetry analysis of healthy organs under real conditions is not feasible. Therefore, computational simulations are used to auxiliary in dose verification in organs of patients submitted to radiotherapy. The goal of this study is to calculate the equivalent dose, due to photons, in surrounding in healthy organs of a patient submitted to radiotherapy for lung cancer, through computational modeling. The simulation was performed using the MCNPX code (Version, 2006], Rex and Regina phantom [ICRP 110, 2008], radiotherapy room, Siemens Oncor Expression accelerator operating at 6 MV and treatment protocol adopted at the Inca (National Cancer Institute, Brazil). The results obtained, considering the dose due to photons for both phantom indicate that organs located inside the thoracic cavity received higher dose, being the bronchi, heart and esophagus more affected, due to the anatomical positioning. Clinical data describe the development of bronchiolitis, esophagitis, and cardiomyopathies with decreased cardiopulmonary function as one of the major effects of lung cancer treatment. In the Regina phantom, the second largest dose was in the region of the breasts with 615,73 mSv / Gy, while in the Rex 514,06 mSv / Gy, event related to the difference of anatomical structure of the organ. Through the t mesh command, a qualitative analysis was performed between the dose deposition profile of the planning system and the simulated treatment, with a similar profile of the dose distribution being verified along the patients body. (Author)
Gómez-Gómez, Enrique; Carrasco-Valiente, Julia; Blanca-Pedregosa, Ana; Barco-Sánchez, Beatriz; Fernandez-Rueda, Jose Luis; Molina-Abril, Helena; Valero-Rosa, Jose; Font-Ugalde, Pilar; Requena-Tapia, Maria José
2017-04-01
To externally validate the European Randomized Study of Screening for Prostate Cancer (ERSPC) risk calculator (RC) and to evaluate its variability between 2 consecutive prostate-specific antigen (PSA) values. We prospectively catalogued 1021 consecutive patients before prostate biopsy for suspicion of prostate cancer (PCa). The risk of PCa and significant PCa (Gleason score ≥7) from 749 patients was calculated according to ERSPC-RC (digital rectal examination-based version 3 of 4) for 2 consecutive PSA tests per patient. The calculators' predictions were analyzed using calibration plots and the area under the receiver operating characteristic curve (area under the curve). Cohen kappa coefficient was used to compare the ability and variability. Of 749 patients, PCa was detected in 251 (33.5%) and significant PCa was detected in 133 (17.8%). Calibration plots showed an acceptable parallelism and similar discrimination ability for both PSA levels with an area under the curve of 0.69 for PCa and 0.74 for significant PCa. The ERSPC showed 226 (30.2%) unnecessary biopsies with the loss of 10 significant PCa. The variability of the RC was 16% for PCa and 20% for significant PCa, and a higher variability was associated with a reduced risk of significant PCa. We can conclude that the performance of the ERSPC-RC in the present cohort shows a high similitude between the 2 PSA levels; however, the RC variability value is associated with a decreased risk of significant PCa. The use of the ERSPC in our cohort detects a high number of unnecessary biopsies. Thus, the incorporation of ERSPC-RC could help the clinical decision to carry out a prostate biopsy. Copyright © 2016 Elsevier Inc. All rights reserved.
Chen, Xueli; Yang, Defu; Qu, Xiaochao; Hu, Hao; Liang, Jimin; Gao, Xinbo; Tian, Jie
2012-06-01
Bioluminescence tomography (BLT) has been successfully applied to the detection and therapeutic evaluation of solid cancers. However, the existing BLT reconstruction algorithms are not accurate enough for cavity cancer detection because of neglecting the void problem. Motivated by the ability of the hybrid radiosity-diffusion model (HRDM) in describing the light propagation in cavity organs, an HRDM-based BLT reconstruction algorithm was provided for the specific problem of cavity cancer detection. HRDM has been applied to optical tomography but is limited to simple and regular geometries because of the complexity in coupling the boundary between the scattering and void region. In the provided algorithm, HRDM was first applied to three-dimensional complicated and irregular geometries and then employed as the forward light transport model to describe the bioluminescent light propagation in tissues. Combining HRDM with the sparse reconstruction strategy, the cavity cancer cells labeled with bioluminescent probes can be more accurately reconstructed. Compared with the diffusion equation based reconstruction algorithm, the essentiality and superiority of the HRDM-based algorithm were demonstrated with simulation, phantom and animal studies. An in vivo gastric cancer-bearing nude mouse experiment was conducted, whose results revealed the ability and feasibility of the HRDM-based algorithm in the biomedical application of gastric cancer detection.
International Nuclear Information System (INIS)
Sewell, Thomas D.; Bennett, Carl M.
2000-01-01
Isothermal-isobaric Monte Carlo calculations were used to obtain predictions of the elastic coefficients and derived engineering moduli and Poisson ratios for crystalline hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX). The elastic coefficients were computed using the strain fluctuation formula due to Rahman and Parrinello [J. Chem. Phys. 76, 2662 (1982)]. Calculations were performed as a function of temperature (218 K≤T≤333 K) and hydrostatic pressure (0 GPa≤p≤4 GPa). The predicted values of the moduli and Poisson ratios under ambient conditions are in accord with general expectations for molecular crystals and with a very recent, unpublished determination for RDX. The moduli exhibit a sensitive pressure dependence whereas the Poisson ratios are relatively independent of pressure. The temperature dependence of the moduli is comparable to the precision of the results. However, the crystal does exhibit thermal softening for most pressures. An additional product of the calculations is information about the pressure-volume-temperature (pVT) equation of state. We obtain near-quantitative agreement with experiment for the case of hydrostatic compression and reasonable, but not quantitative, correspondence for thermal expansion. The results indicate a significant dependence of the thermal expansion coefficients on hydrostatic pressure. (c) 2000 American Institute of Physics
Li, Jonathan G.; Liu, Chihray; Olivier, Kenneth R.; Dempsey, James F.
2009-01-01
The aim of this study was to investigate the relative accuracy of megavoltage photon‐beam dose calculations employing either five bulk densities or independent voxel densities determined by calibration of the CT Houndsfield number. Full‐resolution CT and bulk density treatment plans were generated for 70 lung or esophageal cancer tumors (66 cases) using a commercial treatment planning system with an adaptive convolution dose calculation algorithm (Pinnacle3, Philips Medicals Systems). Bulk densities were applied to segmented regions. Individual and population average densities were compared to the full‐resolution plan for each case. Monitor units were kept constant and no normalizations were employed. Dose volume histograms (DVH) and dose difference distributions were examined for all cases. The average densities of the segmented air, lung, fat, soft tissue, and bone for the entire set were found to be 0.14, 0.26, 0.89, 1.02, and 1.12 g/cm3, respectively. In all cases, the normal tissue DVH agreed to better than 2% in dose. In 62 of 70 DVHs of the planning target volume (PTV), agreement to better than 3% in dose was observed. Six cases demonstrated emphysema, one with bullous formations and one with a hiatus hernia having a large volume of gas. These required the additional assignment of density to the emphysemic lung and inflammatory changes to the lung, the regions of collapsed lung, the bullous formations, and the hernia gas. Bulk tissue density dose calculation provides an accurate method of heterogeneous dose calculation. However, patients with advanced emphysema may require high‐resolution CT studies for accurate treatment planning. PACS number: 87.53.Tf
International Nuclear Information System (INIS)
Glushkov, A.V.; Kol'tsova, N.Yu.
1994-01-01
Equations of motion were solved by a modified method in a quasi-particle representation of the density functional taking into account the most important polarization effects, including the so-called 2p-2h two-particle-two-hole interactions. Based on these calculations, spectroscopic data on energies and oscillator strengths of the helium atom (the test computation), carbon monoxide, nitrogen molecule, and ethylene are presented that refine some previously reported experimental and theoretical results. It is shown that in some cases the inclusion of polarization corrections introduced by 2p-2h effects is of basic importance because it provides up to ∼30% contribution to the energies and oscillator strengths. 23 refs., 5 tabs
Energy Technology Data Exchange (ETDEWEB)
Kocic, A [Institute of Nuclear Sciences Boris Kidric, Vinca, Beograd (Serbia and Montenegro)
1977-07-01
General sampling Monte Carlo scheme for neutron transport equation has been described. Programme TRANSFER for neutron beam transmission analysis has been used to calculate the neutron leakage spectrum, detector efficiency and neutron angular distribution of the example problem (author) [Serbo-Croat] U radu se najpre razmatraju osnovni problemi resavanja transportne jednacine i nacin kako Monte Karlo metoda omogucuje da se prevazidju neki od njih: visedimenzionalnost zadatka, problem dubokog prodiranja i dovoljno fino tretiranje efikasnih preseka. Dalje, govori se o iskustvima sa primenom Monte Karlo metode u Laboratoriji za nuklearnu energetiku i tehnicku fiziku i o primeni ove metode na probleme zastite. Na kraju dati su i analizirani ilustrativni primeri proracuna transporta neutrona kroz ravan sloj zastitnog materijala koriscenjem Monte Karlo programa TRANSFER (author)
International Nuclear Information System (INIS)
Shimada, K; Kai, M
2015-01-01
This paper has proposed that disability-adjusted life year (DALY) can be used as a measure of radiation health risk. DALY is calculated as the sum of years of life lost (YLL) and years lived with disability (YLD). This multidimensional concept can be expressed as a risk index without a probability measure to avoid the misuse of the current radiation detriment at low doses. In this study, we calculated YLL and YLD using Japanese population data by gender. DALY for all cancers in Japan per 1 Gy per person was 0.84 year in men and 1.34 year in women. The DALY for all cancers in the Japanese baseline was 4.8 in men and 3.5 in women. When we calculated the ICRP detriment from the same data, DALYs for the cancer sites were similar to the radiation detriment in the cancer sites, excluding leukemia, breast and thyroid cancer. These results suggested that the ICRP detriment overestimate the weighting fraction of leukemia risk and underestimate the weighting fraction of breast and thyroid cancer. A big advantage over the ICRP detriment is that DALY can calculate the risk components for non-fatal diseases without the data of lethality. This study showed that DALY is a practical tool that can compare many types of diseases encountered in public health. (paper)
International Nuclear Information System (INIS)
Han Tao; Followill, David; Repchak, Roman; Molineu, Andrea; Howell, Rebecca; Salehpour, Mohammad; Mikell, Justin; Mourtada, Firas
2013-01-01
Purpose: The novel deterministic radiation transport algorithm, Acuros XB (AXB), has shown great potential for accurate heterogeneous dose calculation. However, the clinical impact between AXB and other currently used algorithms still needs to be elucidated for translation between these algorithms. The purpose of this study was to investigate the impact of AXB for heterogeneous dose calculation in lung cancer for intensity-modulated radiation therapy (IMRT) and volumetric-modulated arc therapy (VMAT). Methods: The thorax phantom from the Radiological Physics Center (RPC) was used for this study. IMRT and VMAT plans were created for the phantom in the Eclipse 11.0 treatment planning system. Each plan was delivered to the phantom three times using a Varian Clinac iX linear accelerator to ensure reproducibility. Thermoluminescent dosimeters (TLDs) and Gafchromic EBT2 film were placed inside the phantom to measure delivered doses. The measurements were compared with dose calculations from AXB 11.0.21 and the anisotropic analytical algorithm (AAA) 11.0.21. Two dose reporting modes of AXB, dose-to-medium in medium (D m,m ) and dose-to-water in medium (D w,m ), were studied. Point doses, dose profiles, and gamma analysis were used to quantify the agreement between measurements and calculations from both AXB and AAA. The computation times for AAA and AXB were also evaluated. Results: For the RPC lung phantom, AAA and AXB dose predictions were found in good agreement to TLD and film measurements for both IMRT and VMAT plans. TLD dose predictions were within 0.4%–4.4% to AXB doses (both D m,m and D w,m ); and within 2.5%–6.4% to AAA doses, respectively. For the film comparisons, the gamma indexes (±3%/3 mm criteria) were 94%, 97%, and 98% for AAA, AXB Dm,m , and AXB Dw,m , respectively. The differences between AXB and AAA in dose–volume histogram mean doses were within 2% in the planning target volume, lung, heart, and within 5% in the spinal cord. However
Abernathy, Kristen; Burke, Jeremy
2016-01-01
Despite improvements in cancer therapy and treatments, tumor recurrence is a common event in cancer patients. One explanation of recurrence is that cancer therapy focuses on treatment of tumor cells and does not eradicate cancer stem cells (CSCs). CSCs are postulated to behave similar to normal stem cells in that their role is to maintain homeostasis. That is, when the population of tumor cells is reduced or depleted by treatment, CSCs will repopulate the tumor, causing recurrence. In this paper, we study the application of the CSC Hypothesis to the treatment of glioblastoma multiforme by immunotherapy. We extend the work of Kogan et al. (2008) to incorporate the dynamics of CSCs, prove the existence of a recurrence state, and provide an analysis of possible cancerous states and their dependence on treatment levels.
Baltar, Valéria Troncoso; Xun, Wei W; Johansson, Mattias; Ferrari, Pietro; Chuang, Shu-Chun; Relton, Caroline; Ueland, Per Magne; Midttun, Øivind; Slimani, Nadia; Jenab, Mazda; Clavel-Chapelon, Françoise; Boutron-Ruault, Marie-Christine; Fagherazzi, Guy; Kaaks, Rudolf; Rohrmann, Sabine; Boeing, Heiner; Weikert, Cornelia; Bueno-de-Mesquita, Bas; Boshuizen, Hendriek; van Gils, Carla H; Onland-Moret, N Charlotte; Agudo, Antonio; Barricarte, Aurelio; Navarro, Carmen; Rodríguez, Laudina; Castaño, José Maria Huerta; Larrañaga, Nerea; Khaw, Kay-Tee; Wareham, Nick; Allen, Naomi E; Crowe, Francesca; Gallo, Valentina; Norat, Teresa; Krogh, Vittorio; Masala, Giovanna; Panico, Salvatore; Sacerdote, Carlotta; Tumino, Rosario; Trichopoulou, Antonia; Lagiou, Pagona; Trichopoulos, Dimitrios; Rasmuson, Torgny; Hallmans, Göran; Roswall, Nina; Tjønneland, Anne; Riboli, Elio; Brennan, Paul; Vineis, Paolo
2013-08-01
The one-carbon metabolism (OCM) is considered key in maintaining DNA integrity and regulating gene expression, and may be involved in the process of carcinogenesis. Several B-vitamins and amino acids have been implicated in lung cancer risk, via the OCM directly as well as immune system activation. However it is unclear whether these factors act independently or through complex mechanisms. The current study applies structural equations modelling (SEM) to further disentangle the mechanisms involved in lung carcinogenesis. SEM allows simultaneous estimation of linear relations where a variable can be the outcome in one equation and the predictor in another, as well as allowing estimation using latent variables (factors estimated by correlation matrix). A large number of biomarkers have been analysed from 891 lung cancer cases and 1,747 controls nested within the European Prospective Investigation into Cancer and Nutrition (EPIC) cohort. Four putative mechanisms in the OCM and immunity were investigated in relation to lung cancer risk: methionine-homocysteine metabolism, folate cycle, transsulfuration, and mechanisms involved in inflammation and immune activation, all adjusted for tobacco exposure. The hypothesized SEM model confirmed a direct and protective effect for factors representing methionine-homocysteine metabolism (p = 0.020) and immune activation (p = 0.021), and an indirect protective effect of folate cycle (p = 0.019), after adjustment for tobacco smoking. In conclusion, our results show that in the investigation of the involvement of the OCM, the folate cycle and immune system in lung carcinogenesis, it is important to consider complex pathways (by applying SEM) rather than the effects of single vitamins or nutrients (e.g. using traditional multiple regression). In our study SEM were able to suggest a greater role of the methionine-homocysteine metabolism and immune activation over other potential mechanisms.
Directory of Open Access Journals (Sweden)
Chang Wook Jeong
Full Text Available OBJECTIVES: We developed a mobile application-based Seoul National University Prostate Cancer Risk Calculator (SNUPC-RC that predicts the probability of prostate cancer (PC at the initial prostate biopsy in a Korean cohort. Additionally, the application was validated and subjected to head-to-head comparisons with internet-based Western risk calculators in a validation cohort. Here, we describe its development and validation. PATIENTS AND METHODS: As a retrospective study, consecutive men who underwent initial prostate biopsy with more than 12 cores at a tertiary center were included. In the development stage, 3,482 cases from May 2003 through November 2010 were analyzed. Clinical variables were evaluated, and the final prediction model was developed using the logistic regression model. In the validation stage, 1,112 cases from December 2010 through June 2012 were used. SNUPC-RC was compared with the European Randomized Study of Screening for PC Risk Calculator (ERSPC-RC and the Prostate Cancer Prevention Trial Risk Calculator (PCPT-RC. The predictive accuracy was assessed using the area under the receiver operating characteristic curve (AUC. The clinical value was evaluated using decision curve analysis. RESULTS: PC was diagnosed in 1,240 (35.6% and 417 (37.5% men in the development and validation cohorts, respectively. Age, prostate-specific antigen level, prostate size, and abnormality on digital rectal examination or transrectal ultrasonography were significant factors of PC and were included in the final model. The predictive accuracy in the development cohort was 0.786. In the validation cohort, AUC was significantly higher for the SNUPC-RC (0.811 than for ERSPC-RC (0.768, p<0.001 and PCPT-RC (0.704, p<0.001. Decision curve analysis also showed higher net benefits with SNUPC-RC than with the other calculators. CONCLUSIONS: SNUPC-RC has a higher predictive accuracy and clinical benefit than Western risk calculators. Furthermore, it is easy
Faraji, Shirin; Matsika, Spiridoula; Krylov, Anna I.
2018-01-01
We report an implementation of non-adiabatic coupling (NAC) forces within the equation-of-motion coupled-cluster with single and double excitations (EOM-CCSD) framework via the summed-state approach. Using illustrative examples, we compare NAC forces computed with EOM-CCSD and multi-reference (MR) wave functions (for selected cases, we also consider configuration interaction singles). In addition to the magnitude of the NAC vectors, we analyze their direction, which is important for the calculations of the rate of non-adiabatic transitions. Our benchmark set comprises three doublet radical-cations (hexatriene, cyclohexadiene, and uracil), neutral uracil, and sodium-doped ammonia clusters. When the characters of the states agree among different methods, we observe good agreement between the respective NAC vectors, both in the Franck-Condon region and away. In the cases of large discrepancies between the methods, the disagreement can be attributed to the difference in the states' character, which, in some cases, is very sensitive to electron correlation, both within single-reference and multi-reference frameworks. The numeric results confirm that the accuracy of NAC vectors depends critically on the quality of the underlying wave functions. Within their domain of applicability, EOM-CC methods provide a viable alternative to MR approaches.
[Macro-economic calculation of spending versus micro-economic follow-up of costs of breast cancer].
Borella, L; Paraponaris, A
2002-12-01
In the healthcare field, the ability to make economic forecasts requires knowledge of the costs of caring for major diseases. In the case of a semi-chronic condition like cancer, this cost covers all the episodes of care associated with a patient. An evaluation of a macro-economic method of calculating costs for treating non-metastatic cancer, covering all hospital episodes, is proposed. This method is based entirely on the use of annual hospital activity databases, linked to data concerning the incidence of cancer. It allows us to obtain the global cost of care for a neoplasm of a particular site, without the need to reconstruct the whole care pathway of the patients. The model was assessed by comparing it's own results, in the particular case of breast cancer to those issuing from a micro-economic follow-up of 115 patients. Data for macro-economic calculation are extracted from the national French hospital database for the year 1999 and from cancer incidence data. The prospective study was done in 1995, in a comprehensive cancer centre. Macro-economic calculation leads to a cost of 14,555 Euro, for primary breast cancer. Prospective follow-up showed a cost of 14,350 Euro (data corrected, 1999 value). With a difference of 1%, there was a clear cohesion of the two results, while a higher level of divergence was noticed (from 1 to 15%) in the comparison between therapeutic techniques. Accuracy and reliability of results were evaluated. This method may be extended to all types of neoplasms. This method cannot be used instead of follow-up studies, for cost-efficacy or cost-severity analysis, but may be interesting beyond economic forecasts, in the field of payment per pathology.
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
Nair, Kalyani P.; Harkness, Elaine F.; Gadde, Soujanye; Lim, Yit Y.; Maxwell, Anthony J.; Moschidis, Emmanouil; Foden, Philip; Cuzick, Jack; Brentnall, Adam; Evans, D. Gareth; Howell, Anthony; Astley, Susan M.
2017-03-01
Personalised breast screening requires assessment of individual risk of breast cancer, of which one contributory factor is weight. Self-reported weight has been used for this purpose, but may be unreliable. We explore the use of volume of fat in the breast, measured from digital mammograms. Volumetric breast density measurements were used to determine the volume of fat in the breasts of 40,431 women taking part in the Predicting Risk Of Cancer At Screening (PROCAS) study. Tyrer-Cuzick risk using self-reported weight was calculated for each woman. Weight was also estimated from the relationship between self-reported weight and breast fat volume in the cohort, and used to re-calculate Tyrer-Cuzick risk. Women were assigned to risk categories according to 10 year risk (below average =8%) and the original and re-calculated Tyrer-Cuzick risks were compared. Of the 716 women diagnosed with breast cancer during the study, 15 (2.1%) moved into a lower risk category, and 37 (5.2%) moved into a higher category when using weight estimated from breast fat volume. Of the 39,715 women without a cancer diagnosis, 1009 (2.5%) moved into a lower risk category, and 1721 (4.3%) into a higher risk category. The majority of changes were between below average and average risk categories (38.5% of those with a cancer diagnosis, and 34.6% of those without). No individual moved more than one risk group. Automated breast fat measures may provide a suitable alternative to self-reported weight for risk assessment in personalized screening.
Describes equations for bioconcentration, bioaccumulation, biomagnification and biota-sediment accumulation factors used in KABAM V1.0. KABAM is a simulation model used to predict pesticide concentrations in aquatic regions for use in exposure assessments.
National Research Council Canada - National Science Library
Kocher, David C; Apostoaei, Julian A
2007-01-01
This report presents tabulations of equivalent doses of ionizing radiation, referred to as screening doses, that correspond to an estimated probablity of causation of specific cancers of approximately 50% at the upper 99% credibility limit...
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.
Jiang, Yang; Gong, Yuanzheng; Wang, Thomas D.; Seibel, Eric J.
2017-02-01
Multimodal endoscopy, with fluorescence-labeled probes binding to overexpressed molecular targets, is a promising technology to visualize early-stage cancer. T/B ratio is the quantitative analysis used to correlate fluorescence regions to cancer. Currently, T/B ratio calculation is post-processing and does not provide real-time feedback to the endoscopist. To achieve real-time computer assisted diagnosis (CAD), we establish image processing protocols for calculating T/B ratio and locating high-risk fluorescence regions for guiding biopsy and therapy in Barrett's esophagus (BE) patients. Methods: Chan-Vese algorithm, an active contour model, is used to segment high-risk regions in fluorescence videos. A semi-implicit gradient descent method was applied to minimize the energy function of this algorithm and evolve the segmentation. The surrounding background was then identified using morphology operation. The average T/B ratio was computed and regions of interest were highlighted based on user-selected thresholding. Evaluation was conducted on 50 fluorescence videos acquired from clinical video recordings using a custom multimodal endoscope. Results: With a processing speed of 2 fps on a laptop computer, we obtained accurate segmentation of high-risk regions examined by experts. For each case, the clinical user could optimize target boundary by changing the penalty on area inside the contour. Conclusion: Automatic and real-time procedure of calculating T/B ratio and identifying high-risk regions of early esophageal cancer was developed. Future work will increase processing speed to <5 fps, refine the clinical interface, and apply to additional GI cancers and fluorescence peptides.
International Nuclear Information System (INIS)
Choi, Youngmin; Kim, Jeung-Kee; Lee, Hyung-Sik; Hur, Won-Joo; Hong, Young-Seoub; Park, Sungkwang; Ahn, Kijung; Cho, Heunglae
2006-01-01
Background and purpose: To evaluate the effect of an intravenous contrast agent (CA) on dose calculations and its clinical significance in intensity modulated radiation therapy (IMRT) plans for head and neck cancer. Materials and methods: Fifteen patients with head and neck cancer and involved neck nodes were enrolled. Each patient took two sets of computerized tomography (CT) in the same position before and after intravenous CA injections. Target volumes and organs at risk (OAR) were contoured on the enhanced CT, and then an IMRT plan of nine equiangular beams with a 6 MV X-ray was created. After the fusion of non-enhanced and enhanced CTs, the contours and the IMRT plan created from the enhanced CT were copied and placed to the non-enhanced CT. Doses were calculated again from the non-enhanced CT by the same IMRT plan. The radiation doses calculated from the two sets of CTs were compared with regard to planning target volumes (PTV) and the three OARs, both parotid glands and the spinal cord, by Wilcoxon's signed rank test. Results: The doses (maximum, mean, and the dose of 95% of PTV received (D 95% )) of PTV70 and PTV59.4 calculated from the enhanced CTs were lower than those from the non-enhanced CTs (p < 0.05), but the dose differences were less than 1% compared to the doses calculated from the enhanced CTs. The doses of PTV50.4, parotid glands, and spinal cord were not significantly different between the non-enhanced and enhanced CTs. Conclusions: The difference between the doses calculated from the CTs with and without CA enhancement was tolerably small, therefore using intravenous CA could be recommended for the planning CT of head and neck IMRT
Monte Carlo calculations on efficiency of boron neutron capture therapy for brain cancer
International Nuclear Information System (INIS)
Awadalla, Galaleldin Mohamed Suliman
2015-11-01
The search for ways to treat cancer has led to many different treatments, including surgery, chemotherapy, and radiation therapy. Among these treatments, boron neutron capture therapy (BNCT) has shown promising results. BNCT is a radiotherapy treatment modality that has been proposed to treat brain cancer. In this technique, cancerous cells are being injected with 1 0B and irradiated by thermal neutrons to increase the probability of 1 0B (n, a)7 L i reaction to occur. This reaction can potentially deliver a high radiation dose sufficient to kill cancer cells by concentrating boron in them. The short rang of 1 0B (n, a) 7 L i reaction limits the damage to only cancerous cells without affecting healthy tissues. The effectiveness and safety of radiotherapy are dependent on the radiation dose delivered to the tumor and healthy tissues. In this thesis, after reviewing the basics and working principles of boron neutron capture therapy (BNCT), monte Carlo simulations were carried out to model a thermal neutron source suitable for BNCT and to examine the performance of proposed model when used to irradiate a sample of boron containing both 1 0B and 1 1B isotopes. MCNP5 code was used to examine the modeled neutron source through different shielding materials. The results were presented, analyzed and discussed at the end of the work. (author)
Energy Technology Data Exchange (ETDEWEB)
Bodmer, A. R.
1978-01-01
The study of high energy heavy ion reactions includes the three principle a priori approaches used for central collisions, namely, hydrodynamics, cascade--Boltzman equation, and the classical equations of motion. While no clearly justified central or near central collisions are found, the classical equations of motion are used to illustrate some general features of these reactions. It is expected that the hot nuclear matter produced in such collisions is a dense, viscous, and thermally conductive fluid with important nonequilibrium and nonclassical features, rapidity, distribution, noncentral collisions, potential dependent effects for a given two-body scattering, and c.m. cross sections for a central collision with given parameters are among the properties considered. 12 references. (JFP)
Zhang, Hongming; Wei, Jicheng; Yang, Qinke; Baartman, Jantiene E.M.; Gai, Lingtong; Yang, Xiaomei; Li, Shu Qin; Yu, Jiantao; Ritsema, Coen J.; Geissen, Violette
2017-01-01
The Universal Soil Loss Equation (USLE) and its revised version (RUSLE) are often used to estimate soil erosion at regional landscape scales. USLE/RUSLE contain parameters for slope length factor (L) and slope steepness factor (S), usually combined as LS. However a major limitation is the difficulty
Nicewander, W. Alan
2018-01-01
Spearman's correction for attenuation (measurement error) corrects a correlation coefficient for measurement errors in either-or-both of two variables, and follows from the assumptions of classical test theory. Spearman's equation removes all measurement error from a correlation coefficient which translates into "increasing the reliability of…
Borys, Przemysław
2012-06-01
Rat prostate cancer cells have been previously investigated using two cell lines: a highly metastatic one (Mat-Ly-Lu) and a nonmetastatic one (AT-2). It turns out that the highly metastatic Mat-Ly-Lu cells exhibit a phenomenon of cathodal galvanotaxis in an electric field which can be blocked by interrupting the voltage-gated sodium channel (VGSC) activity. The VGSC activity is postulated to be characteristic for metastatic cells and seems to be a reasonable driving force for motile behavior. However, the classical theory of cellular motion depends on calcium ions rather than sodium ions. The current research provides a theoretical connection between cellular sodium inflow and cathodal galvanotaxis of Mat-Ly-Lu cells. Electrical repulsion of intracellular calcium ions by entering sodium ions is proposed after depolarization starting from the cathodal side. The disturbance in the calcium distribution may then drive actin polymerization and myosin contraction. The presented modeling is done within a continuous one-dimensional Poisson-Nernst-Planck equation framework.
Energy Technology Data Exchange (ETDEWEB)
Kim, Jung Min; Kim, Dae Sup; Hong, Dong Ki; Back, Geum Mun; Kwak, Jung Won [Dept. of Radiation Oncology, , Seoul (Korea, Republic of)
2012-03-15
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)
Kim, Jung Min; Kim, Dae Sup; Hong, Dong Ki; Back, Geum Mun; Kwak, Jung Won
2012-01-01
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.
Overdiagnosis in breast cancer screening: The impact of study design and calculations.
Lynge, Elsebeth; Beau, Anna-Belle; Christiansen, Peer; von Euler-Chelpin, My; Kroman, Niels; Njor, Sisse; Vejborg, Ilse
2017-07-01
Overdiagnosis in breast cancer screening is an important issue. A recent study from Denmark concluded that one in three breast cancers diagnosed in screening areas in women aged 50-69 years were overdiagnosed. The purpose of this short communication was to disentangle the study's methodology in order to evaluate the soundness of this conclusion. We found that both the use of absolute differences as opposed to ratios; the sole focus on non-advanced tumours and the crude allocation of tumours and person-years by screening history for women aged 70-84 years, all contributed to the very high estimate of overdiagnosis. Screening affects cohorts of screened women. Danish registers allow very accurate mapping of the fate of every woman. We should be past the phase where studies of overdiagnosis are based on the fixed age groups from routine statistics. Copyright © 2017 The Author(s). Published by Elsevier Ltd.. All rights reserved.
International Nuclear Information System (INIS)
Heydari Azar, A.; Shahshahani, M.; Roshanzamir, M.; Sabouhi, R.
2008-01-01
In this investigation the amount of absorbed doses by the different pathways of Cloud shine, Ground shine, deposition of radioactive materials on skin and cloths, ingestion, inhalation and the consequences of radioactive material releases due to Beyond Design Basis Accidents such as fire, sintering furnace explosion, criticality and earthquake in Esfahan Fuel Production factory by the residents are evaluated. The calculations related to atomic cloud distribution, estimation of delivered dose and decay chains are performed by PCCOSYMA dose. These computations are based on radioactive source terms, distribution height of radioactive materials. actions for reducing the absorbed dose, human body physiological characteristics, metrological condition and population distribution. Finally, the number of peoples who are stricken to mortality and morbidity cancers and risk values are calculated for 1 year and 50 years
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)
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)
Doemer, Anthony; Chetty, Indrin J; Glide-Hurst, Carri; Nurushev, Teamour; Hearshen, David; Pantelic, Milan; Traughber, Melanie; Kim, Joshua; Levin, Kenneth; Elshaikh, Mohamed A; Walker, Eleanor; Movsas, Benjamin
2015-01-01
This study describes initial testing and evaluation of a vertical-field open Magnetic Resonance Imaging (MRI) scanner for the purpose of simulation in radiation therapy for prostate cancer. We have evaluated the clinical workflow of using open MRI as a sole modality for simulation and planning. Relevant results related to MRI alignment (vs. CT) reference dataset with Cone-Beam CT (CBCT) for daily localization are presented. Ten patients participated in an IRB approved study utilizing MRI along with CT simulation with the intent of evaluating the MRI-simulation process. Differences in prostate gland volume, seminal vesicles, and penile bulb were assessed with MRI and compared to CT. To evaluate dose calculation accuracy, bulk-density-assignments were mapped onto respective MRI datasets and treated IMRT plans were re-calculated. For image localization purposes, 400 CBCTs were re-evaluated with MRI as the reference dataset and daily shifts compared against CBCT-to-CT registration. Planning margins based on MRI/CBCT shifts were computed using the van Herk formalism. Significant organ contour differences were noted between MRI and CT. Prostate volumes were on average 39.7% (p = 0.002) larger on CT than MRI. No significant difference was found in seminal vesicle volumes (p = 0.454). Penile bulb volumes were 61.1% higher on CT, without statistical significance (p = 0.074). MRI-based dose calculations with assigned bulk densities produced agreement within 1% with heterogeneity corrected CT calculations. The differences in shift positions for the cohort between CBCT-to-CT registration and CBCT-to-MRI registration are −0.15 ± 0.25 cm (anterior-posterior), 0.05 ± 0.19 cm (superior-inferior), and −0.01 ± 0.14 cm (left-right). This study confirms the potential of using an open-field MRI scanner as primary imaging modality for prostate cancer treatment planning simulation, dose calculations and daily image localization
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)
Danel, J.-F.; Kazandjian, L.
2018-06-01
It is shown that the equation of state (EOS) and the radial distribution functions obtained by density-functional theory molecular dynamics (DFT-MD) obey a simple scaling law. At given temperature, the thermodynamic properties and the radial distribution functions given by a DFT-MD simulation remain unchanged if the mole fractions of nuclei of given charge and the average volume per atom remain unchanged. A practical interest of this scaling law is to obtain an EOS table for a fluid from that already obtained for another fluid if it has the right characteristics. Another practical interest of this result is that an asymmetric mixture made up of light and heavy atoms requiring very different time steps can be replaced by a mixture of atoms of equal mass, which facilitates the exploration of the configuration space in a DFT-MD simulation. The scaling law is illustrated by numerical results.
Directory of Open Access Journals (Sweden)
Hyejoo Kang
2017-07-01
Full Text Available Purpose: The goal is to develop a stand-alone application, which automatically and consistently computes the coordinates of the dose calculation point recommended by the American Brachytherapy Society (i.e., point A based solely on the implanted applicator geometry for cervical cancer brachytherapy. Material and methods: The application calculates point A coordinates from the source dwell geometries in the computed tomography (CT scans, and outputs the 3D coordinates in the left and right directions. The algorithm was tested on 34 CT scans of 7 patients treated with high-dose-rate (HDR brachytherapy using tandem and ovoid applicators. A single experienced user retrospectively and manually inserted point A into each CT scan, whose coordinates were used as the “gold standard” for all comparisons. The gold standard was subtracted from the automatically calculated points, a second manual placement by the same experienced user, and the clinically used point coordinates inserted by multiple planners. Coordinate differences and corresponding variances were compared using nonparametric tests. Results: Automatically calculated, manually placed, and clinically used points agree with the gold standard to < 1 mm, 1 mm, 2 mm, respectively. When compared to the gold standard, the average and standard deviation of the 3D coordinate differences were 0.35 ± 0.14 mm from automatically calculated points, 0.38 ± 0.21 mm from the second manual placement, and 0.71 ± 0.44 mm from the clinically used point coordinates. Both the mean and standard deviations of the 3D coordinate differences were statistically significantly different from the gold standard, when point A was placed by multiple users (p < 0.05 but not when placed repeatedly by a single user or when calculated automatically. There were no statistical differences in doses, which agree to within 1-2% on average for all three groups. Conclusions: The study demonstrates that the automated algorithm
Choi, Garam; Lee, Won Bo
Metal alloys, especially Al-based, are commonly-used materials for various industrial applications. In this paper, the Al-Cu alloys with varying the Al-Cu ratio were investigated based on the first-principle calculation using density functional theory. And the electronic transport properties of the Al-Cu alloys were carried out using Boltzmann transport theory. From the results, the transport properties decrease with Cu-containing ratio at the temperature from moderate to high, but with non-linearity. It is inferred by various scattering effects from the calculation results with relaxation time approximation. For the Al-Cu alloy system, where it is hard to find the reliable experimental data for various alloys, it supports understanding and expectation for the thermal electrical properties from the theoretical prediction. Theoretical and computational soft matters laboratory.
International Nuclear Information System (INIS)
Li, D.
1980-01-01
Reviewed is the effect of heat flux of different system parameters on critical density in order to give an initial view on the value of several parameters. A thorough analysis of different equations is carried out to calculate burnout is steam-water flows in uniformly heated tubes, annular, and rectangular channels and rod bundles. Effect of heat flux density distribution and flux twisting on burnout and storage determination according to burnout are commended [ru
International Nuclear Information System (INIS)
Sumner, H.M.
1969-03-01
The KDF9/EGDON program ZIP MK 2 is the third of a series of programs for off-line digital computer analysis of dynamic systems: it has been designed specifically to cater for the needs of the design or control engineer in having an input scheme which is minimally computer-oriented. It uses numerical algorithms which are as near fool-proof as the author could discover or devise, and has comprehensive diagnostic sections to help the user in the event of faulty data or machine execution. ZIP MK 2 accepts mathematical models comprising first order linear differential and linear algebraic equations, and from these computes and factorises the transfer functions between specified pairs of output and input variables; if desired, the frequency response may be computed from the computed transfer function. The model input scheme is fully compatible with the frequency response programs FRP MK 1 and MK 2, except that, for ZIP MK 2, transport, or time-delays must be converted by the user to Pade or Bode approximations prior to input. ZIP provides the pole-zero plot, (or complex plane analysis), while FRP provides the frequency response and FIFI the time domain analyses. The pole-zero method of analysis has been little used in the past for complex models, especially where transport delays occur, and one of its primary purposes is as a research tool to investigate the usefulness of this method, for process plant, whether nuclear, chemical or other continuous processes. (author)
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.
Jiang, Runqing
uniform dose per fraction (EUDf) and NTCP. The dose distribution including geometric uncertainties was determined from integration of the convolution of the static dose gradient with the PDF. Integration of the convolution of the static dose and derivative of the PDF can also be used to determine the dose including geometric uncertainties although this method was not investigated in detail. Local maximum dose gradient (LMDG) was determined via optimization of dose objective function by manually adjusting DVH control points or selecting beam numbers and directions during IMRT treatment planning. Minimum SD (SDmin) is used when geometric uncertainty is corrected with verification imaging. Maximum SD (SDmax) is used when the geometric uncertainty is known to be large and difficult to manage. SDmax was 4.38 mm in anterior-posterior (AP) direction, 2.70 mm in left-right (LR) direction and 4.35 mm in superior-inferior (SI) direction; SDmin was 1.1 mm in all three directions if less than 2 mm threshold was used for uncorrected fractions in every direction. EUDf is a useful QA parameter for interpreting the biological impact of geometric uncertainties on the static dose distribution. The EUD f has been used as the basis for the time-course NTCP evaluation in the thesis. Relative NTCP values are useful for comparative QA checking by normalizing known complications (e.g. reported in the RTOG studies) to specific DVH control points. For prostate cancer patients, rectal complications were evaluated from specific RTOG clinical trials and detailed evaluation of the treatment techniques (e.g. dose prescription, DVH, number of beams, bean angles). Treatment plans that did not meet DVH constraints represented additional complication risk. Geometric uncertainties improved or worsened rectal NTCP depending on individual internal organ motion within patient.
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.
Maspero, Matteo; van den Berg, Cornelis A. T.; Landry, Guillaume; Belka, Claus; Parodi, Katia; Seevinck, Peter R.; Raaymakers, Bas W.; Kurz, Christopher
2017-12-01
A magnetic resonance (MR)-only radiotherapy workflow can reduce cost, radiation exposure and uncertainties introduced by CT-MRI registration. A crucial prerequisite is generating the so called pseudo-CT (pCT) images for accurate dose calculation and planning. Many pCT generation methods have been proposed in the scope of photon radiotherapy. This work aims at verifying for the first time whether a commercially available photon-oriented pCT generation method can be employed for accurate intensity-modulated proton therapy (IMPT) dose calculation. A retrospective study was conducted on ten prostate cancer patients. For pCT generation from MR images, a commercial solution for creating bulk-assigned pCTs, called MR for Attenuation Correction (MRCAT), was employed. The assigned pseudo-Hounsfield Unit (HU) values were adapted to yield an increased agreement to the reference CT in terms of proton range. Internal air cavities were copied from the CT to minimise inter-scan differences. CT- and MRCAT-based dose calculations for opposing beam IMPT plans were compared by gamma analysis and evaluation of clinically relevant target and organ at risk dose volume histogram (DVH) parameters. The proton range in beam’s eye view (BEV) was compared using single field uniform dose (SFUD) plans. On average, a (2%, 2 mm) gamma pass rate of 98.4% was obtained using a 10% dose threshold after adaptation of the pseudo-HU values. Mean differences between CT- and MRCAT-based dose in the DVH parameters were below 1 Gy (radiotherapy, is feasible following adaptation of the assigned pseudo-HU values.
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.
Sammour, T; Cohen, L; Karunatillake, A I; Lewis, M; Lawrence, M J; Hunter, A; Moore, J W; Thomas, M L
2017-11-01
Recently published data support the use of a web-based risk calculator ( www.anastomoticleak.com ) for the prediction of anastomotic leak after colectomy. The aim of this study was to externally validate this calculator on a larger dataset. Consecutive adult patients undergoing elective or emergency colectomy for colon cancer at a single institution over a 9-year period were identified using the Binational Colorectal Cancer Audit database. Patients with a rectosigmoid cancer, an R2 resection, or a diverting ostomy were excluded. The primary outcome was anastomotic leak within 90 days as defined by previously published criteria. Area under receiver operating characteristic curve (AUROC) was derived and compared with that of the American College of Surgeons National Surgical Quality Improvement Program ® (ACS NSQIP) calculator and the colon leakage score (CLS) calculator for left colectomy. Commercially available artificial intelligence-based analytics software was used to further interrogate the prediction algorithm. A total of 626 patients were identified. Four hundred and fifty-six patients met the inclusion criteria, and 402 had complete data available for all the calculator variables (126 had a left colectomy). Laparoscopic surgery was performed in 39.6% and emergency surgery in 14.7%. The anastomotic leak rate was 7.2%, with 31.0% requiring reoperation. The anastomoticleak.com calculator was significantly predictive of leak and performed better than the ACS NSQIP calculator (AUROC 0.73 vs 0.58) and the CLS calculator (AUROC 0.96 vs 0.80) for left colectomy. Artificial intelligence-predictive analysis supported these findings and identified an improved prediction model. The anastomotic leak risk calculator is significantly predictive of anastomotic leak after colon cancer resection. Wider investigation of artificial intelligence-based analytics for risk prediction is warranted.
Souza, Micheline Tereza Pires; Singer, Pierre; Ozorio, Gislaine Aparecida; Rosa, Vitor Modesto; Alves, Maria Manuela Ferreira; Mendoza López, Rossana Verónica; Waitzberg, Dan L
2018-02-05
Patients with head and neck cancer have changes in body composition and resting energy expenditure (REE) related to significant inflammatory processes. We investigated REE and body composition in a population of patients with head and neck cancer, comparing the measured REE with predicted energy expenditure and deriving an equation of anthropometric values and body composition. This retrospective, observational, descriptive study of a single center included patients with head and neck cancer. We evaluated nutritional status by body mass index (BMI) and Patient-Generated Subjective Global Assessment (PG-SGA), body composition by electric bioimpedance, and REE by indirect calorimetry (IC). We included 140 patients, most of whom were men (80.7%), 60 y or older (58.6%), and had advanced disease (77.9%). Most were malnourished by BMI standards (77.9%) and severely malnourished according to the PG-SGA (49.3%), with a fat-free mass below the ideal values (82.9%) associated with sarcopenia (92.1%). Hypermetabolism was 57%. When comparing REE with the Harris-Benedict formula, we found the agreement limits from -546 613 to 240 708, the mean difference was -152 953 (95% confidence interval [CI], -185 844 to -120 062) and Pitman's variance test was r = -0.294 (P = 0.001). When we included the activity factor and the thermogenesis factor in REE and compared with Harris-Benedict, we found the agreement limits from -764.423 to 337.087, a mean difference of -213.668 (95% CI -259.684 to -167.652), and the Pitman's variance text at r = -0.292 (P = 0.001). Predictive equations, generally recommended by guidelines, are imprecise when compared with IC measures. Therefore, we suggest a new predictive equation. Copyright © 2018 Elsevier Inc. All rights reserved.
Oryu, S; Yamashita, H; Nakazawa, M; Kamada, H
2000-01-01
The hypernucleus subLAMBDA sup 9 Be is investigated in an alpha-alpha-LAMBDA three-body model using the Faddeev formalism. We use an alpha-alpha interaction in which the Pauli-forbidden states are correctly taken into account and we employ some phenomenological potentials between the alpha and LAMBDA particles. We obtained two bound states for J suppi = 1/2 sup + and 3/2 sup + , and three resonance states of (3/2) sub 1 sup - , (3/2) sub 2 sup - , (3/2) sub 3 sup -. We studied the properties of these states by calculating the components and the expectation values of the potential for each partial wave. It is found that a few channels dominate in the 1/2 sup + and 3/2 sup + states, so that the alpha-clusters or the sup 8 Be core are still alive in the nucleus. In a case were the two alpha particles are fixed on an axis the contour plots of the distribution of the LAMBDA particle are shown. With the assistence of these plots one can visually understand that some of them are shell-model-like states while others ...
International Nuclear Information System (INIS)
Santos, William S.; Neves, Lucio P.; Perini, Ana P.; Caldas, Linda V.E.; Maia, Ana F.
2014-01-01
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 2 . The average values of CCs to eight projections (in 10 -4 / Gy.cm 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
Adam, Ahmed; Hellig, Julian C; Perera, Marlon; Bolton, Damien; Lawrentschuk, Nathan
2018-04-01
The use of mobile phone applications (Apps) has modernised the conventional practice of medicine. The diagnostic ability of the current Apps in prostate specific antigen monitoring, and its diagnostic ability within prostate cancer (PCa) risk calculators have not yet been appraised. We aimed to review, rate and assess the everyday functionality, and utility of all the currently available PCa risk calculator Apps. A systematic search on iTunes, Google Play Store, Blackberry World and Windows Apps Store, was performed on 23/11/2017, using the search term 'prostate cancer risk calculator'. After applying the exclusion criteria, each App was individually assessed and rated using pre-set criteria and grading was performed using the validated uMARS scale. In total, 83 Apps were retrieved. After applying our exclusion criteria, only 9 Apps were relevant, with 2 duplicated, and the remaining 7 were suitable for critical review. Data sizes ranged from 414 kb to 10.1 Mb. The cost of the Apps ranged from South African rand (ZAR) 0.00 to ZAR 29.99. The overall mean category uMARS scores ranged from 2.8/5 to 4.5/5. Apps such as Rotterdam Prostate Cancer Risk Calculator, Coral-Prostate Cancer Nomogram Calculator and CPC Risk Calculator, performed the best. The current PCa risk calculator mobile Apps available may be beneficial in counselling the concerned at risk patient. These Apps have potential to assist both the patient and the urologist alike. The PCa risk calculator App 'predictability' may be further enhanced by the incorporation of newly validated risk factors and predictors for PCa.
International Nuclear Information System (INIS)
Nijdam, Wideke; Levendag, Peter; Noever, Inge; Groot, Carin Uyl-de; Agthoven, Michel van
2005-01-01
Background and purpose: This paper presents a model for cost calculation using the different treatment modalities for oropharyngeal (OPh) cancers used in our hospital. We compared full hospital costs, the associated costs of localregional relapses (LRR) and/or treatment related grade III/IV complications. Materials and methods: Patients with OPh cancer are treated in the Erasmus MC preferably by an organ function preservation protocol. That is, by external beam radiation therapy (EBRT) followed by a brachytherapy (BT) boost, and neck dissection in case of N+ disease (BT-group: 157 patients). If BT is not feasible, resection with postoperative EBRT (S-group [S=Surgery]: 110 patients) or EBRT-alone (EBRT-group: 77 patients) is being pursued. Actuarial localregional control (LRC), disease free survival (DFS) and overall survival (OS) at 5-years were calculated according to the Kaplan-Meier method. The mean costs per treatment group for diagnosis, primary Tx per se, follow-up, (salvage of) locoregional relapse (LRR), distant metastasis (DM), and/or grade III/IV complications needing clinical admission, were computed. Results: For the BT-, S-, or EBRT treatment groups, LRC rates at 5-years were 85, 82, and 55%, for the DFS, 61, 48, and 43%, and for the OS 65, 52, and 40%, respectively. The mean costs of primary Tx in case of the BT-group is EURO 13,466; for the S-group EURO 24,219, and EURO 12,502 for the EBRT-group. The mean costs of S (the main salvage modality) for a LRR of the BT group or EBRT-group, were EURO 17,861 and EURO 15,887, respectively. The mean costs of clinical management of Grade III/IV complications were EURO 7184 (BT-group), EURO 16,675 (S-group) and EURO 6437 (EBRT-group). Conclusion: The clinical outcome illustrates excellent LRC rates at 5-years for BT (85%), as well as for S (82%). The relatively low 55% LRC rate at 5-years for EBRT probably reflects a negative selection of patients. It is of interest that the total mean costs of patients alive
Ramezanpour, H R; Setayeshi, S; Akbari, M E
2011-01-01
Determining the optimal and effective scheme for administrating the chemotherapy agents in breast cancer is the main goal of this scientific research. The most important issue here is the amount of drug or radiation administrated in chemotherapy and radiotherapy for increasing patient's survival. This is because in these cases, the therapy not only kills the tumor cells, but also kills some of the healthy tissues and causes serious damages. In this paper we investigate optimal drug scheduling effect for breast cancer model which consist of nonlinear ordinary differential time-delay equations. In this paper, a mathematical model of breast cancer tumors is discussed and then optimal control theory is applied to find out the optimal drug adjustment as an input control of system. Finally we use Sensitivity Approach (SA) to solve the optimal control problem. The goal of this paper is to determine optimal and effective scheme for administering the chemotherapy agent, so that the tumor is eradicated, while the immune systems remains above a suitable level. Simulation results confirm the effectiveness of our proposed procedure. In this paper a new scheme is proposed to design a therapy protocol for chemotherapy in Breast Cancer. In contrast to traditional pulse drug delivery, a continuous process is offered and optimized, according to the optimal control theory for time-delay systems.
Syahidatul Ayuni Mazlan, Mazma; Rosli, Norhayati; Jauhari Arief Ichwan, Solachuddin; Suhaity Azmi, Nina
2017-09-01
A stochastic model is introduced to describe the growth of cancer affected by anti-cancer therapeutics of Chondroitin Sulfate (CS). The parameters values of the stochastic model are estimated via maximum likelihood function. The numerical method of Euler-Maruyama will be employed to solve the model numerically. The efficiency of the stochastic model is measured by comparing the simulated result with the experimental data.
Kim, Peter S; Lee, Peter P
2012-01-01
A next generation approach to cancer envisions developing preventative vaccinations to stimulate a person's immune cells, particularly cytotoxic T lymphocytes (CTLs), to eliminate incipient tumors before clinical detection. The purpose of our study is to quantitatively assess whether such an approach would be feasible, and if so, how many anti-cancer CTLs would have to be primed against tumor antigen to provide significant protection. To understand the relevant dynamics, we develop a two-compartment model of tumor-immune interactions at the tumor site and the draining lymph node. We model interactions at the tumor site using an agent-based model (ABM) and dynamics in the lymph node using a system of delay differential equations (DDEs). We combine the models into a hybrid ABM-DDE system and investigate dynamics over a wide range of parameters, including cell proliferation rates, tumor antigenicity, CTL recruitment times, and initial memory CTL populations. Our results indicate that an anti-cancer memory CTL pool of 3% or less can successfully eradicate a tumor population over a wide range of model parameters, implying that a vaccination approach is feasible. In addition, sensitivity analysis of our model reveals conditions that will result in rapid tumor destruction, oscillation, and polynomial rather than exponential decline in the tumor population due to tumor geometry.
International Nuclear Information System (INIS)
Leenhouts, H.P.; Brugmans, J.P.
2001-01-01
Although the main cause of lung cancer is smoking cigarettes, part of the cases are subscribed to radon exposure, in particular α-radiation from daughter products. However, the relation between lung cancer and radon exposure is rather insecure. Based on international reports (e.g. BEIR VI) and extrapolation of lung cancer incidence in uranium mine workers to the population of the USA and subsequently to the Netherlands, the number of lung cancer cases in the Netherlands is estimated to be circa 800 per year, varying between 200-2000. Results of the analysis are summarized in this article. 10 refs
equateIRT: An R Package for IRT Test Equating
Directory of Open Access Journals (Sweden)
Michela Battauz
2015-12-01
Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.
Shielding calculations using FLUKA
International Nuclear Information System (INIS)
Yamaguchi, Chiri; Tesch, K.; Dinter, H.
1988-06-01
The dose equivalent on the surface of concrete shielding has been calculated using the Monte Carlo code FLUKA86 for incident proton energies from 10 to 800 GeV. The results have been compared with some simple equations. The value of the angular dependent parameter in Moyer's equation has been calculated from the locations where the values of the maximum dose equivalent occur. (author)
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
Park, Yu-Ri; Park, Eun-Young; Kim, Jung-Hee
2017-11-09
According to the self-control model, self-control works as a protective factor and a psychological resource. Although an understanding of the effect(s) of peripheral neuropathy on quality of life is important to healthcare professionals, previous studies do not facilitate broad comprehension in this regard. The purpose of this cross-sectional study was to test the multidimensional assumptions of quality of life of patients with cancer, with focus on their self-control. A structural equation model was tested on patients with cancer at the oncology clinic of a university hospital where patients received chemotherapy. A model was tested using structural equation modeling, which allows the researcher to find the empirical evidence by testing a measurement model and a structural model. The model comprised three variables, self-control, health related quality of life, and chemotherapy-induced peripheral neuropathy. Among the variables, self-control was the endogenous and mediating variable. The proposed models showed good fit indices. Self-control partially mediated chemotherapy-induced peripheral neuropathy and quality of life. It was found that the physical symptoms of peripheral neuropathy influenced health-related quality of life both indirectly and directly. Self-control plays a significant role in the protection and promotion of physical and mental health in various stressful situations, and thus, as a psychological resource, it plays a significant role in quality of life. Our results can be used to develop a quality of life model for patients receiving chemotherapy and as a theoretical foundation for the development of appropriate nursing interventions.
Faller, Hermann; Strahl, André; Richard, Matthias; Niehues, Christiane; Meng, Karin
2017-11-01
Previous research has demonstrated associations between satisfaction with information and reduced emotional distress in cancer patients. However, as most studies were cross-sectional, the direction of this relationship remained unclear. We therefore aimed to test whether information satisfaction predicted subsequent depression and anxiety levels, and, reciprocally, depression and anxiety levels predicted subsequent information satisfaction, thus clarifying the direction of impact. We performed a secondary analysis of a prospective cohort study with 436 female breast cancer patients (mean age 51 years). We measured information satisfaction with 2 self-developed items, symptoms of depression with the 2-item Patient Heath Questionnaire and symptoms of anxiety with the 2-item Generalized Anxiety Disorder Scale. We created 2 structural equation models, 1 for depression and 1 for anxiety, that examined the prediction of 1-year depression (or anxiety) levels by baseline information satisfaction and, in the same model, 1-year information satisfaction by baseline depression (or anxiety) levels (cross-lagged panel analysis). Baseline information satisfaction predicted 1-year levels of both depression (beta = -0.17, P satisfaction, adjusting for its baseline score. Our results suggest a bidirectional relationship between information satisfaction and symptoms of depression and anxiety. Thus, provision of information may reduce subsequent depression and anxiety, while reducing depression and anxiety levels may increase satisfaction with received information. Combining the provision of information with emotional support may be particularly beneficial. Copyright © 2016 John Wiley & Sons, Ltd.
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. Copyright © 2016 Elsevier Ltd. All rights reserved.
Kim, Eric H; Weaver, John K; Shetty, Anup S; Vetter, Joel M; Andriole, Gerald L; Strope, Seth A
2017-04-01
To determine the added value of prostate magnetic resonance imaging (MRI) to the Prostate Cancer Prevention Trial risk calculator. Between January 2012 and December 2015, 339 patients underwent prostate MRI prior to biopsy at our institution. MRI was considered positive if there was at least 1 Prostate Imaging Reporting and Data System 4 or 5 MRI suspicious region. Logistic regression was used to develop 2 models: biopsy outcome as a function of the (1) Prostate Cancer Prevention Trial risk calculator alone and (2) combined with MRI findings. When including all patients, the Prostate Cancer Prevention Trial with and without MRI models performed similarly (area under the curve [AUC] = 0.74 and 0.78, P = .06). When restricting the cohort to patients with estimated risk of high-grade (Gleason ≥7) prostate cancer ≤10%, the model with MRI outperformed the Prostate Cancer Prevention Trial alone model (AUC = 0.69 and 0.60, P = .01). Within this cohort of patients, there was no significant difference in discrimination between models for those with previous negative biopsy (AUC = 0.61 vs 0.63, P = .76), whereas there was a significant improvement in discrimination with the MRI model for biopsy-naïve patients (AUC = 0.72 vs 0.60, P = .01). The use of prostate MRI in addition to the Prostate Cancer Prevention Trial risk calculator provides a significant improvement in clinical risk discrimination for patients with estimated risk of high-grade (Gleason ≥7) prostate cancer ≤10%. Prebiopsy prostate MRI should be strongly considered for these patients. Copyright © 2016 Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Xiao, Jianghong; Li, Yan; Jiang, Qingfeng; Sun, Lan; Henderson Jr, Fraser; Wang, Yongsheng; Jiang, Xiaoqin; Li, Guangjun; Chen, Nianyong
2013-01-01
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
Extraction of dynamical equations from chaotic data
International Nuclear Information System (INIS)
Rowlands, G.; Sprott, J.C.
1991-02-01
A method is described for extracting from a chaotic time series a system of equations whose solution reproduces the general features of the original data even when these are contaminated with noise. The equations facilitate calculation of fractal dimension, Lyapunov exponents and short-term predictions. The method is applied to data derived from numerical solutions of the Logistic equation, the Henon equations, the Lorenz equations and the Roessler equations. 10 refs., 5 figs
Transport equation solving methods
International Nuclear Information System (INIS)
Granjean, P.M.
1984-06-01
This work is mainly devoted to Csub(N) and Fsub(N) methods. CN method: starting from a lemma stated by Placzek, an equivalence is established between two problems: the first one is defined in a finite medium bounded by a surface S, the second one is defined in the whole space. In the first problem the angular flux on the surface S is shown to be the solution of an integral equation. This equation is solved by Galerkin's method. The Csub(N) method is applied here to one-velocity problems: in plane geometry, slab albedo and transmission with Rayleigh scattering, calculation of the extrapolation length; in cylindrical geometry, albedo and extrapolation length calculation with linear scattering. Fsub(N) method: the basic integral transport equation of the Csub(N) method is integrated on Case's elementary distributions; another integral transport equation is obtained: this equation is solved by a collocation method. The plane problems solved by the Csub(N) method are also solved by the Fsub(N) method. The Fsub(N) method is extended to any polynomial scattering law. Some simple spherical problems are also studied. Chandrasekhar's method, collision probability method, Case's method are presented for comparison with Csub(N) and Fsub(N) methods. This comparison shows the respective advantages of the two methods: a) fast convergence and possible extension to various geometries for Csub(N) method; b) easy calculations and easy extension to polynomial scattering for Fsub(N) method [fr
Kido, Kentaro; Kasahara, Kento; Yokogawa, Daisuke; Sato, Hirofumi
2015-07-01
In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein-Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple SN2 reaction (Cl- + CH3Cl → ClCH3 + Cl-) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.
International Nuclear Information System (INIS)
Kido, Kentaro; Kasahara, Kento; Yokogawa, Daisuke; Sato, Hirofumi
2015-01-01
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 N 2 reaction (Cl − + CH 3 Cl → ClCH 3 + Cl − ) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF
Kido, Kentaro; Kasahara, Kento; Yokogawa, Daisuke; Sato, Hirofumi
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 SN2 reaction (Cl(-) + CH3Cl → ClCH3 + Cl(-)) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.
International Nuclear Information System (INIS)
Fraass, Benedick A.; Smathers, James; Deye, James
2003-01-01
Due to the significant interest in Monte Carlo dose calculations for external beam megavoltage radiation therapy from both the research and commercial communities, a workshop was held in October 2001 to assess the status of this computational method with regard to use for clinical treatment planning. The Radiation Research Program of the National Cancer Institute, in conjunction with the Nuclear Data and Analysis Group at the Oak Ridge National Laboratory, gathered a group of experts in clinical radiation therapy treatment planning and Monte Carlo dose calculations, and examined issues involved in clinical implementation of Monte Carlo dose calculation methods in clinical radiotherapy. The workshop examined the current status of Monte Carlo algorithms, the rationale for using Monte Carlo, algorithmic concerns, clinical issues, and verification methodologies. Based on these discussions, the workshop developed recommendations for future NCI-funded research and development efforts. This paper briefly summarizes the issues presented at the workshop and the recommendations developed by the group
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
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)
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)
Directory of Open Access Journals (Sweden)
Roya Sattarzadeh
2018-01-01
Full Text Available Accurate measurement of Mitral Valve Area (MVA is essential to determining the Mitral Stenosis (MS severity and to achieving the best management strategies for this disease. The goal of the present study is to compare mitral valve area (MVA measurement by Continuity Equation (CE and Pressure Half-Time (PHT methods with that of 2D-Planimetry (PL in patients with moderate to severe mitral stenosis (MS. This comparison also was performed in subgroups of patients with significant Aortic Insufficiency (AI, Mitral Regurgitation (MR and Atrial Fibrillation (AF. We studied 70 patients with moderate to severe MS who were referred to echocardiography clinic. MVA was determined by PL, CE and PHT methods. The agreement and correlations between MVA’s obtained from various methods were determined by kappa index, Bland-Altman analysis, and linear regression analysis. The mean values for MVA calculated by CE was 0.81 cm (±0.27 and showed good correlation with those calculated by PL (0.95 cm, ±0.26 in whole population (r=0.771, P<0.001 and MR subgroup (r=0.763, P<0.001 and normal sinus rhythm and normal valve subgroups (r=0.858, P<0.001 and r=0.867, P<0.001, respectively. But CE methods didn’t show any correlation in AF and AI subgroups. MVA measured by PHT had a good correlation with that measured by PL in whole population (r=0.770, P<0.001 and also in NSR (r=0.814, P<0.001 and normal valve subgroup (r=0.781, P<0.001. Subgroup with significant AI and those with significant MR showed moderate correlation (r=0.625, P=0.017 and r=0.595, P=0.041, respectively. Bland Altman Analysis showed that CE would estimate MVA smaller in comparison with PL in the whole population and all subgroups and PHT would estimate MVA larger in comparison with PL in the whole population and all subgroups. The mean bias for CE and PHT are 0.14 cm and -0.06 cm respectively. In patients with moderate to severe mitral stenosis, in the absence of concomitant AF, AI or MR, the accuracy
International Nuclear Information System (INIS)
Yang, Jyisy; Griffiths, Peter R.; Goodwin, Anthony R.H.
2003-01-01
The (ρ,T,p) and (vapor + liquid) equilibria for fluid mixtures containing either CO 2 or H 2 S have been determined from 13 equations of state. The estimated values have been compared with published experimental results. CO 2 and H 2 S were used to represent non-polar and polar fluids, respectively. The equations of state investigated were as follows: (a) the Lee-Kesler equation; (b) two equations that included new reference fluids for the Lee-Kesler method; (c) three so-called extended equations of state; and (d) seven cubic equations of state. After adjustment of the binary interaction parameters the predicted values differed from the experimental data by about 0.8% for CO 2 mixtures while for H 2 S mixtures the uncertainty was about ±2.8%. Somewhat larger errors, although still lower than ±5%, were obtained for co-existing phase densities; the Lee-Kesler method provided results of the highest accuracy. The cubic equations proposed by Schmidt and Wenzel and Valderrama provide the most reliable predictions of both single and co-existing phase densities. Comparison of the predicted (vapor + liquid) equilibrium with experiment shows that each of the seven cubic equations provides results of similar accuracy and all within ±6%
International Nuclear Information System (INIS)
Jamema, S.V.; Deshpande, D.D.; Kirisits, C.; Trnkova, P.; Poetter, R.; Mahantshetty, U.; Shrivastava, S.K.; Dinshaw, K.A.
2008-01-01
In the recent past, inverse planning algorithms were introduced for intracavitary brachytherapy planning (ICBT) for cervical cancer. The loading pattern of these algorithms in comparison with traditional systems may not be similar. The purpose of this study was to objectively compare the loading patterns of traditional systems with the inverse optimization. Based on the outcome of the comparison, an attempt was made to obtain a loading pattern that takes into account the experience made with the inverse optimization
Feynman integrals and difference equations
International Nuclear Information System (INIS)
Moch, S.; Schneider, C.
2007-09-01
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called ΠΣ * -fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)
Feynman integrals and difference equations
Energy Technology Data Exchange (ETDEWEB)
Moch, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation
2007-09-15
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called {pi}{sigma}{sup *}-fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)
DEFF Research Database (Denmark)
Hansen, Christian Rønn; Lübeck Christiansen, Rasmus; Lorenzen, Ebbe Laugaard
2017-01-01
of metal artifact reduction (MAR) in H&N patients in terms of delineation consistency and dose calculation precision in radiation treatment planning. Material and methods: Tumor and OAR delineations were evaluated in planning CT scans of eleven oropharynx patients with streaking artifacts in the tumor...... region preceding curative radiotherapy (RT). The GTV-tumor (GTV-T), GTV-node and parotid glands were contoured by four independent observers on standard CT images and MAR images. Dose calculation was evaluated on thirty H&N patients with dental implants near the treated volume. For each patient, the dose...
Directory of Open Access Journals (Sweden)
João C. F. Borges Júnior
2006-09-01
Full Text Available Em função deste trabalho, objetivou-se desenvolver e testar um programa computacional para calcular os parâmetros das equações de transporte de solutos no solo, com base no ajustamento de modelos teóricos a dados observados, e executar simulações para a variação espacial e temporal da concentração e do balanço de massa de solutos no perfil do solo. Utilizou-se o método dos mínimos quadrados (Levenberg-Marquardt para obtenção dos estimadores dos parâmetros coeficiente dispersivo-difusivo e fator de retardamento. O programa desenvolvido, denominado Disp, possui interface gráfica que torna simples o seu uso quanto aos procedimentos de entrada de dados, execução dos cálculos e acesso aos resultados. Nos formulários de resultados, gráficos e tabelas relacionados às curvas de efluente podem ser gerados além da possibilidade de se executar simulações quanto à variação espacial e temporal da concentração e do balanço de massa de solutos no perfil do solo. Testes comparativos entre o Disp e o programa CXTFIT, relativos aos cálculos dos parâmetros número de Peclet e fator de retardamento, indicaram equivalência entre os dois programas, porém a interface gráfica do Disp o torna de uso mais simples em relação ao CXTFIT.This study aimed to develop and to test a computer program for calculating the parameters of soil solute transport equations, based on adjustment of theoretical models to observed data, as well as to perform simulations for the space and temporary variations of the concentration and balance of the solute mass in the soil profile. The least-squares method (Levenberg-Marquardt was used to obtain the estimators of the diffusion-dispersion coefficient and retardation factor parameters. The developed program, so-called DISP, is provided with a graphic interface that makes possible its use in procedures for data input, accomplishment of calculations and access to results. In the result forms, a number of
Indian Academy of Sciences (India)
regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.
International Nuclear Information System (INIS)
Gross, F.
1986-01-01
Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs
42 CFR 82.18 - How will NIOSH calculate internal dose to the primary cancer site(s)?
2010-10-01
... all available bioassay monitoring information as appropriate, based on assessment of the technical characteristics of the monitoring program. If bioassay monitoring data are unavailable or inadequate, the dose... practices, and incidents involving radiation contamination, as necessary. (b) NIOSH will calculate the dose...
International Nuclear Information System (INIS)
Le Thanh Xuan; Nguyen Thi Cam Thu; Tran Van Nghia; Truong Thi Hong Loan; Vo Thanh Nhon
2015-01-01
The dose distribution calculation is one of the major steps in radiotherapy. In this paper the Monte Carlo code MCNP5 has been applied for simulation 15 MV photon beams emitted from linear accelerator in a case of lung cancer of the General Hospital of Kien Giang. The settings for beam directions, field sizes and isocenter position used in MCNP5 must be the same as those in treatment plan at the hospital to ensure the results from MCNP5 are accurate. We also built a program CODIM by using MATLAB® programming software. This program was used to construct patient model from lung CT images obtained from cancer treatment cases at the General Hospital of Kien Giang and then MCNP5 code was used to simulate the delivered dose in the patient. The results from MCNP5 show that there is a difference of 5% in comparison with Prowess Panther program - a semi-empirical simulation program which is being used for treatment planning in the General Hospital of Kien Giang. The success of the work will help the planners to verify the patient dose distribution calculated from the treatment planning program being used at the hospital. (author)
Electronic representation of wave equation
Energy Technology Data Exchange (ETDEWEB)
Veigend, Petr; Kunovský, Jiří, E-mail: kunovsky@fit.vutbr.cz; Kocina, Filip; Nečasová, Gabriela; Valenta, Václav [University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic); Šátek, Václav [IT4Innovations, VŠB Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava-Poruba (Czech Republic); University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic)
2016-06-08
The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.
Sarigiannis, Dimosthenis A.; Karakitsios, Spyros P.; Gotti, Alberto; Papaloukas, Costas L.; Kassomenos, Pavlos A.; Pilidis, Georgios A.
2009-01-01
The objective of the current study was the development of a reliable modeling platform to calculate in real time the personal exposure and the associated health risk for filling station employees evaluating current environmental parameters (traffic, meteorological and amount of fuel traded) determined by the appropriate sensor network. A set of Artificial Neural Networks (ANNs) was developed to predict benzene exposure pattern for the filling station employees. Furthermore, a Physiology Based...
International Nuclear Information System (INIS)
Koivula, Lauri
2016-01-01
Purpose: Magnetic resonance imaging (MRI) is increasingly used for radiotherapy target delineation, image guidance, and treatment response monitoring. Recent studies have shown that an entire external x-ray radiotherapy treatment planning (RTP) workflow for brain tumor or prostate cancer patients based only on MRI reference images is feasible. This study aims to show that a MRI-only based RTP workflow is also feasible for proton beam therapy plans generated in MRI-based substitute computed tomography (sCT) images of the head and the pelvis. Methods: The sCTs were constructed for ten prostate cancer and ten brain tumor patients primarily by transforming the intensity values of in-phase MR images to Hounsfield units (HUs) with a dual model HU conversion technique to enable heterogeneous tissue representation. HU conversion models for the pelvis were adopted from previous studies, further extended in this study also for head MRI by generating anatomical site-specific conversion models (a new training data set of ten other brain patients). This study also evaluated two other types of simplified sCT: dual bulk density (for bone and water) and homogeneous (water only). For every clinical case, intensity modulated proton therapy (IMPT) plans robustly optimized in standard planning CTs were calculated in sCT for evaluation, and vice versa. Overall dose agreement was evaluated using dose–volume histogram parameters and 3D gamma criteria. Results: In heterogeneous sCTs, the mean absolute errors in HUs were 34 (soft tissues: 13, bones: 92) and 42 (soft tissues: 9, bones: 97) in the head and in the pelvis, respectively. The maximum absolute dose differences relative to CT in the brain tumor clinical target volume (CTV) were 1.4% for heterogeneous sCT, 1.8% for dual bulk sCT, and 8.9% for homogenous sCT. The corresponding maximum differences in the prostate CTV were 0.6%, 1.2%, and 3.6%, respectively. The percentages of dose points in the head and pelvis passing 1% and 1 mm
Energy Technology Data Exchange (ETDEWEB)
Koivula, Lauri [Department of Radiation Oncology, Comprehensive Cancer Center, Helsinki University Central Hospital, P.O. Box 180, Helsinki 00029 HUS (Finland)
2016-08-15
Purpose: Magnetic resonance imaging (MRI) is increasingly used for radiotherapy target delineation, image guidance, and treatment response monitoring. Recent studies have shown that an entire external x-ray radiotherapy treatment planning (RTP) workflow for brain tumor or prostate cancer patients based only on MRI reference images is feasible. This study aims to show that a MRI-only based RTP workflow is also feasible for proton beam therapy plans generated in MRI-based substitute computed tomography (sCT) images of the head and the pelvis. Methods: The sCTs were constructed for ten prostate cancer and ten brain tumor patients primarily by transforming the intensity values of in-phase MR images to Hounsfield units (HUs) with a dual model HU conversion technique to enable heterogeneous tissue representation. HU conversion models for the pelvis were adopted from previous studies, further extended in this study also for head MRI by generating anatomical site-specific conversion models (a new training data set of ten other brain patients). This study also evaluated two other types of simplified sCT: dual bulk density (for bone and water) and homogeneous (water only). For every clinical case, intensity modulated proton therapy (IMPT) plans robustly optimized in standard planning CTs were calculated in sCT for evaluation, and vice versa. Overall dose agreement was evaluated using dose–volume histogram parameters and 3D gamma criteria. Results: In heterogeneous sCTs, the mean absolute errors in HUs were 34 (soft tissues: 13, bones: 92) and 42 (soft tissues: 9, bones: 97) in the head and in the pelvis, respectively. The maximum absolute dose differences relative to CT in the brain tumor clinical target volume (CTV) were 1.4% for heterogeneous sCT, 1.8% for dual bulk sCT, and 8.9% for homogenous sCT. The corresponding maximum differences in the prostate CTV were 0.6%, 1.2%, and 3.6%, respectively. The percentages of dose points in the head and pelvis passing 1% and 1 mm
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)
Energy Technology Data Exchange (ETDEWEB)
Walsh, Linda [Federal Office for Radiation Protection, Department of Radiation Protection and Health, Oberschleissheim (Germany); University of Manchester, The Faculty of Medical and Human Sciences, Manchester (United Kingdom); Schneider, Uwe [University of Zurich, Vetsuisse Faculty, Zurich (Switzerland); Radiotherapy Hirslanden AG, Aarau (Switzerland)
2013-03-15
Radiation-related risks of cancer can be transported from one population to another population at risk, for the purpose of calculating lifetime risks from radiation exposure. Transfer via excess relative risks (ERR) or excess absolute risks (EAR) or a mixture of both (i.e., from the life span study (LSS) of Japanese atomic bomb survivors) has been done in the past based on qualitative weighting. Consequently, the values of the weights applied and the method of application of the weights (i.e., as additive or geometric weighted means) have varied both between reports produced at different times by the same regulatory body and also between reports produced at similar times by different regulatory bodies. Since the gender and age patterns are often markedly different between EAR and ERR models, it is useful to have an evidence-based method for determining the relative goodness of fit of such models to the data. This paper identifies a method, using Akaike model weights, which could aid expert judgment and be applied to help to achieve consistency of approach and quantitative evidence-based results in future health risk assessments. The results of applying this method to recent LSS cancer incidence models are that the relative EAR weighting by cancer solid cancer site, on a scale of 0-1, is zero for breast and colon, 0.02 for all solid, 0.03 for lung, 0.08 for liver, 0.15 for thyroid, 0.18 for bladder and 0.93 for stomach. The EAR weighting for female breast cancer increases from 0 to 0.3, if a generally observed change in the trend between female age-specific breast cancer incidence rates and attained age, associated with menopause, is accounted for in the EAR model. Application of this method to preferred models from a study of multi-model inference from many models fitted to the LSS leukemia mortality data, results in an EAR weighting of 0. From these results it can be seen that lifetime risk transfer is most highly weighted by EAR only for stomach cancer. However
Directory of Open Access Journals (Sweden)
Pavlos A. Kassomenos
2009-02-01
Full Text Available The objective of the current study was the development of a reliable modeling platform to calculate in real time the personal exposure and the associated health risk for filling station employees evaluating current environmental parameters (traffic, meteorological and amount of fuel traded determined by the appropriate sensor network. A set of Artificial Neural Networks (ANNs was developed to predict benzene exposure pattern for the filling station employees. Furthermore, a Physiology Based Pharmaco-Kinetic (PBPK risk assessment model was developed in order to calculate the lifetime probability distribution of leukemia to the employees, fed by data obtained by the ANN model. Bayesian algorithm was involved in crucial points of both model sub compartments. The application was evaluated in two filling stations (one urban and one rural. Among several algorithms available for the development of the ANN exposure model, Bayesian regularization provided the best results and seemed to be a promising technique for prediction of the exposure pattern of that occupational population group. On assessing the estimated leukemia risk under the scope of providing a distribution curve based on the exposure levels and the different susceptibility of the population, the Bayesian algorithm was a prerequisite of the Monte Carlo approach, which is integrated in the PBPK-based risk model. In conclusion, the modeling system described herein is capable of exploiting the information collected by the environmental sensors in order to estimate in real time the personal exposure and the resulting health risk for employees of gasoline filling stations.
Sarigiannis, Dimosthenis A; Karakitsios, Spyros P; Gotti, Alberto; Papaloukas, Costas L; Kassomenos, Pavlos A; Pilidis, Georgios A
2009-01-01
The objective of the current study was the development of a reliable modeling platform to calculate in real time the personal exposure and the associated health risk for filling station employees evaluating current environmental parameters (traffic, meteorological and amount of fuel traded) determined by the appropriate sensor network. A set of Artificial Neural Networks (ANNs) was developed to predict benzene exposure pattern for the filling station employees. Furthermore, a Physiology Based Pharmaco-Kinetic (PBPK) risk assessment model was developed in order to calculate the lifetime probability distribution of leukemia to the employees, fed by data obtained by the ANN model. Bayesian algorithm was involved in crucial points of both model sub compartments. The application was evaluated in two filling stations (one urban and one rural). Among several algorithms available for the development of the ANN exposure model, Bayesian regularization provided the best results and seemed to be a promising technique for prediction of the exposure pattern of that occupational population group. On assessing the estimated leukemia risk under the scope of providing a distribution curve based on the exposure levels and the different susceptibility of the population, the Bayesian algorithm was a prerequisite of the Monte Carlo approach, which is integrated in the PBPK-based risk model. In conclusion, the modeling system described herein is capable of exploiting the information collected by the environmental sensors in order to estimate in real time the personal exposure and the resulting health risk for employees of gasoline filling stations.
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)
Rodriguez, Barbara A.; Borges, Volnei; Vilhena, Marco Tullio
2005-01-01
In this work we would like to obtain a formulation of an analytic method for the solution of the three dimensional transport equation considering Compton scattering and an expression for total doses due to gamma radiation, where the deposited energy by the free electron will be considered. For that, we will work with two equations: the first one for the photon transport, considering the Klein-Nishina kernel and energy multigroup model, and the second one considering the free electron with the screened Rutherford scattering. (author)
Differential Equations Compatible with KZ Equations
International Nuclear Information System (INIS)
Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.
2000-01-01
We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions
International Nuclear Information System (INIS)
Padmanaban, Sriram; Warren, Samantha; Walsh, Anthony; Partridge, Mike; Hawkins, Maria A
2014-01-01
To investigate systematic changes in dose arising when treatment plans optimised using the Anisotropic Analytical Algorithm (AAA) are recalculated using Acuros XB (AXB) in patients treated with definitive chemoradiotherapy (dCRT) for locally advanced oesophageal cancers. We have compared treatment plans created using AAA with those recalculated using AXB. Although the Anisotropic Analytical Algorithm (AAA) is currently more widely used in clinical routine, Acuros XB (AXB) has been shown to more accurately calculate the dose distribution, particularly in heterogeneous regions. Studies to predict clinical outcome should be based on modelling the dose delivered to the patient as accurately as possible. CT datasets from ten patients were selected for this retrospective study. VMAT (Volumetric modulated arc therapy) plans with 2 arcs, collimator rotation ± 5-10° and dose prescription 50 Gy / 25 fractions were created using Varian Eclipse (v10.0). The initial dose calculation was performed with AAA, and AXB plans were created by re-calculating the dose distribution using the same number of monitor units (MU) and multileaf collimator (MLC) files as the original plan. The difference in calculated dose to organs at risk (OAR) was compared using dose-volume histogram (DVH) statistics and p values were calculated using the Wilcoxon signed rank test. The potential clinical effect of dosimetric differences in the gross tumour volume (GTV) was evaluated using three different TCP models from the literature. PTV Median dose was apparently 0.9 Gy lower (range: 0.5 Gy - 1.3 Gy; p < 0.05) for VMAT AAA plans re-calculated with AXB and GTV mean dose was reduced by on average 1.0 Gy (0.3 Gy −1.5 Gy; p < 0.05). An apparent difference in TCP of between 1.2% and 3.1% was found depending on the choice of TCP model. OAR mean dose was lower in the AXB recalculated plan than the AAA plan (on average, dose reduction: lung 1.7%, heart 2.4%). Similar trends were seen for CRT plans
Padmanaban, Sriram; Warren, Samantha; Walsh, Anthony; Partridge, Mike; Hawkins, Maria A
2014-12-23
To investigate systematic changes in dose arising when treatment plans optimised using the Anisotropic Analytical Algorithm (AAA) are recalculated using Acuros XB (AXB) in patients treated with definitive chemoradiotherapy (dCRT) for locally advanced oesophageal cancers. We have compared treatment plans created using AAA with those recalculated using AXB. Although the Anisotropic Analytical Algorithm (AAA) is currently more widely used in clinical routine, Acuros XB (AXB) has been shown to more accurately calculate the dose distribution, particularly in heterogeneous regions. Studies to predict clinical outcome should be based on modelling the dose delivered to the patient as accurately as possible. CT datasets from ten patients were selected for this retrospective study. VMAT (Volumetric modulated arc therapy) plans with 2 arcs, collimator rotation ± 5-10° and dose prescription 50 Gy / 25 fractions were created using Varian Eclipse (v10.0). The initial dose calculation was performed with AAA, and AXB plans were created by re-calculating the dose distribution using the same number of monitor units (MU) and multileaf collimator (MLC) files as the original plan. The difference in calculated dose to organs at risk (OAR) was compared using dose-volume histogram (DVH) statistics and p values were calculated using the Wilcoxon signed rank test. The potential clinical effect of dosimetric differences in the gross tumour volume (GTV) was evaluated using three different TCP models from the literature. PTV Median dose was apparently 0.9 Gy lower (range: 0.5 Gy - 1.3 Gy; p AAA plans re-calculated with AXB and GTV mean dose was reduced by on average 1.0 Gy (0.3 Gy -1.5 Gy; p AAA plan (on average, dose reduction: lung 1.7%, heart 2.4%). Similar trends were seen for CRT plans. Differences in dose distribution are observed with VMAT and CRT plans recalculated with AXB particularly within soft tissue at the tumour/lung interface, where AXB has been shown to more
Energy Technology Data Exchange (ETDEWEB)
Mein, S [Duke University Medical Physics Graduate Program (United States); Gunasingha, R [Department of Radiation Safety, Duke University Medical Center (United States); Nolan, M [Department of Clinical Sciences, College of Veterinary Medicine, North Carolina State University (United States); Oldham, M; Adamson, J [Department of Radiation Oncology, Duke University Medical Center (United States)
2016-06-15
Purpose: X-PACT is an experimental cancer therapy where kV x-rays are used to photo-activate anti-cancer therapeutics through phosphor intermediaries (phosphors that absorb x-rays and re-radiate as UV light). Clinical trials in pet dogs are currently underway (NC State College of Veterinary Medicine) and an essential component is the ability to model the kV dose in these dogs. Here we report the commissioning and characterization of a Monte Carlo (MC) treatment planning simulation tool to calculate X-PACT radiation doses in canine trials. Methods: FLUKA multi-particle MC simulation package was used to simulate a standard X-PACT radiation treatment beam of 80kVp with the Varian OBI x-ray source geometry. The beam quality was verified by comparing measured and simulated attenuation of the beam by various thicknesses of aluminum (2–4.6 mm) under narrow beam conditions (HVL). The beam parameters at commissioning were then corroborated using MC, characterized and verified with empirically collected commissioning data, including: percent depth dose curves (PDD), back-scatter factors (BSF), collimator scatter factor(s), and heel effect, etc. All simulations were conducted for N=30M histories at M=100 iterations. Results: HVL and PDD simulation data agreed with an average percent error of 2.42%±0.33 and 6.03%±1.58, respectively. The mean square error (MSE) values for HVL and PDD (0.07% and 0.50%) were low, as expected; however, longer simulations are required to validate convergence to the expected values. Qualitatively, pre- and post-filtration source spectra matched well with 80kVp references generated via SPEKTR software. Further validation of commissioning data simulation is underway in preparation for first-time 3D dose calculations with canine CBCT data. Conclusion: We have prepared a Monte Carlo simulation capable of accurate dose calculation for use with ongoing X-PACT canine clinical trials. Preliminary results show good agreement with measured data and hold
DEFF Research Database (Denmark)
Dyre, Jeppe
1995-01-01
energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk modelthe energy master equation...... (EME)is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...
Current evaluation of dose rate calculation - analytical method
International Nuclear Information System (INIS)
Tello, Marcos; Vilhena, Marco Tulio
1996-01-01
The accuracy of the dose calculations based on pencil beam formulas such as Fokker-Plank equations and Fermi equations for charged particle transport are studied and a methodology to solve the Boltzmann transport equation is suggested
National Oceanic and Atmospheric Administration, Department of Commerce — Declination is calculated using the current International Geomagnetic Reference Field (IGRF) model. Declination is calculated using the current World Magnetic Model...
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
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.
International Nuclear Information System (INIS)
Shore, B.W.
1981-01-01
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence
International Nuclear Information System (INIS)
Weill, J.; Tellier; Bonnemay; Craigne; Chareton; Di Falco
1969-02-01
After a definition of hybrid calculation (combination of analogue and digital calculation) with a distinction between series and parallel hybrid computing, and a description of a hybrid computer structure and of task sharing between computers, this course proposes a description of hybrid hardware used in Saclay and Cadarache computing centres, and of operations performed by these systems. The next part addresses issues related to programming languages and software. The fourth part describes how a problem is organised for its processing on these computers. Methods of hybrid analysis are then addressed: resolution of optimisation problems, of partial differential equations, and of integral equations by means of different methods (gradient, maximum principle, characteristics, functional approximation, time slicing, Monte Carlo, Neumann iteration, Fischer iteration)
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.
International Nuclear Information System (INIS)
Aydin, H.; Richter, E.; Feyerabend, T.; Bohndorf, W.
1990-01-01
The volumetric analysis of a tumour by CT is a reliable and clinically important method of examination which is rarely used. As for oncology, the importance of this method is based upon the determination of the stage of remission posttherapeutically, especially in those cases which respond to therapy without a roentgenologic change in comparison to pretherapeutic findings. This applies in particular for the evaluation of CT images. In this study 115 CT examinations of 38 patients with recurrent rectal cancer were evaluated and the tumour remission was measured by an exact determination of the tumour volume before and after radiotherapy. The results were compared with the CT findings without volumetric analysis. A change of the tumour size up to 20% of the pretherapeutic volume which eludes from the visual perception can be revealed by a subtle CT-assisted volumetric analysis. Formulas for calculation of the volume or the data concerning length, width and depth of a mass prove to be insufficient or incorrect. Therefore the correct evaluation of a tumour regression or progression shoud be done more often by CT-assisted volumetric analysis. (orig.) [de
Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation
Karney, C. F. F.
1977-01-01
Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.
International Nuclear Information System (INIS)
Sydoriak, S.G.
1976-01-01
Although criteria for cryostatic stability of superconducting magnets cooled by pool boiling of liquid helium have been widely discussed the same cannot be said for magnets cooled by natural convection or forced flow boiling in channels. Boiling in narrow channels is shown to be qualitatively superior to pool boiling because the recovery heat flux equals the breakaway flux for narrow channels, whereas the two are markedly different in pool boiling. A second advantage of channel boiling is that it is well understood and calculable; pool peak nucleate boiling heat flux has been adequately measured only for boiling from the top of an immersed heated body. Peak boiling from the bottom is much less and (probably) depends strongly on the extent of the bottom surface. Equations are presented by which one can calculate the critical boiling heat flux for parallel wall vertical channels subject to either natural convection or forced flow boiling, with one or both walls heated. The one-heated-wall forced flow equation is discussed with regard to design of a spiral wound solenoid (pancake magnet) having a slippery insulating tape between the windings
Equations of multiparticle dynamics
International Nuclear Information System (INIS)
Chao, A.W.
1987-01-01
The description of the motion of charged-particle beams in an accelerator proceeds in steps of increasing complexity. The first step is to consider a single-particle picture in which the beam is represented as a collection on non-interacting test particles moving in a prescribed external electromagnetic field. Knowing the external field, it is then possible to calculate the beam motion to a high accuracy. The real beam consists of a large number of particles, typically 10 11 per beam bunch. It is sometimes inconvenient, or even impossible, to treat the real beam behavior using the single particle approach. One way to approach this problem is to supplement the single particle by another qualitatively different picture. The commonly used tools in accelerator physics for this purpose are the Vlasov and the Fokker-Planck equations. These equations assume smooth beam distributions and are therefore strictly valid in the limit of infinite number of micro-particles, each carrying an infinitesimal charge. The hope is that by studying the two extremes -- the single particle picture and the picture of smooth beam distributions -- we will be able to describe the behavior of our 10 11 -particle system. As mentioned, the most notable use of the smooth distribution picture is the study of collective beam instabilities. However, the purpose of this lecture is not to address this more advanced subject. Rather, it has the limited goal to familiarize the reader with the analytical tools, namely the Vlasov and the Fokker-Planck equations, as a preparation for dealing with the more advanced problems at later times. We will first derive these equations and then illustrate their applications by several examples which allow exact solutions
Directory of Open Access Journals (Sweden)
TAKURO ISODA
2017-01-01
.2% for lung cancer. The corresponding possibility were 14.7% for osteoblastic metastases, 23.9% for mildly osteoblastic metastases, 7.14% for mixedtype metastases, and 16.0% for osteolytic metastases.Conclusion: The lesion-based ANN values calculated by BONENAVI can be influenced by the type of primary cancer and bone metastasis.
Wave equation of hydrogen atom
International Nuclear Information System (INIS)
Suwito.
1977-01-01
The calculation of the energy levels of the hydrogen atom using Bohr, Schroedinger and Dirac theories is reviewed. The result is compared with that obtained from infinite component wave equations theory which developed recently. The conclusion can be stated that the latter theory is better to describe the composit system than the former. (author)
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)
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
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Equating error in observed-score equating
van der Linden, Willem J.
2006-01-01
Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of
Calculation Of Pneumatic Attenuation In Pressure Sensors
Whitmore, Stephen A.
1991-01-01
Errors caused by attenuation of air-pressure waves in narrow tubes calculated by method based on fundamental equations of flow. Changes in ambient pressure transmitted along narrow tube to sensor. Attenuation of high-frequency components of pressure wave calculated from wave equation derived from Navier-Stokes equations of viscous flow in tube. Developed to understand and compensate for frictional attenuation in narrow tubes used to connect aircraft pressure sensors with pressure taps on affected surfaces.
Energy Technology Data Exchange (ETDEWEB)
Zhen, X; Chen, H; Liao, Y; Zhou, L [Southern Medical University, Guangzhou, Guangdong (China); Hrycushko, B; Albuquerque, K; Gu, X [UT Southwestern Medical Center, Dallas, TX (United States)
2016-06-15
Purpose: To study the feasibility of employing deformable registration methods for accurate rectum dose volume parameters calculation and their potentials in revealing rectum dose-toxicity between complication and non-complication cervical cancer patients with brachytherapy treatment. Method and Materials: Data from 60 patients treated with BT including planning images, treatment plans, and follow-up clinical exam were retrospectively collected. Among them, 12 patients complained about hematochezia were further examined with colonoscopy and scored as Grade 1–3 complication (CP). Meanwhile, another 12 non-complication (NCP) patients were selected as a reference group. To seek for potential gains in rectum toxicity prediction when fractional anatomical deformations are account for, the rectum dose volume parameters D0.1/1/2cc of the selected patients were retrospectively computed by three different approaches: the simple “worstcase scenario” (WS) addition method, an intensity-based deformable image registration (DIR) algorithm-Demons, and a more accurate, recent developed local topology preserved non-rigid point matching algorithm (TOP). Statistical significance of the differences between rectum doses of the CP group and the NCP group were tested by a two-tailed t-test and results were considered to be statistically significant if p < 0.05. Results: For the D0.1cc, no statistical differences are found between the CP and NCP group in all three methods. For the D1cc, dose difference is not detected by the WS method, however, statistical differences between the two groups are observed by both Demons and TOP, and more evident in TOP. For the D2cc, the CP and NCP cases are statistically significance of the difference for all three methods but more pronounced with TOP. Conclusion: In this study, we calculated the rectum D0.1/1/2cc by simple WS addition and two DIR methods and seek for gains in rectum toxicity prediction. The results favor the claim that accurate dose
International Nuclear Information System (INIS)
Scholtyssek, W.
1995-01-01
In the first phase of a benchmark comparison, the CONTAIN code was used to calculate an assumed EPR accident 'medium-sized leak in the cold leg', especially for the first two days after initiation of the accident. The results for global characteristics compare well with those of FIPLOC, MELCOR and WAVCO calculations, if the same materials data are used as input. However, significant differences show up for local quantities such as flows through leakages. (orig.)
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 ...
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.
Blakley, G. R.
1982-01-01
Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)
Energy Technology Data Exchange (ETDEWEB)
Latifi, Kujtim, E-mail: Kujtim.Latifi@Moffitt.org [Department of Radiation Oncology, Moffitt Cancer Center, Tampa, Florida (United States); Oliver, Jasmine [Department of Radiation Oncology, Moffitt Cancer Center, Tampa, Florida (United States); Department of Physics, University of South Florida, Tampa, Florida (United States); Baker, Ryan [University of South Florida School of Medicine, Tampa, Florida (United States); Dilling, Thomas J.; Stevens, Craig W. [Department of Radiation Oncology, Moffitt Cancer Center, Tampa, Florida (United States); Kim, Jongphil; Yue, Binglin [Department of Biostatics and Bioinformatics, Moffitt Cancer Center, Tampa, Florida (United States); DeMarco, MaryLou; Zhang, Geoffrey G.; Moros, Eduardo G.; Feygelman, Vladimir [Department of Radiation Oncology, Moffitt Cancer Center, Tampa, Florida (United States)
2014-04-01
Purpose: Pencil beam (PB) and collapsed cone convolution (CCC) dose calculation algorithms differ significantly when used in the thorax. However, such differences have seldom been previously directly correlated with outcomes of lung stereotactic ablative body radiation (SABR). Methods and Materials: Data for 201 non-small cell lung cancer patients treated with SABR were analyzed retrospectively. All patients were treated with 50 Gy in 5 fractions of 10 Gy each. The radiation prescription mandated that 95% of the planning target volume (PTV) receive the prescribed dose. One hundred sixteen patients were planned with BrainLab treatment planning software (TPS) with the PB algorithm and treated on a Novalis unit. The other 85 were planned on the Pinnacle TPS with the CCC algorithm and treated on a Varian linac. Treatment planning objectives were numerically identical for both groups. The median follow-up times were 24 and 17 months for the PB and CCC groups, respectively. The primary endpoint was local/marginal control of the irradiated lesion. Gray's competing risk method was used to determine the statistical differences in local/marginal control rates between the PB and CCC groups. Results: Twenty-five patients planned with PB and 4 patients planned with the CCC algorithms to the same nominal doses experienced local recurrence. There was a statistically significant difference in recurrence rates between the PB and CCC groups (hazard ratio 3.4 [95% confidence interval: 1.18-9.83], Gray's test P=.019). The differences (Δ) between the 2 algorithms for target coverage were as follows: ΔD99{sub GITV} = 7.4 Gy, ΔD99{sub PTV} = 10.4 Gy, ΔV90{sub GITV} = 13.7%, ΔV90{sub PTV} = 37.6%, ΔD95{sub PTV} = 9.8 Gy, and ΔD{sub ISO} = 3.4 Gy. GITV = gross internal tumor volume. Conclusions: Local control in patients receiving who were planned to the same nominal dose with PB and CCC algorithms were statistically significantly different. Possible
Handbook of integral equations
Polyanin, Andrei D
2008-01-01
This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.
International Nuclear Information System (INIS)
Heilbron Filho, P.F.L.; Oliveira Brandao, R. de.
1988-04-01
The theory of Point Kernel applied to a source uniformelly distributed in a cylindrical geometry was utilized to estimated the Cs-137 content of each package of radioactive waste collected. The Taylor equation was employed to calculate the build-up factor and the Green function G was adjusted by means of a least square method. The theory also takes into account factors such as aditional shielding, heterogeneity and humidity of the medium as well as associated uncertanties of the parameters envolved. (author) [pt
Wisniewski, H.; Gourdain, P.-A.
2017-10-01
APOLLO is an online, Linux based plasma calculator. Users can input variables that correspond to their specific plasma, such as ion and electron densities, temperatures, and external magnetic fields. The system is based on a webserver where a FastCGI protocol computes key plasma parameters including frequencies, lengths, velocities, and dimensionless numbers. FastCGI was chosen to overcome security problems caused by JAVA-based plugins. The FastCGI also speeds up calculations over PHP based systems. APOLLO is built upon the WT library, which turns any web browser into a versatile, fast graphic user interface. All values with units are expressed in SI units except temperature, which is in electron-volts. SI units were chosen over cgs units because of the gradual shift to using SI units within the plasma community. APOLLO is intended to be a fast calculator that also provides the user with the proper equations used to calculate the plasma parameters. This system is intended to be used by undergraduates taking plasma courses as well as graduate students and researchers who need a quick reference calculation.
Directory of Open Access Journals (Sweden)
Carels Nicolas
2015-12-01
We propose several novel drug combinations using only the approved drugs for the inactivation of the target identified in this study with the purpose of increasing patient survival and lowering the deleterious side effects of cancer chemotherapy.
Transport equation and shock waves
International Nuclear Information System (INIS)
Besnard, D.
1981-04-01
A multi-group method is derived from a one dimensional transport equation for the slowing down and spatial transport of energetic positive ions in a plasma. This method is used to calculate the behaviour of energetic charged particles in non homogeneous and non stationary plasma, and the effect of energy deposition of the particles on the heating of the plasma. In that purpose, an equation for the density of fast ions is obtained from the Fokker-Planck equation, and a closure condition for the second moment of this equation is deduced from phenomenological considerations. This method leads to a numerical method, simple and very efficient, which doesn't require much computer storage. Two types of numerical results are obtained. First, results on the slowing down of 3.5 MeV alpha particles in a 50 keV plasma plublished by Corman and al and Moses are compared with the results obtained with both our method and a Monte Carlo type method. Good agreement was obtained, even for energy deposition on the ions of the plasma. Secondly, we have calculated propagation of alpha particles heating a cold plasma. These results are in very good agreement with those given by an accurate Monte Carlo method, for both the thermal velocity, and the energy deposition in the plasma
Directory of Open Access Journals (Sweden)
Harminder Singh
2017-06-01
Full Text Available Purpose: The objective of this cross-sectional, noninterventional, 6-month observational study was to assess the adequacy of pain management in patients with cancer admitted to the Oncology Department of Guru Gobind Singh Medical College in Faridkot, India. Methods and Materials: A total of 348 patients with cancer were recruited for evaluation of the prevalence of inadequate cancer pain management using the Brief Pain Inventory Pain Management Index. Results: The current study included 127 males (36.5% and 221 females (63.5%. The most prevalent cancer type was genitourinary; 268 patients (77% had inadequately managed pain. A significant correlation was observed between poorly managed pain and age groups, analgesic used, and body mass index. Conclusion: Our observation of inadequate pain management among 77% of patients indicates that pain management was insufficient in three quarters of the patients in this study. Accumulating data regarding the inadequacy of cancer pain management is crucial to improve symptom management. Better management of pain not only alleviates pain symptoms but also increases the quality of life for patients with cancer.
Numerical calculations near spatial infinity
International Nuclear Information System (INIS)
Zenginoglu, Anil
2007-01-01
After describing in short some problems and methods regarding the smoothness of null infinity for isolated systems, I present numerical calculations in which both spatial and null infinity can be studied. The reduced conformal field equations based on the conformal Gauss gauge allow us in spherical symmetry to calculate numerically the entire Schwarzschild-Kruskal spacetime in a smooth way including spacelike, null and timelike infinity and the domain close to the singularity
BMN correlators by loop equations
International Nuclear Information System (INIS)
Eynard, Bertrand; Kristjansen, Charlotte
2002-01-01
In the BMN approach to N=4 SYM a large class of correlators of interest are expressible in terms of expectation values of traces of words in a zero-dimensional gaussian complex matrix model. We develop a loop-equation based, analytic strategy for evaluating such expectation values to any order in the genus expansion. We reproduce the expectation values which were needed for the calculation of the one-loop, genus one correction to the anomalous dimension of BMN-operators and which were earlier obtained by combinatorial means. Furthermore, we present the expectation values needed for the calculation of the one-loop, genus two correction. (author)
Relative Hazard Calculation Methodology
International Nuclear Information System (INIS)
DL Strenge; MK White; RD Stenner; WB Andrews
1999-01-01
The methodology presented in this document was developed to provide a means of calculating the RH ratios to use in developing useful graphic illustrations. The RH equation, as presented in this methodology, is primarily a collection of key factors relevant to understanding the hazards and risks associated with projected risk management activities. The RH equation has the potential for much broader application than generating risk profiles. For example, it can be used to compare one risk management activity with another, instead of just comparing it to a fixed baseline as was done for the risk profiles. If the appropriate source term data are available, it could be used in its non-ratio form to estimate absolute values of the associated hazards. These estimated values of hazard could then be examined to help understand which risk management activities are addressing the higher hazard conditions at a site. Graphics could be generated from these absolute hazard values to compare high-hazard conditions. If the RH equation is used in this manner, care must be taken to specifically define and qualify the estimated absolute hazard values (e.g., identify which factors were considered and which ones tended to drive the hazard estimation)
International Nuclear Information System (INIS)
Petersen, K.E.
1986-03-01
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)
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...
Relativistic three-particle dynamical equations: I. Theoretical development
International Nuclear Information System (INIS)
Adhikari, S.K.; Tomio, L.; Frederico, T.
1993-11-01
Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, three dimensional scattering integral equations satisfying constrains of relativistic unitarity and covariance are rederived. These equations were first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of variables. Hence it is shown to perform and relate dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, several three dimensional three-particle scattering equations satisfying constraints of relativistic unitary and covariance are derived. Two of these three-particle equations are related by a transformation of variables as in the two-particle case. The three-particle equations obtained are very practical and suitable for performing relativistic scattering calculations. (author)
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
Uraltseva, N N
1995-01-01
This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p
Equations of macrotransport in reactor fuel assemblies
International Nuclear Information System (INIS)
Sorokin, A.P.; Zhukov, A.V.; Kornienko, Yu.N.; Ushakov, P.A.
1986-01-01
The rigorous statement of equations of macrotransport is obtained. These equations are bases for channel-by-channel methods of thermohydraulic calculations of reactor fuel assemblies within the scope of the model of discontinuous multiphase coolant flow (including chemical reactions); they also describe a wide range of problems on thermo-physical reactor fuel assembly justification. It has been carried out by smoothing equations of mass, momentum and enthalpy transfer in cross section of each phase of the elementary fuel assembly subchannel. The equation for cross section flows is obtaind by smoothing the equation of momentum transfer on the interphase. Interaction of phases on the channel boundary is described using the Stanton number. The conclusion is performed using the generalized equation of substance transfer. The statement of channel-by-channel method without the scope of homogeneous flow model is given
Perturbation theory for continuous stochastic equations
International Nuclear Information System (INIS)
Chechetkin, V.R.; Lutovinov, V.S.
1987-01-01
The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probability distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes, stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion-controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and non-equilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered. (author)
Faas, S.; Snijders, Jaap; van Lenthe, J.H.; HernandezLaguna, A; Maruani, J; McWeeny, R; Wilson, S
2000-01-01
In this paper we present the first application of the ZORA (Zeroth Order Regular Approximation of the Dirac Fock equation) formalism in Ab Initio electronic structure calculations. The ZORA method, which has been tested previously in the context of Density Functional Theory, has been implemented in
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.)
International Nuclear Information System (INIS)
Rodricks, J.V.
1992-01-01
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
DEFF Research Database (Denmark)
Petersen, Kurt Erling
1986-01-01
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...
Evaluation of mixing rules for VLE calculations
International Nuclear Information System (INIS)
Adachi, Y.; Chung, W.K.; Lu, B.C.Y.; Yu, J.M.
1983-01-01
This chapter calculates vapor-liquid equilibrium (VLE) values for a number of binary systems of cryogenic interest, including hydrogen- and helium-containing mixtures, by means of several selected cubic equations of state using different sets of mixing rules. The aim is to test the capabilities of these equations for representing VLE values for the selected mixtures, and to identify and recommend the most suitable equation of state together with its compatible mixing rules for the desired data representation. It is determined that the conventional mixing rules together with the modified van der Waals equation, or the four-parameter equation, are suitable for calculating VLE values for the selected systems at cryogenic conditions. The Peng-Robinson and four-parameter equations may yield slightly better results for helium-containing systems
NLOM - a program for nonlocal optical model calculations
International Nuclear Information System (INIS)
Kim, B.T.; Kyum, M.C.; Hong, S.W.; Park, M.H.; Udagawa, T.
1992-01-01
A FORTRAN program NLOM for nonlocal optical model calculations is described. It is based on a method recently developed by Kim and Udagawa, which utilizes the Lanczos technique for solving integral equations derived from the nonlocal Schroedinger equation. (orig.)
International Nuclear Information System (INIS)
Lebedev, D.R.
1979-01-01
Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown
Fractional Schroedinger equation
International Nuclear Information System (INIS)
Laskin, Nick
2002-01-01
Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations
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
International Nuclear Information System (INIS)
Ichiguchi, Katsuji
1998-01-01
A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)
The calculation of Feshbach resonances using coupled propagator equations
International Nuclear Information System (INIS)
Zhan, Hongbin; Zhang, Yinchun; Winkler, P.
1994-01-01
A coupled channel theory of resonances has been formulated within the propagator approach of man-body theory and applied to the 1s3s 2 resonance of e-helium scattering. This system has previously been studied both experimentally and theoretically. These results for the width of the resonance agree well with these earlier findings
The 'strength' of a system of differential equations
International Nuclear Information System (INIS)
Hoenselaers, C.
1977-01-01
A review of Einstein's concept of ''strength'' of a system of differential equations is given. As an example the strength of the Einstein-Maxwell equations for non-null Maxwell field is calculated and shown to be the same as for the pure vacuum Einstein equations. (auth.)
Internal Dosimetric Calculations for Occupationally Exposed Workers
International Nuclear Information System (INIS)
Hussein, M.T.; Farag, H.I.
2005-01-01
The Internal radiation dosimetry calculations are very important to estimate the benefit and the risk of radiation in nuclear medicine field for both patient and worker. MIRD scheme and ICRP model have valid methods in this type of calculations. In this work, a new program called WIRDST the Workers Internal Radiation Dosimetry Simulation for Thyroid gland has been built up by using the Monte Carlo (MC) method to simulate the internal exposure of sodium iodide by inhalation for workers. The working conditions have been taken as the same as found in the hot laboratory of nuclear medicine unit in the National Cancer Institute in Cairo University. The point source equivalent model as a parameterization equation has developed newly by using the fitting model of MC method for uniform distribution of radioactive sodium iodide in the thyroid gland. This model is used for the first time in this type of calculation, and then applied on 3 D coordinates of mathematical geometry for the adult phantom of the reference man. The latest parameters (anatomical data and inhalation metabolic data) of ICRP pamphlets and recommendations have been used in this purpose. Moreover, the latest scheme for iodine decay mode and the latest geometry model for thyroid gland are used also. The results showed that the specific effective energy and the effective dose decrease from the thyroid gland to the nearest organs then decrease gradually until terminated in the organs that have large distance from the thyroid. The Annual Limit of Intake (ALI) has been calculated for a wide range of thyroid uptake (5%, 15%, 25%, 35%, 45%, and 55%) in addition to change of the working time order per week in one year. The results showed that the critical point of intake limits are decreased when the thyroid uptake is increased and/or the number of working time in the hot laboratory per week is increased
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.
Adib, Arash; Poorveis, Davood; Mehraban, Farid
2018-03-01
In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.
Calculation of Critical Temperatures by Empirical Formulae
Directory of Open Access Journals (Sweden)
Trzaska J.
2016-06-01
Full Text Available The paper presents formulas used to calculate critical temperatures of structural steels. Equations that allow calculating temperatures Ac1, Ac3, Ms and Bs were elaborated based on the chemical composition of steel. To elaborate the equations the multiple regression method was used. Particular attention was paid to the collection of experimental data which was required to calculate regression coefficients, including preparation of data for calculation. The empirical data set included more than 500 chemical compositions of structural steel and has been prepared based on information available in literature on the subject.
Derivation of new 3D discrete ordinate equations
International Nuclear Information System (INIS)
Ahrens, C. D.
2012-01-01
The Sn equations have been the workhorse of deterministic radiation transport calculations for many years. Here we derive two new angular discretizations of the 3D transport equation. The first set of equations, derived using Lagrange interpolation and collocation, retains the classical Sn structure, with the main difference being how the scattering source is calculated. Because of the formal similarity with the classical S n equations, it should be possible to modify existing computer codes to take advantage of the new formulation. In addition, the new S n-like equations correctly capture delta function scattering. The second set of equations, derived using a Galerkin technique, does not retain the classical Sn structure because the streaming term is not diagonal. However, these equations can be cast into a form similar to existing methods developed to reduce ray effects. Numerical investigation of both sets of equations is under way. (authors)
Calculation of cell face velocity of non-staggered grid system
Li, Wang; Yu, Bo; Wang, Xinran; Sun, Shuyu
2012-01-01
In this paper, the cell face velocities in the discretization of the continuity equation, the momentum equation, and the scalar equation of a non-staggered grid system are calculated and discussed. Both the momentum interpolation and the linear
The numerical solution of linear multi-term fractional differential equations: systems of equations
Edwards, John T.; Ford, Neville J.; Simpson, A. Charles
2002-11-01
In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.
International Nuclear Information System (INIS)
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 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (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
Resolution of hydrodynamical equations for transverse expansions
International Nuclear Information System (INIS)
Hama, Y.; Pottag, F.W.
1984-01-01
The three-dimensional hydrodynamical expansion is treated with a method similar to that of Milekhin, but more explicit. Although in the final stage one have to appeal to numerical calculation, the partial differential equations governing the transverse expansions are treated without transforming them into ordinary equations with an introduction of averaged quantities. It is only concerned with the formalism and the numerical results will be given in the next paper. (Author) [pt
Resolution of hydrodynamical equations for transverse expansions
International Nuclear Information System (INIS)
Hama, Y.; Pottag, F.W.
1985-01-01
The three-dimensional hydrodynamical expansion is treated with a method similar to that of Milekhin, but more explicit. Although in the final stage we have to appeal to numerical calculation, the partial differential equations governing the transverse expansions are treated without transforming them into ordinary equations with an introduction of averaged quantities. The present paper is concerned with the formalism and the numerical results will be reported in another paper. (Author) [pt
Symmetrized neutron transport equation and the fast Fourier transform method
International Nuclear Information System (INIS)
Sinh, N.Q.; Kisynski, J.; Mika, J.
1978-01-01
The differential equation obtained from the neutron transport equation by the application of the source iteration method in two-dimensional rectangular geometry is transformed into a symmetrized form with respect to one of the angular variables. The discretization of the symmetrized equation leads to finite difference equations based on the five-point scheme and solved by use of the fast Fourier transform method. Possible advantages of the approach are shown on test calculations
Darboux invariants of integrable equations with variable spectral parameters
International Nuclear Information System (INIS)
Shin, H J
2008-01-01
The Darboux transformation for integrable equations with variable spectral parameters is introduced. Darboux invariant quantities are calculated, which are used in constructing the Lax pair of integrable equations. This approach serves as a systematic method for constructing inhomogeneous integrable equations and their soliton solutions. The structure functions of variable spectral parameters determine the integrability and nonlinear coupling terms. Three cases of integrable equations are treated as examples of this approach
Functional equations with causal operators
Corduneanu, C
2003-01-01
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.
Ordinary differential equation for local accumulation time.
Berezhkovskii, Alexander M
2011-08-21
Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation. © 2011 American Institute of Physics
Non-perturbative background field calculations
International Nuclear Information System (INIS)
Stephens, C.R.; Department of Physics, University of Utah, Salt Lake City, Utah 84112)
1988-01-01
New methods are developed for calculating one loop functional determinants in quantum field theory. Instead of relying on a calculation of all the eigenvalues of the small fluctuation equation, these techniques exploit the ability of the proper time formalism to reformulate an infinite dimensional field theoretic problem into a finite dimensional covariant quantum mechanical analog, thereby allowing powerful tools such as the method of Jacobi fields to be used advantageously in a field theory setting. More generally the methods developed herein should be extremely valuable when calculating quantum processes in non-constant background fields, offering a utilitarian alternative to the two standard methods of calculation: perturbation theory in the background field or taking the background field into account exactly. The formalism developed also allows for the approximate calculation of covariances of partial differential equations from a knowledge of the solutions of a homogeneous ordinary differential equation. copyright 1988 Academic Press, Inc
Colorectal Cancer Risk Assessment Tool
... 11/12/2014 Risk Calculator About the Tool Colorectal Cancer Risk Factors Download SAS and Gauss Code Page ... Rectal Cancer: Prevention, Genetics, Causes Tests to Detect Colorectal Cancer and Polyps Cancer Risk Prediction Resources Update November ...
Kinetic equation solution by inverse kinetic method
International Nuclear Information System (INIS)
Salas, G.
1983-01-01
We propose a computer program (CAMU) which permits to solve the inverse kinetic equation. The CAMU code is written in HPL language for a HP 982 A microcomputer with a peripheral interface HP 9876 A ''thermal graphic printer''. The CAMU code solves the inverse kinetic equation by taking as data entry the output of the ionization chambers and integrating the equation with the help of the Simpson method. With this program we calculate the evolution of the reactivity in time for a given disturbance
Complex solutions for generalised fitzhughnagumo equation
International Nuclear Information System (INIS)
Neirameh, A.
2014-01-01
During present investigation, a direct algebraic method on complex solutions of nonlinear partial differential equation is developed and tested in the case of generalized Burgers-Huxley equation. The proposed scheme can be used in a wide class of nonlinear reaction-diffusion equations. These calculations demonstrate that the accuracy of the direct algebraic solutions is quite high even in the case of a small number of grid points. This method is a very reliable, simple, small computation costs, flexible, and convenient alternative method. (author)
Saha's ionization equation for high Z elements
International Nuclear Information System (INIS)
Godwal, B.K.; Sikka, S.K.
1977-01-01
Saha's ionization equation has been solved for high Z elements with the aim of providing input for opacity calculations. Results are presented for two elements, tungsten and uranium. The ionization potentials have been evaluated using the simple Bhor's formula with suitable effective charges for ions. The reliability of the free electron density, ion concentrations, etc., obtained from the Saha's equation solutions has been checked by comparing the P and E computed from them with those given by the Thomas-Fermi-Dirac equation of state. The agreement between the two is good from temperatures above 0.2 keV. (author)
Scalar potentials and the Dirac equation
International Nuclear Information System (INIS)
Bergerhoff, B.; Soff, G.
1994-01-01
The Dirac equation is solved for various types of scalar potentials. Energy eigenvalues and normalized bound-state wave functions are calculated analytically for a scalar 1/r-potential as well as for a mixed scalar and Coulomb 1/r-potential. Also continuum wave functions for positive and negative energies are derived. Similarly, we investigate the solutions of the Dirac equation for a scalar square-well potential. Relativistic wave functions for scalar Yukawa and exponential potentials are determined numerically. Finally, we also discuss solutions of the Dirac equation for scalar linear and quadratic potentials which are frequently used to simulate quark confinement. (orig.)
Equilibrium calculations for helical axis stellarators
International Nuclear Information System (INIS)
Hender, T.C.; Carreras, B.A.
1984-04-01
An average method based on a vacuum flux coordinate system is presented. This average method permits the study of helical axis stellarators with toroidally dominated shifts. An ordering is introduced, and to lowest order the toroidally averaged equilibrium equations are reduced to a Grad-Shafranov equation. Also, to lowest order, a Poisson-type equation is obtained for the toroidally varying corrections to the equilibium. By including these corrections, systems that are toroidally dominated, but with significant helical distortion to the equilibrium, may be studied. Numerical solutions of the average method equations are shown to agree well with three-dimensional calculations
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
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.
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.
Degenerate nonlinear diffusion equations
Favini, Angelo
2012-01-01
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...
Low-density lipoprotein cholesterol and the risk of cancer: a mendelian randomization study
DEFF Research Database (Denmark)
Benn, Marianne; Tybjærg-Hansen, Anne; Stender, Stefan
2011-01-01
cholesterol was calculated using the Friedewald equation in samples in which the triglyceride level was less than 354 mg/dL and measured directly by colorimetry for samples with higher triglyceride levels. Risk of cancer was estimated prospectively using Cox proportional hazards regression analyses and cross...
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.
Reactimeter dispersion equation
A.G. Yuferov
2016-01-01
The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...
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.
International Nuclear Information System (INIS)
Laenen, E.
1995-01-01
We propose a new evolution equation for the gluon density relevant for the region of small x B . 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 multigluon correlations, and allowing for an arbitrary initial gluon distribution in a hadron. We solve the new equation for fixed α s . We find that the effects of multigluon correlations on the deep-inelastic structure function are small. (orig.)
State-dependent neutral delay equations from population dynamics.
Barbarossa, M V; Hadeler, K P; Kuttler, C
2014-10-01
A novel class of state-dependent delay equations is derived from the balance laws of age-structured population dynamics, assuming that birth rates and death rates, as functions of age, are piece-wise constant and that the length of the juvenile phase depends on the total adult population size. The resulting class of equations includes also neutral delay equations. All these equations are very different from the standard delay equations with state-dependent delay since the balance laws require non-linear correction factors. These equations can be written as systems for two variables consisting of an ordinary differential equation (ODE) and a generalized shift, a form suitable for numerical calculations. It is shown that the neutral equation (and the corresponding ODE--shift system) is a limiting case of a system of two standard delay equations.
Scattering integral equations and four nucleon problem
International Nuclear Information System (INIS)
Narodetskii, I.M.
1980-01-01
Existing results from the application of integral equation technique to the four-nucleon bound states and scattering are reviewed. The first numerical calculations of the four-body integral equations have been done ten years ago. Yet, it is still widely believed that these equations are too complicated to solve numerically. The purpose of this review is to provide a clear and elementary introduction in the integral equation method and to demonstrate its usefulness in physical applications. The presentation is based on the quasiparticle approach. This permits a simple interpretation of the equations in terms of quasiparticle scattering. The mathematical basis for the quasiparticle approach is the Hilbert-Schmidt method of the Fredholm integral equation theory. The first part of this review contains a detailed discussion of the Hilbert-Schmidt expansion as applied to the 2-particle amplitudes and to the kernel of the four-body equations. The second part contains the discussion of the four-body quasiparticle equations and of the resed forullts obtain bound states and scattering
Oscillation results for certain fractional difference equations
Directory of Open Access Journals (Sweden)
Zhiyun WANG
2017-08-01
Full Text Available Fractional calculus is a theory that studies the properties and application of arbitrary order differentiation and integration. It can describe the physical properties of some systems more accurately, and better adapt to changes in the system, playing an important role in many fields. For example, it can describe the process of tumor growth (growth stimulation and growth inhibition in biomedical science. The oscillation of solutions of two kinds of fractional difference equations is studied, mainly using the proof by contradiction, that is, assuming the equation has a nonstationary solution. For the first kind of equation, the function symbol is firstly determined, and by constructing the Riccati function, the difference is calculated. Then the condition of the function is used to satisfy the contradiction, that is, the assumption is false, which verifies the oscillation of the solution. For the second kind of equation with initial condition, the equivalent fractional sum form of the fractional difference equation are firstly proved. With considering 0<α≤1 and α>1, respectively, by using the properties of Stirling formula and factorial function, the contradictory is got through enhanced processing, namely the assuming is not established, and the sufficient condition for the bounded solutions of the fractional difference equation is obtained. The above results will optimize the relevant conclusions and enrich the relevant results. The results are applied to the specific equations, and the oscillation of the solutions of equations is proved.
Relativistic wave equations and compton scattering
International Nuclear Information System (INIS)
Sutanto, S.H.; Robson, B.A.
1998-01-01
Full text: Recently an eight-component relativistic wave equation for spin-1/2 particles was proposed.This equation was obtained from a four-component spin-1/2 wave equation (the KG1/2 equation), which contains second-order derivatives in both space and time, by a procedure involving a linearisation of the time derivative analogous to that introduced by Feshbach and Villars for the Klein-Gordon equation. This new eight-component equation gives the same bound-state energy eigenvalue spectra for hydrogenic atoms as the Dirac equation but has been shown to predict different radiative transition probabilities for the fine structure of both the Balmer and Lyman a-lines. Since it has been shown that the new theory does not always give the same results as the Dirac theory, it is important to consider the validity of the new equation in the case of other physical problems. One of the early crucial tests of the Dirac theory was its application to the scattering of a photon by a free electron: the so-called Compton scattering problem. In this paper we apply the new theory to the calculation of Compton scattering to order e 2 . It will be shown that in spite of the considerable difference in the structure of the new theory and that of Dirac the cross section is given by the Klein-Nishina formula
Direct Discrete Method for Neutronic Calculations
International Nuclear Information System (INIS)
Vosoughi, Naser; Akbar Salehi, Ali; Shahriari, Majid
2002-01-01
The objective of this paper is to introduce a new direct method for neutronic calculations. This method which is named Direct Discrete Method, is simpler than the neutron Transport equation and also more compatible with physical meaning of problems. This method is based on physic of problem and with meshing of the desired geometry, writing the balance equation for each mesh intervals and with notice to the conjunction between these mesh intervals, produce the final discrete equations series without production of neutron transport differential equation and mandatory passing from differential equation bridge. We have produced neutron discrete equations for a cylindrical shape with two boundary conditions in one group energy. The correction of the results from this method are tested with MCNP-4B code execution. (authors)
Thermohydraulic calculations of PWR primary circuits
International Nuclear Information System (INIS)
Botelho, D.A.
1984-01-01
Some mathematical and numerical models from Retran computer codes aiming to simulate reactor transients, are presented. The equations used for calculating one-dimensional flow are integrated using mathematical methods from Flash code, with steam code to correlate the variables from thermodynamic state. The algorithm obtained was used for calculating a PWR reactor. (E.G.) [pt
Manca, V.; Salibra, A.; Scollo, Giuseppe
1990-01-01
Equational type logic is an extension of (conditional) equational logic, that enables one to deal in a single, unified framework with diverse phenomena such as partiality, type polymorphism and dependent types. In this logic, terms may denote types as well as elements, and atomic formulae are either
Alternative equations of gravitation
International Nuclear Information System (INIS)
Pinto Neto, N.
1983-01-01
It is shown, trough a new formalism, that the quantum fluctuation effects of the gravitational field in Einstein's equations are analogs to the effects of a continuum medium in Maxwell's Electrodynamics. Following, a real example of the applications of these equations is studied. Qunatum fluctuations effects as perturbation sources in Minkowski and Friedmann Universes are examined. (L.C.) [pt
Energy Technology Data Exchange (ETDEWEB)
Yagi, M. [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Horton, W. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies
1993-11-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite {beta} that we solve the perpendicular component of Ohm`s law to conserve the physical energy while ensuring the relation {del} {center_dot} j = 0.
International Nuclear Information System (INIS)
Yagi, M.; Horton, W.
1993-11-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that we solve the perpendicular component of Ohm's law to conserve the physical energy while ensuring the relation ∇ · j = 0
International Nuclear Information System (INIS)
Yagi, M.; Horton, W.
1994-01-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that the perpendicular component of Ohm's law be solved to ensure ∇·j=0 for energy conservation
African Journals Online (AJOL)
The currently proposed model compaction equation was derived from data sourced from the. Niger Delta and it relates porosity to depth for sandstones under hydrostatic pressure condition. The equation is useful in predicting porosity and compaction trend in hydrostatic sands of the. Niger Delta. GEOLOGICAL SETTING OF ...
M. Hazewinkel (Michiel)
1995-01-01
textabstractDedication: 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
The generalized Fermat equation
Beukers, F.
2006-01-01
This article will be devoted to generalisations of Fermat’s equation xn + yn = zn. Very soon after the Wiles and Taylor proof of Fermat’s Last Theorem, it was wondered what would happen if the exponents in the three term equation would be chosen differently. Or if coefficients other than 1 would
Rotor calculations for neutron spectroscopy
International Nuclear Information System (INIS)
Gobert, G.
1968-01-01
The determination of stress in a rotating disk plane of symmetry normal to the axis of rotation has been studied by a number of investigators. In a recent paper Reich gives an operating process for an analytical solution in an asymmetric rotating disk. In the report we give the calculation of finite difference stress solutions applicable to the two rotating disks. The equations are then programmed for the 360.75 computer by Fortran methods concerning the rotors of choppers. (author) [fr
Configuration space Faddeev calculations
International Nuclear Information System (INIS)
Payne, G.L.; Klink, W.H.; Polyzou, W.N.
1989-01-01
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
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...
Hamming generalized corrector for reactivity calculation
International Nuclear Information System (INIS)
Suescun-Diaz, Daniel; Ibarguen-Gonzalez, Maria C.; Figueroa-Jimenez, Jorge H.
2014-01-01
This work presents the Hamming method generalized corrector for numerically resolving the differential equation of delayed neutron precursor concentration from the point kinetics equations for reactivity calculation, without using the nuclear power history or the Laplace transform. A study was carried out of several correctors with their respective modifiers with different time step calculations, to offer stability and greater precision. Better results are obtained for some correctors than with other existing methods. Reactivity can be calculated with precision of the order h 5 , where h is the time step. (orig.)
Deriving the bond pricing equation
Directory of Open Access Journals (Sweden)
Kožul Nataša
2014-01-01
Full Text Available Given the recent focus on Eurozone debt crisis and the credit rating downgrade not only of US debt, but that of other countries and many UK major banking institutions, this paper aims to explain the concept of bond yield, its different measures and bond pricing equation. Yields on capital market instruments are rarely quoted on the same basis, which makes direct comparison between different as investment choices impossible. Some debt instruments are quoted on discount basis, whilst coupon-bearing ones accrue interest differently, offer different compounding opportunities, have different coupon payment frequencies, and manage non-business day maturity dates differently. Moreover, rules governing debt vary across countries, markets and currencies, making yield calculation and comparison a rather complex issue. Thus, some fundamental concepts applicable to debt instrument yield measurement, with focus on bond equation, are presented here. In addition, bond equation expressed in annuity form and used to apply Newton-Raphson algorithm to derive true bond yield is also shown.
International Nuclear Information System (INIS)
Briere, J.; Philippon, B.
1979-01-01
An LiF dosimeter placed inside the uterus will only give an approximate value of the dose delivered to gonads during therapy by iodine-131. But it was easily demonstrated that the dose measured by LTD dosimeter does not significantly differ for uterus and for ovaries, because of the similar position of the source organs. Consequently a LiF dosimeter was placed in volunteer patients inside the uterus. Experimental results were compared to the dose calculated by Robertson and Gorman (J. Nucl. Med. 17, 826, (1976)) method for ovaries and for uterus. (author)
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.
Nuclear fission with a Langevin equation
International Nuclear Information System (INIS)
Boilley, D.; Suraud, E.; Abe, Yasuhisa
1992-01-01
A microscopically derived Langevin equation is applied to thermally induced nuclear fission. An important memory effect is pointed out and discussed. A strong friction coefficient, estimated from microscopic quantities, tends to decrease the stationary limit of the fission rate and to increase the transient time. The calculations are performed with a collective mass depending on the collective variable and with a constant mass. Fission rates calculated at different temperatures are shown and compared with previous available results. (author) 23 refs.; 7 figs
Gravitational closure of matter field equations
Düll, Maximilian; Schuller, Frederic P.; Stritzelberger, Nadine; Wolz, Florian
2018-04-01
The requirement that both the matter and the geometry of a spacetime canonically evolve together, starting and ending on shared Cauchy surfaces and independently of the intermediate foliation, leaves one with little choice for diffeomorphism-invariant gravitational dynamics that can equip the coefficients of a given system of matter field equations with causally compatible canonical dynamics. Concretely, we show how starting from any linear local matter field equations whose principal polynomial satisfies three physicality conditions, one may calculate coefficient functions which then enter an otherwise immutable set of countably many linear homogeneous partial differential equations. Any solution of these so-called gravitational closure equations then provides a Lagrangian density for any type of tensorial geometry that features ultralocally in the initially specified matter Lagrangian density. Thus the given system of matter field equations is indeed closed by the so obtained gravitational equations. In contrast to previous work, we build the theory on a suitable associated bundle encoding the canonical configuration degrees of freedom, which allows one to include necessary constraints on the geometry in practically tractable fashion. By virtue of the presented mechanism, one thus can practically calculate, rather than having to postulate, the gravitational theory that is required by specific matter field dynamics. For the special case of standard model matter one obtains general relativity.
Directory of Open Access Journals (Sweden)
Jean Paolo Gomes Minella
2010-08-01
Full Text Available Métodos de representação espacial para o cálculo do fator topográfico (LS da Equação Universal de Perda de Solo Revisada (RUSLE têm sido utilizados para estimar a erosão do solo e a produção de sedimentos em bacias hidrográficas. Esses procedimentos baseiam-se nas equações tradicionalmente empregadas para determinação do fator LS e em informações que caracterizam a forma das vertentes derivadas do modelo numérico de elevação (MNE. Neste estudo foram analisados dois métodos de representação espacial utilizados no cálculo do fator LS em modelos matemáticos de erosão e produção de sedimentos em bacias hidrográficas. A análise foi realizada em quatro bacias rurais de relevo movimentado. Os valores de LS obtidos pelos métodos de representação espacial foram comparados entre si e com valores de LS determinados pelo método tradicional com levantamento em campo. Resultados mostraram que os valores de LS gerados pelos métodos de representação espacial apresentam diferenças significativas entre si, sendo dependentes do procedimento de cálculo e do método utilizado para determinar a direção de fluxo no MNE. Também foi verificado que os valores numéricos do fator LS determinados pelos métodos de representação espacial apresentam diferenças em relação àqueles estimados pelo método tradicional.Methods of spatial representation to calculate the topographic factor (LS of the Revised Universal Soil Loss Equation (USLE have been used to estimate soil erosion and sediment yield of watersheds. These procedures are based on equations traditionally used to determine the LS factor and information that characterize the hillslope forms and processes, derived from the Digital Elevation Model (DEM. Two computational methods commonly used to calculate LS factor in soil erosion and sediment yield models were analyzed in this study. The analysis was performed in four small rural watersheds with hilly terrain. The LS values
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
Integration of Chandrasekhar's integral equation
International Nuclear Information System (INIS)
Tanaka, Tasuku
2003-01-01
We solve Chandrasekhar's integration equation for radiative transfer in the plane-parallel atmosphere by iterative integration. The primary thrust in radiative transfer has been to solve the forward problem, i.e., to evaluate the radiance, given the optical thickness and the scattering phase function. In the area of satellite remote sensing, our problem is the inverse problem: to retrieve the surface reflectance and the optical thickness of the atmosphere from the radiance measured by satellites. In order to retrieve the optical thickness and the surface reflectance from the radiance at the top-of-the atmosphere (TOA), we should express the radiance at TOA 'explicitly' in the optical thickness and the surface reflectance. Chandrasekhar formalized radiative transfer in the plane-parallel atmosphere in a simultaneous integral equation, and he obtained the second approximation. Since then no higher approximation has been reported. In this paper, we obtain the third approximation of the scattering function. We integrate functions derived from the second approximation in the integral interval from 1 to ∞ of the inverse of the cos of zenith angles. We can obtain the indefinite integral rather easily in the form of a series expansion. However, the integrals at the upper limit, ∞, are not yet known to us. We can assess the converged values of those series expansions at ∞ through calculus. For integration, we choose coupling pairs to avoid unnecessary terms in the outcome of integral and discover that the simultaneous integral equation can be deduced to the mere integral equation. Through algebraic calculation, we obtain the third approximation as a polynomial of the third degree in the atmospheric optical thickness
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
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
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
Supersymmetric quasipotential equations
International Nuclear Information System (INIS)
Zaikov, R.P.
1981-01-01
A supersymmetric extension of the Logunov-Tavkhelidze quasipotential approach is suggested. The supersymmetric Bethe- Salpeter equation is an initial equation. The transition from the four-time to the two-time Green function is made in the super- center-of-mass system. The two-time Green function has no inverse function in the whole spinor space. The resolvent operator if found using the Majorana character of the spinor wave function. The supersymmetric quasipotential equation is written. The consideration is carried out in the framework of the theory of chiral scalar superfields [ru
Local instant conservation equations
International Nuclear Information System (INIS)
Delaje, Dzh.
1984-01-01
Local instant conservation equations for two-phase flow are derived. Derivation of the equation starts from the recording of integral laws of conservation for a fixed reference volume, containing both phases. Transformation of the laws, using the Leibniz rule and Gauss theory permits to obtain the sum of two integrals as to the volume and integral as to the surface. Integrals as to the volume result in local instant differential equations, in particular derivatives for each phase, and integrals as to the surface reflect local instant conditions of a jump on interface surface
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
Ordinary differential equations
Miller, Richard K
1982-01-01
Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,
Uncertain differential equations
Yao, Kai
2016-01-01
This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.
40 CFR 98.363 - Calculating GHG emissions.
2010-07-01
... combustion device (metric tons CH4/yr). V = Average annual volumetric flow rate, calculated in Equation JJ-7... CH4 flow to digester combustion device, as calculated in Equation JJ-6 of this section (metric tons CH4). DE = CH4 destruction efficiency from flaring or burning in engine (lesser of manufacturer's...
Electron transfer dynamics: Zusman equation versus exact theory
International Nuclear Information System (INIS)
Shi Qiang; Chen Liping; Nan Guangjun; Xu Ruixue; Yan Yijing
2009-01-01
The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations.
Equations of motion for train derailment dynamics
2007-09-11
This paper describes a planar or two-dimensional model to : examine the gross motions of rail cars in a generalized train : derailment. Three coupled, second-order differential equations : are derived from Newton's Laws to calculate rigid-body car : ...
Self-similar solutions of the modified nonlinear schrodinger equation
International Nuclear Information System (INIS)
Kitaev, A.V.
1986-01-01
This paper considers a 2 x 2 matrix linear ordinary differential equation with large parameter t and irregular singular point of fourth order at infinity. The leading order of the monodromy data of this equation is calculated in terms of its coefficients. Isomonodromic deformations of the equation are self-similar solutions of the modified nonlinear Schrodinger equation, and therefore inversion of the expressions obtained for the monodromy data gives the leading term in the time-asymptotic behavior of the self-similar solution. The application of these results to the type IV Painleve equation is considered in detail
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.
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...
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.
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.
Equations For Rotary Transformers
Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.
1988-01-01
Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.
Problems in differential equations
Brenner, J L
2013-01-01
More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.
Applied partial differential equations
DuChateau, Paul
2012-01-01
Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.
Nonlinear differential equations
International Nuclear Information System (INIS)
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
Saaty, Thomas L
1981-01-01
Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.
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.
Structural Equations and Causation
Hall, Ned
2007-01-01
Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.
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.
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…
Equations of radiation hydrodynamics
International Nuclear Information System (INIS)
Mihalas, D.
1982-01-01
The purpose of this paper is to give an overview of the role of radiation in the transport of energy and momentum in a combined matter-radiation fluid. The transport equation for a moving radiating fluid is presented in both a fully Eulerian and a fully Lagrangian formulation, along with conservation equations describing the dynamics of the fluid. Special attention is paid to the problem of deriving equations that are mutually consistent in each frame, and between frames, to 0(v/c). A detailed analysis is made to show that in situations of broad interest, terms that are formally of 0(v/c) actually dominate the solution, demonstrating that it is esential (1) to pay scrupulous attention to the question of the frame dependence in formulating the equations; and (2) to solve the equations to 0(v/c) in quite general circumstances. These points are illustrated in the context of the nonequilibrium radiation diffusion limit, and a sketch of how the Lagrangian equations are to be solved will be presented
Quantum linear Boltzmann equation
International Nuclear Information System (INIS)
Vacchini, Bassano; Hornberger, Klaus
2009-01-01
We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.
Covariant field equations in supergravity
Energy Technology Data Exchange (ETDEWEB)
Vanhecke, Bram [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium); Ghent University, Faculty of Physics, Gent (Belgium); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)
2017-12-15
Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Covariant field equations in supergravity
International Nuclear Information System (INIS)
Vanhecke, Bram; Proeyen, Antoine van
2017-01-01
Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Differential Equation over Banach Algebra
Kleyn, Aleks
2018-01-01
In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.
Zero Temperature Hope Calculations
International Nuclear Information System (INIS)
Rozsnyai, B. F.
2002-01-01
The primary purpose of the HOPE code is to calculate opacities over a wide temperature and density range. It can also produce equation of state (EOS) data. Since the experimental data at the high temperature region are scarce, comparisons of predictions with the ample zero temperature data provide a valuable physics check of the code. In this report we show a selected few examples across the periodic table. Below we give a brief general information about the physics of the HOPE code. The HOPE code is an ''average atom'' (AA) Dirac-Slater self-consistent code. The AA label in the case of finite temperature means that the one-electron levels are populated according to the Fermi statistics, at zero temperature it means that the ''aufbau'' principle works, i.e. no a priory electronic configuration is set, although it can be done. As such, it is a one-particle model (any Hartree-Fock model is a one particle model). The code is an ''ion-sphere'' model, meaning that the atom under investigation is neutral within the ion-sphere radius. Furthermore, the boundary conditions for the bound states are also set at the ion-sphere radius, which distinguishes the code from the INFERNO, OPAL and STA codes. Once the self-consistent AA state is obtained, the code proceeds to generate many-electron configurations and proceeds to calculate photoabsorption in the ''detailed configuration accounting'' (DCA) scheme. However, this last feature is meaningless at zero temperature. There is one important feature in the HOPE code which should be noted; any self-consistent model is self-consistent in the space of the occupied orbitals. The unoccupied orbitals, where electrons are lifted via photoexcitation, are unphysical. The rigorous way to deal with that problem is to carry out complete self-consistent calculations both in the initial and final states connecting photoexcitations, an enormous computational task. The Amaldi correction is an attempt to address this problem by distorting the
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.
The polaron problem and the Boltzmann equation
International Nuclear Information System (INIS)
Devreese, J.
1979-01-01
A mobility theory for the Feynman polaron is developed. It is shown that the Boltzmann equation for polarons is valid for weak coupling and not too high electric fields. The analytical results indicate that for E → 0 the relaxation time approximation is valid. A comparison is made of three methods to calculate the mobility in a linear electron transport theory. An approximation to the Kubo formula, a mobility calculation using path integrals by Feynman and a calculation based on the displaced Maxwell distribution function are considered. The three methods lead to equivalent results in the weak scattering and small electric field limit
New nonlinear methods for linear transport calculations
International Nuclear Information System (INIS)
Adams, M.L.
1993-01-01
We present a new family of methods for the numerical solution of the linear transport equation. With these methods an iteration consists of an 'S N sweep' followed by an 'S 2 -like' calculation. We show, by analysis as well as numerical results, that iterative convergence is always rapid. We show that this rapid convergence does not depend on a consistent discretization of the S 2 -like equations - they can be discretized independently from the S N equations. We show further that independent discretizations can offer significant advantages over consistent ones. In particular, we find that in a wide range of problems, an accurate discretization of the S 2 -like equation can be combined with a crude discretization of the S N equations to produce an accurate S N answer. We demonstrate this by analysis as well as numerical results. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Roosta, Sara [Molecular Simulation Research Laboratory, Department of Chemistry, Iran University of Science & Technology, Tehran (Iran, Islamic Republic of); Hashemianzadeh, Seyed Majid, E-mail: hashemianzadeh@iust.ac.ir [Molecular Simulation Research Laboratory, Department of Chemistry, Iran University of Science & Technology, Tehran (Iran, Islamic Republic of); Ketabi, Sepideh, E-mail: sepidehketabi@yahoo.com [Department of Chemistry, East Tehran Branch, Islamic Azad University, Tehran (Iran, Islamic Republic of)
2016-10-01
Encapsulation of cisplatin anticancer drug into the single walled (10, 0) carbon nanotube and (10, 0) boron-nitride nanotube was investigated by quantum mechanical calculations and Monte Carlo Simulation in aqueous solution. Solvation free energies and complexation free energies of the cisplatin@ carbon nanotube and cisplatin@ boron-nitride nanotube complexes was determined as well as radial distribution functions of entitled compounds. Solvation free energies of cisplatin@ carbon nanotube and cisplatin@ boron-nitride nanotube were − 4.128 kcal mol{sup −1} and − 2457.124 kcal mol{sup −1} respectively. The results showed that cisplatin@ boron-nitride nanotube was more soluble species in water. In addition electrostatic contribution of the interaction of boron- nitride nanotube complex and solvent was − 281.937 kcal mol{sup −1} which really more than Van der Waals and so the electrostatic interactions play a distinctive role in the solvation free energies of boron- nitride nanotube compounds. On the other hand electrostatic part of the interaction of carbon nanotube complex and solvent were almost the same as Van der Waals contribution. Complexation free energies were also computed to study the stability of related structures and the free energies were negative (− 374.082 and − 245.766 kcal mol{sup −1}) which confirmed encapsulation of drug into abovementioned nanotubes. However, boron-nitride nanotubes were more appropriate for encapsulation due to their larger solubility in aqueous solution. - Highlights: • Solubility of cisplatin@ boron-nitride nanotube is larger than cisplatin@ carbon nanotube. • Boron- nitride nanotube complexes have larger electrostatic contribution in solvation free energy. • Complexation free energies confirm encapsulation of drug into the nanotubes in aqueous solution. • Boron- nitride nanotubes are appropriate drug delivery systems compared with carbon nanotubes.
International Nuclear Information System (INIS)
Roosta, Sara; Hashemianzadeh, Seyed Majid; Ketabi, Sepideh
2016-01-01
Encapsulation of cisplatin anticancer drug into the single walled (10, 0) carbon nanotube and (10, 0) boron-nitride nanotube was investigated by quantum mechanical calculations and Monte Carlo Simulation in aqueous solution. Solvation free energies and complexation free energies of the cisplatin@ carbon nanotube and cisplatin@ boron-nitride nanotube complexes was determined as well as radial distribution functions of entitled compounds. Solvation free energies of cisplatin@ carbon nanotube and cisplatin@ boron-nitride nanotube were − 4.128 kcal mol"−"1 and − 2457.124 kcal mol"−"1 respectively. The results showed that cisplatin@ boron-nitride nanotube was more soluble species in water. In addition electrostatic contribution of the interaction of boron- nitride nanotube complex and solvent was − 281.937 kcal mol"−"1 which really more than Van der Waals and so the electrostatic interactions play a distinctive role in the solvation free energies of boron- nitride nanotube compounds. On the other hand electrostatic part of the interaction of carbon nanotube complex and solvent were almost the same as Van der Waals contribution. Complexation free energies were also computed to study the stability of related structures and the free energies were negative (− 374.082 and − 245.766 kcal mol"−"1) which confirmed encapsulation of drug into abovementioned nanotubes. However, boron-nitride nanotubes were more appropriate for encapsulation due to their larger solubility in aqueous solution. - Highlights: • Solubility of cisplatin@ boron-nitride nanotube is larger than cisplatin@ carbon nanotube. • Boron- nitride nanotube complexes have larger electrostatic contribution in solvation free energy. • Complexation free energies confirm encapsulation of drug into the nanotubes in aqueous solution. • Boron- nitride nanotubes are appropriate drug delivery systems compared with carbon nanotubes.
The shallow water equations in Lagrangian coordinates
International Nuclear Information System (INIS)
Mead, J.L.
2004-01-01
Recent advances in the collection of Lagrangian data from the ocean and results about the well-posedness of the primitive equations have led to a renewed interest in solving flow equations in Lagrangian coordinates. We do not take the view that solving in Lagrangian coordinates equates to solving on a moving grid that can become twisted or distorted. Rather, the grid in Lagrangian coordinates represents the initial position of particles, and it does not change with time. We apply numerical methods traditionally used to solve differential equations in Eulerian coordinates, to solve the shallow water equations in Lagrangian coordinates. The difficulty with solving in Lagrangian coordinates is that the transformation from Eulerian coordinates results in solving a highly nonlinear partial differential equation. The non-linearity is mainly due to the Jacobian of the coordinate transformation, which is a precise record of how the particles are rotated and stretched. The inverse Jacobian must be calculated, thus Lagrangian coordinates cannot be used in instances where the Jacobian vanishes. For linear (spatial) flows we give an explicit formula for the Jacobian and describe the two situations where the Lagrangian shallow water equations cannot be used because either the Jacobian vanishes or the shallow water assumption is violated. We also prove that linear (in space) steady state solutions of the Lagrangian shallow water equations have Jacobian equal to one. In the situations where the shallow water equations can be solved in Lagrangian coordinates, accurate numerical solutions are found with finite differences, the Chebyshev pseudospectral method, and the fourth order Runge-Kutta method. The numerical results shown here emphasize the need for high order temporal approximations for long time integrations
International Nuclear Information System (INIS)
Kotikov, A.V.
1993-01-01
A new method of massive Feynman diagrams calculation is presented. It provides a fairly simple procedure to obtain the result without the D-space integral calculation (for the dimensional regularization). Some diagrams are calculated as an illustration of this method capacities. (author). 7 refs
Sensitivity of rocky planet structures to the equation of state
International Nuclear Information System (INIS)
Swift, D.C.
2009-01-01
Structures were calculated for Mercury, Venus, Earth, the Moon, and Mars, using a core-mantle model and adjusting the core radius to reproduce the observed mass and diameter of each body. Structures were calculated using Fe and basalt equations of state of different degrees of sophistication for the core and mantle. The choice of equation of state had a significant effect on the inferred structure. For each structure, the moment of inertia ratio was calculated and compared with observed values. Linear Grueneisen equations of state fitted to limited portions of shock data reproduced the observed moments of inertia significantly better than did more detailed equations of state incorporating phase transitions, presumably reflecting the actual compositions of the bodies. The linear Grueneisen equations of state and corresponding structures seem however to be a reasonable starting point for comparative simulations of large-scale astrophysical impacts.
Energy Technology Data Exchange (ETDEWEB)
Wang, X. [Radiology Department, Peking Union Medical College Hospital, Chinese Academy of Medical Sciences, Beijing (China); Henzler, T., E-mail: thomas.henzler@medma.uni-heidelberg.de [Institute of Clinical Radiology and Nuclear Medicine, University Medical Center Mannheim, Medical Faculty Mannheim, Heidelberg University (Germany); Gawlitza, J.; Diehl, S. [Institute of Clinical Radiology and Nuclear Medicine, University Medical Center Mannheim, Medical Faculty Mannheim, Heidelberg University (Germany); Wilhelm, T. [Department of Surgery, University Medical Center Mannheim, Medical Faculty Mannheim, Heidelberg University (Germany); Schoenberg, S.O. [Institute of Clinical Radiology and Nuclear Medicine, University Medical Center Mannheim, Medical Faculty Mannheim, Heidelberg University (Germany); Jin, Z.Y.; Xue, H.D. [Radiology Department, Peking Union Medical College Hospital, Chinese Academy of Medical Sciences, Beijing (China); Smakic, A. [Institute of Clinical Radiology and Nuclear Medicine, University Medical Center Mannheim, Medical Faculty Mannheim, Heidelberg University (Germany)
2016-11-15
Purpose: Dynamic volume perfusion CT (dVPCT) provides valuable information on tissue perfusion in patients with hepatocellular carcinoma (HCC) and pancreatic cancer. However, currently dVPCT is often performed in addition to conventional CT acquisitions due to the limited morphologic image quality of dose optimized dVPCT protocols. The aim of this study was to prospectively compare objective and subjective image quality, lesion detectability and radiation dose between mean temporal arterial (mTA) and mean temporal portal venous (mTPV) images calculated from low dose dynamic volume perfusion CT (dVPCT) datasets with linearly blended 120-kVp arterial and portal venous datasets in patients with HCC and pancreatic cancer. Materials and methods: All patients gave written informed consent for this institutional review board–approved HIPAA compliant study. 27 consecutive patients (18 men, 9 women, mean age, 69.1 years ± 9.4) with histologically proven HCC or suspected pancreatic cancer were prospectively enrolled. The study CT protocol included a dVPCT protocol performed with 70 or 80 kVp tube voltage (18 spiral acquisitions, 71.2 s total acquisition times) and standard dual-energy (90/150 kVpSn) arterial and portal venous acquisition performed 25 min after the dVPCT. The mTA and mTPV images were manually reconstructed from the 3 to 5 best visually selected single arterial and 3 to 5 best single portal venous phases dVPCT dataset. The linearly blended 120-kVp images were calculated from dual-energy CT (DECT) raw data. Image noise, SNR, and CNR of the liver, abdominal aorta (AA) and main portal vein (PV) were compared between the mTA/mTPV and the linearly blended 120-kVp dual-energy arterial and portal venous datasets, respectively. Subjective image quality was evaluated by two radiologists regarding subjective image noise, sharpness and overall diagnostic image quality using a 5-point Likert Scale. In addition, liver lesion detectability was performed for each liver
International Nuclear Information System (INIS)
Wang, X.; Henzler, T.; Gawlitza, J.; Diehl, S.; Wilhelm, T.; Schoenberg, S.O.; Jin, Z.Y.; Xue, H.D.; Smakic, A.
2016-01-01
Purpose: Dynamic volume perfusion CT (dVPCT) provides valuable information on tissue perfusion in patients with hepatocellular carcinoma (HCC) and pancreatic cancer. However, currently dVPCT is often performed in addition to conventional CT acquisitions due to the limited morphologic image quality of dose optimized dVPCT protocols. The aim of this study was to prospectively compare objective and subjective image quality, lesion detectability and radiation dose between mean temporal arterial (mTA) and mean temporal portal venous (mTPV) images calculated from low dose dynamic volume perfusion CT (dVPCT) datasets with linearly blended 120-kVp arterial and portal venous datasets in patients with HCC and pancreatic cancer. Materials and methods: All patients gave written informed consent for this institutional review board–approved HIPAA compliant study. 27 consecutive patients (18 men, 9 women, mean age, 69.1 years ± 9.4) with histologically proven HCC or suspected pancreatic cancer were prospectively enrolled. The study CT protocol included a dVPCT protocol performed with 70 or 80 kVp tube voltage (18 spiral acquisitions, 71.2 s total acquisition times) and standard dual-energy (90/150 kVpSn) arterial and portal venous acquisition performed 25 min after the dVPCT. The mTA and mTPV images were manually reconstructed from the 3 to 5 best visually selected single arterial and 3 to 5 best single portal venous phases dVPCT dataset. The linearly blended 120-kVp images were calculated from dual-energy CT (DECT) raw data. Image noise, SNR, and CNR of the liver, abdominal aorta (AA) and main portal vein (PV) were compared between the mTA/mTPV and the linearly blended 120-kVp dual-energy arterial and portal venous datasets, respectively. Subjective image quality was evaluated by two radiologists regarding subjective image noise, sharpness and overall diagnostic image quality using a 5-point Likert Scale. In addition, liver lesion detectability was performed for each liver
Relativistic few body calculations
International Nuclear Information System (INIS)
Gross, F.
1988-01-01
A modern treatment of the nuclear few-body problem must take into account both the quark structure of baryons and mesons, which should be important at short range, and the relativistic exchange of mesons, which describes the long range, peripheral interactions. A way to model both of these aspects is described. The long range, peripheral interactions are calculated using the spectator model, a general approach in which the spectators to nucleon interactions are put on their mass-shell. Recent numerical results for a relativistic OBE model of the NN interaction, obtained by solving a relativistic equation with one-particle on mass-shell, will be presented and discussed. Two meson exchange models, one with only four mesons (π,σ,/rho/,ω) but with a 25% admixture of γ 5 coupling for the pion, and a second with six mesons (π,σ,/rho/,ω,δ,/eta/) but pure γ 5 γ/sup μ/ pion coupling, are shown to give very good quantitative fits to the NN scattering phase shifts below 400 MeV, and also a good description of the /rvec p/ 40 Ca elastic scattering observables. Applications of this model to electromagnetic interactions of the two body system, with emphasis on the determination of relativistic current operators consistent with the dynamics and the exact treatment of current conservation in the presence of phenomenological form factors, will be described. 18 refs., 8 figs
Configuration space Faddeev calculations
International Nuclear Information System (INIS)
Payne, G.L.; Klink, W.H.; Ployzou, W.N.
1991-01-01
The detailed study of few-body systems provides one of the most precise tools for studying the dynamics of nuclei. Our research program consists of a careful theoretical study of the nuclear few-body systems. During the past year we have completed several aspects of this program. We have continued our program of using the trinucleon system to investigate the validity of various realistic nucleon-nucleon potentials. Also, the effects of meson-exchange currents in nuclear systems have been studied. Initial calculations using the configuration-space Faddeev equations for nucleon-deuteron scattering have been completed. With modifications to treat relativistic systems, few-body methods can be applied to phenomena that are sensitive to the structure of the individual hadrons. We have completed a review of Relativistic Hamiltonian Dynamics in Nuclear and Particle Physics for Advances in Nuclear Physics. Although it is called a review, it is a large document that contains a significant amount of new research
Quantum - statistical equation of state
International Nuclear Information System (INIS)
Kalitkin, N.N.; Kuz'mina, L.V.
1976-01-01
An atom model is considered which allows uniform description of the equation of an equilibrium plasma state in the range of densities from gas to superhigh ones and in the temperature range from 1-5 eV to a ten of keV. Quantum and exchange corrections to the Thomas-Fermi thermodynamic functions at non zero temperatures have been calculated. The calculated values have been compared with experimental data and with calculations performed by more accurate models. The differences result from the fact that a quantum approach does not allow for shell effects. The evaluation of these differences makes it possible to indicate the limits of applicability of the Thomas-Fermi model with quantum and exchange corrections. It turns out that if at zero temperature the model may be applied only for high compressions, at the temperature more than 1 eV it well describes the behaviour of plasma in a very wide range of densities and agrees satisfactorily with experiment even for non-ideal plasma
Vedder, Moniek M; de Bekker-Grob, Esther W; Lilja, Hans G; Vickers, Andrew J; van Leenders, Geert J L H; Steyerberg, Ewout W; Roobol, Monique J
2014-12-01
Prostate-specific antigen (PSA) testing has limited accuracy for the early detection of prostate cancer (PCa). To assess the value added by percentage of free to total PSA (%fPSA), prostate cancer antigen 3 (PCA3), and a kallikrein panel (4k-panel) to the European Randomised Study of Screening for Prostate Cancer (ERSPC) multivariable prediction models: risk calculator (RC) 4, including transrectal ultrasound, and RC 4 plus digital rectal examination (4+DRE) for prescreened men. Participants were invited for rescreening between October 2007 and February 2009 within the Dutch part of the ERSPC study. Biopsies were taken in men with a PSA level ≥3.0 ng/ml or a PCA3 score ≥10. Additional analyses of the 4k-panel were done on serum samples. Outcome was defined as PCa detectable by sextant biopsy. Receiver operating characteristic curve and decision curve analyses were performed to compare the predictive capabilities of %fPSA, PCA3, 4k-panel, the ERSPC RCs, and their combinations in logistic regression models. PCa was detected in 119 of 708 men. The %fPSA did not perform better univariately or added to the RCs compared with the RCs alone. In 202 men with an elevated PSA, the 4k-panel discriminated better than PCA3 when modelled univariately (area under the curve [AUC]: 0.78 vs. 0.62; p=0.01). The multivariable models with PCA3 or the 4k-panel were equivalent (AUC: 0.80 for RC 4+DRE). In the total population, PCA3 discriminated better than the 4k-panel (univariate AUC: 0.63 vs. 0.56; p=0.05). There was no statistically significant difference between the multivariable model with PCA3 (AUC: 0.73) versus the model with the 4k-panel (AUC: 0.71; p=0.18). The multivariable model with PCA3 performed better than the reference model (0.73 vs. 0.70; p=0.02). Decision curves confirmed these patterns, although numbers were small. Both PCA3 and, to a lesser extent, a 4k-panel have added value to the DRE-based ERSPC RC in detecting PCa in prescreened men. We studied the added
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.
On the hierarchy of partially invariant submodels of differential equations
Golovin, Sergey V.
2007-01-01
It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ...
Navier-Stokes-like equations for traffic flow.
Velasco, R M; Marques, W
2005-10-01
The macroscopic traffic flow equations derived from the reduced Paveri-Fontana equation are closed starting with the maximization of the informational entropy. The homogeneous steady state taken as a reference is obtained for a specific model of the desired velocity and a kind of Chapman-Enskog method is developed to calculate the traffic pressure at the Navier-Stokes level. Numerical solution of the macroscopic traffic equations is obtained and its characteristics are analyzed.
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.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Boussinesq evolution equations
DEFF Research Database (Denmark)
Bredmose, Henrik; Schaffer, H.; Madsen, Per A.
2004-01-01
This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...
On the monodromy group for the super Schwarzian differential equation
International Nuclear Information System (INIS)
Uehara, Shozo; Yasui, Yukinori.
1991-03-01
We calculate the first variation of the monodromy group associated with a super Schwarzian differential equation. The relation between the monodromy period and the Fenchel-Nielsen deformation of a super Riemann surface is presented. (author)
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.
On the solution of the Liouville equation over a rectangle
Directory of Open Access Journals (Sweden)
A. M. Arthurs
1996-01-01
Full Text Available Methods for integral equations are used to derive pointwise bounds for the solution of a boundary value problem for the nonlinear Liouville partial differential equation over a rectangle. Several test calculations are performed and the resulting solutions are more accurate than those obtained previously by other methods.
Parametric Equations: Push 'Em Back, Push 'Em Back, Way Back!
Cieply, Joseph F.
1993-01-01
Stresses using the features of graphing calculators to teach parametric equations much earlier in the curriculum than is presently done. Examples using parametric equations to teach slopes and lines in beginning algebra, inverse functions in advanced algebra, the wrapping function, and simulations of physical phenomena are presented. (MAZ)
Perfect fluid cosmological Universes: One equation of state and the ...
Indian Academy of Sciences (India)
Anadijiban Das
2018-01-04
Jan 4, 2018 ... equation of state, one may calculate the geometric vari- ables, such as the ... connected by any analytic function ψ, the evolutions equations, mainly ... [3] J E Marsden and A J Tromba, Vector calculus, 3rd edn. (W. H. Freeman ...
Relativistic hydrodynamics with QHD-I equation of state
International Nuclear Information System (INIS)
Menezes, D.P.
1993-04-01
We derive the equation of state of the QHD-I lagrangian in a classical approach. The obtained equation of state is then used as input in a relativistic hydrodynamical numerical routine. Rapidity and transverse momentum distributions are calculated and compared with experimental data on heavy ion collisions obtained at BNL-AGS and CERN-SPS. (orig.). 7 figs
Dressing symmetry of the uniformization solution of Liouville equation
International Nuclear Information System (INIS)
Shen Jianmin.
1994-10-01
In this paper, the relations between monodromy group and dressing group for Liouville equation in uniformization theorem are discussed. The representation of monodromy transformation, acting on the chiral components of the solution of Liouville equation, is obtained. The non-trivial exchange algebra for monodromy transformation is calculated. (author). 14 refs
Explicit presentation of the Colebrook's friction factor equation ...
African Journals Online (AJOL)
Two explicit and very accurate equations for calculating the friction factor of pipes over the entire range of relative roughness and Reynold's Number covered by the Colebrook's Equation have been developed. A rectangular array of relative Roughness and Reynold's Number was used to test the accuracy of the new ...
Equations of 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
Iteration of adjoint equations
International Nuclear Information System (INIS)
Lewins, J.D.
1994-01-01
Adjoint functions are the basis of variational methods and now widely used for perturbation theory and its extension to higher order theory as used, for example, in modelling fuel burnup and optimization. In such models, the adjoint equation is to be solved in a critical system with an adjoint source distribution that is not zero but has special properties related to ratios of interest in critical systems. Consequently the methods of solving equations by iteration and accumulation are reviewed to show how conventional methods may be utilized in these circumstances with adequate accuracy. (author). 3 refs., 6 figs., 3 tabs
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....
Partial differential equations
Agranovich, M S
2002-01-01
Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplectic geometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and gener
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
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
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
Guiding Center Equations in Toroidal Equilibria
International Nuclear Information System (INIS)
White, Roscoe; Zakharov, Leonid
2002-01-01
Guiding center equations for particle motion in a general toroidal magnetic equilibrium configuration are derived using magnetic coordinates. Previous derivations made use of Boozer coordinates, in which the poloidal and toroidal angle variables are chosen so that the Jacobian is inversely proportional to the square of the magnetic field. It is shown that the equations for guiding center motion in any equilibrium possessing nested flux surfaces have exactly the same simple form as those derived in this special case. This allows the use of more spatially uniform coordinates instead of the Boozer coordinates, greatly increasing the accuracy of calculations in large beta and strongly shaped equilibria
Sobolev gradients and differential equations
Neuberger, J W
2010-01-01
A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair p...
Analysis of wave equation in electromagnetic field by Proca equation
International Nuclear Information System (INIS)
Pamungkas, Oky Rio; Soeparmi; Cari
2017-01-01
This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)
Comparison of Kernel Equating and Item Response Theory Equating Methods
Meng, Yu
2012-01-01
The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…
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...
B-splines and Faddeev equations
International Nuclear Information System (INIS)
Huizing, A.J.
1990-01-01
Two numerical methods for solving the three-body equations describing relativistic pion deuteron scattering have been investigated. For separable two body interactions these equations form a set of coupled one-dimensional integral equations. They are plagued by singularities which occur in the kernel of the integral equations as well as in the solution. The methods to solve these equations differ in the way they treat the singularities. First the Fuda-Stuivenberg method is discussed. The basic idea of this method is an one time iteration of the set of integral equations to treat the logarithmic singularities. In the second method, the spline method, the unknown solution is approximated by splines. Cubic splines have been used with cubic B-splines as basis. If the solution is approximated by a linear combination of basis functions, an integral equation can be transformed into a set of linear equations for the expansion coefficients. This set of linear equations is solved by standard means. Splines are determined by points called knots. A proper choice of splines to approach the solution stands for a proper choice of the knots. The solution of the three-body scattering equations has a square root behaviour at a certain point. Hence it was investigated how the knots should be chosen to approximate the square root function by cubic B-splines in an optimal way. Before applying this method to solve numerically the three-body equations describing pion-deuteron scattering, an analytically solvable example has been constructed with a singularity structure of both kernel and solution comparable to those of the three-body equations. The accuracy of the numerical solution was determined to a large extent by the accuracy of the approximation of the square root part. The results for a pion laboratory energy of 47.4 MeV agree very well with those from literature. In a complete calculation for 47.7 MeV the spline method turned out to be a factor thousand faster than the Fuda
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.
Analytical solution to the hybrid diffusion-transport equation
International Nuclear Information System (INIS)
Nanneh, M.M.; Williams, M.M.R.
1986-01-01
A special integral equation was derived in previous work using a hybrid diffusion-transport theory method for calculating the flux distribution in slab lattices. In this paper an analytical solution of this equation has been carried out on a finite reactor lattice. The analytical results of disadvantage factors are shown to be accurate in comparison with the numerical results and accurate transport theory calculations. (author)
Reaction rate calculations via transmission coefficients
International Nuclear Information System (INIS)
Feit, M.D.; Alder, B.J.
1985-01-01
The transmission coefficient of a wavepacket traversing a potential barrier can be determined by steady state calculations carried out in imaginary time instead of by real time dynamical calculations. The general argument is verified for the Eckart barrier potential by a comparison of transmission coefficients calculated from real and imaginary time solutions of the Schroedinger equation. The correspondence demonstrated here allows a formulation for the reaction rate that avoids difficulties due to both rare events and explicitly time dependent calculations. 5 refs., 2 figs
Directory of Open Access Journals (Sweden)
Luciano Melo Coutinho
2014-01-01
Full Text Available Erosion is considered the main cause of depletion of agricultural land, which generates approximate annual losses of billions of dollars in Brazil. Water erosion is the most common, caused by effective precipitation basin, since its potential is the main agent of reshaping the land. Universal Equation Soil Loss (USLE show great applicability to estimate erosion in watersheds from their physical and geographical elements (PS = R*K*L*S*C*P. The intensity of erosion can be influenced by the profile of the slope, measured by the length (L and grade of slope (S. The topographic factor (LS of the USLE is the most difficult to obtain for large and/or diverse relief areas. We calculated the spatial map of the LS factor Silver watershed (Castelo-ES from the processing of cartographic data in environment Geographic Information Systems (GIS. The relief of the study area was represented by interpolation from contour lines supported mapped hydrography, give the digital elevation model hydrologically consistent (MDEHC and declivity map. For generation of the LS factor was used to equation developed by Bertoni and Lombardi Neto (2005, suitable for slopes of different length and declivity. The Silver watershed has diversified relief, marked by flat and steep declivity areas, which indicates erosive vulnerability. The main values of LS were identified minimum (0, medium (8.2 and maximum (80.5. = A erosão é apontada como a principal causa do depauperamento de terras agrícolas, o que gera prejuízos anuais aproximados da ordem de bilhões de dólares no Brasil. A erosão hídrica é a mais comum, ocasionada pela precipitação efetiva em bacias, que devido ao seu potencial erosivo é o principal agente de remodelagem do terreno. A Equação Universal de Perdas de Solos (EUPS mostra-se de grande aplicabilidade para estimar a erosão de bacias hidrográficas a partir de seus elementos físicos e geográficos (PS = R*K*L*S*C*P. A intensidade da erosão pode sofrer
Kleinert, H.; Zatloukal, V.
2013-11-01
The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.
Indian Academy of Sciences (India)
The Raychaudhuri equation is central to the understanding of gravitational attraction in ... of K Gödel on the ideas of shear and vorticity in cosmology (he defines the shear. (eq. (8) in [1]) .... which follows from the definition of the scale factor l.
Generalized reduced magnetohydrodynamic equations
International Nuclear Information System (INIS)
Kruger, S.E.
1999-01-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics
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.
Indian Academy of Sciences (India)
research, teaching and practice related to the analysis and design ... its variants, are present in a large number of ma- chines used in daily ... with advanced electronics, sensors, control systems and computing ... ted perfectly well with the rapidly developing comput- .... velopment of the Freudenstein equation using Figure 3.
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
ABSTRACT. Analysis of underground circular cylindrical shell is carried out in this work. The forth order differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the assumptions of P. L Pasternak. Laplace transformation was used to solve the governing ...
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe 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
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.
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…
ANTHROPOMETRIC PREDICTIVE EQUATIONS FOR ...
African Journals Online (AJOL)
Keywords: Anthropometry, Predictive Equations, Percentage Body Fat, Nigerian Women, Bioelectric Impedance ... such as Asians and Indians (Pranav et al., 2009), ... size (n) of at least 3o is adjudged as sufficient for the ..... of people, gender and age (Vogel eta/., 1984). .... Fish Sold at Ile-Ife Main Market, South West Nigeria.
Indian Academy of Sciences (India)
However, one can associate the term with any solution of nonlinear partial differential equations (PDEs) which (i) represents a wave of permanent form, (ii) is localized ... In the past several decades, many methods have been proposed for solving nonlinear PDEs, such as ... space–time fractional derivative form of eq. (1) and ...
Fay, Temple H.
2010-01-01
Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…
Guiding center drift equations
International Nuclear Information System (INIS)
Boozer, A.H.
1979-03-01
The quations for particle guiding center drift orbits are given in a new magnetic coordinate system. This form of the equations not only separates the fast motion along the lines from the slow motion across, but also requires less information about the magnetic field than many other formulations of the problem
dimensional nonlinear evolution equations
Indian Academy of Sciences (India)
in real-life situations, it is important to find their exact solutions. Further, in ... But only little work is done on the high-dimensional equations. .... Similarly, to determine the values of d and q, we balance the linear term of the lowest order in eq.
Stochastic nonlinear beam equations
Czech Academy of Sciences Publication Activity Database
Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan
2005-01-01
Roč. 132, č. 1 (2005), s. 119-149 ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005
Savoy, L. G.
1988-01-01
Describes a study of students' ability to balance equations. Answers to a test on this topic were analyzed to determine the level of understanding and processes used by the students. Presented is a method to teach this skill to high school chemistry students. (CW)
FIPRED Project - Experiments and calculations
International Nuclear Information System (INIS)
Ohai, D.; Dumitrescu, I.; Doca, C.; Meleg, T.; Benga, D.
2009-01-01
Full text: The FIPRED (Fission Products Release from Debris Bed) Project was developed by INR in the framework of EC FP6 SARNET (2004-2008) and will be continued in EC FP6 SARNET2 (2009-2013). The project objective is the evaluation of fission product release from debris bed resulted after reactor severe accident by natural UO 2 sintered pellets self disintegration by oxidation. A large experimental program was performed covering the main parameters influencing granulometric distribution of powders (fragments) resulted from UO 2 sintered pellets self disintegration by air oxidation. The paper presents experimental results obtained and material equation obtained by mathematical calculations. (authors)
Lectures on partial differential equations
Petrovsky, I G
1992-01-01
Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.
Quantum equations from Brownian motions
International Nuclear Information System (INIS)
Rajput, B.S.
2011-01-01
Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows it's classical counter part on applying Heisenberg uncertainly principle between energy and time without applying any analytical continuation. (author)
Program for TI programmable 59 calculator for calculation of 3H concentration of water samples
International Nuclear Information System (INIS)
Hussain, S.D.; Asghar, G.
1982-09-01
A program has been developed for TI Programmable 59 Calculator of Texas Instruments Inc. to calculate from the observed parameters such as count rate etc. the 3 H (tritium) concentration of water samples processed with/without prior electrolytic enrichment. Procedure to use the program has been described in detail. A brief description of the laboratory treatment of samples and the mathematical equations used in the calculations have been given. (orig./A.B.)
Elements of partial differential equations
Sneddon, Ian Naismith
1957-01-01
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
On generalized fractional vibration equation
International Nuclear Information System (INIS)
Dai, Hongzhe; Zheng, Zhibao; Wang, Wei
2017-01-01
Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.
Swarm analysis by using transport equations, 1
International Nuclear Information System (INIS)
Dote, Toshihiko; Shimada, Masatoshi
1980-01-01
By evolving Maxwell-Boltzmann transport equations, various quantities on swarm of charged particles have been analyzed. Although this treatment is properly general, and common transport equations for charged particles ought to be given, in particular, equations only for electrons were presented here. The relation between the random energy and the drift energy was first derived and the general expression of the electron velocity was deduced too. For a simple example, one dimensional steady-state electron swarm in a uniform medium was treated. Electron swarm characteristics numerically calculated in He, Ne or Ar exhibited some interesting properties, which were physically clearly elucidated. These results were also compared with several data already published. Agreements between them were qualitatively rather well in detailed structures. (author)
Complete integrability of the difference evolution equations
International Nuclear Information System (INIS)
Gerdjikov, V.S.; Ivanov, M.I.; Kulish, P.P.
1980-01-01
The class of exactly solvable nonlinear difference evolution equations (DEE) related to the discrete analog of the one-dimensional Dirac problem L is studied. For this starting from L we construct a special linear non-local operator Λ and obtain the expansions of w and σ 3 deltaw over its eigenfunctions, w being the potential in L. This allows us to obtain compact expressions for the integrals of motion and to prove that these DEE are completely integrable Hamiltonian systems. Moreover, it is shown that there exists a hierarchy of Hamiltonian structures, generated by Λ, and the action-angle variables are explicity calculated. As particular cases the difference analog of the non-linear Schroedinger equation and the modified Korteweg-de-Vries equation are considered. The quantization of these Hamiltonian system through the use of the quantum inverse scattering method is briefly discussed [ru
Effective field equations for expectation values
International Nuclear Information System (INIS)
Jordan, R.D.
1986-01-01
We discuss functional methods which allow calculation of expectation values, rather than the usual in-out amplitudes, from a path integral. The technique, based on Schwinger's idea of summing over paths which go from the past to the future and then back to the past, provides effective field equations satisfied by the expectation value of the field. These equations are shown to be real and causal for a general theory up to two-loop order, and unitarity is checked to this order. These methods are applied to a simple quantum-mechanical example to illustrate the differences between the new formalism and the standard theory. When applied to the gravitational field, the new effective field equations should be useful for studies of quantum cosmology
Broyden's method in nuclear structure calculations
International Nuclear Information System (INIS)
Baran, Andrzej; Bulgac, Aurel; Forbes, Michael McNeil; Hagen, Gaute; Nazarewicz, Witold; Schunck, Nicolas; Stoitsov, Mario V.
2008-01-01
Broyden's method, widely used in quantum chemistry electronic-structure calculations for the numerical solution of nonlinear equations in many variables, is applied in the context of the nuclear many-body problem. Examples include the unitary gas problem, the nuclear density functional theory with Skyrme functionals, and the nuclear coupled-cluster theory. The stability of the method, its ease of use, and its rapid convergence rates make Broyden's method a tool of choice for large-scale nuclear structure calculations
Methods for Equating Mental Tests.
1984-11-01
1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth
Nodal spectrum method for solving neutron diffusion equation
International Nuclear Information System (INIS)
Sanchez, D.; Garcia, C. R.; Barros, R. C. de; Milian, D.E.
1999-01-01
Presented here is a new numerical nodal method for solving static multidimensional neutron diffusion equation in rectangular geometry. Our method is based on a spectral analysis of the nodal diffusion equations. These equations are obtained by integrating the diffusion equation in X, Y directions and then considering flat approximations for the current. These flat approximations are the only approximations that are considered in this method, as a result the numerical solutions are completely free from truncation errors. We show numerical results to illustrate the methods accuracy for coarse mesh calculations
BCS equations in the continuum
International Nuclear Information System (INIS)
Sandulescu, N.; Liotta, R. J.; Wyss, R.
1998-01-01
The properties of nuclei close to the drip line are significantly influenced by the continuum part of the single-particle spectrum. The main role is played by the resonant states which are largely confined in the region of nuclear potential and therefore stronger coupled with the bound states in an excitation process. Resonant states are also important in the nuclei beyond the drip line. In this case the decay properties of the nucleus can be directly related to the widths of the narrow resonances occupied by the unbound nucleons. The aim of this work is to propose an alternative for evaluating the effect of the resonant part of single-particle spectrum on the pairing correlations calculated within the BCS approximation. We estimated the role of resonances in the case of the isotope 170 Sn. The Resonant-BCS (RBCS) equations are solved for the case of a seniority force. The BCS approximation based on a seniority force cannot be applied in the case of a nucleus immersed in a box if all discrete states simulating the continuum are considered. In such a case the pairing correlations will increase with the number of states in the box. In our case one can still apply a seniority force with RBCS because the effect of the continuum appears here through a finite number of physical resonances, well defined by the given mean field. Because these resonances have a spatial distribution concentrated within the region of the nuclear potential, one expects that the localization probability of nucleons, far out from the nuclear surface, to be small. The gap obtained taking correctly the contribution of resonances, according to RBCS equations, is about 1.3 MeV, while pairing gap calculated only with the bound single-particle spectrum has the value Δ = 1.10 MeV. If we introduce also the resonant states, neglecting completely their widths, the gap will increase to the value Δ = 1.880 MeV. Therefore, one cannot estimate properly the pairing correlations by supplementing the spectrum
Spurious solutions in few-body equations. II. Numerical investigations
International Nuclear Information System (INIS)
Adhikari, S.K.
1979-01-01
A recent analytic study of spurious solutions in few-body equations by Adhikari and Gloeckle is here complemented by numerical investigations. As proposed by Adhikari and Gloeckle we study numerically the spurious solutions in the three-body Weinberg type equations and draw some general conclusions about the existence of spurious solutions in three-body equations with the Weinberg kernel and in other few-body formulations. In particular we conclude that for most of the potentials we encounter in problems of nuclear physics the three-body Weinberg type equation will not have a spurious solution which may interfere with the bound state or scattering calculation. Hence, if proven convenient, the three-body Weinberg type equation can be used in practical calculations. The same conclusion is true for the three-body channel coupling array scheme of Kouri, Levin, and Tobocman. In the case of the set of six coupled four-body equations proposed by Rosenberg et al. and the set of the Bencze-Redish-Sloan equations a careful study of the possible spurious solutions is needed before using these equations in practical calculations
Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2018-01-01
We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.
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, ...
Flavored quantum Boltzmann equations
International Nuclear Information System (INIS)
Cirigliano, Vincenzo; Lee, Christopher; Ramsey-Musolf, Michael J.; Tulin, Sean
2010-01-01
We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and CP-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the CP asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.
Causal electromagnetic interaction equations
International Nuclear Information System (INIS)
Zinoviev, Yury M.
2011-01-01
For the electromagnetic interaction of two particles the relativistic causal quantum mechanics equations are proposed. These equations are solved for the case when the second particle moves freely. The initial wave functions are supposed to be smooth and rapidly decreasing at the infinity. This condition is important for the convergence of the integrals similar to the integrals of quantum electrodynamics. We also consider the singular initial wave functions in the particular case when the second particle mass is equal to zero. The discrete energy spectrum of the first particle wave function is defined by the initial wave function of the free-moving second particle. Choosing the initial wave functions of the free-moving second particle it is possible to obtain a practically arbitrary discrete energy spectrum.
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Directory of Open Access Journals (Sweden)
Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
Electroweak evolution equations
International Nuclear Information System (INIS)
Ciafaloni, Paolo; Comelli, Denis
2005-01-01
Enlarging a previous analysis, where only fermions and transverse gauge bosons were taken into account, we write down infrared-collinear evolution equations for the Standard Model of electroweak interactions computing the full set of splitting functions. Due to the presence of double logs which are characteristic of electroweak interactions (Bloch-Nordsieck violation), new infrared singular splitting functions have to be introduced. We also include corrections related to the third generation Yukawa couplings
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
Damped nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Nicholson, D.R.; Goldman, M.V.
1976-01-01
High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time
Fun with Differential Equations
Indian Academy of Sciences (India)
IAS Admin
tion of ® with ¼=2. One can use the uniqueness of solutions of differential equations to prove the addition formulae for sin(t1 +t2), etc. But instead of continuing with this thought process, let us do something more interesting. Now we shall consider another system. Fix 0 < < 1. I am looking for three real-valued functions x(t), ...
National Oceanic and Atmospheric Administration, Department of Commerce — The Magnetic Field Calculator will calculate the total magnetic field, including components (declination, inclination, horizontal intensity, northerly intensity,...
Shock Spectrum Calculation from Acceleration Time Histories
1980-09-01
accurate and economical . If the velocity is desired, it can be calculated with Equation A-8b. As it stands it is exact. Approx- imation will be...Washington DC; DAEN-MCE.D (R L Wight) Washington DC; DAEN.MPE-D Washington DC; DAEN- MPU . Washington DC; DARCOM; ERADCOM Tech Supp Dir. (DELSD-L) Ft