Some fundamental considerations of the equation of radiative transfer

International Nuclear Information System (INIS)

Kuriyan, J.G.; Sudarshan, E.C.G.

1978-10-01

The radiation transfer of the vector electromagnetic field was first formulated by Chandrasekhar while deriving the polarization characteristics of a sunlit sky. There are two subtle problems underlying this treatment. The first concerns the crucial identification of a Stokes parameter with the specific intensity of radiation. While both depend on position in 3-D space, the latter has, intrinsic to it, an additional angular dependence defining the flow of the radiation field. How can this inadequacy be remedied without damaging the results obtained heretofore from Chandrasekhar's formalism. The second problem arises from the fact that the radiative transfer equation describes the transport of an incoherent radiation field through space. This, however, seems to contradict the results of the Van Cittert-Zernike-Wolf theorem which implies that an incoherent field develops coherence as it passes through free space implying, of course, that the radiative transfer equation must involve not incoherent but partially coherent fields. The vector transfer equation of the direct beam (Beer's law) is derived from first principles. The analysis of this equation provides a satisfactory resolution of these two problems. The result also shows that the Beer's law will have to be modified to a matrix law to accommodate systems that are not spherically symmetric. 13 references

The Transport Equation in Optically Thick Media: Discussion of IMC and its Diffusion Limit

Energy Technology Data Exchange (ETDEWEB)

Szoke, A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Brooks, E. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2016-07-12

We discuss the limits of validity of the Implicit Monte Carlo (IMC) method for the transport of thermally emitted radiation. The weakened coupling between the radiation and material energy of the IMC method causes defects in handling problems with strong transients. We introduce an approach to asymptotic analysis for the transport equation that emphasizes the fact that the radiation and material temperatures are always different in time-dependent problems, and we use it to show that IMC does not produce the correct diffusion limit. As this is a defect of IMC in the continuous equations, no improvement to its discretization can remedy it.

Radiation transport calculation methods in BNCT

International Nuclear Information System (INIS)

Koivunoro, H.; Seppaelae, T.; Savolainen, S.

2000-01-01

Boron neutron capture therapy (BNCT) is used as a radiotherapy for malignant brain tumours. Radiation dose distribution is necessary to determine individually for each patient. Radiation transport and dose distribution calculations in BNCT are more complicated than in conventional radiotherapy. Total dose in BNCT consists of several different dose components. The most important dose component for tumour control is therapeutic boron dose D B . The other dose components are gamma dose D g , incident fast neutron dose D f ast n and nitrogen dose D N . Total dose is a weighted sum of the dose components. Calculation of neutron and photon flux is a complex problem and requires numerical methods, i.e. deterministic or stochastic simulation methods. Deterministic methods are based on the numerical solution of Boltzmann transport equation. Such are discrete ordinates (SN) and spherical harmonics (PN) methods. The stochastic simulation method for calculation of radiation transport is known as Monte Carlo method. In the deterministic methods the spatial geometry is partitioned into mesh elements. In SN method angular integrals of the transport equation are replaced with weighted sums over a set of discrete angular directions. Flux is calculated iteratively for all these mesh elements and for each discrete direction. Discrete ordinates transport codes used in the dosimetric calculations are ANISN, DORT and TORT. In PN method a Legendre expansion for angular flux is used instead of discrete direction fluxes, land the angular dependency comes a property of vector function space itself. Thus, only spatial iterations are required for resulting equations. A novel radiation transport code based on PN method and tree-multigrid technique (TMG) has been developed at VTT (Technical Research Centre of Finland). Monte Carlo method solves the radiation transport by randomly selecting neutrons and photons from a prespecified boundary source and following the histories of selected particles

Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements

International Nuclear Information System (INIS)

Surya Mohan, P.; Tarvainen, Tanja; Schweiger, Martin; Pulkkinen, Aki; Arridge, Simon R.

2011-01-01

Highlights: → We developed a variable order global basis scheme to solve light transport in 3D. → Based on finite elements, the method can be applied to a wide class of geometries. → It is computationally cheap when compared to the fixed order scheme. → Comparisons with local basis method and other models demonstrate its accuracy. → Addresses problems encountered n modeling of light transport in human brain. - Abstract: We propose the P N approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P N approximation is compared against Monte Carlo simulations and other state-of-the-art methods.

Time-dependent simplified PN approximation to the equations of radiative transfer

International Nuclear Information System (INIS)

Frank, Martin; Klar, Axel; Larsen, Edward W.; Yasuda, Shugo

2007-01-01

The steady-state simplified P N approximation to the radiative transport equation has been successfully applied to many problems involving radiation. This paper presents the derivation of time-dependent simplified P N (SP N ) equations (up to N = 3) via two different approaches. First, we use an asymptotic analysis, similar to the asymptotic derivation of the steady-state SP N equations. Second, we use an approach similar to the original derivation of the steady-state SP N equations and we show that both approaches lead to similar results. Special focus is put on the well-posedness of the equations and the question whether it can be guaranteed that the solution satisfies the correct physical bounds. Several numerical test cases are shown, including an analytical benchmark due to Su and Olson [B. Su, G.L. Olson, An analytical benchmark for non-equilibrium radiative transfer in an isotropically scattering medium, Ann. Nucl. Energy 24 (1997) 1035-1055.

Path Toward a Unified Geometry for Radiation Transport

Science.gov (United States)

Lee, Kerry

The Direct Accelerated Geometry for Radiation Analysis and Design (DAGRAD) element of the RadWorks Project under Advanced Exploration Systems (AES) within the Space Technology Mission Directorate (STMD) of NASA will enable new designs and concepts of operation for radiation risk assessment, mitigation and protection. This element is designed to produce a solution that will allow NASA to calculate the transport of space radiation through complex CAD models using the state-of-the-art analytic and Monte Carlo radiation transport codes. Due to the inherent hazard of astronaut and spacecraft exposure to ionizing radiation in low-Earth orbit (LEO) or in deep space, risk analyses must be performed for all crew vehicles and habitats. Incorporating these analyses into the design process can minimize the mass needed solely for radiation protection. Transport of the radiation fields as they pass through shielding and body materials can be simulated using Monte Carlo techniques or described by the Boltzmann equation, which is obtained by balancing changes in particle fluxes as they traverse a small volume of material with the gains and losses caused by atomic and nuclear collisions. Deterministic codes that solve the Boltzmann transport equation, such as HZETRN (high charge and energy transport code developed by NASA LaRC), are generally computationally faster than Monte Carlo codes such as FLUKA, GEANT4, MCNP(X) or PHITS; however, they are currently limited to transport in one dimension, which poorly represents the secondary light ion and neutron radiation fields. NASA currently uses HZETRN space radiation transport software, both because it is computationally efficient and because proven methods have been developed for using this software to analyze complex geometries. Although Monte Carlo codes describe the relevant physics in a fully three-dimensional manner, their computational costs have thus far prevented their widespread use for analysis of complex CAD models, leading

Self-consistent collisional-radiative model for hydrogen atoms: Atom–atom interaction and radiation transport

International Nuclear Information System (INIS)

Colonna, G.; Pietanza, L.D.; D’Ammando, G.

2012-01-01

Graphical abstract: Self-consistent coupling between radiation, state-to-state kinetics, electron kinetics and fluid dynamics. Highlight: ► A CR model of shock-wave in hydrogen plasma has been presented. ► All equations have been coupled self-consistently. ► Non-equilibrium electron and level distributions are obtained. ► The results show non-local effects and non-equilibrium radiation. - Abstract: A collisional-radiative model for hydrogen atom, coupled self-consistently with the Boltzmann equation for free electrons, has been applied to model a shock tube. The kinetic model has been completed considering atom–atom collisions and the vibrational kinetics of the ground state of hydrogen molecules. The atomic level kinetics has been also coupled with a radiative transport equation to determine the effective adsorption and emission coefficients and non-local energy transfer.

Mixed-hybrid finite element method for the transport equation and diffusion approximation of transport problems

International Nuclear Information System (INIS)

Cartier, J.

2006-04-01

This thesis focuses on mathematical analysis, numerical resolution and modelling of the transport equations. First of all, we deal with numerical approximation of the solution of the transport equations by using a mixed-hybrid scheme. We derive and study a mixed formulation of the transport equation, then we analyse the related variational problem and present the discretization and the main properties of the scheme. We particularly pay attention to the behavior of the scheme and we show its efficiency in the diffusion limit (when the mean free path is small in comparison with the characteristic length of the physical domain). We present academical benchmarks in order to compare our scheme with other methods in many physical configurations and validate our method on analytical test cases. Unstructured and very distorted meshes are used to validate our scheme. The second part of this thesis deals with two transport problems. The first one is devoted to the study of diffusion due to boundary conditions in a transport problem between two plane plates. The second one consists in modelling and simulating radiative transfer phenomenon in case of the industrial context of inertial confinement fusion. (author)

The gBL transport equations

International Nuclear Information System (INIS)

Mynick, H.E.

1989-05-01

The transport equations arising from the ''generalized Balescu- Lenard'' (gBL) collision operator are obtained, and some of their properties examined. The equations contain neoclassical and turbulent transport as two special cases, having the same structure. The resultant theory offers potential explanation for a number of results not well understood, including the anomalous pinch, observed ratios of Q/ΓT on TFTR, and numerical reproduction of ASDEX profiles by a model for turbulent transport invoked without derivation, but by analogy to neoclassical theory. The general equations are specialized to consideration of a number of particular transport mechanisms of interest. 10 refs

ipole: Semianalytic scheme for relativistic polarized radiative transport

Science.gov (United States)

Moscibrodzka, Monika; Gammie, Charles F.

2018-04-01

ipole is a ray-tracing code for covariant, polarized radiative transport particularly useful for modeling Event Horizon Telescope sources, though may also be used for other relativistic transport problems. The code extends the ibothros scheme for covariant, unpolarized transport using two representations of the polarized radiation field: in the coordinate frame, it parallel transports the coherency tensor, and in the frame of the plasma, it evolves the Stokes parameters under emission, absorption, and Faraday conversion. The transport step is as spacetime- and coordinate- independent as possible; the emission, absorption, and Faraday conversion step is implemented using an analytic solution to the polarized transport equation with constant coefficients. As a result, ipole is stable, efficient, and produces a physically reasonable solution even for a step with high optical depth and Faraday depth.

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

International Nuclear Information System (INIS)

Matthes, W.K.

1998-01-01

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

Dispersive effects in radiation transport and radiation hydrodynamics in matter at high density

International Nuclear Information System (INIS)

Crowley, B.J.B.

1983-01-01

In a recent research program (reported in AWRE 0 20/82) I have investigated the generalisation of the equations of radiation hydrodynamics when electromagnetic radiation is assumed to obey a linear-response dispersion relation of the form nω=kc where the refractive index n depends on the frequency ω and/or wave number k. From the application of the Boltzmann-Liouville transport theory to photons in the short-wavelength (geometrical optics) limit, I derive the energy and momentum equations which, when combined with a classical (Euler-Lagrange-Navier-Stokes) treatment of a fluid material medium in LTE, yield a complete dynamical theory of linear interactions (+ stimulated processes) between incoherent (thermal) radiation and dense, locally isotropic matter. The theory includes an account of pondero-motive forces and electro (magneto) striction. Moreover, it is apparently capable of being generalised to non-linear interactions in which the refractive index depends on the local specific intensity of the radiation field, and, to some extent, to the treatment of high-frequency coherent radiation. The generalisation of various approximated forms of radiation-transport theory (esp. diffusion) has been considered in detail. Some problems remain however. One such is the treatment of anomalous dispersion. Current research work is concentrating on the interesting atomic physics aspects of electromagnetic (esp. radiative) properties of a dispersive material medium

Mixed-hybrid finite element method for the transport equation and diffusion approximation of transport problems; Resolution de l'equation du transport par une methode d'elements finis mixtes-hybrides et approximation par la diffusion de problemes de transport

Energy Technology Data Exchange (ETDEWEB)

Cartier, J

2006-04-15

This thesis focuses on mathematical analysis, numerical resolution and modelling of the transport equations. First of all, we deal with numerical approximation of the solution of the transport equations by using a mixed-hybrid scheme. We derive and study a mixed formulation of the transport equation, then we analyse the related variational problem and present the discretization and the main properties of the scheme. We particularly pay attention to the behavior of the scheme and we show its efficiency in the diffusion limit (when the mean free path is small in comparison with the characteristic length of the physical domain). We present academical benchmarks in order to compare our scheme with other methods in many physical configurations and validate our method on analytical test cases. Unstructured and very distorted meshes are used to validate our scheme. The second part of this thesis deals with two transport problems. The first one is devoted to the study of diffusion due to boundary conditions in a transport problem between two plane plates. The second one consists in modelling and simulating radiative transfer phenomenon in case of the industrial context of inertial confinement fusion. (author)

Radiation Transport Around Axisymmetric Blunt Body Vehicles Using a Modified Differential Approximation

Science.gov (United States)

Hartung, Lin C.; Hassan, H. A.

1992-01-01

A moment method for computing 3-D radiative transport is applied to axisymmetric flows in thermochemical nonequilibrium. Such flows are representative of proposed aerobrake missions. The method uses the P-1 approximation to reduce the governing system of integro-di erential equations to a coupled set of partial di erential equations. A numerical solution method for these equations given actual variations of the radiation properties in thermochemical nonequilibrium blunt body flows is developed. Initial results from the method are shown and compared to tangent slab calculations. The agreement between the transport methods is found to be about 10 percent in the stagnation region, with the difference increasing along the flank of the vehicle.

Development of interfacial area transport equation

International Nuclear Information System (INIS)

Kim, Seung Jin; Ishii, Mamoru; Kelly, Joseph

2005-01-01

The interfacial area transport equation dynamically models the changes in interfacial structures along the flow field by mechanistically modeling the creation and destruction of dispersed phase. Hence, when employed in the numerical thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Accounting for the substantial differences in the transport mechanism for various sizes of bubbles, the transport equation is formulated for two characteristic groups of bubbles. The group 1 equation describes the transport of small-dispersed bubbles, whereas the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. To evaluate the feasibility and reliability of interfacial area transport equation available at present, it is benchmarked by an extensive database established in various two-phase flow configurations spanning from bubbly to churn-turbulent flow regimes. The geometrical effect in interfacial area transport is examined by the data acquired in vertical air-water two-phase flow through round pipes of various sizes and a confined flow duct, and by those acquired in vertical co-current downward air-water two-phase flow through round pipes of two different sizes

The use of symbolic computation in radiative, energy, and neutron transport calculations

Science.gov (United States)

Frankel, J. I.

This investigation uses symbolic computation in developing analytical methods and general computational strategies for solving both linear and nonlinear, regular and singular, integral and integro-differential equations which appear in radiative and combined mode energy transport. This technical report summarizes the research conducted during the first nine months of the present investigation. The use of Chebyshev polynomials augmented with symbolic computation has clearly been demonstrated in problems involving radiative (or neutron) transport, and mixed-mode energy transport. Theoretical issues related to convergence, errors, and accuracy have also been pursued. Three manuscripts have resulted from the funded research. These manuscripts have been submitted to archival journals. At the present time, an investigation involving a conductive and radiative medium is underway. The mathematical formulation leads to a system of nonlinear, weakly-singular integral equations involving the unknown temperature and various Legendre moments of the radiative intensity in a participating medium. Some preliminary results are presented illustrating the direction of the proposed research.

DIAPHANE: A portable radiation transport library for astrophysical applications

Science.gov (United States)

Reed, Darren S.; Dykes, Tim; Cabezón, Rubén; Gheller, Claudio; Mayer, Lucio

2018-05-01

One of the most computationally demanding aspects of the hydrodynamical modelingof Astrophysical phenomena is the transport of energy by radiation or relativistic particles. Physical processes involving energy transport are ubiquitous and of capital importance in many scenarios ranging from planet formation to cosmic structure evolution, including explosive events like core collapse supernova or gamma-ray bursts. Moreover, the ability to model and hence understand these processes has often been limited by the approximations and incompleteness in the treatment of radiation and relativistic particles. The DIAPHANE project has focused on developing a portable and scalable library that handles the transport of radiation and particles (in particular neutrinos) independently of the underlying hydrodynamic code. In this work, we present the computational framework and the functionalities of the first version of the DIAPHANE library, which has been successfully ported to three different smoothed-particle hydrodynamic codes, GADGET2, GASOLINE and SPHYNX. We also present validation of different modules solving the equations of radiation and neutrino transport using different numerical schemes.

Induced Compton-scattering effects in radiation-transport approximations

International Nuclear Information System (INIS)

Gibson, D.R. Jr.

1982-02-01

The method of characteristics is used to solve radiation transport problems with induced Compton scattering effects included. The methods used to date have only addressed problems in which either induced Compton scattering is ignored, or problems in which linear scattering is ignored. Also, problems which include both induced Compton scattering and spatial effects have not been considered previously. The introduction of induced scattering into the radiation transport equation results in a quadratic nonlinearity. Methods are developed to solve problems in which both linear and nonlinear Compton scattering are important. Solutions to scattering problems are found for a variety of initial photon energy distributions

Quantum-mechanical transport equation for atomic systems.

Science.gov (United States)

Berman, P. R.

1972-01-01

A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

Mixed-hybrid finite element method for the transport equation and diffusion approximation of transport problems; Resolution de l'equation du transport par une methode d'elements finis mixtes-hybrides et approximation par la diffusion de problemes de transport

Energy Technology Data Exchange (ETDEWEB)

Cartier, J

2006-04-15

This thesis focuses on mathematical analysis, numerical resolution and modelling of the transport equations. First of all, we deal with numerical approximation of the solution of the transport equations by using a mixed-hybrid scheme. We derive and study a mixed formulation of the transport equation, then we analyse the related variational problem and present the discretization and the main properties of the scheme. We particularly pay attention to the behavior of the scheme and we show its efficiency in the diffusion limit (when the mean free path is small in comparison with the characteristic length of the physical domain). We present academical benchmarks in order to compare our scheme with other methods in many physical configurations and validate our method on analytical test cases. Unstructured and very distorted meshes are used to validate our scheme. The second part of this thesis deals with two transport problems. The first one is devoted to the study of diffusion due to boundary conditions in a transport problem between two plane plates. The second one consists in modelling and simulating radiative transfer phenomenon in case of the industrial context of inertial confinement fusion. (author)

Laser radiation in active amplifying media treated as a transport problem - Transfer equation derived and exactly solved

Science.gov (United States)

Gupta, S. R. D.; Gupta, Santanu D.

1991-10-01

The flow of laser radiation in a plane-parallel cylindrical slab of active amplifying medium with axial symmetry is treated as a problem in radiative transfer. The appropriate one-dimensional transfer equation describing the transfer of laser radiation has been derived by an appeal to Einstein's A, B coefficients (describing the processes of stimulated line absorption, spontaneous line emission, and stimulated line emission sustained by population inversion in the medium) and considering the 'rate equations' to completely establish the rational of the transfer equation obtained. The equation is then exactly solved and the angular distribution of the emergent laser beam intensity is obtained; its numerically computed values are given in tables and plotted in graphs showing the nature of peaks of the emerging laser beam intensity about the axis of the laser cylinder.

The 'generalized Balescu-Lenard' transport equations

International Nuclear Information System (INIS)

Mynick, H.E.

1990-01-01

The transport equations arising from the 'generalized Balescu-Lenard' collision operator are obtained and some of their properties examined. The equations contain neoclassical and turbulent transport as two special cases having the same structure. The resultant theory offers a possible explanation for a number of results not well understood, including the anomalous pinch, observed ratios of Q/ΓT on TFTR, and numerical reproduction of ASDEX profiles by a model for turbulent transport invoked without derivation, but by analogy with neoclassical theory. The general equations are specialized to consideration of a number of particular transport mechanisms of interest. (author). Letter-to-the-editor. 10 refs

A FORMALISM FOR COVARIANT POLARIZED RADIATIVE TRANSPORT BY RAY TRACING

International Nuclear Information System (INIS)

Gammie, Charles F.; Leung, Po Kin

2012-01-01

We write down a covariant formalism for polarized radiative transfer appropriate for ray tracing through a turbulent plasma. The polarized radiation field is represented by the polarization tensor (coherency matrix) N αβ ≡ (a α k a* β k ), where a k is a Fourier coefficient for the vector potential. Using Maxwell's equations, the Liouville-Vlasov equation, and the WKB approximation, we show that the transport equation in vacuo is k μ ∇ μ N αβ = 0. We show that this is equivalent to Broderick and Blandford's formalism based on invariant Stokes parameters and a rotation coefficient, and suggest a modification that may reduce truncation error in some situations. Finally, we write down several alternative approaches to integrating the transfer equation.

Induced Compton scattering effects in radiation transport approximations

International Nuclear Information System (INIS)

Gibson, D.R. Jr.

1982-01-01

In this thesis the method of characteristics is used to solve radiation transport problems with induced Compton scattering effects included. The methods used to date have only addressed problems in which either induced Compton scattering is ignored, or problems in which linear scattering is ignored. Also, problems which include both induced Compton scattering and spatial effects have not been considered previously. The introduction of induced scattering into the radiation transport equation results in a quadratic nonlinearity. Methods are developed to solve problems in which both linear and nonlinear Compton scattering are important. Solutions to scattering problems are found for a variety of initial photon energy distributions

Solution of the radiative heat transfer equation with internal energy sources in a slab by the GFD method for anisotropic albedo

Energy Technology Data Exchange (ETDEWEB)

Azevedo, Fabio Souto de, E-mail: fabio.azevedo@ufrgs.b [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Inst. de Matematica; Sauter, Esequia, E-mail: esequia.sauter@canoas.ifrs.edu.b [Instituto Federal do Rio Grande do Sul (IFRS), Canoas, RS (Brazil); Thompson, Mark; Vilhena, Marco Tulio B., E-mail: mark.thompson@mat.ufrgs.b, E-mail: vilhena@mat.ufrgs.b [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada

2011-07-01

In this work we apply the Green Function Decomposition Method the radiative transport equation in a slab. The method consists in converting the radiative transport equation into a integral equation and projecting the integral operators involved into a finite dimensional space. This methodology does not involve an a priori discretization on the angular variable {mu}, requiring only that the kernel is numerically integrated on {mu}. Numerical results are provided for isotropic, linearly anisotropic, and Rayleigh scattering near the unitary albedo. (author)

The Laplace transformation of adjoint transport equations

International Nuclear Information System (INIS)

Hoogenboom, J.E.

1985-01-01

A clarification is given of the difference between the equation adjoint to the Laplace-transformed time-dependent transport equation and the Laplace-transformed time-dependent adjoint transport equation. Proper procedures are derived to obtain the Laplace transform of the instantaneous detector response. (author)

Asymptotic diffusion limit of cell temperature discretisation schemes for thermal radiation transport

Energy Technology Data Exchange (ETDEWEB)

Smedley-Stevenson, Richard P., E-mail: richard.smedley-stevenson@awe.co.uk [AWE PLC, Aldermaston, Reading, Berkshire, RG7 4PR (United Kingdom); Department of Earth Science and Engineering, Imperial College London, SW7 2AZ (United Kingdom); McClarren, Ryan G., E-mail: rmcclarren@ne.tamu.edu [Department of Nuclear Engineering, Texas A & M University, College Station, TX 77843-3133 (United States)

2015-04-01

This paper attempts to unify the asymptotic diffusion limit analysis of thermal radiation transport schemes, for a linear-discontinuous representation of the material temperature reconstructed from cell centred temperature unknowns, in a process known as ‘source tilting’. The asymptotic limits of both Monte Carlo (continuous in space) and deterministic approaches (based on linear-discontinuous finite elements) for solving the transport equation are investigated in slab geometry. The resulting discrete diffusion equations are found to have nonphysical terms that are proportional to any cell-edge discontinuity in the temperature representation. Based on this analysis it is possible to design accurate schemes for representing the material temperature, for coupling thermal radiation transport codes to a cell centred representation of internal energy favoured by ALE (arbitrary Lagrange–Eulerian) hydrodynamics schemes.

Asymptotic diffusion limit of cell temperature discretisation schemes for thermal radiation transport

International Nuclear Information System (INIS)

Smedley-Stevenson, Richard P.; McClarren, Ryan G.

2015-01-01

This paper attempts to unify the asymptotic diffusion limit analysis of thermal radiation transport schemes, for a linear-discontinuous representation of the material temperature reconstructed from cell centred temperature unknowns, in a process known as ‘source tilting’. The asymptotic limits of both Monte Carlo (continuous in space) and deterministic approaches (based on linear-discontinuous finite elements) for solving the transport equation are investigated in slab geometry. The resulting discrete diffusion equations are found to have nonphysical terms that are proportional to any cell-edge discontinuity in the temperature representation. Based on this analysis it is possible to design accurate schemes for representing the material temperature, for coupling thermal radiation transport codes to a cell centred representation of internal energy favoured by ALE (arbitrary Lagrange–Eulerian) hydrodynamics schemes

An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations

Energy Technology Data Exchange (ETDEWEB)

Sun, Wenjun, E-mail: sun_wenjun@iapcm.ac.cn [Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China); Jiang, Song, E-mail: jiang@iapcm.ac.cn [Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China); Xu, Kun, E-mail: makxu@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Hong Kong (China); Li, Shu, E-mail: li_shu@iapcm.ac.cn [Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China)

2015-12-01

This paper presents an extension of previous work (Sun et al., 2015 [22]) of the unified gas kinetic scheme (UGKS) for the gray radiative transfer equations to the frequency-dependent (multi-group) radiative transfer system. Different from the gray radiative transfer equations, where the optical opacity is only a function of local material temperature, the simulation of frequency-dependent radiative transfer is associated with additional difficulties from the frequency-dependent opacity. For the multiple frequency radiation, the opacity depends on both the spatial location and the frequency. For example, the opacity is typically a decreasing function of frequency. At the same spatial region the transport physics can be optically thick for the low frequency photons, and optically thin for high frequency ones. Therefore, the optical thickness is not a simple function of space location. In this paper, the UGKS for frequency-dependent radiative system is developed. The UGKS is a finite volume method and the transport physics is modeled according to the ratio of the cell size to the photon's frequency-dependent mean free path. When the cell size is much larger than the photon's mean free path, a diffusion solution for such a frequency radiation will be obtained. On the other hand, when the cell size is much smaller than the photon's mean free path, a free transport mechanism will be recovered. In the regime between the above two limits, with the variation of the ratio between the local cell size and photon's mean free path, the UGKS provides a smooth transition in the physical and frequency space to capture the corresponding transport physics accurately. The seemingly straightforward extension of the UGKS from the gray to multiple frequency radiation system is due to its intrinsic consistent multiple scale transport modeling, but it still involves lots of work to properly discretize the multiple groups in order to design an asymptotic preserving (AP

On an integral equation arising in the transport of radiation through a slab involving internal reflection

International Nuclear Information System (INIS)

Williams, M.M.R.

2005-01-01

The integral equation derived by Nieuwenhuizen and Luck for transmission of radiation through an optically thick diffusive medium is reconsidered in the light of radiative transfer theory and extended to slabs of arbitrary thickness. (author)

Fractional Boltzmann equation for multiple scattering of resonance radiation in low-temperature plasma

Energy Technology Data Exchange (ETDEWEB)

Uchaikin, V V; Sibatov, R T, E-mail: vuchaikin@gmail.com, E-mail: ren_sib@bk.ru [Ulyanovsk State University, 432000, 42 Leo Tolstoy str., Ulyanovsk (Russian Federation)

2011-04-08

The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start with the standard Boltzmann equation; averaging over photon frequencies leads to the appearance of a fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of a fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solving the obtained equation and demonstrate numerical results in some simple cases.

Fractional Boltzmann equation for multiple scattering of resonance radiation in low-temperature plasma

International Nuclear Information System (INIS)

Uchaikin, V V; Sibatov, R T

2011-01-01

The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start with the standard Boltzmann equation; averaging over photon frequencies leads to the appearance of a fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of a fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solving the obtained equation and demonstrate numerical results in some simple cases.

Advantages of Analytical Transformations in Monte Carlo Methods for Radiation Transport

International Nuclear Information System (INIS)

McKinley, M S; Brooks III, E D; Daffin, F

2004-01-01

Monte Carlo methods for radiation transport typically attempt to solve an integral by directly sampling analog or weighted particles, which are treated as physical entities. Improvements to the methods involve better sampling, probability games or physical intuition about the problem. We show that significant improvements can be achieved by recasting the equations with an analytical transform to solve for new, non-physical entities or fields. This paper looks at one such transform, the difference formulation for thermal photon transport, showing a significant advantage for Monte Carlo solution of the equations for time dependent transport. Other related areas are discussed that may also realize significant benefits from similar analytical transformations

Modeling Blazar Spectra by Solving an Electron Transport Equation

Science.gov (United States)

Lewis, Tiffany; Finke, Justin; Becker, Peter A.

2018-01-01

Blazars are luminous active galaxies across the entire electromagnetic spectrum, but the spectral formation mechanisms, especially the particle acceleration, in these sources are not well understood. We develop a new theoretical model for simulating blazar spectra using a self-consistent electron number distribution. Specifically, we solve the particle transport equation considering shock acceleration, adiabatic expansion, stochastic acceleration due to MHD waves, Bohm diffusive particle escape, synchrotron radiation, and Compton radiation, where we implement the full Compton cross-section for seed photons from the accretion disk, the dust torus, and 26 individual broad lines. We used a modified Runge-Kutta method to solve the 2nd order equation, including development of a new mathematical method for normalizing stiff steady-state ordinary differential equations. We show that our self-consistent, transport-based blazar model can qualitatively fit the IR through Fermi g-ray data for 3C 279, with a single-zone, leptonic configuration. We use the solution for the electron distribution to calculate multi-wavelength SED spectra for 3C 279. We calculate the particle and magnetic field energy densities, which suggest that the emitting region is not always in equipartition (a common assumption), but sometimes matter dominated. The stratified broad line region (based on ratios in quasar reverberation mapping, and thus adding no free parameters) improves our estimate of the location of the emitting region, increasing it by ~5x. Our model provides a novel view into the physics at play in blazar jets, especially the relative strength of the shock and stochastic acceleration, where our model is well suited to distinguish between these processes, and we find that the latter tends to dominate.

Transport-constrained extensions of collision and track length estimators for solutions of radiative transport problems

International Nuclear Information System (INIS)

Kong, Rong; Spanier, Jerome

2013-01-01

In this paper we develop novel extensions of collision and track length estimators for the complete space-angle solutions of radiative transport problems. We derive the relevant equations, prove that our new estimators are unbiased, and compare their performance with that of more conventional estimators. Such comparisons based on numerical solutions of simple one dimensional slab problems indicate the the potential superiority of the new estimators for a wide variety of more general transport problems

IPOLE - semi-analytic scheme for relativistic polarized radiative transport

Science.gov (United States)

Mościbrodzka, M.; Gammie, C. F.

2018-03-01

We describe IPOLE, a new public ray-tracing code for covariant, polarized radiative transport. The code extends the IBOTHROS scheme for covariant, unpolarized transport using two representations of the polarized radiation field: In the coordinate frame, it parallel transports the coherency tensor; in the frame of the plasma it evolves the Stokes parameters under emission, absorption, and Faraday conversion. The transport step is implemented to be as spacetime- and coordinate- independent as possible. The emission, absorption, and Faraday conversion step is implemented using an analytic solution to the polarized transport equation with constant coefficients. As a result, IPOLE is stable, efficient, and produces a physically reasonable solution even for a step with high optical depth and Faraday depth. We show that the code matches analytic results in flat space, and that it produces results that converge to those produced by Dexter's GRTRANS polarized transport code on a complicated model problem. We expect IPOLE will mainly find applications in modelling Event Horizon Telescope sources, but it may also be useful in other relativistic transport problems such as modelling for the IXPE mission.

Neutron transport equation - indications on homogenization and neutron diffusion

International Nuclear Information System (INIS)

Argaud, J.P.

1992-06-01

In PWR nuclear reactor, the practical study of the neutrons in the core uses diffusion equation to describe the problem. On the other hand, the most correct method to describe these neutrons is to use the Boltzmann equation, or neutron transport equation. In this paper, we give some theoretical indications to obtain a diffusion equation from the general transport equation, with some simplifying hypothesis. The work is organised as follows: (a) the most general formulations of the transport equation are presented: integro-differential equation and integral equation; (b) the theoretical approximation of this Boltzmann equation by a diffusion equation is introduced, by the way of asymptotic developments; (c) practical homogenization methods of transport equation is then presented. In particular, the relationships with some general and useful methods in neutronic are shown, and some homogenization methods in energy and space are indicated. A lot of other points of view or complements are detailed in the text or the remarks

Transport of Terrestrial gamma-Radiation in Plane Semi-Infinite Geometry

DEFF Research Database (Denmark)

Kirkegaard, Peter; Løvborg, Leif

1980-01-01

The plane one-dimensional photon transport equation is solved for the scattered γ-radiation flux in the case of two adjacent media. One medium represents a natural ground with uniformly distributed potassium, uranium, and thorium γ-ray emitters. The other medium is air with no radioactive contami...

Swarm analysis by using transport equations

International Nuclear Information System (INIS)

Dote, Toshihiko.

1985-01-01

As the basis of weak ionization plasma phenomena, the motion, i.e. swarm, of charged particles in the gas is analyzed by use of the transport equations, from which basic nature of the swarm is discussed. The present report is an overview of the studies made in the past several years. Described are principally the most basic aspects concerning behaviors of the electrons and positive ions, that is, the basic equations and their significance, characteristics of the behaviors of the electron and positive ion swarms as revealed by solving the equations, and various characteristics of the swarm parameters. Contents are: Maxwell-Boltzmann's transport equations, behavior of the electron swarm, energy loss of the electrons, and behavior of the positive ion swarm. (Mori, K.)

High-order discontinuous Galerkin nonlocal transport and energy equations scheme for radiation hydrodynamics

Czech Academy of Sciences Publication Activity Database

Holec, M.; Limpouch, J.; Liska, R.; Weber, Stefan A.

2017-01-01

Roč. 83, č. 10 (2017), s. 779-797 ISSN 0271-2091 R&D Projects: GA MŠk EF15_008/0000162; GA MŠk LQ1606 Grant - others:ELI Beamlines(XE) CZ.02.1.01/0.0/0.0/15_008/0000162 Institutional support: RVO:68378271 Keywords : radiation hydrodynamics * nonlocal transport * Knudsen number * multigroup diffusion * radiation coupling Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders OBOR OECD: Nuclear physics Impact factor: 1.652, year: 2016

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

Range of validity of transport equations

International Nuclear Information System (INIS)

Berges, Juergen; Borsanyi, Szabolcs

2006-01-01

Transport equations can be derived from quantum field theory assuming a loss of information about the details of the initial state and a gradient expansion. While the latter can be systematically improved, the assumption about a memory loss is not known to be controlled by a small expansion parameter. We determine the range of validity of transport equations for the example of a scalar g 2 Φ 4 theory. We solve the nonequilibrium time evolution using the three-loop 2PI effective action. The approximation includes off-shell and memory effects and assumes no gradient expansion. This is compared to transport equations to lowest order (LO) and beyond (NLO). We find that the earliest time for the validity of transport equations is set by the characteristic relaxation time scale t damp =-2ω/Σ ρ (eq) , where -Σ ρ (eq) /2 denotes the on-shell imaginary-part of the self-energy. This time scale agrees with the characteristic time for partial memory loss, but is much shorter than thermal equilibration times. For times larger than about t damp the gradient expansion to NLO is found to describe the full results rather well for g 2 (less-or-similar sign)1

Spatial discretizations for self-adjoint forms of the radiative transfer equations

International Nuclear Information System (INIS)

Morel, Jim E.; Adams, B. Todd; Noh, Taewan; McGhee, John M.; Evans, Thomas M.; Urbatsch, Todd J.

2006-01-01

There are three commonly recognized second-order self-adjoint forms of the neutron transport equation: the even-parity equations, the odd-parity equations, and the self-adjoint angular flux equations. Because all of these equations contain second-order spatial derivatives and are self-adjoint for the mono-energetic case, standard continuous finite-element discretization techniques have proved quite effective when applied to the spatial variables. We first derive analogs of these equations for the case of time-dependent radiative transfer. The primary unknowns for these equations are functions of the angular intensity rather than the angular flux, hence the analog of the self-adjoint angular flux equation is referred to as the self-adjoint angular intensity equation. Then we describe a general, arbitrary-order, continuous spatial finite-element approach that is applied to each of the three equations in conjunction with backward-Euler differencing in time. We refer to it as the 'standard' technique. We also introduce an alternative spatial discretization scheme for the self-adjoint angular intensity equation that requires far fewer unknowns than the standard method, but appears to give comparable accuracy. Computational results are given that demonstrate the validity of both of these discretization schemes

Saturation and linear transport equation

International Nuclear Information System (INIS)

Kutak, K.

2009-03-01

We show that the GBW saturation model provides an exact solution to the one dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting term in the diffusive approximation are balanced by the nonlinear term. (orig.)

Non-classical radiation transport in random media with fluctuating densities

International Nuclear Information System (INIS)

Dyuldya, S.V.; Bratchenko, M.I.

2012-01-01

The ensemble averaged propagation kernels of the non-classical radiation transport are studied by means of the proposed application of the stochastic differential equation random medium generators. It is shown that the non-classical transport is favored in long-correlated weakly fluctuating media. The developed kernel models have been implemented in GEANT4 and validated against the d ouble Monte Carlo m odeling of absorptions curves of disperse neutron absorbers and γ-albedos from a scatterer/absorber random mix

Unconditionally stable diffusion-acceleration of the transport equation

International Nuclear Information System (INIS)

Larsen, E.W.

1982-01-01

The standard iterative procedure for solving fixed-source discrete-ordinates problems converges very slowly for problems in optically large regions with scattering ratios c near unity. The diffusion-synthetic acceleration method has been proposed to make use of the fact that for this class of problems the diffusion equation is often an accurate approximation to the transport equation. However, stability difficulties have historically hampered the implementation of this method for general transport differencing schemes. In this article we discuss a recently developed procedure for obtaining unconditionally stable diffusion-synthetic acceleration methods for various transport differencing schemes. We motivate the analysis by first discussing the exact transport equation; then we illustrate the procedure by deriving a new stable acceleration method for the linear discontinuous transport differencing scheme. We also provide some numerical results

Unconditionally stable diffusion-acceleration of the transport equation

International Nuclear Information System (INIS)

Larson, E.W.

1982-01-01

The standard iterative procedure for solving fixed-source discrete-ordinates problems converges very slowly for problems in optically thick regions with scattering ratios c near unity. The diffusion-synthetic acceleration method has been proposed to make use of the fact that for this class of problems, the diffusion equation is often an accurate approximation to the transport equation. However, stability difficulties have historically hampered the implementation of this method for general transport differencing schemes. In this article we discuss a recently developed procedure for obtaining unconditionally stable diffusion-synthetic acceleration methods for various transport differencing schemes. We motivate the analysis by first discussing the exact transport equation; then we illustrate the procedure by deriving a new stable acceleration method for the linear discontinuous transport differencing scheme. We also provide some numerical results

Simulation of transport equations with Monte Carlo

International Nuclear Information System (INIS)

Matthes, W.

1975-09-01

The main purpose of the report is to explain the relation between the transport equation and the Monte Carlo game used for its solution. The introduction of artificial particles carrying a weight provides one with high flexibility in constructing many different games for the solution of the same equation. This flexibility opens a way to construct a Monte Carlo game for the solution of the adjoint transport equation. Emphasis is laid mostly on giving a clear understanding of what to do and not on the details of how to do a specific game

Introduction to radiation transport

International Nuclear Information System (INIS)

Olson, G.L.

1998-01-01

This lecture will present time-dependent radiation transport where the radiation is coupled to a static medium, i.e., the material is not in motion. In reality, radiation exerts a pressure on the materials it propagates through and will accelerate the material in the direction of the radiation flow. This fully coupled problem with radiation transport and materials in motion is referred to as radiation-hydrodynamics (or in a shorthand notation: rad-hydro) and is beyond the scope of this lecture

Exact solution of the neutron transport equation in spherical geometry

Energy Technology Data Exchange (ETDEWEB)

Anli, Fikret; Akkurt, Abdullah; Yildirim, Hueseyin; Ates, Kemal [Kahramanmaras Suetcue Imam Univ. (Turkey). Faculty of Sciences and Letters

2017-03-15

Solution of the neutron transport equation in one dimensional slab geometry construct a basis for the solution of neutron transport equation in a curvilinear geometry. Therefore, in this work, we attempt to derive an exact analytical benchmark solution for both neutron transport equations in slab and spherical medium by using P{sub N} approximation which is widely used in neutron transport theory.

2D deterministic radiation transport with the discontinuous finite element method

International Nuclear Information System (INIS)

Kershaw, D.; Harte, J.

1993-01-01

This report provides a complete description of the analytic and discretized equations for 2D deterministic radiation transport. This computational model has been checked against a wide variety of analytic test problems and found to give excellent results. We make extensive use of the discontinuous finite element method

Approximate radiative solutions of the Einstein equations

International Nuclear Information System (INIS)

Kuusk, P.; Unt, V.

1976-01-01

In this paper the external field of a bounded source emitting gravitational radiation is considered. A successive approximation method is used to integrate the Einstein equations in Bondi's coordinates (Bondi et al, Proc. R. Soc.; A269:21 (1962)). A method of separation of angular variables is worked out and the approximate Einstein equations are reduced to key equations. The losses of mass, momentum, and angular momentum due to gravitational multipole radiation are found. It is demonstrated that in the case of proper treatment a real mass occurs instead of a mass aspect in a solution of the Einstein equations. In an appendix Bondi's new function is given in terms of sources. (author)

Diffusion equation and spin drag in spin-polarized transport

DEFF Research Database (Denmark)

Flensberg, Karsten; Jensen, Thomas Stibius; Mortensen, Asger

2001-01-01

We study the role of electron-electron interactions for spin-polarized transport using the Boltzmann equation, and derive a set of coupled transport equations. For spin-polarized transport the electron-electron interactions are important, because they tend to equilibrate the momentum of the two-s...

Hybrid formulation of radiation transport in optically thick divertor plasmas

Energy Technology Data Exchange (ETDEWEB)

Rosato, J.; Marandet, Y.; Bufferand, H.; Stamm, R. [PIIM, UMR 7345 Aix-Marseille Universite / CNRS, Centre de St-Jerome, Marseille (France); Reiter, D. [IEK-4 Plasmaphysik, Forschungszentrum Juelich GmbH, Juelich (Germany)

2016-08-15

Kinetic Monte Carlo simulations of coupled atom-radiation transport in optically thick divertor plasmas can be computationally very demanding, in particular in ITER relevant conditions or even larger devices, e.g. for power plant divertor studies. At high (∝ 10{sup 15} cm{sup -3}) atomic densities, it can be shown that sufficiently large divertors behave in certain areas like a black body near the first resonance line of hydrogen (Lyman α). This suggests that, at least in part, the use of continuum model (radiation hydrodynamics) can be sufficiently accurate, while being less time consuming. In this work, we report on the development of a hybrid model devoted to switch automatically between a kinetic and a continuum description according to the plasma conditions. Calculations of the photo-excitation rate in a homogeneous slab are performed as an illustration. The outlined hybrid concept might be also applicable to neutral atom transport, due to mathematical analogy of transport equations for neutrals and radiation. (copyright 2016 The Authors. Contributions to Plasma Physics published by Wiley-VCH Verlag GmbH and Co. KGaA Weinheim. This)

Two split cell numerical methods for solving 2-D non-equilibrium radiation transport equations

International Nuclear Information System (INIS)

Feng Tinggui

2004-11-01

Two numerically positive methods, the step characteristic integral method and subcell balance method, for solving radiative transfer equations on quadrilateral grids are presented. Numerical examples shows that the schemes presented are feasible on non-rectangle grid computation, and that the computing results by the schemes presented are comparative to that by the discrete ordinate diamond scheme on rectangle grid. (author)

A non-local-thermodynamic equilibrium formulation of the transport equation for polarized light in the presence of weak magnetic fields. Doctoral thesis

International Nuclear Information System (INIS)

McNamara, D.J.

1977-01-01

The present work is motivated by the desire to better understand solar magnetism. Just as stellar astrophysics and radiative transfer have been coupled in the history of research in physics, so too has the study of radiative transfer of polarized light in magnetic fields and solar magnetism been a history of mutual growth. The Stokes parameters characterize the state of polarization of a beam of radiation. The author considers the changes in polarization, and therefore in the Stokes parameters, due to the transport of a beam through an optically thick medium in a weak magnetic field. The transport equation is derived from a general density matrix equation of motion. This allows the possibility of interference effects arising from the mixing of atomic sublevels in a weak magnetic field to be taken into account. The statistical equilibrium equations are similarly derived. Finally, the coupled system of equations is presented, and the order of magnitude of the interference effects, shown. Collisional effects are not considered. The magnitude of the interference effects in magnetic field measurements of the sun may be evaluated

Monte Carlo closure for moment-based transport schemes in general relativistic radiation hydrodynamic simulations

Science.gov (United States)

Foucart, Francois

2018-04-01

General relativistic radiation hydrodynamic simulations are necessary to accurately model a number of astrophysical systems involving black holes and neutron stars. Photon transport plays a crucial role in radiatively dominated accretion discs, while neutrino transport is critical to core-collapse supernovae and to the modelling of electromagnetic transients and nucleosynthesis in neutron star mergers. However, evolving the full Boltzmann equations of radiative transport is extremely expensive. Here, we describe the implementation in the general relativistic SPEC code of a cheaper radiation hydrodynamic method that theoretically converges to a solution of Boltzmann's equation in the limit of infinite numerical resources. The algorithm is based on a grey two-moment scheme, in which we evolve the energy density and momentum density of the radiation. Two-moment schemes require a closure that fills in missing information about the energy spectrum and higher order moments of the radiation. Instead of the approximate analytical closure currently used in core-collapse and merger simulations, we complement the two-moment scheme with a low-accuracy Monte Carlo evolution. The Monte Carlo results can provide any or all of the missing information in the evolution of the moments, as desired by the user. As a first test of our methods, we study a set of idealized problems demonstrating that our algorithm performs significantly better than existing analytical closures. We also discuss the current limitations of our method, in particular open questions regarding the stability of the fully coupled scheme.

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

Development and preliminary verification of 2-D transport module of radiation shielding code ARES

International Nuclear Information System (INIS)

Zhang Penghe; Chen Yixue; Zhang Bin; Zang Qiyong; Yuan Longjun; Chen Mengteng

2013-01-01

The 2-D transport module of radiation shielding code ARES is two-dimensional neutron and radiation shielding code. The theory model was based on the first-order steady state neutron transport equation, adopting the discrete ordinates method to disperse direction variables. Then a set of differential equations can be obtained and solved with the source iteration method. The 2-D transport module of ARES was capable of calculating k eff and fixed source problem with isotropic or anisotropic scattering in x-y geometry. The theoretical model was briefly introduced and series of benchmark problems were verified in this paper. Compared with the results given by the benchmark, the maximum relative deviation of k eff is 0.09% and the average relative deviation of flux density is about 0.60% in the BWR cells benchmark problem. As for the fixed source problem with isotropic and anisotropic scattering, the results of the 2-D transport module of ARES conform with DORT very well. These numerical results of benchmark problems preliminarily demonstrate that the development process of the 2-D transport module of ARES is right and it is able to provide high precision result. (authors)

Dynamic modeling of interfacial structures via interfacial area transport equation

International Nuclear Information System (INIS)

Seungjin, Kim; Mamoru, Ishii

2005-01-01

The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the numerical thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right-hand-side of the transport equations have been established by mechanistically modeling the creation and destruction of bubbles due to major bubble interaction mechanisms. In the present paper, the interfacial area transport equations currently available are reviewed to address the feasibility and reliability of the model along with extensive experimental results. These include the data from adiabatic upward air-water two-phase flow in round tubes of various sizes, from a rectangular duct, and from adiabatic co-current downward air-water two-phase flow in round pipes of two sizes. (authors)

Implicit Monte Carlo methods and non-equilibrium Marshak wave radiative transport

International Nuclear Information System (INIS)

Lynch, J.E.

1985-01-01

Two enhancements to the Fleck implicit Monte Carlo method for radiative transport are described, for use in transparent and opaque media respectively. The first introduces a spectral mean cross section, which applies to pseudoscattering in transparent regions with a high frequency incident spectrum. The second provides a simple Monte Carlo random walk method for opaque regions, without the need for a supplementary diffusion equation formulation. A time-dependent transport Marshak wave problem of radiative transfer, in which a non-equilibrium condition exists between the radiation and material energy fields, is then solved. These results are compared to published benchmark solutions and to new discrete ordinate S-N results, for both spatially integrated radiation-material energies versus time and to new spatially dependent temperature profiles. Multigroup opacities, which are independent of both temperature and frequency, are used in addition to a material specific heat which is proportional to the cube of the temperature. 7 refs., 4 figs

Transport methods: general. 8. Formulation of Transport Equation in a Split Form

International Nuclear Information System (INIS)

Stancic, V.

2001-01-01

The singular eigenfunction expansion method has enabled the application of functional analysis methods in transport theory. However, when applying it, the users were discouraged, since in most problems, including slab problems, an extra problem has occurred. It appears necessary to solve the Fredholm integral equation in order to determine the expansion coefficients. There are several reasons for this difficulty. One reason might be the use of the full-range expansion techniques even in the regions where the function is singular. Such an example is the free boundary condition that requires the distribution to be equal to zero. Moreover, at μ = 0, the transport equation becomes an integral one. Both reasons motivated us to redefine the transport equation in a more natural way. Similar to scattering theory, here we define the flux distribution as a direct sum of forward- and backward-directed neutrons, e.g., μ ≥ 0 and μ < 0, respectively. As a result, the plane geometry transport equation is being split into coupled-pair equations. Further, using an appropriate transformation, this pair of equations reduces to a self-adjoint one having the same form as the known full-range single flux. It is interesting that all the methods of full-range theory are applicable here provided the flux as well as the transformed transport operator are two-dimensional matrices. Applying this to the slab problem, we find explicit expressions for reflected and transmitted particles caused by an arbitrary plane source. That is the news in this paper. Because of space constraints, only fundamentals of this approach will be presented here. We assume that the reader is familiar with this field; therefore, the applications are noted only at the end. (author)

Hot electrons in superlattices: quantum transport versus Boltzmann equation

DEFF Research Database (Denmark)

Wacker, Andreas; Jauho, Antti-Pekka; Rott, S.

1999-01-01

A self-consistent solution of the transport equation is presented for semiconductor superlattices within different approaches: (i) a full quantum transport model based on nonequilibrium Green functions, (ii) the semiclassical Boltzmann equation for electrons in a miniband, and (iii) Boltzmann...

The plasma transport equations derived by multiple time-scale expansions and turbulent transport. I. General theory

International Nuclear Information System (INIS)

Edenstrasser, J.W.

1995-01-01

A multiple time-scale derivative expansion scheme is applied to the dimensionless Fokker--Planck equation and to Maxwell's equations, where the parameter range of a typical fusion plasma was assumed. Within kinetic theory, the four time scales considered are those of Larmor gyration, particle transit, collisions, and classical transport. The corresponding magnetohydrodynamic (MHD) time scales are those of ion Larmor gyration, Alfven, MHD collision, and resistive diffusion. The solution of the zeroth-order equations results in the force-free equilibria and ideal Ohm's law. The solution of the first-order equations leads under the assumption of a weak collisional plasma to the ideal MHD equations. On the MHD-collision time scale, not only the full set of the MHD transport equations is obtained, but also turbulent terms, where the related transport quantities are one order in the expansion parameter larger than those of classical transport. Finally, at the resistive diffusion time scale the known transport equations are arrived at including, however, also turbulent contributions. copyright 1995 American Institute of Physics

Numerical simulations for radiation hydrodynamics. 2: Transport limit

International Nuclear Information System (INIS)

Dai, W.W.; Woodward, P.R.

2000-01-01

A finite difference scheme is proposed for two-dimensional radiation hydrodynamical equations in the transport limit. The scheme is of Godunov-type, in which the set of time-averaged flux needed in the scheme is calculated through Riemann problems solved. In the scheme, flow signals are explicitly treated, while radiation signals are implicitly treated. Flow fields and radiation fields are updated simultaneously. An iterative approach is proposed to solve the set of nonlinear algebraic equations arising from the implicitness of the scheme. The sweeping method used in the scheme significantly reduces the number of iterations or computer CPU time needed. A new approach to further accelerate the convergence is proposed, which further reduces the number of iterations needed by more than one order. No matter how many cells radiation signals propagate in one time step, only an extremely small number of iterations are needed in the scheme, and each iteration costs only about 0.8% of computer CPU time which is needed for one time step of a second order accurate and fully explicit scheme. Two-dimensional problems are treated through a dimensionally split technique. Therefore, iterations for solving the set of algebraic equations are carried out only in each one-dimensional sweep. Through numerical examples it is shown that the scheme keeps the principle advantages of Godunov schemes for flow motion. In the time scale of flow motion numerical results are the same as those obtained from a second order accurate and fully explicit scheme. The acceleration of the convergence proposed in this paper may be directly applied to other hyperbolic systems. This study is important for laser fusion and astrophysics

Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas

International Nuclear Information System (INIS)

Zawaideh, E.S.

1985-01-01

A new set of two-fluid equations which are valid from collisional to weakly collisional limits are derived. Starting from gyrokinetic equations in flux coordinates with no zeroth order drifts, a set of moment equations describing plasma transport along the field lines of a space and time dependent magnetic field are derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii while in the weakly collisional limit, they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations. The new transport equations are used to study the effects of collisionality, magnetic field structure, and plasma anisotropy on plasma parallel transport. Numerical examples comparing these equations with conventional transport equations show that the conventional equations may contain large errors near the sound speed (M approx. = 1). It is also found that plasma anisotropy, which is not included in the conventional equations, is a critical parameter in determining plasma transport in varying magnetic field. The new transport equations are also used to study axial confinement in multiple mirror devices from the strongly to weakly collisional regime. A new ion conduction model was worked out to extend the regime of validity of the transport equations to the low density multiple mirror regime

Approximate solution of the transport equation by methods of Galerkin type

International Nuclear Information System (INIS)

Pitkaranta, J.

1977-01-01

Questions of the existence, uniqueness, and convergence of approximate solutions of transport equations by methods of the Galerkin type (where trial and weighting functions are the same) are discussed. The results presented do not exclude the infinite-dimensional case. Two strategies can be followed in the variational approximation of the transport operator: one proceeds from the original form of the transport equation, while the other is based on the partially symmetrized equation. Both principles are discussed in this paper. The transport equation is assumed in a discretized multigroup form

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)

Accurate and efficient radiation transport in optically thick media -- by means of the Symbolic Implicit Monte Carlo method in the difference formulation

International Nuclear Information System (INIS)

Szoke, A; Brooks, E D; McKinley, M; Daffin, F

2005-01-01

The equations of radiation transport for thermal photons are notoriously difficult to solve in thick media without resorting to asymptotic approximations such as the diffusion limit. One source of this difficulty is that in thick, absorbing media thermal emission is almost completely balanced by strong absorption. In a previous publication [SB03], the photon transport equation was written in terms of the deviation of the specific intensity from the local equilibrium field. We called the new form of the equations the difference formulation. The difference formulation is rigorously equivalent to the original transport equation. It is particularly advantageous in thick media, where the radiation field approaches local equilibrium and the deviations from the Planck distribution are small. The difference formulation for photon transport also clarifies the diffusion limit. In this paper, the transport equation is solved by the Symbolic Implicit Monte Carlo (SIMC) method and a comparison is made between the standard formulation and the difference formulation. The SIMC method is easily adapted to the derivative source terms of the difference formulation, and a remarkable reduction in noise is obtained when the difference formulation is applied to problems involving thick media

Minimum entropy production closure of the photo-hydrodynamic equations for radiative heat transfer

International Nuclear Information System (INIS)

Christen, Thomas; Kassubek, Frank

2009-01-01

In the framework of a two-moment photo-hydrodynamic modelling of radiation transport, we introduce a concept for the determination of effective radiation transport coefficients based on the minimization of the local entropy production rate of radiation and (generally nongrey) matter. The method provides the nonequilibrium photon distribution from which the effective (variable) absorption coefficients and the variable Eddington factor (VEF) can be calculated. For a single band model, the photon distribution depends explicitly on the frequency dependence of the absorption coefficient. Without introducing artificial fit parameters, multi-group or multi-band concepts, our approach reproduces the exact results in both limits of optically thick (Rosseland mean) and optically thin (Planck mean) media, in contrast to the maximum entropy method. Also the results for general nonequilibrium radiation between the limits of diffusive and ballistic photons are reasonable. We conjecture that the reason for the success of our approach lies in the linearity of the underlying Boltzmann equation of the photon gas. The method is illustrated and discussed for grey matter and for a simple example of nongrey matter with a two-band absorption spectrum. The method is also briefly compared with the maximum entropy concept.

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)

Fundaments of transport equation splitting and the eigenvalue problem

International Nuclear Information System (INIS)

Stancic, V.

2000-01-01

In order to remove some singularities concerning the boundary conditions of one dimensional transport equation, a split form of transport equation describing the forward i.e. μ≥0, and a backward μ<0 directed neutrons is being proposed here. The eigenvalue problem has also been considered here (author)

The use of symbolic computation in radiative, energy, and neutron transport calculations. Technical report, 15 August 1992--14 August 1994

International Nuclear Information System (INIS)

Frankel, J.I.

1995-01-01

This investigation uses symbolic computation in developing analytical methods and general computational strategies for solving both linear and nonlinear, regular and singular, integral and integro-differential equations which appear in radiative and combined mode energy transport. This technical report summarizes the research conducted during the first nine months of the present investigation. The use of Chebyshev polynomials augmented with symbolic computation has clearly been demonstrated in problems involving radiative (or neutron) transport, and mixed-mode energy transport. Theoretical issues related to convergence, errors, and accuracy have also been pursued. Three manuscripts have resulted from the funded research. These manuscripts have been submitted to archival journals. At the present time, an investigation involving a conductive and radiative medium is underway. The mathematical formulation leads to a system of nonlinear, weakly-singular integral equations involving the unknown temperature and various Legendre moments of the radiative intensity in a participating medium. Some preliminary results are presented illustrating the direction of the proposed research

Dynamic modeling of interfacial structures via interfacial area transport equation

International Nuclear Information System (INIS)

Seungjin, Kim; Mamoru, Ishii

2004-01-01

Full text of publication follows:In the current thermal-hydraulic system analysis codes using the two-fluid model, the empirical correlations that are based on the two-phase flow regimes and regime transition criteria are being employed as closure relations for the interfacial transfer terms. Due to its inherent shortcomings, however, such static correlations are inaccurate and present serious problems in the numerical analysis. In view of this, a new dynamic approach employing the interfacial area transport equation has been studied. The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Therefore, the interfacial area transport equation can make a leapfrog improvement in the current capability of the two-fluid model from both scientific and practical point of view. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right hand-side of the transport equations have been established by mechanistically modeling the creation and destruction of bubbles due to major bubble interaction mechanisms. The coalescence mechanisms include the random collision driven by turbulence, and the entrainment of trailing bubbles in the wake region of the preceding bubble. The disintegration mechanisms include the break-up by turbulence impact, shearing-off at the rim of large cap bubbles and the break-up of large cap

Diffusive limits for linear transport equations

International Nuclear Information System (INIS)

Pomraning, G.C.

1992-01-01

The authors show that the Hibert and Chapman-Enskog asymptotic treatments that reduce the nonlinear Boltzmann equation to the Euler and Navier-Stokes fluid equations have analogs in linear transport theory. In this linear setting, these fluid limits are described by diffusion equations, involving familiar and less familiar diffusion coefficients. Because of the linearity extant, one can carry out explicitly the initial and boundary layer analyses required to obtain asymptotically consistent initial and boundary conditions for the diffusion equations. In particular, the effects of boundary curvature and boundary condition variation along the surface can be included in the boundary layer analysis. A brief review of heuristic (nonasymptotic) diffusion description derivations is also included in our discussion

A new computational method for simulation of charge transport in semiconductor radiation detectors

International Nuclear Information System (INIS)

Holban, I.

1993-01-01

An effective computational method for simulation of charge transport in semiconductor radiation detectors is the purpose of the present work. Basic equations for analysis include (1) Poisson's equations, (2) continuity equation for electrons and holes, (3) rate equations for deep levels, (4) current equation for electrons and holes and (5) boundary conditions. The system of equations is discretized and equidistant space and time grids is brought. The nonlinearity of the problem is overcome by using Newton-Raphson iteration scheme. Instead of solving a nonlinear boundary problem we resolve a linear matrix equation. Our computation procedure becomes very efficient using a sparse matrix. The computed program allows to calculate the charge collection efficiency and transient response for arbitrary electric fields when trapping and detrapping effects are present. The earlier literature results are reproduced. (Author)

Regulatory practices of radiation safety of SNF transportation in Russia

International Nuclear Information System (INIS)

Kuryndina, Lidia; Kuryndin, Anton; Stroganov, Anatoly

2008-01-01

This paper overviews current regulatory practices for the assurance of nuclear and radiation safety during railway transportation of SNF on the territory of Russian Federation from NPPs to longterm-storage of reprocessing sites. The legal and regulatory requirements (mostly compliant with IAEA ST-1), licensing procedure for NM transportation are discussed. The current procedure does not require a regulatory approval for each particular shipment if the SNF fully comply with the Rosatom's branch standard and is transported in approved casks. It has been demonstrated that SNF packages compliant with the branch standard, which is knowingly provide sufficient safety margin, will conform to the federal level regulations. The regulatory approval is required if a particular shipment does not comply with the branch standard. In this case, the shipment can be approved only after regulatory review of Applicant's documents to demonstrate that the shipment still conformant to the higher level (federal) regulations. The regulatory review frequently needs a full calculation test of the radiation safety assurance. This test can take a lot of time. That's why the special calculation tools were created in SEC NRS. These tools aimed for precision calculation of the radiation safety parameters by SNF transportation use preliminary calculated Green's functions. Such approach allows quickly simulate any source distribution and optimize spent fuel assemblies placement in cask due to the transport equation property of linearity relatively the source. The short description of calculation tools are presented. Also, the paper discusses foreseen implications related to transportation of mixed-oxide SNF. (author)

A modular spherical harmonics approach to the neutron transport equation

International Nuclear Information System (INIS)

Inanc, F.; Rohach, A.F.

1989-01-01

A modular nodal method was developed for solving the neutron transport equation in 2-D xy coordinates. The spherical harmonic expansion was used for approximating the second-order even-parity form of the neutron transport equation. The boundary conditions of the spherical harmonics approximation were derived in a form to have forms analogous to the partial currents in the neutron diffusion equation. Relations were developed for generating both the second-order spherical harmonic equations and the boundary conditions in an automated computational algorithm. Nodes using different orders of the spherical harmonics approximation to the transport equation were interfaced through mixed-type boundary conditions. The determination of spherical harmonic orders implemented in the nodes were determined by the scheme in an automated manner. Results of the method compared favorably to benchmark problems. (author)

Generalized heat-transport equations: parabolic and hyperbolic models

Science.gov (United States)

Rogolino, Patrizia; Kovács, Robert; Ván, Peter; Cimmelli, Vito Antonio

2018-03-01

We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman-Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.

Unified formulation of radiation conditions for the wave equation

DEFF Research Database (Denmark)

Krenk, Steen

2002-01-01

A family of radiation conditions for the wave equation is derived by truncating a rational function approxiamtion of the corresponding plane wave representation, and it is demonstrated how these boundary conditions can be formulated in terms of fictitious surface densities, governed by second......-order wave equations on the radiating surface. Several well-established radiation boundary conditions appear as special cases, corresponding to different choice of the coefficients in the rational approximation. The relation between these choices is established, and an explicit formulation in terms...

Homogenization of the critically spectral equation in neutron transport

International Nuclear Information System (INIS)

Allaire, G.; Paris-6 Univ., 75; Bal, G.

1998-01-01

We address the homogenization of an eigenvalue problem for the neutron transport equation in a periodic heterogeneous domain, modeling the criticality study of nuclear reactor cores. We prove that the neutron flux, corresponding to the first and unique positive eigenvector, can be factorized in the product of two terms, up to a remainder which goes strongly to zero with the period. On terms is the first eigenvector of the transport equation in the periodicity cell. The other term is the first eigenvector of a diffusion equation in the homogenized domain. Furthermore, the corresponding eigenvalue gives a second order corrector for the eigenvalue of the heterogeneous transport problem. This result justifies and improves the engineering procedure used in practice for nuclear reactor cores computations. (author)

Homogenization of the critically spectral equation in neutron transport

Energy Technology Data Exchange (ETDEWEB)

Allaire, G. [CEA Saclay, 91 - Gif-sur-Yvette (France). Dept. de Mecanique et de Technologie]|[Paris-6 Univ., 75 (France). Lab. d' Analyse Numerique; Bal, G. [Electricite de France (EDF), 92 - Clamart (France). Direction des Etudes et Recherches

1998-07-01

We address the homogenization of an eigenvalue problem for the neutron transport equation in a periodic heterogeneous domain, modeling the criticality study of nuclear reactor cores. We prove that the neutron flux, corresponding to the first and unique positive eigenvector, can be factorized in the product of two terms, up to a remainder which goes strongly to zero with the period. On terms is the first eigenvector of the transport equation in the periodicity cell. The other term is the first eigenvector of a diffusion equation in the homogenized domain. Furthermore, the corresponding eigenvalue gives a second order corrector for the eigenvalue of the heterogeneous transport problem. This result justifies and improves the engineering procedure used in practice for nuclear reactor cores computations. (author)

From statistic mechanic outside equilibrium to transport equations

International Nuclear Information System (INIS)

Balian, R.

1995-01-01

This lecture notes give a synthetic view on the foundations of non-equilibrium statistical mechanics. The purpose is to establish the transport equations satisfied by the relevant variables, starting from the microscopic dynamics. The Liouville representation is introduced, and a projection associates with any density operator , for given choice of relevant observables, a reduced density operator. An exact integral-differential equation for the relevant variables is thereby derived. A short-memory approximation then yields the transport equations. A relevant entropy which characterizes the coarseness of the description is associated with each level of description. As an illustration, the classical gas, with its three levels of description and with the Chapman-Enskog method, is discussed. (author). 3 figs., 5 refs

Quadratic inner element subgrid scale discretisation of the Boltzmann transport equation

International Nuclear Information System (INIS)

Baker, C.M.J.; Buchan, A.G.; Pain, C.C.; Tollit, B.; Eaton, M.D.; Warner, P.

2012-01-01

This paper explores the application of the inner element subgrid scale method to the Boltzmann transport equation using quadratic basis functions. Previously, only linear basis functions for both the coarse scale and the fine scale were considered. This paper, therefore, analyses the advantages of using different coarse and subgrid basis functions for increasing the accuracy of the subgrid scale method. The transport of neutral particle radiation may be described by the Boltzmann transport equation (BTE) which, due to its 7 dimensional phase space, is computationally expensive to resolve. Multi-scale methods offer an approach to efficiently resolve the spatial dimensions of the BTE by separating the solution into its coarse and fine scales and formulating a solution whereby only the computationally efficient coarse scales need to be solved. In previous work an inner element subgrid scale method was developed that applied a linear continuous and discontinuous finite element method to represent the solution’s coarse and fine scale components. This approach was shown to generate efficient and stable solutions, and so this article continues its development by formulating higher order quadratic finite element expansions over the continuous and discontinuous scales. Here it is shown that a solution’s convergence can be improved significantly using higher order basis functions. Furthermore, by using linear finite elements to represent coarse scales in combination with quadratic fine scales, convergence can also be improved with only a modest increase in computational expense.

Gray and multigroup radiation transport models for two-dimensional binary stochastic media using effective opacities

International Nuclear Information System (INIS)

Olson, Gordon L.

2016-01-01

One-dimensional models for the transport of radiation through binary stochastic media do not work in multi-dimensions. Authors have attempted to modify or extend the 1D models to work in multidimensions without success. Analytic one-dimensional models are successful in 1D only when assuming greatly simplified physics. State of the art theories for stochastic media radiation transport do not address multi-dimensions and temperature-dependent physics coefficients. Here, the concept of effective opacities and effective heat capacities is found to well represent the ensemble averaged transport solutions in cases with gray or multigroup temperature-dependent opacities and constant or temperature-dependent heat capacities. In every case analyzed here, effective physics coefficients fit the transport solutions over a useful range of parameter space. The transport equation is solved with the spherical harmonics method with angle orders of n=1 and 5. Although the details depend on what order of solution is used, the general results are similar, independent of angular order. - Highlights: • Gray and multigroup radiation transport is done through 2D stochastic media. • Approximate models for the mean radiation field are found for all test problems. • Effective opacities are adjusted to fit the means of stochastic media transport. • Test problems include temperature dependent opacities and heat capacities • Transport solutions are done with angle orders n=1 and 5.

Liouville's equation and radiative acceleration in general relativity

International Nuclear Information System (INIS)

Keane, A.J.

1999-01-01

This thesis examines thoroughly the general motion of a material charged particle in the intense radiation field of a static spherically symmetric compact object with spherical emitting surface outside the Schwarzschild radius. Such a test particle will be pulled in by the gravitational attraction of the compact object and pushed out by the radiation pressure force, therefore the types of trajectory admitted will depend the gravitational field, the radiation field and the particle cross-section. The presence of a strong gravitational field demands a fully general relativistic treatment of the problem. This type of calculation is interesting not only as a formal problem in general relativity but also since it has important astrophysical implications, for example, application to astrophysical discs and jets. In chapter 1 we review the classical radiation force problem and outline the transition to a fully general relativistic scenario. We discuss the method for obtaining the radiation pressure force and calculating the particle trajectories. We review previous work in this area and outline the aims of the thesis. Then we consider some astrophysical applications and discuss how realistic our calculations are. In chapter 2 we give an introduction and overview of differential geometry as this is necessary for an accurate description of tensors on a curved manifold. Then we review the general theory of relativity and in particular obtain the Schwarzschild metric describing a static spherically symmetric vacuum spacetime. Chapter 3 deals with test particle motion through a curved spacetime. Liouville's equation describes the statistical distribution in phase space of a collection of test particles and is based upon a Hamiltonian formulation of the dynamical system - this material also relies heavily upon the concepts of differential geometry introduced in chapter 2. In particular we are interested in photon transport and find the general solutions for some symmetric

Basic equations of interfacial area transport in gas-liquid two-phase flow

International Nuclear Information System (INIS)

Kataoka, I.; Yoshida, K.; Naitoh, M.; Okada, H.; Morii, T.

2011-01-01

The rigorous and consistent formulations of basic equations of interfacial area transport were derived using correlation functions of characteristic function of each phase and velocities of each phase. Turbulent transport term of interfacial area concentration was consistently derived and related to the difference between interfacial velocity and averaged velocity of each phase. Constitutive equations of turbulent transport terms of interfacial area concentration were proposed for bubbly flow. New transport model and constitutive equations were developed for churn flow. These models and constitutive equations are validated by experimental data of radial distributions of interfacial area concentration in bubbly and churn flow. (author)

General particle transport equation. Final report

International Nuclear Information System (INIS)

Lafi, A.Y.; Reyes, J.N. Jr.

1994-12-01

The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence

The use of symbolic computation in radiative, energy, and neutron transport calculations. Final report

International Nuclear Information System (INIS)

Frankel, J.I.

1997-01-01

This investigation used sysmbolic manipulation in developing analytical methods and general computational strategies for solving both linear and nonlinear, regular and singular integral and integro-differential equations which appear in radiative and mixed-mode energy transport. Contained in this report are seven papers which present the technical results as individual modules

A simple Boltzmann transport equation for ballistic to diffusive transient heat transport

International Nuclear Information System (INIS)

Maassen, Jesse; Lundstrom, Mark

2015-01-01

Developing simplified, but accurate, theoretical approaches to treat heat transport on all length and time scales is needed to further enable scientific insight and technology innovation. Using a simplified form of the Boltzmann transport equation (BTE), originally developed for electron transport, we demonstrate how ballistic phonon effects and finite-velocity propagation are easily and naturally captured. We show how this approach compares well to the phonon BTE, and readily handles a full phonon dispersion and energy-dependent mean-free-path. This study of transient heat transport shows (i) how fundamental temperature jumps at the contacts depend simply on the ballistic thermal resistance, (ii) that phonon transport at early times approach the ballistic limit in samples of any length, and (iii) perceived reductions in heat conduction, when ballistic effects are present, originate from reductions in temperature gradient. Importantly, this framework can be recast exactly as the Cattaneo and hyperbolic heat equations, and we discuss how the key to capturing ballistic heat effects is to use the correct physical boundary conditions

Quantum Non-Markovian Langevin Equations and Transport Coefficients

International Nuclear Information System (INIS)

Sargsyan, V.V.; Antonenko, N.V.; Kanokov, Z.; Adamian, G.G.

2005-01-01

Quantum diffusion equations featuring explicitly time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytic expressions for calculating the friction and diffusion coefficients in nuclear processes are obtained. The asymptotic behavior of the transport coefficients and correlation functions for a damped harmonic oscillator that is linearly coupled in momentum to a heat bath is studied. The coupling to a heat bath in momentum is responsible for the appearance of the diffusion coefficient in coordinate. The problem of regression of correlations in quantum dissipative systems is analyzed

Transport methods: general. 7. Formulation of a Fourier-Boltzmann Transformation to Solve the Three-Dimensional Transport Equation

International Nuclear Information System (INIS)

Stancic, V.

2001-01-01

This paper presents some elements of a new approach to solve analytically the linearized three-dimensional (3-D) transport equation of neutral particles. Since this task is of such special importance, we present some results of a paper that is still in progress. The most important is that using this transformation, an integro-differential equation with an analytical solution is obtained. For this purpose, a simplest 3-D equation is being considered which describes the transport process in an infinite medium. Until now, this equation has been analytically considered either using the Laplace transform with respect to time parameter t or applying the Fourier transform over the space coordinate. Both of them reduce the number of differential terms in the equation; however, evaluation of the inverse transformation is complicated. In this paper, we introduce for the first time a Fourier transform induced by the Boltzmann operator. For this, we use a complete set of 3-D eigenfunctions of the Boltzmann transport operator defined in a similar way as those that have been already used in 3-D transport theory as a basic set to transform the transport equation. This set consists of a continuous part and a discrete one with spectral measure. The density distribution equation shows the known form asymptotic behavior. Several applications are to be performed using this equation and compared to the benchmark one. Such an analysis certainly would be out of the available space

Deterministic methods in radiation transport

International Nuclear Information System (INIS)

Rice, A.F.; Roussin, R.W.

1992-06-01

The Seminar on Deterministic Methods in Radiation Transport was held February 4--5, 1992, in Oak Ridge, Tennessee. Eleven presentations were made and the full papers are published in this report, along with three that were submitted but not given orally. These papers represent a good overview of the state of the art in the deterministic solution of radiation transport problems for a variety of applications of current interest to the Radiation Shielding Information Center user community

Some results on the neutron transport and the coupling of equations; Quelques resultats sur le transport neutronique et le couplage d`equations

Energy Technology Data Exchange (ETDEWEB)

Bal, G. [Electricite de France (EDF), Direction des Etudes et Recherches, 92 - Clamart (France)

1997-12-31

Neutron transport in nuclear reactors is well modeled by the linear Boltzmann transport equation. Its resolution is relatively easy but very expensive. To achieve whole core calculations, one has to consider simpler models, such as diffusion or homogeneous transport equations. However, the solutions may become inaccurate in particular situations (as accidents for instance). That is the reason why we wish to solve the equations on small area accurately and more coarsely on the remaining part of the core. It is than necessary to introduce some links between different discretizations or modelizations. In this note, we give some results on the coupling of different discretizations of all degrees of freedom of the integral-differential neutron transport equation (two degrees for the angular variable, on for the energy component, and two or three degrees for spatial position respectively in 2D (cylindrical symmetry) and 3D). Two chapters are devoted to the coupling of discrete ordinates methods (for angular discretization). The first one is theoretical and shows the well posing of the coupled problem, whereas the second one deals with numerical applications of practical interest (the results have been obtained from the neutron transport code developed at the R and D, which has been modified for introducing the coupling). Next, we present the nodal scheme RTN0, used for the spatial discretization. We show well posing results for the non-coupled and the coupled problems. At the end, we deal with the coupling of energy discretizations for the multigroup equations obtained by homogenization. Some theoretical results of the discretization of the velocity variable (well-posing of problems), which do not deal directly with the purposes of coupling, are presented in the annexes. (author). 34 refs.

Radiation transport code with adaptive Mesh Refinement: acceleration techniques and applications

International Nuclear Information System (INIS)

Velarde, Pedro; Garcia-Fernaandez, Carlos; Portillo, David; Barbas, Alfonso

2011-01-01

We present a study of acceleration techniques for solving Sn radiation transport equations with Adaptive Mesh Refinement (AMR). Both DSA and TSA are considered, taking into account the influence of the interaction between different levels of the mesh structure and the order of approximation in angle. A Hybrid method is proposed in order to obtain better convergence rate and lower computer times. Some examples are presented relevant to ICF and X ray secondary sources. (author)

A hybrid transport-diffusion Monte Carlo method for frequency-dependent radiative-transfer simulations

International Nuclear Information System (INIS)

Densmore, Jeffery D.; Thompson, Kelly G.; Urbatsch, Todd J.

2012-01-01

Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Implicit Monte Carlo radiative-transfer simulations in optically thick media. In DDMC, particles take discrete steps between spatial cells according to a discretized diffusion equation. Each discrete step replaces many smaller Monte Carlo steps, thus improving the efficiency of the simulation. In this paper, we present an extension of DDMC for frequency-dependent radiative transfer. We base our new DDMC method on a frequency-integrated diffusion equation for frequencies below a specified threshold, as optical thickness is typically a decreasing function of frequency. Above this threshold we employ standard Monte Carlo, which results in a hybrid transport-diffusion scheme. With a set of frequency-dependent test problems, we confirm the accuracy and increased efficiency of our new DDMC method.

Moment equation approach to neoclassical transport theory

International Nuclear Information System (INIS)

Hirshman, S.P.

1978-01-01

The neoclassical cross-field fluxes for a toroidally confined, axisymmetric plasma are calculated in terms of the thermodynamic forces from the fluid continuity and momentum balance equations. This macroscopic formulation of neoclassical transport theory unifies the numerous complex expressions for the transport coefficients, previously obtained by solving the Fokker--Planck equation, and elucidates their physical basis. In the large aspect ratio limit, the continuous transition in the scaling of the diffusion coefficient throughout various collisionality regimes is shown to depend on the ratio of parallel viscosity coefficients of the plasma species. Comparison of the present results with the kinetic theory expressions for the neoclassical fluxes determines the parallel viscosity coefficients for a multispecies plasma in the long-mean-free-path regime

Variational formulation and projectional methods for the second order transport equation

International Nuclear Information System (INIS)

Borysiewicz, M.; Stankiewicz, R.

1979-01-01

Herein the variational problem for a second-order boundary value problem for the neutron transport equation is formulated. The projectional methods solving the problem are examined. The approach is compared with that based on the original untransformed form of the neutron transport equation

Neutronics methods for thermal radiative transfer

International Nuclear Information System (INIS)

Larsen, E.W.

1988-01-01

The equations of thermal radiative transfer are time discretized in a semi-implicit manner, yielding a linear transport problem for each time step. The governing equation in this problem has the form of a neutron transport equation with fission but no scattering. Numerical methods are described, whose origins lie in neutron transport, and that have been successfully adapted to this new problem. Acceleration methods that have been developed specifically for the radiative transfer problem, but may have generalizations applicable in neutronics problems, are also discussed

General Eulerian formulation of the comoving-frame equation of radiative transfer

International Nuclear Information System (INIS)

Riffert, H.

1986-01-01

For a wide range of problems in radiation hydrodynamics the motion of the matter is best described in an Eulerian coordinate system, and here a comoving-frame equation of radiation transfer in such fixed coordinates is derived, using the radiation quantities measured in the comoving frame. The choice of coordinates is arbitrary, and the equation is given explicitly for an arbitrary diagonal metric, correct to all orders in v/c. All comoving frame equations derived earlier are included as special cases. An example is given for the case of a spherically symmetric flow in a Schwarzschild metric. 9 references

Interference-exact radiative transfer equation

DEFF Research Database (Denmark)

Partanen, Mikko; Haÿrynen, Teppo; Oksanen, Jani

2017-01-01

Maxwell's equations with stochastic or quantum optical source terms accounting for the quantum nature of light. We show that both the nonlocal wave and local particle features associated with interference and emission of propagating fields in stratified geometries can be fully captured by local damping...... and scattering coefficients derived from the recently introduced quantized fluctuational electrodynamics (QFED) framework. In addition to describing the nonlocal optical interference processes as local directionally resolved effects, this allows reformulating the well known and widely used radiative transfer...... equation (RTE) as a physically transparent interference-exact model that extends the useful range of computationally efficient and quantum optically accurate interference-aware optical models from simple structures to full optical devices....

A hybrid transport-diffusion method for Monte Carlo radiative-transfer simulations

International Nuclear Information System (INIS)

Densmore, Jeffery D.; Urbatsch, Todd J.; Evans, Thomas M.; Buksas, Michael W.

2007-01-01

Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Monte Carlo particle-transport simulations in diffusive media. If standard Monte Carlo is used in such media, particle histories will consist of many small steps, resulting in a computationally expensive calculation. In DDMC, particles take discrete steps between spatial cells according to a discretized diffusion equation. Each discrete step replaces many small Monte Carlo steps, thus increasing the efficiency of the simulation. In addition, given that DDMC is based on a diffusion equation, it should produce accurate solutions if used judiciously. In practice, DDMC is combined with standard Monte Carlo to form a hybrid transport-diffusion method that can accurately simulate problems with both diffusive and non-diffusive regions. In this paper, we extend previously developed DDMC techniques in several ways that improve the accuracy and utility of DDMC for nonlinear, time-dependent, radiative-transfer calculations. The use of DDMC in these types of problems is advantageous since, due to the underlying linearizations, optically thick regions appear to be diffusive. First, we employ a diffusion equation that is discretized in space but is continuous in time. Not only is this methodology theoretically more accurate than temporally discretized DDMC techniques, but it also has the benefit that a particle's time is always known. Thus, there is no ambiguity regarding what time to assign a particle that leaves an optically thick region (where DDMC is used) and begins transporting by standard Monte Carlo in an optically thin region. Also, we treat the interface between optically thick and optically thin regions with an improved method, based on the asymptotic diffusion-limit boundary condition, that can produce accurate results regardless of the angular distribution of the incident Monte Carlo particles. Finally, we develop a technique for estimating radiation momentum deposition during the

Numerical solution of the transport equation describing the radon transport from subsurface soil to buildings

International Nuclear Information System (INIS)

Savovic, S.; Djordjevich, A.; Ristic, G.

2012-01-01

A theoretical evaluation of the properties and processes affecting the radon transport from subsurface soil into buildings is presented in this work. The solution of the relevant transport equation is obtained using the explicit finite difference method (EFDM). Results are compared with analytical steady-state solution reported in the literature. Good agreement is found. It is shown that EFDM is effective and accurate for solving the equation that describes radon diffusion, advection and decay during its transport from subsurface to buildings, which is especially important when arbitrary initial and boundary conditions are required. (authors)

Accuracy analysis of automodel solutions for Lévy flight-based transport: from resonance radiative transfer to a simple general model

Science.gov (United States)

Kukushkin, A. B.; Sdvizhenskii, P. A.

2017-12-01

The results of accuracy analysis of automodel solutions for Lévy flight-based transport on a uniform background are presented. These approximate solutions have been obtained for Green’s function of the following equations: the non-stationary Biberman-Holstein equation for three-dimensional (3D) radiative transfer in plasma and gases, for various (Doppler, Lorentz, Voigt and Holtsmark) spectral line shapes, and the 1D transport equation with a simple longtailed step-length probability distribution function with various power-law exponents. The results suggest the possibility of substantial extension of the developed method of automodel solution to other fields far beyond physics.

Effects of radiation transport on mass ablation rate and conversion efficiency in numerical simulations of inertial confinement fusion

International Nuclear Information System (INIS)

Gupta, N.K.

2002-01-01

The effects of radiation transport on hydrodynamic parameters of laser produced plasmas are studied. LTE and non-LTE atomic models are used to calculate multi group opacities and emissivities. Screened hydrogenic atom model is used to calculate the energy levels. The population densities of neutral to fully ionized ions are obtained by solving the steady state rate equations. Radiation transport is treated in multi-group diffusion or Sn method. A comparison is made between 1 and 100 group radiation transport and LTE and non-LTE models. For aluminium, multi group radiation transport leads to much higher mass ablation as compared to the 1 group and no radiation transport cases. This in turn leads to higher ablation pressures. However, for gold gray approximation gives higher mass ablation as compared to multi group simulations. LTE conversion efficiency of laser light into x-rays is more than the non-LTE estimates. For LTE as well as non-LTE cases, the one group approximation over-predicts the conversion efficiency Multi group non-LTE simulations predict that the conversion efficiency increases with laser intensity up to a maximum and then it decreases. (author)

An Implementation of Interfacial Transport Equation into the CUPID code

Energy Technology Data Exchange (ETDEWEB)

Park, Ik Kyu; Cho, Heong Kyu; Yoon, Han Young; Jeong, Jae Jun

2009-11-15

A component scale thermal hydraulic analysis code, CUPID (Component Unstructured Program for Interfacial Dynamics), is being developed for the analysis of components for a nuclear reactor, such as reactor vessel, steam generator, containment, etc. It adopted a three-dimensional, transient, two phase and three-field model. In order to develop the numerical schemes for the three-field model, various numerical schemes have been examined including the SMAS, semi-implicit ICE, SIMPLE. The governing equations for a 2-phase flow are composed of mass, momentum, and energy conservation equations for each phase. These equation sets are closed by the interfacial transfer rate of mass, momentum, and energy. The interfacial transfer of mass, momentum, and energy occurs through the interfacial area, and this area plays an important role in the transfer rate. The flow regime based correlations are used for calculating the interracial area in the traditional style 2-phase flow model. This is dependent upon the flow regime and is limited to the fully developed 2-phase flow region. Its application to the multi-dimensional 2-phase flow has some limitation because it adopts the measured results of 2-phase flow in the 1-dimensional tube. The interfacial area concentration transport equation had been suggested in order to calculate the interfacial area without the interfacial area correlations. The source terms to close the interfacial area transport equation should be further developed for a wide ranger usage of it. In this study, the one group interfacial area concentration transport equation has been implemented into the CUPID code. This interfacial area concentration transport equation can be used instead of the interfacial area concentration correlations for the bubbly flow region.

An Implementation of Interfacial Transport Equation into the CUPID code

International Nuclear Information System (INIS)

Park, Ik Kyu; Cho, Heong Kyu; Yoon, Han Young; Jeong, Jae Jun

2009-11-01

A component scale thermal hydraulic analysis code, CUPID (Component Unstructured Program for Interfacial Dynamics), is being developed for the analysis of components for a nuclear reactor, such as reactor vessel, steam generator, containment, etc. It adopted a three-dimensional, transient, two phase and three-field model. In order to develop the numerical schemes for the three-field model, various numerical schemes have been examined including the SMAS, semi-implicit ICE, SIMPLE. The governing equations for a 2-phase flow are composed of mass, momentum, and energy conservation equations for each phase. These equation sets are closed by the interfacial transfer rate of mass, momentum, and energy. The interfacial transfer of mass, momentum, and energy occurs through the interfacial area, and this area plays an important role in the transfer rate. The flow regime based correlations are used for calculating the interracial area in the traditional style 2-phase flow model. This is dependent upon the flow regime and is limited to the fully developed 2-phase flow region. Its application to the multi-dimensional 2-phase flow has some limitation because it adopts the measured results of 2-phase flow in the 1-dimensional tube. The interfacial area concentration transport equation had been suggested in order to calculate the interfacial area without the interfacial area correlations. The source terms to close the interfacial area transport equation should be further developed for a wide ranger usage of it. In this study, the one group interfacial area concentration transport equation has been implemented into the CUPID code. This interfacial area concentration transport equation can be used instead of the interfacial area concentration correlations for the bubbly flow region

Modified two-fluid model for the two-group interfacial area transport equation

International Nuclear Information System (INIS)

Sun Xiaodong; Ishii, Mamoru; Kelly, Joseph M.

2003-01-01

This paper presents a modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not practical to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model

Nodal collocation approximation for the multidimensional PL equations applied to transport source problems

Energy Technology Data Exchange (ETDEWEB)

Verdu, G. [Departamento de Ingenieria Quimica Y Nuclear, Universitat Politecnica de Valencia, Cami de Vera, 14, 46022. Valencia (Spain); Capilla, M.; Talavera, C. F.; Ginestar, D. [Dept. of Nuclear Engineering, Departamento de Matematica Aplicada, Universitat Politecnica de Valencia, Cami de Vera, 14, 46022. Valencia (Spain)

2012-07-01

PL equations are classical high order approximations to the transport equations which are based on the expansion of the angular dependence of the angular neutron flux and the nuclear cross sections in terms of spherical harmonics. A nodal collocation method is used to discretize the PL equations associated with a neutron source transport problem. The performance of the method is tested solving two 1D problems with analytical solution for the transport equation and a classical 2D problem. (authors)

Nodal collocation approximation for the multidimensional PL equations applied to transport source problems

International Nuclear Information System (INIS)

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

2012-01-01

PL equations are classical high order approximations to the transport equations which are based on the expansion of the angular dependence of the angular neutron flux and the nuclear cross sections in terms of spherical harmonics. A nodal collocation method is used to discretize the PL equations associated with a neutron source transport problem. The performance of the method is tested solving two 1D problems with analytical solution for the transport equation and a classical 2D problem. (authors)

Dynamics of radiating fluids

International Nuclear Information System (INIS)

Mihalas, D.; Weaver, R.

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 essential (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 is presented

The Method of Manufactured Solutions for RattleSnake A SN Radiation Transport Solver Inside the MOOSE Framework

International Nuclear Information System (INIS)

Wang, Yaqi

2012-01-01

The Method of Manufactured Solutions (MMS) is an accepted technique to verify that a numerical discretization for the radiation transport equation has been implemented correctly. This technique offers a few advantages over other methods such as benchmark problems or analytical solutions. The solution can be manufactured such that properties for the angular flux are either stressed or preserved. For radiation transport, these properties can include desired smoothness, positiveness and arbitrary order of anisotropy in angle. Another advantage is that the angular flux solution can be manufactured for multidimensional problems where analytical solutions are difficult to obtain in general.

Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

Energy Technology Data Exchange (ETDEWEB)

Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)

2013-01-01

In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

The transport equation in general geometry

International Nuclear Information System (INIS)

Pomraning, G.C.

1990-01-01

As stated in the introduction to the paper, the motivation for this work was to obtain an explicit form for the streaming operator in the transport equation, which could be used to compute curvature effects in an asymptotic analysis leading to diffusion theory. This sign error was discovered while performing this analysis

Differential equation of exospheric lateral transport and its application to terrestrial hydrogen

Science.gov (United States)

Hodges, R. R., Jr.

1973-01-01

The differential equation description of exospheric lateral transport of Hodges and Johnson is reformulated to extend its utility to light gases. Accuracy of the revised equation is established by applying it to terrestrial hydrogen. The resulting global distributions for several static exobase models are shown to be essentially the same as those that have been computed by Quessette using an integral equation approach. The present theory is subsequently used to elucidate the effects of nonzero lateral flow, exobase rotation, and diurnal tidal winds on the hydrogen distribution. Finally it is shown that the differential equation of exospheric transport is analogous to a diffusion equation. Hence it is practical to consider exospheric transport as a continuation of thermospheric diffusion, a concept that alleviates the need for an artificial exobase dividing thermosphere and exosphere.

Exactly averaged equations for flow and transport in random media

International Nuclear Information System (INIS)

Shvidler, Mark; Karasaki, Kenzi

2001-01-01

It is well known that exact averaging of the equations of flow and transport in random porous media can be realized only for a small number of special, occasionally exotic, fields. On the other hand, the properties of approximate averaging methods are not yet fully understood. For example, the convergence behavior and the accuracy of truncated perturbation series. Furthermore, the calculation of the high-order perturbations is very complicated. These problems for a long time have stimulated attempts to find the answer for the question: Are there in existence some exact general and sufficiently universal forms of averaged equations? If the answer is positive, there arises the problem of the construction of these equations and analyzing them. There exist many publications related to these problems and oriented on different applications: hydrodynamics, flow and transport in porous media, theory of elasticity, acoustic and electromagnetic waves in random fields, etc. We present a method of finding the general form of exactly averaged equations for flow and transport in random fields by using (1) an assumption of the existence of Green's functions for appropriate stochastic problems, (2) some general properties of the Green's functions, and (3) the some basic information about the random fields of the conductivity, porosity and flow velocity. We present a general form of the exactly averaged non-local equations for the following cases. 1. Steady-state flow with sources in porous media with random conductivity. 2. Transient flow with sources in compressible media with random conductivity and porosity. 3. Non-reactive solute transport in random porous media. We discuss the problem of uniqueness and the properties of the non-local averaged equations, for the cases with some types of symmetry (isotropic, transversal isotropic, orthotropic) and we analyze the hypothesis of the structure non-local equations in general case of stochastically homogeneous fields. (author)

Self-Adjoint Angular Flux Equation for Coupled Electron-Photon Transport

International Nuclear Information System (INIS)

Liscum-Powell, J.L.; Lorence, L.J. Jr.; Morel, J.E.; Prinja, A.K.

1999-01-01

Recently, Morel and McGhee described an alternate second-order form of the transport equation called the self adjoint angular flux (SAAF) equation that has the angular flux as its unknown. The SAAF formulation has all the advantages of the traditional even- and odd-parity self-adjoint equations, with the added advantages that it yields the full angular flux when it is numerically solved, it is significantly easier to implement reflective and reflective-like boundary conditions, and in the appropriate form it can be solved in void regions. The SAAF equation has the disadvantage that the angular domain is the full unit sphere and, like the even- and odd- parity form, S n source iteration cannot be implemented using the standard sweeping algorithm. Also, problems arise in pure scattering media. Morel and McGhee demonstrated the efficacy of the SAAF formulation for neutral particle transport. Here we apply the SAAF formulation to coupled electron-photon transport problems using multigroup cross-sections from the CEPXS code and S n discretization

Self-adjoint angular flux equation for coupled electron-photon transport

International Nuclear Information System (INIS)

Liscum-Powell, J.L.; Prinja, A.K.; Morel, J.E.; Lorence, L.J. Jr.

1999-01-01

Recently, Morel and McGhee described an alternate second-order form of the transport equation called the self-adjoint angular flux (SAAF) equation that has the angular flux as its unknown. The SAAF formulation has all the advantages of the traditional even- and odd-parity self-adjoint equations, with the added advantages that it yields the full angular flux when it is numerically solved, it is significantly easier to implement reflective and reflective-like boundary conditions, and in the appropriate form it can be solved in void regions. The SAAF equation has the disadvantage that the angular domain is the full unit sphere, and, like the even- and odd-parity form, S n source iteration cannot be implemented using the standard sweeping algorithm. Also, problems arise in pure scattering media. Morel and McGhee demonstrated the efficacy of the SAAF formulation for neutral particle transport. Here, the authors apply the SAAF formulation to coupled electron-photon transport problems using multigroup cross sections from the CEPXS code and S n discretization

Coupling of neutron transport equations. First results; Couplage d`equations en transport neutronique. premiere approche 1D monocinetique

Energy Technology Data Exchange (ETDEWEB)

Bal, G.

1995-07-01

To achieve whole core calculations of the neutron transport equation, we have to follow this 2 step method: space and energy homogenization of the assemblies; resolution of the homogenized equation on the whole core. However, this is no more valid when accidents occur (for instance depressurization causing locally strong heterogeneous media). One solution consists then in coupling two kinds of resolutions: a fine computation on the damaged cell (fine mesh, high number of energy groups) coupled with a coarse one everywhere else. We only deal here with steady state solutions (which already live in 6D spaces). We present here two such methods: The coupling by transmission of homogenized sections and the coupling by transmission of boundary conditions. To understand what this coupling is, we first restrict ourselves to 1D with respect to space in one energy group. The first two chapters deal with a recall of basic properties of the neutron transport equation. We give at chapter 3 some indications of the behaviour of the flux with respect to the cross sections. We present at chapter 4 some couplings and give some properties. Chapter 5 is devoted to a presentation of some numerical applications. (author). 9 refs., 7 figs.

A moving mesh finite difference method for equilibrium radiation diffusion equations

Energy Technology Data Exchange (ETDEWEB)

Yang, Xiaobo, E-mail: xwindyb@126.com [Department of Mathematics, College of Science, China University of Mining and Technology, Xuzhou, Jiangsu 221116 (China); Huang, Weizhang, E-mail: whuang@ku.edu [Department of Mathematics, University of Kansas, Lawrence, KS 66045 (United States); Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn [School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, Fujian 361005 (China)

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.

A moving mesh finite difference method for equilibrium radiation diffusion equations

International Nuclear Information System (INIS)

Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian

2015-01-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation

Utilization of a photon transport code to investigate radiation therapy treatment planning quantities and techniques

International Nuclear Information System (INIS)

Palta, J.R.

1981-01-01

A versatile computer program MORSE, based on neutron and photon transport theory has been utilzed to investigate radiation therapy treatment planning quantities and techniques. A multi-energy group representation of transport equation provides a concise approach in utilizing Monte Carlo numerical techniques to multiple radiation therapy treatment planning problems. Central axis total and scattered dose distributions for homogeneous and inhomogeneous water phantoms are calculated and the correction factor for lung and bone inhomogeneities are also evaluated. Results show that Monte Carlo calculations based on multi-energy group tansport theory predict the depth dose distributions that are in good agreement with available experimental data. Central axis depth dose distributions for a bremsstrahlung spectrum from a linear accelerator is also calculated to exhibit the versatility of the computer program in handling multiple radiation therapy problems. A novel approach is undertaken to study the dosimetric properties of brachytherapy sources

Radiative transfer equation for graded index medium in cylindrical and spherical coordinate systems

International Nuclear Information System (INIS)

Liu, L.H.; Zhang, L.; Tan, H.P.

2006-01-01

In graded index medium, the ray goes along a curved path determined by Fermat principle, and the curved ray-tracing is very difficult and complex. To avoid the complicated and time-consuming computation of curved ray trajectory, the methods not based on ray-tracing technique need to be developed for the solution of radiative transfer in graded index medium. For this purpose, in this paper the streaming operator along a curved ray trajectory in original radiative transfer equation for graded index medium is transformed and expressed in spatial and angular ordinates and the radiative transfer equation for graded index medium in cylindrical and spherical coordinate systems are derived. The conservative and the non-conservative forms of radiative transfer equation for three-dimensional graded index medium are given, which can be used as base equations to develop the numerical simulation methods, such as finite volume method, discrete ordinates method, and finite element method, for radiative transfer in graded index medium in cylindrical and spherical coordinate systems

Variance estimates for transport in stochastic media by means of the master equation

International Nuclear Information System (INIS)

Pautz, S. D.; Franke, B. C.; Prinja, A. K.

2013-01-01

The master equation has been used to examine properties of transport in stochastic media. It has been shown previously that not only may the Levermore-Pomraning (LP) model be derived from the master equation for a description of ensemble-averaged transport quantities, but also that equations describing higher-order statistical moments may be obtained. We examine in greater detail the equations governing the second moments of the distribution of the angular fluxes, from which variances may be computed. We introduce a simple closure for these equations, as well as several models for estimating the variances of derived transport quantities. We revisit previous benchmarks for transport in stochastic media in order to examine the error of these new variance models. We find, not surprisingly, that the errors in these variance estimates are at least as large as the corresponding estimates of the average, and sometimes much larger. We also identify patterns in these variance estimates that may help guide the construction of more accurate models. (authors)

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

Advances in the solution of three-dimensional nodal neutron transport equation

International Nuclear Information System (INIS)

Pazos, Ruben Panta; Hauser, Eliete Biasotto; Vilhena, Marco Tullio de

2003-01-01

In this paper we study the three-dimensional nodal discrete-ordinates approximations of neutron transport equation in a convex domain with piecewise smooth boundaries. We use the combined collocation method of the angular variables and nodal approach for the spatial variables. By nodal approach we mean the iterated transverse integration of the S N equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTS N method, first applying the Laplace transform to the set of the nodal S N equations and then obtaining the solution by symbolic computation. We include the LTS N method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTS N approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation. We give numerical results obtained with an algebraic computer system (for N up to 8) and with a code for higher values of N. We compare our results for the geometry of a box with a source in a vertex and a leakage zone in the opposite with others techniques used in this problem. (author)

A NUMERICAL SCHEME FOR SPECIAL RELATIVISTIC RADIATION MAGNETOHYDRODYNAMICS BASED ON SOLVING THE TIME-DEPENDENT RADIATIVE TRANSFER EQUATION

Energy Technology Data Exchange (ETDEWEB)

Ohsuga, Ken; Takahashi, Hiroyuki R. [National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588 (Japan)

2016-02-20

We develop a numerical scheme for solving the equations of fully special relativistic, radiation magnetohydrodynamics (MHDs), in which the frequency-integrated, time-dependent radiation transfer equation is solved to calculate the specific intensity. The radiation energy density, the radiation flux, and the radiation stress tensor are obtained by the angular quadrature of the intensity. In the present method, conservation of total mass, momentum, and energy of the radiation magnetofluids is guaranteed. We treat not only the isotropic scattering but also the Thomson scattering. The numerical method of MHDs is the same as that of our previous work. The advection terms are explicitly solved, and the source terms, which describe the gas–radiation interaction, are implicitly integrated. Our code is suitable for massive parallel computing. We present that our code shows reasonable results in some numerical tests for propagating radiation and radiation hydrodynamics. Particularly, the correct solution is given even in the optically very thin or moderately thin regimes, and the special relativistic effects are nicely reproduced.

PBMC: Pre-conditioned Backward Monte Carlo code for radiative transport in planetary atmospheres

Science.gov (United States)

García Muñoz, A.; Mills, F. P.

2017-08-01

PBMC (Pre-Conditioned Backward Monte Carlo) solves the vector Radiative Transport Equation (vRTE) and can be applied to planetary atmospheres irradiated from above. The code builds the solution by simulating the photon trajectories from the detector towards the radiation source, i.e. in the reverse order of the actual photon displacements. In accounting for the polarization in the sampling of photon propagation directions and pre-conditioning the scattering matrix with information from the scattering matrices of prior (in the BMC integration order) photon collisions, PBMC avoids the unstable and biased solutions of classical BMC algorithms for conservative, optically-thick, strongly-polarizing media such as Rayleigh atmospheres.

Solving the equation of neutron transport

International Nuclear Information System (INIS)

Nasfi, Rim

2009-01-01

This work is devoted to the study of some numerical methods of resolution of the problem of transport of the neutrons. We started by introducing the equation integro-differential transport of the neutrons. Then we applied the finite element method traditional for stationary and nonstationary linear problems in 2D. A great part is reserved for the presentation of the mixed numerical diagram and mixed hybrid with two types of uniform grids: triangular and rectangular. Thereafter we treated some numerical examples by implementations in Matlab in order to test the convergence of each method. To finish, we had results of simulation by the Monte Carlo method on a problem of two-dimensional transport with an aim of comparing them with the results resulting from the finite element method mixed hybrids. Some remarks and prospects conclude this work.

Stable solutions of nonlocal electron heat transport equations

International Nuclear Information System (INIS)

Prasad, M.K.; Kershaw, D.S.

1991-01-01

Electron heat transport equations with a nonlocal heat flux are in general ill-posed and intrinsically unstable, as proved by the present authors [Phys. Fluids B 1, 2430 (1989)]. A straightforward numerical solution of these equations will therefore lead to absurd results. It is shown here that by imposing a minimal set of constraints on the problem it is possible to arrive at a globally stable, consistent, and energy conserving numerical solution

Parallel processing Monte Carlo radiation transport codes

International Nuclear Information System (INIS)

McKinney, G.W.

1994-01-01

Issues related to distributed-memory multiprocessing as applied to Monte Carlo radiation transport are discussed. Measurements of communication overhead are presented for the radiation transport code MCNP which employs the communication software package PVM, and average efficiency curves are provided for a homogeneous virtual machine

On linear transport problems

International Nuclear Information System (INIS)

Ignatovich, V.K.

1989-01-01

The equations. governing the transport of radiation in plane media of finite thickness are formulated and solved in terms reflection and extintion of radiation inthe case of semi infinite media. 13 refs

An integral equation arising in two group neutron transport theory

International Nuclear Information System (INIS)

Cassell, J S; Williams, M M R

2003-01-01

An integral equation describing the fuel distribution necessary to maintain a flat flux in a nuclear reactor in two group transport theory is reduced to the solution of a singular integral equation. The formalism developed enables the physical aspects of the problem to be better understood and its relationship with the corresponding diffusion theory model is highlighted. The integral equation is solved by reducing it to a non-singular Fredholm equation which is then evaluated numerically

Aspheric surface testing by irradiance transport equation

Science.gov (United States)

Shomali, Ramin; Darudi, Ahmad; Nasiri, Sadollah; Asgharsharghi Bonab, Armir

2010-10-01

In this paper a method for aspheric surface testing is presented. The method is based on solving the Irradiance Transport Equation (ITE).The accuracy of ITE normally depends on the amount of the pick to valley of the phase distribution. This subject is investigated by a simulation procedure.

Nonrelativistic grey Sn-transport radiative-shock solutions

International Nuclear Information System (INIS)

Ferguson, J. M.; Morel, J. E.; Lowrie, R. B.

2017-01-01

We present semi-analytic radiative-shock solutions in which grey Sn-transport is used to model the radiation, and we include both constant cross sections and cross sections that depend on temperature and density. These new solutions solve for a variable Eddington factor (VEF) across the shock domain, which allows for interesting physics not seen before in radiative-shock solutions. Comparisons are made with the grey nonequilibrium-diffusion radiative-shock solutions of Lowrie and Edwards [1], which assumed that the Eddington factor is constant across the shock domain. It is our experience that the local Mach number is monotonic when producing nonequilibrium-diffusion solutions, but that this monotonicity may disappear while integrating the precursor region to produce Sn-transport solutions. For temperature- and density-dependent cross sections we show evidence of a spike in the VEF in the far upstream portion of the radiative-shock precursor. We show evidence of an adaptation zone in the precursor region, adjacent to the embedded hydrodynamic shock, as conjectured by Drake [2, 3], and also confirm his expectation that the precursor temperatures adjacent to the Zel’dovich spike take values that are greater than the downstream post-shock equilibrium temperature. We also show evidence that the radiation energy density can be nonmonotonic under the Zel’dovich spike, which is indicative of anti-diffusive radiation flow as predicted by McClarren and Drake [4]. We compare the angle dependence of the radiation flow for the Sn-transport and nonequilibriumdiffusion radiation solutions, and show that there are considerable differences in the radiation flow between these models across the shock structure. Lastly, we analyze the radiation flow to understand the cause of the adaptation zone, as well as the structure of the Sn-transport radiation-intensity solutions across the shock structure.

Solution of the transport equation with account for inelastic collisions

International Nuclear Information System (INIS)

Kalashnikov, N.P.; Remizovich, V.S.; Ryazanov, M.I.

1980-01-01

The theory of charged particle scattering in a matter with account for inelastic collisions is considered. In ''directly-forward'' approximation the transport equation at the absence of elastic collisions is obtained. The solution of the transport equation is made without and with account for fluctuation of energy losses. Formulas for path-energy relation are given. Energy spectrum and distribution of fast charged particles with respect to paths are studied. The problem of quantum mechanical approach to the theory of multiple scattering of fast charged particles in a matter is discussed briefly

Radiation transport phenomena and modeling - part A: Codes

International Nuclear Information System (INIS)

Lorence, L.J.

1997-01-01

The need to understand how particle radiation (high-energy photons and electrons) from a variety of sources affects materials and electronics has motivated the development of sophisticated computer codes that describe how radiation with energies from 1.0 keV to 100.0 GeV propagates through matter. Predicting radiation transport is the necessary first step in predicting radiation effects. The radiation transport codes that are described here are general-purpose codes capable of analyzing a variety of radiation environments including those produced by nuclear weapons (x-rays, gamma rays, and neutrons), by sources in space (electrons and ions) and by accelerators (x-rays, gamma rays, and electrons). Applications of these codes include the study of radiation effects on electronics, nuclear medicine (imaging and cancer treatment), and industrial processes (food disinfestation, waste sterilization, manufacturing.) The primary focus will be on coupled electron-photon transport codes, with some brief discussion of proton transport. These codes model a radiation cascade in which electrons produce photons and vice versa. This coupling between particles of different types is important for radiation effects. For instance, in an x-ray environment, electrons are produced that drive the response in electronics. In an electron environment, dose due to bremsstrahlung photons can be significant once the source electrons have been stopped

Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas

International Nuclear Information System (INIS)

Zawaideh, E.; Najmabadi, F.; Conn, R.W.

1986-01-01

A new set of two-fluid equations that are valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates with no zero-order drifts, a set of moment equations describing plasma transport along the field lines of a space- and time-dependent magnetic field is derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii, while in the weakly collisional limit they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations [Proc. R. Soc. London, Ser. A 236, 112 (1956)]. The new set of equations also exhibits a physical singularity at the sound speed. This singularity is used to derive and compute the sound speed. Numerical examples comparing these equations with conventional transport equations show that in the limit where the ratio of the mean free path lambda to the scale length of the magnetic field gradient L/sub B/ approaches zero, there is no significant difference between the solution of the new and conventional transport equations. However, conventional fluid equations, ordinarily expected to be correct to the order (lambda/L/sub B/) 2 , are found to have errors of order (lambda/L/sub u/) 2 = (lambda/L/sub B/) 2 /(1-M 2 ) 2 , where L/sub u/ is the scale length of the flow velocity gradient and M is the Mach number. As such, the conventional equations may contain large errors near the sound speed (Mroughly-equal1)

Normal and adjoint integral and integrodifferential neutron transport equations. Pt. 2

International Nuclear Information System (INIS)

Velarde, G.

1976-01-01

Using the simplifying hypotheses of the integrodifferential Boltzmann equations of neutron transport, given in JEN 334 report, several integral equations, and theirs adjoint ones, are obtained. Relations between the different normal and adjoint eigenfunctions are established and, in particular, proceeding from the integrodifferential Boltzmann equation it's found out the relation between the solutions of the adjoint equation of its integral one, and the solutions of the integral equation of its adjoint one (author)

An anisotropic diffusion approximation to thermal radiative transfer

International Nuclear Information System (INIS)

Johnson, Seth R.; Larsen, Edward W.

2011-01-01

This paper describes an anisotropic diffusion (AD) method that uses transport-calculated AD coefficients to efficiently and accurately solve the thermal radiative transfer (TRT) equations. By assuming weak gradients and angular moments in the radiation intensity, we derive an expression for the radiation energy density that depends on a non-local function of the opacity. This nonlocal function is the solution of a transport equation that can be solved with a single steady-state transport sweep once per time step, and the function's second angular moment is the anisotropic diffusion tensor. To demonstrate the AD method's efficacy, we model radiation flow down a channel in 'flatland' geometry. (author)

Study of the sensitivity of the radiation transport problem in a scattering medium

International Nuclear Information System (INIS)

Nunes, Rogerio Chaffin

2002-03-01

In this work, the system of differential equations obtained by the angular approach of the two-dimensional transport equation by the discrete ordinates method is solved through the formulation of finite elements with the objective of investigating the sensitivity of the outgoing flux of radiation with the incoming flux and the properties of absorption and scattering of the medium. The variational formulation for the system of differential equations of second order with the generalized boundary conditions of Neumann (third type) allows an easy implementation of the method of the finite elements with triangular mesh and approximation space of first order. The geometry chosen for the simulations is a circle with a non homogeneous circular form in its interior. The mapping of Dirichlet-Neumann is studied through various simulations involving the incoming flux, the outgoing flux and the properties of the medium. (author)

Survey of radiation protection programmes for transport

International Nuclear Information System (INIS)

Lizot, M.T.; Perrin, M.L.; Sert, G.; Lange, F.; Schwarz, G.; Feet, H.J.; Christ, R.; Shaw, K.B.; Hughes, J.S.; Gelder, R.

2001-07-01

The survey of radiation protection programmes for transport has been jointly performed by three scientific organisations I.P.S.N. (France), G.R.S. ( Germany), and N.R.P.B. (United kingdom) on behalf of the European Commission and the pertaining documentation summarises the findings and conclusions of the work that was undertaken with the principal objectives to provide guidance on the establishment, implementation and application of radiation protection programmes for the transport of radioactive materials by operators and the assessment and evaluation of such programmes by the competent authority and to review currently existing radiation protection programmes for the transport of radioactive materials. (N.C.)

A method for solving neutron transport equation

International Nuclear Information System (INIS)

Dimitrijevic, Z.

1993-01-01

The procedure for solving the transport equation by directly integrating for case one-dimensional uniform multigroup medium is shown. The solution is expressed in terms of linear combination of function H n (x,μ), and the coefficient is determined from given conditions. The solution is applied for homogeneous slab of critical thickness. (author)

Least-squares finite element discretizations of neutron transport equations in 3 dimensions

Energy Technology Data Exchange (ETDEWEB)

Manteuffel, T.A [Univ. of Colorado, Boulder, CO (United States); Ressel, K.J. [Interdisciplinary Project Center for Supercomputing, Zurich (Switzerland); Starkes, G. [Universtaet Karlsruhe (Germany)

1996-12-31

The least-squares finite element framework to the neutron transport equation introduced in is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. Here we report on some practical aspects of this approach for neutron transport calculations in three space dimensions. The systems of partial differential equations resulting from a P{sub 1} and P{sub 2} approximation of the angular dependence are derived. In the diffusive limit, the system is essentially a Poisson equation for zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. We report on the numerical results obtained for the minimum of the least-squares functional augmented by an additional boundary term using trilinear finite elements on a uniform tesselation into cubes.

Assessment of Haar Wavelet-Quasilinearization Technique in Heat Convection-Radiation Equations

Directory of Open Access Journals (Sweden)

Umer Saeed

2014-01-01

Full Text Available We showed that solutions by the Haar wavelet-quasilinearization technique for the two problems, namely, (i temperature distribution equation in lumped system of combined convection-radiation in a slab made of materials with variable thermal conductivity and (ii cooling of a lumped system by combined convection and radiation are strongly reliable and also more accurate than the other numerical methods and are in good agreement with exact solution. According to the Haar wavelet-quasilinearization technique, we convert the nonlinear heat transfer equation to linear discretized equation with the help of quasilinearization technique and apply the Haar wavelet method at each iteration of quasilinearization technique to get the solution. The main aim of present work is to show the reliability of the Haar wavelet-quasilinearization technique for heat transfer equations.

Solution of charged particle transport equation by Monte-Carlo method in the BRANDZ code system

International Nuclear Information System (INIS)

Artamonov, S.N.; Androsenko, P.A.; Androsenko, A.A.

1992-01-01

Consideration is given to the issues of Monte-Carlo employment for the solution of charged particle transport equation and its implementation in the BRANDZ code system under the conditions of real 3D geometry and all the data available on radiation-to-matter interaction in multicomponent and multilayer targets. For the solution of implantation problem the results of BRANDZ data comparison with the experiments and calculations by other codes in complexes systems are presented. The results of direct nuclear pumping process simulation for laser-active media by a proton beam are also included. 4 refs.; 7 figs

Implementation and testing of a multivariate inverse radiation transport solver

International Nuclear Information System (INIS)

Mattingly, John; Mitchell, Dean J.

2012-01-01

Detection, identification, and characterization of special nuclear materials (SNM) all face the same basic challenge: to varying degrees, each must infer the presence, composition, and configuration of the SNM by analyzing a set of measured radiation signatures. Solutions to this problem implement inverse radiation transport methods. Given a set of measured radiation signatures, inverse radiation transport estimates properties of the source terms and transport media that are consistent with those signatures. This paper describes one implementation of a multivariate inverse radiation transport solver. The solver simultaneously analyzes gamma spectrometry and neutron multiplicity measurements to fit a one-dimensional radiation transport model with variable layer thicknesses using nonlinear regression. The solver's essential components are described, and its performance is illustrated by application to benchmark experiments conducted with plutonium metal. - Highlights: ► Inverse problems, specifically applied to identifying and characterizing radiation sources . ► Radiation transport. ► Analysis of gamma spectroscopy and neutron multiplicity counting measurements. ► Experimental testing of the inverse solver against measurements of plutonium.

Novel Parallel Numerical Methods for Radiation and Neutron Transport

International Nuclear Information System (INIS)

Brown, P N

2001-01-01

In many of the multiphysics simulations performed at LLNL, transport calculations can take up 30 to 50% of the total run time. If Monte Carlo methods are used, the percentage can be as high as 80%. Thus, a significant core competence in the formulation, software implementation, and solution of the numerical problems arising in transport modeling is essential to Laboratory and DOE research. In this project, we worked on developing scalable solution methods for the equations that model the transport of photons and neutrons through materials. Our goal was to reduce the transport solve time in these simulations by means of more advanced numerical methods and their parallel implementations. These methods must be scalable, that is, the time to solution must remain constant as the problem size grows and additional computer resources are used. For iterative methods, scalability requires that (1) the number of iterations to reach convergence is independent of problem size, and (2) that the computational cost grows linearly with problem size. We focused on deterministic approaches to transport, building on our earlier work in which we performed a new, detailed analysis of some existing transport methods and developed new approaches. The Boltzmann equation (the underlying equation to be solved) and various solution methods have been developed over many years. Consequently, many laboratory codes are based on these methods, which are in some cases decades old. For the transport of x-rays through partially ionized plasmas in local thermodynamic equilibrium, the transport equation is coupled to nonlinear diffusion equations for the electron and ion temperatures via the highly nonlinear Planck function. We investigated the suitability of traditional-solution approaches to transport on terascale architectures and also designed new scalable algorithms; in some cases, we investigated hybrid approaches that combined both

Some results on the neutron transport and the coupling of equations

International Nuclear Information System (INIS)

Bal, G.

1997-01-01

Neutron transport in nuclear reactors is well modeled by the linear Boltzmann transport equation. Its resolution is relatively easy but very expensive. To achieve whole core calculations, one has to consider simpler models, such as diffusion or homogeneous transport equations. However, the solutions may become inaccurate in particular situations (as accidents for instance). That is the reason why we wish to solve the equations on small area accurately and more coarsely on the remaining part of the core. It is than necessary to introduce some links between different discretizations or modelizations. In this note, we give some results on the coupling of different discretizations of all degrees of freedom of the integral-differential neutron transport equation (two degrees for the angular variable, on for the energy component, and two or three degrees for spatial position respectively in 2D (cylindrical symmetry) and 3D). Two chapters are devoted to the coupling of discrete ordinates methods (for angular discretization). The first one is theoretical and shows the well posing of the coupled problem, whereas the second one deals with numerical applications of practical interest (the results have been obtained from the neutron transport code developed at the R and D, which has been modified for introducing the coupling). Next, we present the nodal scheme RTN0, used for the spatial discretization. We show well posing results for the non-coupled and the coupled problems. At the end, we deal with the coupling of energy discretizations for the multigroup equations obtained by homogenization. Some theoretical results of the discretization of the velocity variable (well-posing of problems), which do not deal directly with the purposes of coupling, are presented in the annexes. (author)

Kinetic Boltzmann, Vlasov and Related Equations

CERN Document Server

Sinitsyn, Alexander; Vedenyapin, Victor

2011-01-01

Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in

Application of the Radiative Transfer Equation (RTE) to Scattering by ...

African Journals Online (AJOL)

Application of the Radiative Transfer Equation (RTE) to Scattering by a Dust Aerosol Layer. ... Incident radiation in its journey through the atmosphere before reaching the earth surface encounters particles of different sizes and composition such as dust aerosols resulting in interactions that lead to absorption and scattering.

Application of the finite element method to the neutron transport equation

International Nuclear Information System (INIS)

Martin, W.R.

1976-01-01

This paper examines the theoretical and practical application of the finite element method to the neutron transport equation. It is shown that in principle the system of equations obtained by application of the finite element method can be solved with certain physical restrictions concerning the criticality of the medium. The convergence of this approximate solution to the exact solution with mesh refinement is examined, and a non-optical estimate of the convergence rate is obtained analytically. It is noted that the numerical results indicate a faster convergence rate and several approaches to obtain this result analytically are outlined. The practical application of the finite element method involved the development of a computer code capable of solving the neutron transport equation in 1-D plane geometry. Vacuum, reflecting, or specified incoming boundary conditions may be analyzed, and all are treated as natural boundary conditions. The time-dependent transport equation is also examined and it is shown that the application of the finite element method in conjunction with the Crank-Nicholson time discretization method results in a system of algebraic equations which is readily solved. Numerical results are given for several critical slab eigenvalue problems, including anisotropic scattering, and the results compare extremely well with benchmark results. It is seen that the finite element code is more efficient than a standard discrete ordinates code for certain problems. A problem with severe heterogeneities is considered and it is shown that the use of discontinuous spatial and angular elements results in a marked improvement in the results. Finally, time-dependent problems are examined and it is seen that the phenomenon of angular mode separation makes the numerical treatment of the transport equation in slab geometry a considerable challenge, with the result that the angular mesh has a dominant effect on obtaining acceptable solutions

Methodology for obtaining a solution for the three-dimensional Boltzmann transport equation and an expression for the calculation of the total doses considering Compton scattering simulated by Klein-Nishina

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)

Two-scale approach to oscillatory singularly perturbed transport equations

CERN Document Server

Frénod, Emmanuel

2017-01-01

This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master’s and PhD students interested in homogenization and numerics, as well as to the Iter community.

Transport equations in an enzymatic glucose fuel cell

Science.gov (United States)

Jariwala, Soham; Krishnamurthy, Balaji

2018-01-01

A mathematical model is developed to study the effects of convective flux and operating temperature on the performance of an enzymatic glucose fuel cell with a membrane. The model assumes isothermal operating conditions and constant feed rate of glucose. The glucose fuel cell domain is divided into five sections, with governing equations describing transport characteristics in each region, namely - anode diffusion layer, anode catalyst layer (enzyme layer), membrane, cathode catalyst layer and cathode diffusion layer. The mass transport is assumed to be one-dimensional and the governing equations are solved numerically. The effects flow rate of glucose feed on the performance of the fuel cell are studied as it contributes significantly to the convective flux. The effects of operating temperature on the performance of a glucose fuel cell are also modeled. The cell performances are compared using cell polarization curves, which were found compliant with experimental observations.

Two analytic transport equation solutions for particular cases of particle history

International Nuclear Information System (INIS)

Simovic, R.

1997-01-01

For anisotropic scattering and plane geometry, the linear transport equation of particles generated by a monodirectional unit source A(x,μ) = δ(x-0)δ(μ - μ 0 ) > 0, can be stated in the form of an integral equation

A stochastic solution of the advective transport equation with uncertainty

International Nuclear Information System (INIS)

Williams, M.M.R.

1991-01-01

A model has been developed for calculating the transport of water-borne radionuclides through layers of porous materials, such as rock or clay. The model is based upon a purely advective transport equation, in which the fluid velocity is a random variable, thereby simulating dispersion in a more realistic manner than the ad hoc introduction of a dispersivity. In addition to a random velocity field, which is an observable physical phenomenon, allowance is made for uncertainty in our knowledge of the parameters which enter the equation, e.g. the retardation coefficient. This too, is assumed to be a random variable and contributes to the stochasticity of the resulting partial differential equation of transport. The stochastic differential equation can be solved analytically and then ensemble averages taken over the associated probability distribution of velocity and retardation coefficient. A method based upon a novel form of the central limit theorem of statistics is employed to obtain tractable solutions of a system consisting of many serial legs of varying properties. One interesting conclusion is that the total flux out of a medium is significantly underestimated by using the deterministic solution with an average transit time compared with that from the stochastically averaged solution. The theory is illustrated numerically for a number of physically relevant cases. (author) 8 figs., 4 tabs., 7 refs

Transport equations, Level Set and Eulerian mechanics. Application to fluid-structure coupling

International Nuclear Information System (INIS)

Maitre, E.

2008-11-01

My works were devoted to numerical analysis of non-linear elliptic-parabolic equations, to neutron transport equation and to the simulation of fabrics draping. More recently I developed an Eulerian method based on a level set formulation of the immersed boundary method to deal with fluid-structure coupling problems arising in bio-mechanics. Some of the more efficient algorithms to solve the neutron transport equation make use of the splitting of the transport operator taking into account its characteristics. In the present work we introduced a new algorithm based on this splitting and an adaptation of minimal residual methods to infinite dimensional case. We present the case where the velocity space is of dimension 1 (slab geometry) and 2 (plane geometry) because the splitting is simpler in the former

Radiation transport: Progress report, July 1, 1987-September 30, 1987

International Nuclear Information System (INIS)

O'Dell, R.D.; Nagy, A.

1988-05-01

Research and development progress in radiation transport for the Los Alamos National Laboratory's Group S-6 for the fourth quarter of FY 87 is reported. Included are unclassified tasks in the areas of Deterministic Radiation Transport, Monte Carlo Radiation Transport, and Cross Sections and Physics. 23 refs., 9 figs

Available computer codes and data for radiation transport analysis

International Nuclear Information System (INIS)

Trubey, D.K.; Maskewitz, B.F.; Roussin, R.W.

1975-01-01

The Radiation Shielding Information Center (RSIC), sponsored and supported by the Energy Research and Development Administration (ERDA) and the Defense Nuclear Agency (DNA), is a technical institute serving the radiation transport and shielding community. It acquires, selects, stores, retrieves, evaluates, analyzes, synthesizes, and disseminates information on shielding and ionizing radiation transport. The major activities include: (1) operating a computer-based information system and answering inquiries on radiation analysis, (2) collecting, checking out, packaging, and distributing large computer codes, and evaluated and processed data libraries. The data packages include multigroup coupled neutron-gamma-ray cross sections and kerma coefficients, other nuclear data, and radiation transport benchmark problem results

Radiative transport-based frequency-domain fluorescence tomography

International Nuclear Information System (INIS)

Joshi, Amit; Rasmussen, John C; Sevick-Muraca, Eva M; Wareing, Todd A; McGhee, John

2008-01-01

We report the development of radiative transport model-based fluorescence optical tomography from frequency-domain boundary measurements. The coupled radiative transport model for describing NIR fluorescence propagation in tissue is solved by a novel software based on the established Attila(TM) particle transport simulation platform. The proposed scheme enables the prediction of fluorescence measurements with non-contact sources and detectors at a minimal computational cost. An adjoint transport solution-based fluorescence tomography algorithm is implemented on dual grids to efficiently assemble the measurement sensitivity Jacobian matrix. Finally, we demonstrate fluorescence tomography on a realistic computational mouse model to locate nM to μM fluorophore concentration distributions in simulated mouse organs

Photonuclear Physics in Radiation Transport - II: Implementation

International Nuclear Information System (INIS)

White, M.C.; Little, R.C.; Chadwick, M.B.; Young, P.G.; MacFarlane, R.E.

2003-01-01

This is the second of two companion papers. The first paper describes model calculations and nuclear data evaluations of photonuclear reactions on isotopes of C, O, Al, Si, Ca, Fe, Cu, Ta, W, and Pb for incident photon energies up to 150 MeV. This paper describes the steps taken to process these files into transport libraries and to update the Monte Carlo N-Particle (MCNP) and MCNPX radiation transport codes to use tabular photonuclear reaction data. The evaluated photonuclear data files are created in the standard evaluated nuclear data file (ENDF) format. These files must be processed by the NJOY data processing system into A Compact ENDF (ACE) files suitable for radiation transport calculations. MCNP and MCNPX have been modified to use these new data in a self-consistent and fully integrated manner. Verification problems were used at each step along the path to check the integrity of the methodology. The resulting methodology and tools provide a comprehensive system for using photonuclear data in radiation transport calculations. Also described are initial validation simulations used to benchmark several of the photonuclear transport tables

Evaluation of Clear-Sky Incoming Radiation Estimating Equations Typically Used in Remote Sensing Evapotranspiration Algorithms

Directory of Open Access Journals (Sweden)

Ted W. Sammis

2013-09-01

Full Text Available Net radiation is a key component of the energy balance, whose estimation accuracy has an impact on energy flux estimates from satellite data. In typical remote sensing evapotranspiration (ET algorithms, the outgoing shortwave and longwave components of net radiation are obtained from remote sensing data, while the incoming shortwave (RS and longwave (RL components are typically estimated from weather data using empirical equations. This study evaluates the accuracy of empirical equations commonly used in remote sensing ET algorithms for estimating RS and RL radiation. Evaluation is carried out through comparison of estimates and observations at five sites that represent different climatic regions from humid to arid. Results reveal (1 both RS and RL estimates from all evaluated equations well correlate with observations (R2 ≥ 0.92, (2 RS estimating equations tend to overestimate, especially at higher values, (3 RL estimating equations tend to give more biased values in arid and semi-arid regions, (4 a model that parameterizes the diffuse component of radiation using two clearness indices and a simple model that assumes a linear increase of atmospheric transmissivity with elevation give better RS estimates, and (5 mean relative absolute errors in the net radiation (Rn estimates caused by the use of RS and RL estimating equations varies from 10% to 22%. This study suggests that Rn estimates using recommended incoming radiation estimating equations could improve ET estimates.

Variable transformation of calibration equations for radiation dosimetry

International Nuclear Information System (INIS)

Watanabe, Yoichi

2005-01-01

For radiation dosimetry, dosimetric equipment must be calibrated by using known doses. The calibration is done to determine an equation that relates the absorbed dose to a physically measurable quantity. Since the calibration equation is accompanied by unavoidable uncertainties, the doses estimated with such equations suffer from inherent uncertainties. We presented mathematical formulation of the calibration when the calibration relation is either linear or nonlinear. We also derived equations for the uncertainty of the estimated dose as a function of the uncertainties of the parameters in the equations and the measured physical quantity. We showed that a dosimeter with a linear calibration equation with zero dose-offset enables us to perform relative dosimetry without calibration data. Furthermore, a linear equation justifies useful data manipulations such as rescaling the dose and changing the dose-offset for comparing dose distributions. Considering that some dosimeters exhibit linear response with a large dose-offset or often nonlinear response, we proposed variable transformations of the measured physical quantity, namely, linear- and log-transformation methods. The proposed methods were tested with Kodak X-Omat V radiographic film and BANG (registered) polymer gel dosimeter. We demonstrated that the variable transformation methods could lead to linear equations with zero dose-offset and could reduce the uncertainty of the estimated dose

A multigroup flux-limited asymptotic diffusion Fokker-Planck equation

International Nuclear Information System (INIS)

Liu Chengan

1987-01-01

A more perfrect flux-limited method is applied to combine with asymptotic diffusion theory of the radiation transpore, and the high peaked component in the scattering angle is treated with Fokker-Planck methods, thus the flux-limited asymptotic diffusion Fokker-Planck equation has been founded. Since the equation is of diffusion form, it retains the simplity and the convenience of the classical diffusion theory, and improves precision in describing radiation transport problems

Renormalization-group approach to nonlinear radiation-transport problems

International Nuclear Information System (INIS)

Chapline, G.F.

1980-01-01

A Monte Carlo method is derived for solving nonlinear radiation-transport problems that allows one to average over the effects of many photon absorptions and emissions at frequencies where the opacity is large. This method should allow one to treat radiation-transport problems with large optical depths, e.g., line-transport problems, with little increase in computational effort over that which is required for optically thin problems

Alternative formulation of the monokinetic transport equation

International Nuclear Information System (INIS)

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

1985-01-01

After recalling a technique already exploited in stationary neutron transport, the dynamic linear monokinetic equation for general geometry is cast into an integro-differential form where a second order space Laplace operator and both a second and first time derivatives appear. The introduced unknowns are given a physical interpretation for plane geometry and their relations with the total flux and current are derived

The accuracy of time dependent transport equation ergodic approximation

International Nuclear Information System (INIS)

Stancic, V.

1995-01-01

In order to predict the accuracy of the ergodic approximation for solving the time dependent transport equation, a comparison with respect to multiple collision and time finite difference methods, has been considered. (author)

Cable Connected Spinning Spacecraft, 1. the Canonical Equations, 2. Urban Mass Transportation, 3

Science.gov (United States)

Sitchin, A.

1972-01-01

Work on the dynamics of cable-connected spinning spacecraft was completed by formulating the equations of motion by both the canonical equations and Lagrange's equations and programming them for numerical solution on a digital computer. These energy-based formulations will permit future addition of the effect of cable mass. Comparative runs indicate that the canonical formulation requires less computer time. Available literature on urban mass transportation was surveyed. Areas of the private rapid transit concept of urban transportation are also studied.

Solution and study of nodal neutron transport equation applying the LTSN-DiagExp method

International Nuclear Information System (INIS)

Hauser, Eliete Biasotto; Pazos, Ruben Panta; Vilhena, Marco Tullio de; Barros, Ricardo Carvalho de

2003-01-01

In this paper we report advances about the three-dimensional nodal discrete-ordinates approximations of neutron transport equation for Cartesian geometry. We use the combined collocation method of the angular variables and nodal approach for the spatial variables. By nodal approach we mean the iterated transverse integration of the S N equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTS N method, first applying the Laplace transform to the set of the nodal S N equations and then obtained the solution by symbolic computation. We include the LTS N method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTS N approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation. (author)

A non-linear optimal Discontinuous Petrov-Galerkin method for stabilising the solution of the transport equation

International Nuclear Information System (INIS)

Merton, S. R.; Smedley-Stevenson, R. P.; Pain, C. C.; Buchan, A. G.; Eaton, M. D.

2009-01-01

This paper describes a new Non-Linear Discontinuous Petrov-Galerkin (NDPG) method and application to the one-speed Boltzmann Transport Equation (BTE) for space-time problems. The purpose of the method is to remove unwanted oscillations in the transport solution which occur in the vicinity of sharp flux gradients, while improving computational efficiency and numerical accuracy. This is achieved by applying artificial dissipation in the solution gradient direction, internal to an element using a novel finite element (FE) Riemann approach. The amount of dissipation added acts internal to each element. This is done using a gradient-informed scaling of the advection velocities in the stabilisation term. This makes the method in its most general form non-linear. The method is designed to be independent of angular expansion framework. This is demonstrated for the both discrete ordinates (S N ) and spherical harmonics (P N ) descriptions of the angular variable. Results show the scheme performs consistently well in demanding time dependent and multi-dimensional radiation transport problems. (authors)

Statistics of Monte Carlo methods used in radiation transport calculation

International Nuclear Information System (INIS)

Datta, D.

2009-01-01

Radiation transport calculation can be carried out by using either deterministic or statistical methods. Radiation transport calculation based on statistical methods is basic theme of the Monte Carlo methods. The aim of this lecture is to describe the fundamental statistics required to build the foundations of Monte Carlo technique for radiation transport calculation. Lecture note is organized in the following way. Section (1) will describe the introduction of Basic Monte Carlo and its classification towards the respective field. Section (2) will describe the random sampling methods, a key component of Monte Carlo radiation transport calculation, Section (3) will provide the statistical uncertainty of Monte Carlo estimates, Section (4) will describe in brief the importance of variance reduction techniques while sampling particles such as photon, or neutron in the process of radiation transport

Radiation transport. Progress report, April 1-December 31, 1983

International Nuclear Information System (INIS)

O'Dell, R.D.

1984-10-01

Research and development progress in radiation transport by the Los Alamos National Laboratory's Group X-6 for the last nine months of CY 83 is reported. Included are unclassified tasks in the areas of Fission Reactor Neutronics, Deterministic Transport Methods, Monte Carlo Radiation Transport, and Cross Sections and Physics

Solving the transport equation with quadratic finite elements: Theory and applications

International Nuclear Information System (INIS)

Ferguson, J.M.

1997-01-01

At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids

New diffusion-like solutions of one-speed transport equations in spherical geometry

International Nuclear Information System (INIS)

Sahni, D.C.

1988-01-01

Stationary, one-speed, spherically symmetric transport equations are considered in a conservative medium. Closed-form expressions are obtained for the angular flux ψ(r, μ) that yield a total flux varying as 1/r by using Sonine transforms. Properties of this solution are studied and it is shown that the solution can not be identified as a diffusion mode solution of the transport equation. Limitations of the Sonine transform technique are noted. (author)

Development of comprehensive models for opacities and radiation transport for IFE systems

International Nuclear Information System (INIS)

Tolkach, V.; Morozov, V.; Hassanein, A.

2003-01-01

An ignition in an inertial confinement fusion (ICF) reactor results in X-ray spectra and ion fluxes moving toward the chamber wall with different velocities. During flight, parts of the energy will be deposited either in the residual and/or protective chamber gas or in the initial vapor cloud developed near the wall surface from vaporization. The deposited energy will be re-radiated to the chamber wall long after the ignition process. The exact amount of energy deposited/radiated and time of deposition are key issues in evaluating the chamber response and the economical feasibility of an ICF reactor. The radiation processes in the protective gas layer or in the vapor cloud developed above the first wall play an important role in the overall dynamics of the ICF chamber. A self-consistent field method has been developed to calculate ionization potentials, atom and ion energy levels, transition probabilities, and other atomic properties used to calculate thermodynamic and optical characteristics of the plasma by means of collisional-radiation equilibrium (CRE). The methodology of solving radiation transport equations in spherical geometry and the dependence of results on the chosen theoretical model are demonstrated using the method of inward/outward directions

A modified two-fluid model for the application of two-group interfacial area transport equation

International Nuclear Information System (INIS)

Sun, X.; Ishii, M.; Kelly, J.

2003-01-01

This paper presents the modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not desirable to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model

Elliptic random-walk equation for suspension and tracer transport in porous media

DEFF Research Database (Denmark)

Shapiro, Alexander; Bedrikovetsky, P. G.

2008-01-01

. The new theory predicts delay of the maximum of the tracer, compared to the velocity of the flow, while its forward "tail" contains much more particles than in the solution of the classical parabolic (advection-dispersion) equation. This is in agreement with the experimental observations and predictions......We propose a new approach to transport of the suspensions and tracers in porous media. The approach is based on a modified version of the continuous time random walk (CTRW) theory. In the framework of this theory we derive an elliptic transport equation. The new equation contains the time...... of the CTRW theory. (C) 2008 Elsevier B.V. All rights reserved....

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)

A multigroup treatment of radiation transport

International Nuclear Information System (INIS)

Tahir, N.A.; Laing, E.W.; Nicholas, D.J.

1980-12-01

A multi-group radiation package is outlined which will accurately handle radiation transfer problems in laser-produced plasmas. Bremsstrahlung, recombination and line radiation are included as well as fast electron Bremsstrahlung radiation. The entire radiation field is divided into a large number of groups (typically 20), which diffuse radiation energy in real space as well as in energy space, the latter occurring via electron-radiation interaction. Using this model a radiation transport code will be developed to be incorporated into MEDUSA. This modified version of MEDUSA will be used to study radiative preheat effects in laser-compression experiments at the Central Laser Facility, Rutherford Laboratory. The model is also relevant to heavy ion fusion studies. (author)

A Green function of neutron transport equation

International Nuclear Information System (INIS)

Simovic, R.

1993-01-01

In this paper the angularly dependent Green function of the neutron transport equation is derived analytically and approximately. By applying the analytical FDPN approximation up to eighth order, numerical values of the Green functions are obtained with the accuracy of six significant figures in the whole range of parameter c, angle cosine μ and distances x up to the ten optical lengths from the neutron source. (author)

Analytical solution for the transport equation for neutral particles in cylindrical and Cartesian geometry

International Nuclear Information System (INIS)

Goncalves, Glenio Aguiar

2003-01-01

In this work, we are reported analytical solutions for the transport equation for neutral particles in cylindrical and cartesian geometry. For the cylindrical geometry, it is applied the Hankel transform of order zero in the S N approximation of the one-dimensional cylindrical transport equation, assuming azimuthal symmetry and isotropic scattering. This procedure is coined HTSN method. The anisotropic problem is handled using the decomposition method, generating a recursive approach, which the HTSN solution is used as initial condition. For cartesian geometry, the one and two dimensional transport equation is derived in the angular variable as many time as the degree of the anisotropic scattering. This procedure leads to set of integro-differential plus one differential equation that can be really solved by the variable separation method. Following this procedure, it was possible to come out with the Case solution for the one-dimensional problem. Numerical simulations are reported for the cylindrical transport problem both isotropic and anisotropic case of quadratic degree. (author)

Radiological emergency: road map for radiation accident victim transport

International Nuclear Information System (INIS)

Costa, V.S.G.; Alcantara, Y.P.; Lima, C.M.A.; Silva, F. C. A. da

2017-01-01

During a radiological or nuclear emergency, a number of necessary actions are taken, both within the radiation protection of individuals and the environment, involving many institutions and highly specialized personnel. Among them it is possible to emphasize the air transportation of radiation accident victims.The procedures and measures for the safe transport of these radiation accident victims are generally the responsibility of the armed forces, specifically the Aeronautics, with the action denominated 'Aeromedical Military Evacuation of Radiation Accident Victims'. The experience with the Radiological Accident of Goiânia demonstrated the importance of adequate preparation and response during a radiological emergency and the need for procedures and measures with regard to the transport of radiation victims are clearly defined and clearly presented for the effectiveness of the actions. This work presents the necessary actions for the transport of radiation accident victim during a radiological emergency, through the road map technique, which has been widely used in scientific technical area to facilitate understanding and show the way to be followed to reach the proposed objectives

Discrete energy formulation of neutron transport theory applied to solving the discrete ordinates equations

International Nuclear Information System (INIS)

Ching, J.; Oblow, E.M.; Goldstein, H.

1976-01-01

An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated that allows the development of a discrete energy, discrete ordinates method for the solution of radiation transport problems. In the discrete energy method, the group averaging required in the cross-section processing for multigroup calculations is replaced by a faster numerical quadrature scheme capable of generating transfer cross sections describing all the physical processes of interest on a fine point-energy grid. Test calculations in which the discrete energy method is compared with the multigroup method show that, for the same energy grid, the discrete energy method is much faster, although somewhat less accurate, than the multigroup method. However, the accuracy of the discrete energy method increases rapidly as the spacing between energy grid points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum, the discrete energy method is therefore expected to be far more economical than the multigroup technique for equivalent accuracy solutions. This advantage of the point method is demonstrated by application to the study of neutron transport in a thick iron slab

A high-order Petrov-Galerkin method for the Boltzmann transport equation

International Nuclear Information System (INIS)

Pain, C.C.; Candy, A.S.; Piggott, M.D.; Buchan, A.; Eaton, M.D.; Goddard, A.J.H.; Oliveira, C.R.E. de

2005-01-01

We describe a new Petrov-Galerkin method using high-order terms to introduce dissipation in a residual-free formulation. The method is developed following both a Taylor series analysis and a variational principle, and the result has much in common with traditional Petrov-Galerkin, Self Adjoint Angular Flux (SAAF) and Even Parity forms of the Boltzmann transport equation. In addition, we consider the subtleties in constructing appropriate boundary conditions. In sub-grid scale (SGS) modelling of fluids the advantages of high-order dissipation are well known. Fourth-order terms, for example, are commonly used as a turbulence model with uniform dissipation. They have been shown to have superior properties to SGS models based upon second-order dissipation or viscosity. Even higher-order forms of dissipation (e.g. 16.-order) can offer further advantages, but are only easily realised by spectral methods because of the solution continuity requirements that these higher-order operators demand. Higher-order operators are more effective, bringing a higher degree of representation to the solution locally. Second-order operators, for example, tend to relax the solution to a linear variation locally, whereas a high-order operator will tend to relax the solution to a second-order polynomial locally. The form of the dissipation is also important. For example, the dissipation may only be applied (as it is in this work) in the streamline direction. While for many problems, for example Large Eddy Simulation (LES), simply adding a second or fourth-order dissipation term is a perfectly satisfactory SGS model, it is well known that a consistent residual-free formulation is required for radiation transport problems. This motivated the consideration of a new Petrov-Galerkin method that is residual-free, but also benefits from the advantageous features that SGS modelling introduces. We close with a demonstration of the advantages of this new discretization method over standard Petrov

Sn approach applied to the solution of transport equation

International Nuclear Information System (INIS)

Lopes, J.P.

1973-09-01

In this work the origin of the Transport Theory is considered and the Transport Equation for the movement of the neutron in a system is established in its more general form, using the laws of nuclear physics. This equation is used as the starting point for development, under adequate assumptions, of simpler models that render the problem suitable for numerical solution. Representation of this model in different geometries is presented. The different processes of nuclear physics are introduced briefly and discussed. In addition, the boundary conditions for the different cases and a general procedure for the application of the Conservation Law are stated. The last chapter deals specifically with the S n method, its development, definitions and generalities. Computational schemes for obtaining the S n solution in spherical and cylindrical geometry, and convergence acceleration methods are also developed. (author)

Solution and Study of the Two-Dimensional Nodal Neutron Transport Equation

International Nuclear Information System (INIS)

Panta Pazos, Ruben; Biasotto Hauser, Eliete; Tullio de Vilhena, Marco

2002-01-01

In the last decade Vilhena and coworkers reported an analytical solution to the two-dimensional nodal discrete-ordinates approximations of the neutron transport equation in a convex domain. The key feature of these works was the application of the combined collocation method of the angular variable and nodal approach in the spatial variables. By nodal approach we mean the transverse integration of the SN equations. This procedure leads to a set of one-dimensional S N equations for the average angular fluxes in the variables x and y. These equations were solved by the old version of the LTS N method, which consists in the application of the Laplace transform to the set of nodal S N equations and solution of the resulting linear system by symbolic computation. It is important to recall that this procedure allow us to increase N the order of S N up to 16. To overcome this drawback we step forward performing a spectral painstaking analysis of the nodal S N equations for N up to 16 and we begin the convergence of the S N nodal equations defining an error for the angular flux and estimating the error in terms of the truncation error of the quadrature approximations of the integral term. Furthermore, we compare numerical results of this approach with those of other techniques used to solve the two-dimensional discrete approximations of the neutron transport equation. (authors)

On the Boltzmann Equation of Thermal Transport for Interacting Phonons and Electrons

Directory of Open Access Journals (Sweden)

Amelia Carolina Sparavigna

2016-05-01

Full Text Available The thermal transport in a solid can be determined by means of the Boltzmann equations regarding its distributions of phonons and electrons, when the solid is subjected to a thermal gradient. After solving the coupled equations, the related thermal conductivities can be obtained. Here we show how to determine the coupled equations for phonons and electrons.

The Schrödinger Equation, the Zero-Point Electromagnetic Radiation, and the Photoelectric Effect

Science.gov (United States)

França, H. M.; Kamimura, A.; Barreto, G. A.

2016-04-01

A Schrödinger type equation for a mathematical probability amplitude Ψ( x, t) is derived from the generalized phase space Liouville equation valid for the motion of a microscopic particle, with mass M and charge e, moving in a potential V( x). The particle phase space probability density is denoted Q( x, p, t), and the entire system is immersed in the "vacuum" zero-point electromagnetic radiation. We show, in the first part of the paper, that the generalized Liouville equation is reduced to a simpler Liouville equation in the equilibrium limit where the small radiative corrections cancel each other approximately. This leads us to a simpler Liouville equation that will facilitate the calculations in the second part of the paper. Within this second part, we address ourselves to the following task: Since the Schrödinger equation depends on hbar , and the zero-point electromagnetic spectral distribution, given by ρ 0{(ω )} = hbar ω 3/2 π 2 c3, also depends on hbar , it is interesting to verify the possible dynamical connection between ρ 0( ω) and the Schrödinger equation. We shall prove that the Planck's constant, present in the momentum operator of the Schrödinger equation, is deeply related with the ubiquitous zero-point electromagnetic radiation with spectral distribution ρ 0( ω). For simplicity, we do not use the hypothesis of the existence of the L. de Broglie matter-waves. The implications of our study for the standard interpretation of the photoelectric effect are discussed by considering the main characteristics of the phenomenon. We also mention, briefly, the effects of the zero-point radiation in the tunneling phenomenon and the Compton's effect.

Radiation protection programmes for the transport of radioactive material. Safety guide

International Nuclear Information System (INIS)

2007-01-01

This Safety Guide provides guidance on meeting the requirements for the establishment of radiation protection programmes (RPPs) for the transport of radioactive material, to optimize radiation protection in order to meet the requirements for radiation protection that underlie the Regulations for the Safe Transport of Radioactive Material. This Guide covers general aspects of meeting the requirements for radiation protection, but does not cover criticality safety or other possible hazardous properties of radioactive material. The annexes of this Guide include examples of RPPs, relevant excerpts from the Transport Regulations, examples of total dose per transport index handled, a checklist for road transport, specific segregation distances and emergency instructions for vehicle operators

On similarity and scaling of the radiative transfer equation

International Nuclear Information System (INIS)

Mitrescu, C.; Stephens, G.L.

2004-01-01

The present paper shows how the well-known similarity and scaling concepts are properties of the radiative transfer equation and not specifically of the degree of anisotropy of the phase function. It is shown that the key assumption regarding the angular dependence of the radiative field is essential in determining both the value for the parameter used to scale the radiative transfer, as well as the number of streams used in calculating the radiances for various atmospheric problems. Simulations performed on realistic type of cirrus clouds, characterized by strongly anisotropic functions, demonstrates the superior computational advantage for accurately simulating radiances. A new approach for determining the scaling parameter is introduced

Anti-diffusive radiation flow in the cooling layer of a radiating shock

International Nuclear Information System (INIS)

McClarren, Ryan G.; Paul Drake, R.

2010-01-01

This paper shows that for systems with optically thin, hot layers, such as those that occur in radiating shocks, radiation will flow uphill: radiation will flow from low to high radiation energy density. These are systems in which the angular distribution of the radiation intensity changes rapidly in space, and in which the radiation in some region has a pancaked structure, whose effect on the mean intensity will be much larger than the effect on the scalar radiation pressure. The salient feature of the solution to the radiative transfer equation in these circumstances is that the gradient of the radiation energy density is in the same direction as the radiation flux, i.e. radiation energy is flowing uphill. Such an anti-diffusive flow of energy cannot be captured by a model where the spatial variation of the Eddington factor is not accounted for, as in flux-limited diffusion models or the P 1 equations. The qualitative difference between the two models leads to a monotonic mean intensity for the diffusion model whereas the transport mean intensity has a global maximum in the hot layer. Mathematical analysis shows that the discrepancy between the diffusion model and the transport solution is due to an approximation of exponential integrals using a simple exponential.

Solution of the stellar structure equations in Eulerian coordinates

International Nuclear Information System (INIS)

Deupree, R.G.

1976-01-01

The equations of hydrostatic and thermal equilibrium, assuming only radiative energy transport and spherical symmetry, are solved in Eulerian coordinates by a suitable modification of the Henyey method. An Eulerian approach may possibly be more suitably extended to more spatial dimensions than the usual Lagrangian procedure. The principle advantage of this method is that the equations of hydrostatic and thermal equilibrium and Poisson's equation may be solved simultaneously

Correction of the wavefront using the irradiance transport equation

Science.gov (United States)

García, M.; Granados, F.; Cornejo, A.

2008-07-01

The correction of the wavefront in optical systems implies the use of wavefront sensors, software, and auxiliary optical systems. We propose evaluated the wavefront using the fact that the wavefront and its intensity are related in the mathematical expression the irradiance transport equation (ITE)

Effect of localized surface-plasmon mode on exciton transport and radiation emission in carbon nanotubes.

Science.gov (United States)

Roslyak, Oleksiy; Cherqui, Charles; Dunlap, David H; Piryatinski, Andrei

2014-07-17

We report on a general theoretical approach to study exciton transport and emission in a single-walled carbon nanotube (SWNT) in the presence of a localized surface-plasmon (SP) mode within a metal nanoparticle interacting via near-field coupling. We derive a set of quantum mechanical equations of motion and approximate rate equations that account for the exciton, SP, and the environmental degrees of freedom. The material equations are complemented by an expression for the radiated power that depends on the exciton and SP populations and coherences, allowing for an examination of the angular distribution of the emitted radiation that would be measured in experiment. Numerical simulations for a (6,5) SWNT and cone-shaped Ag metal tip (MT) have been performed using this methodology. Comparison with physical parameters shows that the near-field interaction between the exciton-SP occurs in a weak coupling regime, with the diffusion processes being much faster than the exciton-SP population exchange. In such a case, the effect of the exciton population transfer to the MT with its subsequent dissipation (i.e., the Förster energy transfer) is to modify the exciton steady state distribution while reducing the equilibration time for excitons to reach a steady sate distribution. We find that the radiation distribution is dominated by SP emission for a SWNT-MT separation of a few tens of nanometers due to the fast SP emission rate, whereas the exciton-SP coherences can cause its rotation.

Transport of radioactivity and radiation

International Nuclear Information System (INIS)

De Beer, G.P.

1988-01-01

The movement of radioactivity and radiation is of prime importance in a wide variety of fields and the present advanced degree of knowledge of transport mechanisms is due largely to the application of sophisticated computer techniques

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

International Nuclear Information System (INIS)

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

1982-01-01

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

Approximate solutions for the two-dimensional integral transport equation. The critically mixed methods of resolution

International Nuclear Information System (INIS)

Sanchez, Richard.

1980-11-01

This work is divided into two part the first part (note CEA-N-2165) deals with the solution of complex two-dimensional transport problems, the second one treats the critically mixed methods of resolution. These methods are applied for one-dimensional geometries with highly anisotropic scattering. In order to simplify the set of integral equation provided by the integral transport equation, the integro-differential equation is used to obtain relations that allow to lower the number of integral equation to solve; a general mathematical and numerical study is presented [fr

Molecular representation of molar domain (volume), evolution equations, and linear constitutive relations for volume transport.

Science.gov (United States)

Eu, Byung Chan

2008-09-07

In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel.

A multi scale approximation solution for the time dependent Boltzmann-transport equation

International Nuclear Information System (INIS)

Merk, B.

2004-03-01

The basis of all transient simulations for nuclear reactor cores is the reliable calculation of the power production. The local power distribution is generally calculated by solving the space, time, energy and angle dependent neutron transport equation known as Boltzmann equation. The computation of exact solutions of the Boltzmann equation is very time consuming. For practical numerical simulations approximated solutions are usually unavoidable. The objective of this work is development of an effective multi scale approximation solution for the Boltzmann equation. Most of the existing methods are based on separation of space and time. The new suggested method is performed without space-time separation. This effective approximation solution is developed on the basis of an expansion for the time derivative of different approximations to the Boltzmann equation. The method of multiple scale expansion is used for the expansion of the time derivative, because the problem of the stiff time behaviour can't be expressed by standard expansion methods. This multiple scale expansion is used in this work to develop approximation solutions for different approximations of the Boltzmann equation, starting from the expansion of the point kinetics equations. The resulting analytic functions are used for testing the applicability and accuracy of the multiple scale expansion method for an approximation solution with 2 delayed neutron groups. The results are tested versus the exact analytical results for the point kinetics equations. Very good agreement between both solutions is obtained. The validity of the solution with 2 delayed neutron groups to approximate the behaviour of the system with 6 delayed neutron groups is demonstrated in an additional analysis. A strategy for a solution with 4 delayed neutron groups is described. A multiple scale expansion is performed for the space-time dependent diffusion equation for one homogenized cell with 2 delayed neutron groups. The result is

Los Alamos radiation transport code system on desktop computing platforms

International Nuclear Information System (INIS)

Briesmeister, J.F.; Brinkley, F.W.; Clark, B.A.; West, J.T.

1990-01-01

The Los Alamos Radiation Transport Code System (LARTCS) consists of state-of-the-art Monte Carlo and discrete ordinates transport codes and data libraries. These codes were originally developed many years ago and have undergone continual improvement. With a large initial effort and continued vigilance, the codes are easily portable from one type of hardware to another. The performance of scientific work-stations (SWS) has evolved to the point that such platforms can be used routinely to perform sophisticated radiation transport calculations. As the personal computer (PC) performance approaches that of the SWS, the hardware options for desk-top radiation transport calculations expands considerably. The current status of the radiation transport codes within the LARTCS is described: MCNP, SABRINA, LAHET, ONEDANT, TWODANT, TWOHEX, and ONELD. Specifically, the authors discuss hardware systems on which the codes run and present code performance comparisons for various machines

Numerical simulation for fractional order stationary neutron transport equation using Haar wavelet collocation method

Energy Technology Data Exchange (ETDEWEB)

Saha Ray, S., E-mail: santanusaharay@yahoo.com; Patra, A.

2014-10-15

Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet collocation method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: In this paper the numerical solution for the fractional order stationary neutron transport equation is presented using Haar wavelet Collocation Method (HWCM). Haar wavelet collocation method is efficient and powerful in solving wide class of linear and nonlinear differential equations. This paper intends to provide an application of Haar wavelets to nuclear science problems. This paper describes the application of Haar wavelets for the numerical solution of fractional order stationary neutron transport equation in homogeneous medium with isotropic scattering. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency and applicability of the method, two test problems are discussed.

Study of the sensitivity of the radiation transport problem in a scattering medium; Estudo da sensibilidade do problema de transporte de radiacao em meio espalhador

Energy Technology Data Exchange (ETDEWEB)

Nunes, Rogerio Chaffin

2002-03-15

In this work, the system of differential equations obtained by the angular approach of the two-dimensional transport equation by the discrete ordinates method is solved through the formulation of finite elements with the objective of investigating the sensitivity of the outgoing flux of radiation with the incoming flux and the properties of absorption and scattering of the medium. The variational formulation for the system of differential equations of second order with the generalized boundary conditions of Neumann (third type) allows an easy implementation of the method of the finite elements with triangular mesh and approximation space of first order. The geometry chosen for the simulations is a circle with a non homogeneous circular form in its interior. The mapping of Dirichlet-Neumann is studied through various simulations involving the incoming flux, the outgoing flux and the properties of the medium. (author)

Parallel thermal radiation transport in two dimensions

International Nuclear Information System (INIS)

Smedley-Stevenson, R.P.; Ball, S.R.

2003-01-01

This paper describes the distributed memory parallel implementation of a deterministic thermal radiation transport algorithm in a 2-dimensional ALE hydrodynamics code. The parallel algorithm consists of a variety of components which are combined in order to produce a state of the art computational capability, capable of solving large thermal radiation transport problems using Blue-Oak, the 3 Tera-Flop MPP (massive parallel processors) computing facility at AWE (United Kingdom). Particular aspects of the parallel algorithm are described together with examples of the performance on some challenging applications. (author)

Parallel thermal radiation transport in two dimensions

Energy Technology Data Exchange (ETDEWEB)

Smedley-Stevenson, R.P.; Ball, S.R. [AWE Aldermaston (United Kingdom)

2003-07-01

This paper describes the distributed memory parallel implementation of a deterministic thermal radiation transport algorithm in a 2-dimensional ALE hydrodynamics code. The parallel algorithm consists of a variety of components which are combined in order to produce a state of the art computational capability, capable of solving large thermal radiation transport problems using Blue-Oak, the 3 Tera-Flop MPP (massive parallel processors) computing facility at AWE (United Kingdom). Particular aspects of the parallel algorithm are described together with examples of the performance on some challenging applications. (author)

An inverse method for radiation transport

Energy Technology Data Exchange (ETDEWEB)

Favorite, J. A. (Jeffrey A.); Sanchez, R. (Richard)

2004-01-01

Adjoint functions have been used with forward functions to compute gradients in implicit (iterative) solution methods for inverse problems in optical tomography, geoscience, thermal science, and other fields, but only once has this approach been used for inverse solutions to the Boltzmann transport equation. In this paper, this approach is used to develop an inverse method that requires only angle-independent flux measurements, rather than angle-dependent measurements as was done previously. The method is applied to a simplified form of the transport equation that does not include scattering. The resulting procedure uses measured values of gamma-ray fluxes of discrete, characteristic energies to determine interface locations in a multilayer shield. The method was implemented with a Newton-Raphson optimization algorithm, and it worked very well in numerical one-dimensional spherical test cases. A more sophisticated optimization method would better exploit the potential of the inverse method.

Finite element approximation to the even-parity transport equation

International Nuclear Information System (INIS)

Lewis, E.E.

1981-01-01

This paper studies the finite element method, a procedure for reducing partial differential equations to sets of algebraic equations suitable for solution on a digital computer. The differential equation is cast into the form of a variational principle, the resulting domain then subdivided into finite elements. The dependent variable is then approximated by a simple polynomial, and these are linked across inter-element boundaries by continuity conditions. The finite element method is tailored to a variety of transport problems. Angular approximations are formulated, and the extent of ray effect mitigation is examined. Complex trial functions are introduced to enable the inclusion of buckling approximations. The ubiquitous curved interfaces of cell calculations, and coarse mesh methods are also treated. A concluding section discusses limitations of the work to date and suggests possible future directions

Comparison of neutronic transport equation resolution nodal methods

International Nuclear Information System (INIS)

Zamonsky, O.M.; Gho, C.J.

1990-01-01

In this work, some transport equation resolution nodal methods are comparatively studied: the constant-constant (CC), linear-nodal (LN) and the constant-quadratic (CQ). A nodal scheme equivalent to finite differences has been used for its programming, permitting its inclusion in existing codes. Some bidimensional problems have been solved, showing that linear-nodal (LN) are, in general, obtained with accuracy in CPU shorter times. (Author) [es

TLC scheme for numerical solution of the transport equation on equilateral triangular meshes

International Nuclear Information System (INIS)

Walters, W.F.

1983-01-01

A new triangular linear characteristic TLC scheme for numerically solving the transport equation on equilateral triangular meshes has been developed. This scheme uses the analytic solution of the transport equation in the triangle as its basis. The data on edges of the triangle are assumed linear as is the source representation. A characteristic approach or nodal approach is used to obtain the analytic solution. Test problems indicate that the new TLC is superior to the widely used DITRI scheme for accuracy

Terahertz radiation induced chaotic electron transport in semiconductor superlattices with a tilted magnetic field

Energy Technology Data Exchange (ETDEWEB)

Wang, C., E-mail: cwang@mail.sim.ac.cn; Wang, F.; Cao, J. C., E-mail: jccao@mail.sim.ac.cn [Key Laboratory of Terahertz Solid-State Technology, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050 (China)

2014-09-01

Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation.

Terahertz radiation induced chaotic electron transport in semiconductor superlattices with a tilted magnetic field

International Nuclear Information System (INIS)

Wang, C.; Wang, F.; Cao, J. C.

2014-01-01

Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation

Terahertz radiation induced chaotic electron transport in semiconductor superlattices with a tilted magnetic field.

Science.gov (United States)

Wang, C; Wang, F; Cao, J C

2014-09-01

Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation.

Measurement of Membrane Characteristics Using the Phenomenological Equation and the Overall Mass Transport Equation in Ion-Exchange Membrane Electrodialysis of Saline Water

Directory of Open Access Journals (Sweden)

Yoshinobu Tanaka

2012-01-01

Full Text Available The overall membrane pair characteristics included in the overall mass transport equation are understandable using the phenomenological equations expressed in the irreversible thermodynamics. In this investigation, the overall membrane pair characteristics (overall transport number , overall solute permeability , overall electro-osmotic permeability and overall hydraulic permeability were measured by seawater electrodialysis changing current density, temperature and salt concentration, and it was found that occasionally takes minus value. For understanding the above phenomenon, new concept of the overall concentration reflection coefficient ∗ is introduced from the phenomenological equation. This is the aim of this investigation. ∗ is defined for describing the permselectivity between solutes and water molecules in the electrodialysis system just after an electric current interruption. ∗ is expressed by the function of and . ∗ is generally larger than 1 and is positive, but occasionally ∗ becomes less than 1 and becomes negative. Negative means that ions are transferred with water molecules (solvent from desalting cells toward concentrating cells just after an electric current interruption, indicating up-hill transport or coupled transport between water molecules and solutes.

Radiation inactivation studies of renal brush border water and urea transport

International Nuclear Information System (INIS)

Verkman, A.S.; Dix, J.A.; Seifter, J.L.; Skorecki, K.L.; Jung, C.Y.; Ausiello, D.A.

1985-01-01

Radiation inactivation was used to determine the nature and molecular weight of water and urea transport pathways in brush border membrane vesicles (BBMV) isolated from rabbit renal cortex. BBMV were frozen to -50 degrees C, irradiated with 1.5 MeV electrons, thawed, and assayed for transport or enzyme activity. The freezing process had no effect on enzyme or transport kinetics. BBMV alkaline phosphatase activity gave linear ln(activity) vs. radiation dose plots with a target size of 68 +/- 3 kDa, similar to previously reported values. Water and solute transport were measured using the stopped-flow light-scattering technique. The rates of acetamide and osmotic water transport did not depend on radiation dose (0-7 Mrad), suggesting that transport of these substances does not require a protein carrier. In contrast, urea and thiourea transport gave linear ln(activity) vs. dose curves with a target size of 125-150 kDa; 400 mM urea inhibited thiourea flux by -50% at 0 and 4.7 Mrad, showing that radiation does not affect inhibitor binding to surviving transporters. These studies suggest that BBMV urea transport requires a membrane protein, whereas osmotic water transport does not

Solution and study of nodal neutron transport equation applying the LTS{sub N}-DiagExp method

Energy Technology Data Exchange (ETDEWEB)

Hauser, Eliete Biasotto; Pazos, Ruben Panta [Pontificia Univ. Catolica do Rio Grande do Sul, Porto Alegre, RS (Brazil). Faculdade de Matematica]. E-mail: eliete@pucrs.br; rpp@mat.pucrs.br; Vilhena, Marco Tullio de [Pontificia Univ. Catolica do Rio Grande do Sul, Porto Alegre, RS (Brazil). Instituto de Matematica]. E-mail: vilhena@mat.ufrgs.br; Barros, Ricardo Carvalho de [Universidade do Estado, Nova Friburgo, RJ (Brazil). Instituto Politecnico]. E-mail: ricardo@iprj.uerj.br

2003-07-01

In this paper we report advances about the three-dimensional nodal discrete-ordinates approximations of neutron transport equation for Cartesian geometry. We use the combined collocation method of the angular variables and nodal approach for the spatial variables. By nodal approach we mean the iterated transverse integration of the S{sub N} equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTS{sub N} method, first applying the Laplace transform to the set of the nodal S{sub N} equations and then obtained the solution by symbolic computation. We include the LTS{sub N} method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTS{sub N} approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation. (author)

Relativistic transport equation for a discontinuity wave of multiplicity one

Energy Technology Data Exchange (ETDEWEB)

Giambo, S; Palumbo, A [Istituto di Matematica, Universita degli Studi, Messina (Italy)

1980-04-14

In the framework of the theory of the singular hypersurfaces, the transport equation for the amplitude of a discontinuity wave, corresponding to a simple characteristic of a quasi-linear hyperbolic system, is established in the context of special relativity.

Comparison of preconditioned generalized conjugate gradient methods to two-dimensional neutron and photon transport equation

International Nuclear Information System (INIS)

Chen, G.S.

1997-01-01

We apply and compare the preconditioned generalized conjugate gradient methods to solve the linear system equation that arises in the two-dimensional neutron and photon transport equation in this paper. Several subroutines are developed on the basis of preconditioned generalized conjugate gradient methods for time-independent, two-dimensional neutron and photon transport equation in the transport theory. These generalized conjugate gradient methods are used. TFQMR (transpose free quasi-minimal residual algorithm), CGS (conjuage gradient square algorithm), Bi-CGSTAB (bi-conjugate gradient stabilized algorithm) and QMRCGSTAB (quasi-minimal residual variant of bi-conjugate gradient stabilized algorithm). These sub-routines are connected to computer program DORT. Several problems are tested on a personal computer with Intel Pentium CPU. (author)

Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.

Science.gov (United States)

Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung

2018-01-01

A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.

A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media

Energy Technology Data Exchange (ETDEWEB)

Zhao, J.M., E-mail: jmzhao@hit.edu.cn [School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, People' s Republic of China (China); Tan, J.Y., E-mail: tanjy@hit.edu.cn [School of Auto Engineering, Harbin Institute of Technology at Weihai, 2 West Wenhua Road, Weihai 264209, People' s Republic of China (China); Liu, L.H., E-mail: lhliu@hit.edu.cn [School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, People' s Republic of China (China); School of Auto Engineering, Harbin Institute of Technology at Weihai, 2 West Wenhua Road, Weihai 264209, People' s Republic of China (China)

2013-01-01

A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J.E. Morel, B.T. Adams, T. Noh, J.M. McGhee, T.M. Evans, T.J. Urbatsch, Spatial discretizations for self-adjoint forms of the radiative transfer equations, J. Comput. Phys. 214 (1) (2006) 12-40 (where it was termed SAAI), J.M. Zhao, L.H. Liu, Second order radiative transfer equation and its properties of numerical solution using finite element method, Numer. Heat Transfer B 51 (2007) 391-409] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. The MSORTE contains a naturally introduced diffusion (or second order) term which provides better numerical property than the classic first order radiative transfer equation (RTE). The stability and convergence characteristics of the MSORTE discretized by central difference scheme is analyzed theoretically, and the better numerical stability of the second order form radiative transfer equations than the RTE when discretized by the central difference type method is proved. A collocation meshless method is developed based on the MSORTE to solve radiative transfer in inhomogeneous media. Several critical test cases are taken to verify the performance of the presented method. The collocation meshless method based on the MSORTE is demonstrated to be capable of stably and accurately solve radiative transfer in strongly inhomogeneous media, media with void region and even with discontinuous extinction coefficient.

Optical properties reconstruction using the adjoint method based on the radiative transfer equation

Science.gov (United States)

Addoum, Ahmad; Farges, Olivier; Asllanaj, Fatmir

2018-01-01

An efficient algorithm is proposed to reconstruct the spatial distribution of optical properties in heterogeneous media like biological tissues. The light transport through such media is accurately described by the radiative transfer equation in the frequency-domain. The adjoint method is used to efficiently compute the objective function gradient with respect to optical parameters. Numerical tests show that the algorithm is accurate and robust to retrieve simultaneously the absorption μa and scattering μs coefficients for lowly and highly absorbing medium. Moreover, the simultaneous reconstruction of μs and the anisotropy factor g of the Henyey-Greenstein phase function is achieved with a reasonable accuracy. The main novelty in this work is the reconstruction of g which might open the possibility to image this parameter in tissues as an additional contrast agent in optical tomography.

Numerical solution of neutron transport equations in discrete ordinates and slab geometry

International Nuclear Information System (INIS)

Serrano Pedraza, F.

1985-01-01

An unified formalism to solve numerically, between other equation, the neutron transport in discrete ordinates, slab geometry, several energy groups and independents of time, has been developed recently. Such a formalism cover some of the conventional schemes as diamond difference, (WDD) characteristic step (SC) lineal characteristic (LC), quadratic characteristic (QC) and lineal discontinuous. Unified formation gives before hand the convergence order of the previously selected scheme. In fact it allows besides to generate a big amount of numerical schemes, with which is also possible to solve numerical equations as soon as neutron transport. The essential purpose of this work was to solve the neutron transport equations in slab geometry and discrete ordinates considering several energy groups without to take under advisement time dependence based in the above mentioned unified formalism. To reach this purpose it was necesary to design a computer code with the name TNOD1 (Neutron transport in discrete ordinates and 1 dimension) which includes each one of the schemes already pointed out. there exist two numerical schemes, also recently developed, quadratic continuous (QC) and cubic continuous (CN), although covered by unified formalism, it has been possible to include them inside this computer code without make substantial changes in its structure. In chapter I, derivative of neutron transport equation independent of time is taken, for angular flux, including boundary conditions and discontinuity. In chapter II the neutron transport equations are obtained in multigroups, independents of time, for approximation of discrete ordinates. Description of theory related with unified formalism and its relationship with mentioned discretization schemes is presented in chapter III. Chapter IV describes the computer code developed and finally, in chapter V different numerical results obtained with TNOD1 program are shown. In Appendix A theorems and mathematical arguments used

Two-dimensional radiation shielding optimization analysis of spent fuel transport container

International Nuclear Information System (INIS)

Tian Yingnan; Chen Yixue; Yang Shouhai

2013-01-01

The intelligent radiation shielding optimization design software platform is a one-dimensional multi-target radiation shielding optimization program which is developed on the basis of the genetic algorithm program and one-dimensional discrete ordinate program-ANISN. This program was applied in the optimization design analysis of the spent fuel transport container radiation shielding. The multi-objective optimization calculation model of the spent fuel transport container radiation shielding was established, and the optimization calculation of the spent fuel transport container weight and radiation dose rate was carried by this program. The calculation results were checked by Monte-Carlo program-MCNP/4C. The results show that the weight of the optimized spent fuel transport container decreases to 81.1% of the origin and the radiation dose rate decreases to below 65.4% of the origin. The maximum deviation between the calculated values from the program and the MCNP is below 5%. The results show that the optimization design scheme is feasible and the calculation result is correct. (authors)

Dirac equation of spin particles and tunneling radiation from a Kinnersly black hole

Energy Technology Data Exchange (ETDEWEB)

Li, Guo-Ping; Zu, Xiao-Tao [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Feng, Zhong-Wen [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); China West Normal University, College of Physics and Space Science, Nanchong (China); Li, Hui-Ling [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Shenyang Normal University, College of Physics Science and Technology, Shenyang (China)

2017-04-15

In curved space-time, the Hamilton-Jacobi equation is a semi-classical particle equation of motion, which plays an important role in the research of black hole physics. In this paper, starting from the Dirac equation of spin 1/2 fermions and the Rarita-Schwinger equation of spin 3/2 fermions, respectively, we derive a Hamilton-Jacobi equation for the non-stationary spherically symmetric gravitational field background. Furthermore, the quantum tunneling of a charged spherically symmetric Kinnersly black hole is investigated by using the Hamilton-Jacobi equation. The result shows that the Hamilton-Jacobi equation is helpful to understand the thermodynamic properties and the radiation characteristics of a black hole. (orig.)

The RAGE radiation-hydrodynamic code

International Nuclear Information System (INIS)

Gittings, Michael; Clover, Michael; Betlach, Thomas; Byrne, Nelson; Ranta, Dale; Weaver, Robert; Coker, Robert; Dendy, Edward; Hueckstaedt, Robert; New, Kim; Oakes, W Rob; Stefan, Ryan

2008-01-01

We describe RAGE, the 'radiation adaptive grid Eulerian' radiation-hydrodynamics code, including its data structures, its parallelization strategy and performance, its hydrodynamic algorithm(s), its (gray) radiation diffusion algorithm, and some of the considerable amount of verification and validation efforts. The hydrodynamics is a basic Godunov solver, to which we have made significant improvements to increase the advection algorithm's robustness and to converge stiffnesses in the equation of state. Similarly, the radiation transport is a basic gray diffusion, but our treatment of the radiation-material coupling, wherein we converge nonlinearities in a novel manner to allow larger timesteps and more robust behavior, can be applied to any multi-group transport algorithm

Cellular neural network to the spherical harmonics approximation of neutron transport equation in x–y geometry

International Nuclear Information System (INIS)

Pirouzmand, Ahmad; Hadad, Kamal

2012-01-01

Highlights: ► This paper describes the solution of time-dependent neutron transport equation. ► We use a novel method based on cellular neural networks (CNNs) coupled with the spherical harmonics method. ► We apply the CNN model to simulate step and ramp perturbation transients in a core. ► The accuracy and capabilities of the CNN model are examined for x–y geometry. - Abstract: In an earlier paper we utilized a novel method using cellular neural networks (CNNs) coupled with spherical harmonics method to solve the steady state neutron transport equation in x–y geometry. Here, the previous work is extended to the study of time-dependent neutron transport equation. To achieve this goal, an equivalent electrical circuit based on a second-order form of time-dependent neutron transport equation and one equivalent group of neutron precursor density is obtained by the CNN method. The CNN model is used to simulate step and ramp perturbation transients in a typical 2D core.

Resolution of the neutron transport equation by a three-dimensional least square method

International Nuclear Information System (INIS)

Varin, Elisabeth

2001-01-01

The knowledge of space and time distribution of neutrons with a certain energy or speed allows the exploitation and control of a nuclear reactor and the assessment of the irradiation dose about an irradiated nuclear fuel storage site. The neutron density is described by a transport equation. The objective of this research thesis is to develop a software for the resolution of this stationary equation in a three-dimensional Cartesian domain by means of a deterministic method. After a presentation of the transport equation, the author gives an overview of the different deterministic resolution approaches, identifies their benefits and drawbacks, and discusses the choice of the Ressel method. The least square method is precisely described and then applied. Numerical benchmarks are reported for validation purposes

Study of Radiation Shielding Analysis for Low-Intermediate Level Waste Transport Ship

Energy Technology Data Exchange (ETDEWEB)

Kim, Dohyung; Lee, Unjang; Song, Yangsoo; Kim, Sukhoon; Ko, Jaehoon [Korea Nuclear Engineering and Service Corporation, Seoul (Korea, Republic of)

2007-07-01

In Korea, it is planed to transport Low-Intermediate Level Radioactive Waste (LILW) from each nuclear power plant site to Kyongju LILW repository after 2009. Transport through the sea using ship is one of the most prospective ways of LILW transport for current situation in Korea. There are domestic and international regulations for radiation dose limit for radioactive material transport. In this article, radiation shielding analysis for LILW transport ship is performed using 3-D computer simulation code, MCNP. As a result, the thickness and materials for radiation shielding walls next to cargo in the LILW transport ship are determined.

Solving the radiation diffusion and energy balance equations using pseudo-transient continuation

International Nuclear Information System (INIS)

Shestakov, A.I.; Greenough, J.A.; Howell, L.H.

2005-01-01

We develop a scheme for the system coupling the radiation diffusion and matter energy balance equations. The method is based on fully implicit, first-order, backward Euler differencing; Picard-Newton iterations solve the nonlinear system. We show that iterating on the radiation energy density and the emission source is more robust. Since the Picard-Newton scheme may not converge for all initial conditions and time steps, pseudo-transient continuation (Ψtc) is introduced. The combined Ψtc-Picard-Newton scheme is analyzed. We derive conditions on the Ψtc parameter that guarantee physically meaningful iterates, e.g., positive energies. Successive Ψtc iterates are bounded and the radiation energy density and emission source tend to equilibrate. The scheme is incorporated into a multiply dimensioned, massively parallel, Eulerian, radiation-hydrodynamic computer program with automatic mesh refinement (AMR). Three examples are presented that exemplify the scheme's performance. (1) The Pomraning test problem that models radiation flow into cold matter. (2) A similar, but more realistic problem simulating the propagation of an ionization front into tenuous hydrogen gas with a Saha model for the equation-of-state. (3) A 2D axisymmetric (R,Z) simulation with real materials featuring jetting, radiatively driven, interacting shocks

Solution of linear transport equation using Chebyshev polynomials and Laplace transform

International Nuclear Information System (INIS)

Cardona, A.V.; Vilhena, M.T.M.B. de

1994-01-01

The Chebyshev polynomials and the Laplace transform are combined to solve, analytically, the linear transport equation in planar geometry, considering isotropic scattering and the one-group model. Numerical simulation is presented. (author)

A new approach to radiative transfer theory using Jones's vectors. I

International Nuclear Information System (INIS)

Fymat, A.L.; Vasudevan, R.

1975-01-01

Radiative transfer of partially polarized radiation in an anisotropically scattering, inhomogeneous atmosphere containing arbitrary polydispersion of particles is described using Jones's amplitude vectors and matrices. This novel approach exploits the close analogy between the quantum mechanical states of spin 1/2 systems and the polarization states of electromagnetic radiation described by Jones's vector, and draws on the methodology of such spin 1/2 systems. The complete equivalence between the transport equation for Jones's vectors and the classical radiative transfer equation for Stokes's intensity vectors is demonstrated in two independent ways after deriving the transport equations for the polarization coherency matrices and for the quaternions corresponding to the Jones's vectors. A compact operator formulation of the theory is provided, and used to derive the necessary equations for both a local and a global description of the transport of Jones's vectors. Lastly, the integro-differential equations for the amplitude reflection and transmission matrices are derived, and related to the usual corresponding equations. The present formulation is the most succinct and the most convenient one for both theoretical and experimental studies. It yields a simpler analysis than the classical formulation since it reduces by a factor of two the dimensionality of transfer problems. It preserves information on phases, and thus can be used directly across the entire electromagnetic spectrum without any further conversion into intensities. (Auth.)

Radiation safety in sea transport of radioactive material in Japan

International Nuclear Information System (INIS)

Odano, N.; Yanagi, H.

2004-01-01

Radiation safety for sea transport of radioactive material in Japan has been discussed based on records of the exposed dose of sea transport workers and measured data of dose rate equivalents distribution inboard exclusive radioactive material shipping vessels. Recent surveyed records of the exposed doses of workers who engaged in sea transport operation indicate that exposed doses of transport workers are significantly low. Measured distribution of the exposed dose equivalents inboard those vessels indicates that dose rate equivalents inside those vessels are lower than levels regulated by the transport regulations of Japan. These facts clarify that radiation safety of inboard environment and handling of transport casks in sea transport of radioactive material in Japan are assured

Radiation safety in sea transport of radioactive material in Japan

Energy Technology Data Exchange (ETDEWEB)

Odano, N. [National Maritime Research Inst., Tokyo (Japan); Yanagi, H. [Nuclear Fuel Transport Co., Ltd., Tokyo (Japan)

2004-07-01

Radiation safety for sea transport of radioactive material in Japan has been discussed based on records of the exposed dose of sea transport workers and measured data of dose rate equivalents distribution inboard exclusive radioactive material shipping vessels. Recent surveyed records of the exposed doses of workers who engaged in sea transport operation indicate that exposed doses of transport workers are significantly low. Measured distribution of the exposed dose equivalents inboard those vessels indicates that dose rate equivalents inside those vessels are lower than levels regulated by the transport regulations of Japan. These facts clarify that radiation safety of inboard environment and handling of transport casks in sea transport of radioactive material in Japan are assured.

Use of implicit Monte Carlo radiation transport with hydrodynamics and compton scattering

International Nuclear Information System (INIS)

Fleck, J.A. Jr.

1971-03-01

It is shown that the combination of implicit radiation transport and hydrodynamics, Compton scattering, and any other energy transport can be simply carried out by a ''splitting'' procedure. Contributions to material energy exchange can be reckoned separately for hydrodynamics, radiation transport without scattering, Compton scattering, plus any other possible energy exchange mechanism. The radiation transport phase of the calculation would be implicit, but the hydrodynamics and Compton portions would not, leading to possible time step controls. The time step restrictions which occur on radiation transfer due to large Planck mean absorption cross-sections would not occur

Adomian decomposition method for solving the telegraph equation in charged particle transport

International Nuclear Information System (INIS)

Abdou, M.A.

2005-01-01

In this paper, the analysis for the telegraph equation in case of isotropic small angle scattering from the Boltzmann transport equation for charged particle is presented. The Adomian decomposition is used to solve the telegraph equation. By means of MAPLE the Adomian polynomials of obtained series (ADM) solution have been calculated. The behaviour of the distribution function are shown graphically. The results reported in this article provide further evidence of the usefulness of Adomain decomposition for obtaining solution of linear and nonlinear problems

Maximal stochastic transport in the Lorenz equations

Energy Technology Data Exchange (ETDEWEB)

Agarwal, Sahil, E-mail: sahil.agarwal@yale.edu [Program in Applied Mathematics, Yale University, New Haven (United States); Wettlaufer, J.S., E-mail: john.wettlaufer@yale.edu [Program in Applied Mathematics, Yale University, New Haven (United States); Departments of Geology & Geophysics, Mathematics and Physics, Yale University, New Haven (United States); Mathematical Institute, University of Oxford, Oxford (United Kingdom); Nordita, Royal Institute of Technology and Stockholm University, Stockholm (Sweden)

2016-01-08

We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh–Bénard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [1], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity depends on the number of realizations in the ensemble; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits, the degree of which depends on the degree to which the ensemble represents the ergodic set. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations and the numerical convergence of the noise correlations. The numerical convergence of both the ensemble and time averages of the noise correlations is sufficiently slow that it is the limiting aspect of the realization of these bounds. Finally, we note that the full solutions of the stochastic equations demonstrate that the effect of noise is equivalent to the effect of chaos.

Collapsing radiating stars with various equations of state

Science.gov (United States)

Brassel, Byron P.; Goswami, Rituparno; Maharaj, Sunil D.

2017-06-01

We study the gravitational collapse of radiating stars in the context of the cosmic censorship conjecture. We consider a generalized Vaidya spacetime with three concentric regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. We outline the general mathematical framework to study the conditions on the mass function so that future-directed nonspacelike geodesics can terminate at the singularity in the past. Mass functions for several equations of state are analyzed using this framework and it is shown that the collapse in each case terminates at a locally naked central singularity. We calculate the strength of these singularities to show that they are strong curvature singularities which implies that no extension of spacetime through them is possible.

Application of Trotter approximation for solving time dependent neutron transport equation

International Nuclear Information System (INIS)

Stancic, V.

1987-01-01

A method is proposed to solve multigroup time dependent neutron transport equation with arbitrary scattering anisotropy. The recurrence relation thus obtained is simple, numerically stable and especially suitable for treatment of complicated geometries. (author)

Experimental verification of theoretical equations for acoustic radiation force on compressible spherical particles in traveling waves

Science.gov (United States)

Johnson, Kennita A.; Vormohr, Hannah R.; Doinikov, Alexander A.; Bouakaz, Ayache; Shields, C. Wyatt; López, Gabriel P.; Dayton, Paul A.

2016-05-01

Acoustophoresis uses acoustic radiation force to remotely manipulate particles suspended in a host fluid for many scientific, technological, and medical applications, such as acoustic levitation, acoustic coagulation, contrast ultrasound imaging, ultrasound-assisted drug delivery, etc. To estimate the magnitude of acoustic radiation forces, equations derived for an inviscid host fluid are commonly used. However, there are theoretical predictions that, in the case of a traveling wave, viscous effects can dramatically change the magnitude of acoustic radiation forces, which make the equations obtained for an inviscid host fluid invalid for proper estimation of acoustic radiation forces. To date, experimental verification of these predictions has not been published. Experimental measurements of viscous effects on acoustic radiation forces in a traveling wave were conducted using a confocal optical and acoustic system and values were compared with available theories. Our results show that, even in a low-viscosity fluid such as water, the magnitude of acoustic radiation forces is increased manyfold by viscous effects in comparison with what follows from the equations derived for an inviscid fluid.

The discontinuous finite element method for solving Eigenvalue problems of transport equations

International Nuclear Information System (INIS)

Yang, Shulin; Wang, Ruihong

2011-01-01

In this paper, the multigroup transport equations for solving the eigenvalues λ and K_e_f_f under two dimensional cylindrical coordinate are discussed. Aimed at the equations, the discretizing way combining discontinuous finite element method (DFE) with discrete ordinate method (SN) is developed, and the iterative algorithms and steps are studied. The numerical results show that the algorithms are efficient. (author)

The H-N method for solving linear transport equation: theory and application

International Nuclear Information System (INIS)

Kaskas, A.; Gulecyuz, M.C.; Tezcan, C.

2002-01-01

The system of singular integral equation which is obtained from the integro-differential form of the linear transport equation as a result of Placzec lemma is solved. Application are given using the exit distributions and the infinite medium Green's function. The same theoretical results are also obtained with the use of the singular eigenfunction of the method of elementary solutions

Predicting fractional bed load transport rates: Application of the Wilcock‐Crowe equations to a regulated gravel bed river

Science.gov (United States)

Gaeuman, David; Andrews, E.D.; Krause, Andreas; Smith, Wes

2009-01-01

Bed load samples from four locations in the Trinity River of northern California are analyzed to evaluate the performance of the Wilcock‐Crowe bed load transport equations for predicting fractional bed load transport rates. Bed surface particles become smaller and the fraction of sand on the bed increases with distance downstream from Lewiston Dam. The dimensionless reference shear stress for the mean bed particle size (τ*rm) is largest near the dam, but varies relatively little between the more downstream locations. The relation between τ*rm and the reference shear stresses for other size fractions is constant across all locations. Total bed load transport rates predicted with the Wilcock‐Crowe equations are within a factor of 2 of sampled transport rates for 68% of all samples. The Wilcock‐Crowe equations nonetheless consistently under‐predict the transport of particles larger than 128 mm, frequently by more than an order of magnitude. Accurate prediction of the transport rates of the largest particles is important for models in which the evolution of the surface grain size distribution determines subsequent bed load transport rates. Values of τ*rm estimated from bed load samples are up to 50% larger than those predicted with the Wilcock‐Crowe equations, and sampled bed load transport approximates equal mobility across a wider range of grain sizes than is implied by the equations. Modifications to the Wilcock‐Crowe equation for determining τ*rm and the hiding function used to scale τ*rm to other grain size fractions are proposed to achieve the best fit to observed bed load transport in the Trinity River.

Academic Training - The use of Monte Carlo radiation transport codes in radiation physics and dosimetry

CERN Multimedia

Françoise Benz

2006-01-01

2005-2006 ACADEMIC TRAINING PROGRAMME LECTURE SERIES 27, 28, 29 June 11:00-12:00 - TH Conference Room, bldg. 4 The use of Monte Carlo radiation transport codes in radiation physics and dosimetry F. Salvat Gavalda,Univ. de Barcelona, A. FERRARI, CERN-AB, M. SILARI, CERN-SC Lecture 1. Transport and interaction of electromagnetic radiation F. Salvat Gavalda,Univ. de Barcelona Interaction models and simulation schemes implemented in modern Monte Carlo codes for the simulation of coupled electron-photon transport will be briefly reviewed. Different schemes for simulating electron transport will be discussed. Condensed algorithms, which rely on multiple-scattering theories, are comparatively fast, but less accurate than mixed algorithms, in which hard interactions (with energy loss or angular deflection larger than certain cut-off values) are simulated individually. The reliability, and limitations, of electron-interaction models and multiple-scattering theories will be analyzed. Benchmark comparisons of simu...

A time dependent mixing model to close PDF equations for transport in heterogeneous aquifers

Science.gov (United States)

Schüler, L.; Suciu, N.; Knabner, P.; Attinger, S.

2016-10-01

Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the concentration variance, used in moment methods. The mixing model, describing the transport of the PDF in concentration space, is essential for both methods. Finding a satisfactory mixing model is still an open question and due to the rather elaborate PDF methods, a difficult undertaking. Both the PDF equation and the concentration variance equation depend on the same mixing model. This connection is used to find and test an improved mixing model for the much easier to handle concentration variance. Subsequently, this mixing model is transferred to the PDF equation and tested. The newly proposed mixing model yields significantly improved results for both variance modelling and PDF modelling.

Intense radiative heat transport across a nano-scale gap

International Nuclear Information System (INIS)

Budaev, Bair V.; Ghafari, Amin; Bogy, David B.

2016-01-01

In this paper, we analyze the radiative heat transport in layered structures. The analysis is based on our prior description of the spectrum of thermally excited waves in systems with a heat flux. The developed method correctly predicts results for all known special cases for both large and closing gaps. Numerical examples demonstrate the applicability of our approach to the calculation of the radiative heat transport coefficient across various layered structures.

The RAGE radiation-hydrodynamic code

Energy Technology Data Exchange (ETDEWEB)

Gittings, Michael; Clover, Michael; Betlach, Thomas; Byrne, Nelson; Ranta, Dale [Science Applications International Corp. MS A-1, 10260 Campus Point Drive, San Diego, CA 92121 (United States); Weaver, Robert; Coker, Robert; Dendy, Edward; Hueckstaedt, Robert; New, Kim; Oakes, W Rob [Los Alamos National Laboratory, MS T087, PO Box 1663, Los Alamos, NM 87545 (United States); Stefan, Ryan [TaylorMade-adidas Golf, 5545 Fermi Court, Carlsbad, CA 92008-7324 (United States)], E-mail: michael.r.clover@saic.com

2008-10-01

We describe RAGE, the 'radiation adaptive grid Eulerian' radiation-hydrodynamics code, including its data structures, its parallelization strategy and performance, its hydrodynamic algorithm(s), its (gray) radiation diffusion algorithm, and some of the considerable amount of verification and validation efforts. The hydrodynamics is a basic Godunov solver, to which we have made significant improvements to increase the advection algorithm's robustness and to converge stiffnesses in the equation of state. Similarly, the radiation transport is a basic gray diffusion, but our treatment of the radiation-material coupling, wherein we converge nonlinearities in a novel manner to allow larger timesteps and more robust behavior, can be applied to any multi-group transport algorithm.

Radiative transfer equation accounting for rotational Raman scattering and its solution by the discrete-ordinates method

International Nuclear Information System (INIS)

Rozanov, Vladimir V.; Vountas, Marco

2014-01-01

Rotational Raman scattering of solar light in Earth's atmosphere leads to the filling-in of Fraunhofer and telluric lines observed in the reflected spectrum. The phenomenological derivation of the inelastic radiative transfer equation including rotational Raman scattering is presented. The different forms of the approximate radiative transfer equation with first-order rotational Raman scattering terms are obtained employing the Cabannes, Rayleigh, and Cabannes–Rayleigh scattering models. The solution of these equations is considered in the framework of the discrete-ordinates method using rigorous and approximate approaches to derive particular integrals. An alternative forward-adjoint technique is suggested as well. A detailed description of the model including the exact spectral matching and a binning scheme that significantly speeds up the calculations is given. The considered solution techniques are implemented in the radiative transfer software package SCIATRAN and a specified benchmark setup is presented to enable readers to compare with own results transparently. -- Highlights: • We derived the radiative transfer equation accounting for rotational Raman scattering. • Different approximate radiative transfer approaches with first order scattering were used. • Rigorous and approximate approaches are shown to derive particular integrals. • An alternative forward-adjoint technique is suggested as well. • An additional spectral binning scheme which speeds up the calculations is presented

Transport methods: general. 3. An Additive Angular-Dependent Re-balance Acceleration Method for Neutron Transport Equations

International Nuclear Information System (INIS)

Cho, Nam Zin; Park, Chang Je

2001-01-01

An additive angular-dependent re-balance (AADR) factor acceleration method is described to accelerate the source iteration of discrete ordinates transport calculation. The formulation of the AADR method follows that of the angular-dependent re-balance (ADR) method in that the re-balance factor is defined only on the cell interface and in that the low-order equation is derived by integrating the transport equation (high-order equation) over angular subspaces. But, the re-balance factor is applied additively. While the AADR method is similar to the boundary projection acceleration and the alpha-weighted linear acceleration, it is more general and does have distinct features. The method is easily extendible to DP N and low-order S N re-balancing, and it does not require consistent discretizations between the high- and low-order equations as in diffusion synthetic acceleration. We find by Fourier analysis and numerical results that the AADR method with a chosen form of weighting functions is unconditionally stable and very effective. There also exists an optimal weighting parameter that leads to the smallest spectral radius. The AADR acceleration method described in this paper is simple to implement, unconditionally stable, and very effective. It uses a physically based weighting function with an optimal parameter, leading to the best spectral radius of ρ<0.1865, compared to ρ<0.2247 of DSA. The application of the AADR acceleration method with the LMB scheme on a test problem shows encouraging results

Fire Intensity Data for Validation of the Radiative Transfer Equation

Energy Technology Data Exchange (ETDEWEB)

Blanchat, Thomas K. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Jernigan, Dann A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2016-01-01

A set of experiments and test data are outlined in this report that provides radiation intensity data for the validation of models for the radiative transfer equation. The experiments were performed with lightly-sooting liquid hydrocarbon fuels that yielded fully turbulent fires 2 m diameter). In addition, supplemental measurements of air flow and temperature, fuel temperature and burn rate, and flame surface emissive power, wall heat, and flame height and width provide a complete set of boundary condition data needed for validation of models used in fire simulations.

Global existence of a generalized solution for the radiative transfer equations

International Nuclear Information System (INIS)

Golse, F.; Perthame, B.

1984-01-01

We prove global existence of a generalized solution of the radiative transfer equations, extending Mercier's result to the case of a layer with an initially cold area. Our Theorem relies on the results of Crandall and Ligett [fr

Exponentially-convergent Monte Carlo for the 1-D transport equation

International Nuclear Information System (INIS)

Peterson, J. R.; Morel, J. E.; Ragusa, J. C.

2013-01-01

We define a new exponentially-convergent Monte Carlo method for solving the one-speed 1-D slab-geometry transport equation. This method is based upon the use of a linear discontinuous finite-element trial space in space and direction to represent the transport solution. A space-direction h-adaptive algorithm is employed to restore exponential convergence after stagnation occurs due to inadequate trial-space resolution. This methods uses jumps in the solution at cell interfaces as an error indicator. Computational results are presented demonstrating the efficacy of the new approach. (authors)

Transport of radioactive wastes to the planned final waste repository Konrad: Radiation exposure resulting from normal transport and radiological risks from transport accidents

International Nuclear Information System (INIS)

Lange, F.; Fett, H.J.; Gruendler, D.; Schwarz, G.

1993-01-01

Radiation exposures of members of critical groups of the general population and of transport personnel resulting from normal transport of radioactive wastes to the planned final waste repository Konrad have been evaluated in detail. By applying probabilistic safety assessment techniques radiological risks from transport accidents have been analysed by quantifying potential radiation exposures and contaminations of the biosphere in connection with their expected frequencies of occurrence. The Konrad transport study concentrates on the local region of the waste repository, where all transports converge. (orig.) [de

Problem on primary radiation filtration effect on form of coupling equations during X-ray fluorescence analysis

International Nuclear Information System (INIS)

Lavrent'ev, Yu.G.; Kuznetsova, A.I.

1976-01-01

A simplified method for x-ray fluorescence analysis is given. It is shown that the system of coupling equations with constant coefficients and with the number of equations equal to the number of unknown elements allows to obtain the same accuracy of the analysis as with the considerably more complex equations with variable coefficients which take into account the filtration of the primary radiation in a direct way. The system can even be more simplified by using linear equations with constant coefficients. In order to test these systems and to compare them with known coupling equations experimental data for the determination of zirconium and niobium from 16 artificial preparations with fillers of variable composition are presented. The calculation of the absorption of the secondary as well as the primary radiation by means of the proposed equations with constant coefficients is sufficiently good

Discontinuous Galerkin finite element methods for radiative transfer in spherical symmetry

Science.gov (United States)

Kitzmann, D.; Bolte, J.; Patzer, A. B. C.

2016-11-01

The discontinuous Galerkin finite element method (DG-FEM) is successfully applied to treat a broad variety of transport problems numerically. In this work, we use the full capacity of the DG-FEM to solve the radiative transfer equation in spherical symmetry. We present a discontinuous Galerkin method to directly solve the spherically symmetric radiative transfer equation as a two-dimensional problem. The transport equation in spherical atmospheres is more complicated than in the plane-parallel case owing to the appearance of an additional derivative with respect to the polar angle. The DG-FEM formalism allows for the exact integration of arbitrarily complex scattering phase functions, independent of the angular mesh resolution. We show that the discontinuous Galerkin method is able to describe accurately the radiative transfer in extended atmospheres and to capture discontinuities or complex scattering behaviour which might be present in the solution of certain radiative transfer tasks and can, therefore, cause severe numerical problems for other radiative transfer solution methods.

An introduction to the Boltzmann equation and transport processes in gases

CERN Document Server

Kremer, Gilberto M; Colton, David

2010-01-01

This book covers classical kinetic theory of gases, presenting basic principles in a self-contained framework and from a more rigorous approach based on the Boltzmann equation. Uses methods in kinetic theory for determining the transport coefficients of gases.

Reactor Dosimetry Applications Using RAPTOR-M3G:. a New Parallel 3-D Radiation Transport Code

Science.gov (United States)

Longoni, Gianluca; Anderson, Stanwood L.

2009-08-01

The numerical solution of the Linearized Boltzmann Equation (LBE) via the Discrete Ordinates method (SN) requires extensive computational resources for large 3-D neutron and gamma transport applications due to the concurrent discretization of the angular, spatial, and energy domains. This paper will discuss the development RAPTOR-M3G (RApid Parallel Transport Of Radiation - Multiple 3D Geometries), a new 3-D parallel radiation transport code, and its application to the calculation of ex-vessel neutron dosimetry responses in the cavity of a commercial 2-loop Pressurized Water Reactor (PWR). RAPTOR-M3G is based domain decomposition algorithms, where the spatial and angular domains are allocated and processed on multi-processor computer architectures. As compared to traditional single-processor applications, this approach reduces the computational load as well as the memory requirement per processor, yielding an efficient solution methodology for large 3-D problems. Measured neutron dosimetry responses in the reactor cavity air gap will be compared to the RAPTOR-M3G predictions. This paper is organized as follows: Section 1 discusses the RAPTOR-M3G methodology; Section 2 describes the 2-loop PWR model and the numerical results obtained. Section 3 addresses the parallel performance of the code, and Section 4 concludes this paper with final remarks and future work.

A non linear half space problem for radiative transfer equations. Application to the Rosseland approximation

International Nuclear Information System (INIS)

Sentis, R.

1984-07-01

The radiative transfer equations may be approximated by a non linear diffusion equation (called Rosseland equation) when the mean free paths of the photons are small with respect to the size of the medium. Some technical assomptions are made, namely about the initial conditions, to avoid any problem of initial layer terms

Numerical evaluation of the intensity transport equation for well-known wavefronts and intensity distributions

Science.gov (United States)

Campos-García, Manuel; Granados-Agustín, Fermín.; Cornejo-Rodríguez, Alejandro; Estrada-Molina, Amilcar; Avendaño-Alejo, Maximino; Moreno-Oliva, Víctor Iván.

2013-11-01

In order to obtain a clearer interpretation of the Intensity Transport Equation (ITE), in this work, we propose an algorithm to solve it for some particular wavefronts and its corresponding intensity distributions. By simulating intensity distributions in some planes, the ITE is turns into a Poisson equation with Neumann boundary conditions. The Poisson equation is solved by means of the iterative algorithm SOR (Simultaneous Over-Relaxation).

Solution of the Boltzmann-Fokker-Planck transport equation using exponential nodal schemes

International Nuclear Information System (INIS)

Ortega J, R.; Valle G, E. del

2003-01-01

There are carried out charge and energy calculations deposited due to the interaction of electrons with a plate of a certain material, solving numerically the electron transport equation for the Boltzmann-Fokker-Planck approach of first order in plate geometry with a computer program denominated TEOD-NodExp (Transport of Electrons in Discreet Ordinates, Nodal Exponentials), using the proposed method by the Dr. J. E. Morel to carry out the discretization of the variable energy and several spatial discretization schemes, denominated exponentials nodal. It is used the Fokker-Planck equation since it represents an approach of the Boltzmann transport equation that is been worth whenever it is predominant the dispersion of small angles, that is to say, resulting dispersion in small dispersion angles and small losses of energy in the transport of charged particles. Such electrons could be those that they face with a braking plate in a device of thermonuclear fusion. In the present work its are considered electrons of 1 MeV that impact isotropically on an aluminum plate. They were considered three different thickness of plate that its were designated as problems 1, 2 and 3. In the calculations it was used the discrete ordinate method S 4 with expansions of the dispersion cross sections until P 3 order. They were considered 25 energy groups of uniform size between the minimum energy of 0.1 MeV and the maximum of 1.0 MeV; the one spatial intervals number it was considered variable and it was assigned the values of 10, 20 and 30. (Author)

Spatially adaptive hp refinement approach for PN neutron transport equation using spectral element method

International Nuclear Information System (INIS)

Nahavandi, N.; Minuchehr, A.; Zolfaghari, A.; Abbasi, M.

2015-01-01

Highlights: • Powerful hp-SEM refinement approach for P N neutron transport equation has been presented. • The method provides great geometrical flexibility and lower computational cost. • There is a capability of using arbitrary high order and non uniform meshes. • Both posteriori and priori local error estimation approaches have been employed. • High accurate results are compared against other common adaptive and uniform grids. - Abstract: In this work we presented the adaptive hp-SEM approach which is obtained from the incorporation of Spectral Element Method (SEM) and adaptive hp refinement. The SEM nodal discretization and hp adaptive grid-refinement for even-parity Boltzmann neutron transport equation creates powerful grid refinement approach with high accuracy solutions. In this regard a computer code has been developed to solve multi-group neutron transport equation in one-dimensional geometry using even-parity transport theory. The spatial dependence of flux has been developed via SEM method with Lobatto orthogonal polynomial. Two commonly error estimation approaches, the posteriori and the priori has been implemented. The incorporation of SEM nodal discretization method and adaptive hp grid refinement leads to high accurate solutions. Coarser meshes efficiency and significant reduction of computer program runtime in comparison with other common refining methods and uniform meshing approaches is tested along several well-known transport benchmarks

Fully implicit 1D radiation hydrodynamics: Validation and verification

International Nuclear Information System (INIS)

Ghosh, Karabi; Menon, S.V.G.

2010-01-01

A fully implicit finite difference scheme has been developed to solve the hydrodynamic equations coupled with radiation transport. Solution of the time-dependent radiation transport equation is obtained using the discrete ordinates method and the energy flow into the Lagrangian meshes as a result of radiation interaction is fully accounted for. A tridiagonal matrix system is solved at each time step to determine the hydrodynamic variables implicitly. The results obtained from this fully implicit radiation hydrodynamics code in the planar geometry agrees well with the scaling law for radiation driven strong shock propagation in aluminium. For the point explosion problem the self similar solutions are compared with results for pure hydrodynamic case in spherical geometry. Results obtained when radiation interaction is also accounted agree with those of point explosion with heat conduction for lower input energies. Having, thus, benchmarked the code, self convergence of the method w.r.t. time step is studied in detail for both the planar and spherical problems. Spatial as well as temporal convergence rates are ≅1 as expected from the difference forms of mass, momentum and energy conservation equations. This shows that the asymptotic convergence rate of the code is realized properly.

Master equations for degenerate systems: electron radiative cascade in a Coulomb potential

International Nuclear Information System (INIS)

Uskov, D B; Pratt, R H

2004-01-01

We examine the effects of degeneracy and its lifting for the problem of electron radiative cascade, described by master equations of the Lindblad form (quantum optical master equations). A weak external field approximation is used to study the resulting gradual transformation of cascade dynamics between degenerate and non-degenerate forms. Exploiting the spherical symmetry properties of the system we demonstrate significant difference between perturbations commuting with angular momentum and perturbations breaking the spherical symmetry, such as a homogeneous external field. We discuss the possibility and the general approach for reduction of the Lindblad master equations in the case of spectral degeneracy to the Pauli balance equations. This determines the appropriate choice of basis as, for example, spherical or parabolic

Nature of complex time eigenvalues of the one speed transport equation in a homogeneous sphere

International Nuclear Information System (INIS)

Dahl, E.B.; Sahni, D.C.

1990-01-01

The complex time eigenvalues of the transport equation have been studied for one speed neutrons, scattered isotropically in a homogeneous sphere with vacuum boundary conditions. It is shown that the complex decay constants vary continuously with the radius of the sphere. Our earlier conjecture (Dahl and Sahni (1983-84)) regarding disjoint arcs is thus shown to be true. We also indicate that complex decay constants exist even for large assemblies, though with rapid oscillations in the corresponding eigenvectors. These modes cannot be predicted by the diffusion equation as this behaviour of the eigenvectors contradicts the assumption of 'slowly varying flux' needed to derive the diffusion approximation from the transport equation. For an infinite system, the existence of complex modes is related to the solution of a homogeneous equation. (author)

Development of a polynomial nodal model to the multigroup transport equation in one dimension

International Nuclear Information System (INIS)

Feiz, M.

1986-01-01

A polynomial nodal model that uses Legendre polynomial expansions was developed for the multigroup transport equation in one dimension. The development depends upon the least-squares minimization of the residuals using the approximate functions over the node. Analytical expressions were developed for the polynomial coefficients. The odd moments of the angular neutron flux over the half ranges were used at the internal interfaces, and the Marshak boundary condition was used at the external boundaries. Sample problems with fine-mesh finite-difference solutions of the diffusion and transport equations were used for comparison with the model

LDRD Final Review: Radiation Transport Calculations

Energy Technology Data Exchange (ETDEWEB)

Goorley, John Timothy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Morgan, George Lake [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Lestone, John Paul [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2017-06-22

Both high-fidelity & toy simulations are being used to understand measured signals and improve the Area 11 NDSE diagnostic. We continue to gain more and more confidence in the ability for MCNP to simulate neutron and photon transport from source to radiation detector.

High-order solution methods for grey discrete ordinates thermal radiative transfer

Energy Technology Data Exchange (ETDEWEB)

Maginot, Peter G., E-mail: maginot1@llnl.gov [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States); Morel, Jim E., E-mail: morel@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States)

2016-12-15

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.

Radiation doses from the transport of radioactive materials

International Nuclear Information System (INIS)

Shaw, K.B.; Holyoak, B.

1983-01-01

A summary is given of a study on radiation exposure resulting from the transport of radioactive materials within the United Kingdom. It was concluded that the transport of technetium generators for hospital use accounts for about 49% of the occupational exposure for the normal transport of radioactive materials. Other isotopes for medical and industrial use contribute about 38% of the occupational exposure and the remainder can be attributed to transportation as a result of the nuclear fuel cycle including the transport of irradiated nuclear fuel. The occupational collective dose for all modes of transport is estimated at 1 man Sv y -1 . (UK)

Analysis of an upstream weighted collocation approximation to the transport equation

International Nuclear Information System (INIS)

Shapiro, A.; Pinder, G.F.

1981-01-01

The numerical behavior of a modified orthogonal collocation method, as applied to the transport equations, can be examined through the use of a Fourier series analysis. The necessity of such a study becomes apparent in the analysis of several techniques which emulate classical upstream weighting schemes. These techniques are employed in orthogonal collocation and other numerical methods as a means of handling parabolic partial differential equations with significant first-order terms. Divergent behavior can be shown to exist in one upstream weighting method applied to orthogonal collocation

A multilevel method for conductive-radiative heat transfer

Energy Technology Data Exchange (ETDEWEB)

Banoczi, J.M.; Kelley, C.T. [North Carolina State Univ., Raleigh, NC (United States)

1996-12-31

We present a fast multilevel algorithm for the solution of a system of nonlinear integro-differential equations that model steady-state combined radiative-conductive heat transfer. The equations can be formulated as a compact fixed point problem with a fixed point map that requires both a solution of the linear transport equation and the linear heat equation for its evaluation. We use fast transport solvers developed by the second author, to construct an efficient evaluation of the fixed point map and then apply the Atkinson-Brakhage, method, with Newton-GMRES as the coarse mesh solver, to the full nonlinear system.

New numerical method for solving the solute transport equation

International Nuclear Information System (INIS)

Ross, B.; Koplik, C.M.

1978-01-01

The solute transport equation can be solved numerically by approximating the water flow field by a network of stream tubes and using a Green's function solution within each stream tube. Compared to previous methods, this approach permits greater computational efficiency and easier representation of small discontinuities, and the results are easier to interpret physically. The method has been used to study hypothetical sites for disposal of high-level radioactive waste

Experimental validation of GADRAS's coupled neutron-photon inverse radiation transport solver

International Nuclear Information System (INIS)

Mattingly, John K.; Mitchell, Dean James; Harding, Lee T.

2010-01-01

Sandia National Laboratories has developed an inverse radiation transport solver that applies nonlinear regression to coupled neutron-photon deterministic transport models. The inverse solver uses nonlinear regression to fit a radiation transport model to gamma spectrometry and neutron multiplicity counting measurements. The subject of this paper is the experimental validation of that solver. This paper describes a series of experiments conducted with a 4.5 kg sphere of α-phase, weapons-grade plutonium. The source was measured bare and reflected by high-density polyethylene (HDPE) spherical shells with total thicknesses between 1.27 and 15.24 cm. Neutron and photon emissions from the source were measured using three instruments: a gross neutron counter, a portable neutron multiplicity counter, and a high-resolution gamma spectrometer. These measurements were used as input to the inverse radiation transport solver to evaluate the solver's ability to correctly infer the configuration of the source from its measured radiation signatures.

Department of Environmental and Radiation Transport Physics - Overview

International Nuclear Information System (INIS)

Woznicka, U.

2001-01-01

Full text: We deal with environmental physics and the radiation transport physics, both theoretically and experimentally. Some results find their way to practical applications. Our environmental physics research encompasses hydrogeological problems as well as measurements of trace elements in the atmosphere and in the water. Theoretical (analytical and numerical) and experimental issues of the radiation transport and radiation fields are our main field of research. The interest in radiation transport phenomena is stimulated by their importance for the environmental physics, industrial and nuclear facilities and methods of geophysical. Environmental isotopes and noble gases are used in the investigation of water-bearing geological formations in order to determine the origin and age of groundwater. The papers listed below and three ''Reports on research'' present recent achievements in this field. The gas chromatography methods are used for monitoring the anthropogenic trace gases (SF 6 and freons), which participate in the Earth green-house effect. A very high detection level of SF 6 in water, 0.0028 fg/cm 3 H 2 0, has been reached as required for hydrogeological purposes. A preliminary verification of the SF 6 tracer method for dating young groundwaters by the tritium method has been carried out. We carried on the work on a method of radon measurement in soil in connection with geological conditions. The national seminar ''Radon in Environment'' organized at the INP aroused an interest of Polish scientific centres in that field. The seminar gathered 60 participants who presented 24 oral reports and 8 posters. Within the scope of the radiation transport physics we studied thermal neutron transport in finite hydrogenous media. Advantages and limitations of a Monte Carlo code (MCNP) in thermal neutron transport simulations have been examined by both the analytical solution and the experiment on the INP pulsed neutron generator. An interesting contribution to the

Radiation transport in MEDUSA

International Nuclear Information System (INIS)

Rose, S.J.; Evans, R.G.

1983-09-01

The transport of energy by X-ray photons has been included in the lD Lagrangian hydrodynamics code, MEDUSA. Calculations of the implosion by 0.53 μm laser irradiation of plastic and glass microballoons of current interest at the Central Laser Facility show that radiation preheats the fill gas and alters the temperature and density profiles during the implosion. A lower maximum gas temperature is obtained and this results, for a DT gas fill, in a greatly reduced neutron yield. (author)

Finite moments approach to the time-dependent neutron transport equation

International Nuclear Information System (INIS)

Kim, Sang Hyun

1994-02-01

Currently, nodal techniques are widely used in solving the multidimensional diffusion equation because of savings in computing time and storage. Thanks to the development of computer technology, one can now solve the transport equation instead of the diffusion equation to obtain more accurate solution. The finite moments method, one of the nodal methods, attempts to represent the fluxes in the cell and on cell surfaces more rigorously by retaining additional spatial moments. Generally, there are two finite moments schemes to solve the time-dependent transport equation. In one, the time variable is treated implicitly with finite moments method in space variable (implicit finite moments method), the other method uses finite moments method in both space and time (space-time finite moments method). In this study, these two schemes are applied to two types of time-dependent neutron transport problems. One is a fixed source problem, the other a heterogeneous fast reactor problem with delayed neutrons. From the results, it is observed that the two finite moments methods give almost the same solutions in both benchmark problems. However, the space-time finite moments method requires a little longer computing time than that of the implicit finite moments method. In order to reduce the longer computing time in the space-time finite moments method, a new iteration strategy is exploited, where a few time-stepwise calculation, in which original time steps are grouped into several coarse time divisions, is performed sequentially instead of performing iterations over the entire time steps. This strategy results in significant reduction of the computing time and we observe that 2-or 3-stepwise calculation is preferable. In addition, we propose a new finite moments method which is called mixed finite moments method in this thesis. Asymptotic analysis for the finite moments method shows that accuracy of the solution in a heterogeneous problem mainly depends on the accuracy of the

CACTUS, a characteristics solution to the neutron transport equations in complicated geometries

International Nuclear Information System (INIS)

Halsall, M.J.

1980-04-01

CACTUS has been written to solve the multigroup neutron transport equation in a general two-dimensional geometry. The method is based upon a characteristics formulation for the problem in which the transport equation is integrated explicitly along straight line tracks that are suitably distributed throughout the problem. Source distributions and scattering are assumed to be isotropic, but the only restriction on geometry is that the outer boundary should be rectangular. Within this rectangular boundary the user is free to build his problem geometry using any combination of intersecting straight lines and circular arcs. The theory of the method is described, followed by some details of a coding, a sensitivity study on the number of tracks required to integrate fluxes in a particular problem, a user's guide, and a few test cases. (author)

C5 Benchmark Problem with Discrete Ordinate Radiation Transport Code DENOVO

Energy Technology Data Exchange (ETDEWEB)

Yesilyurt, Gokhan [ORNL; Clarno, Kevin T [ORNL; Evans, Thomas M [ORNL; Davidson, Gregory G [ORNL; Fox, Patricia B [ORNL

2011-01-01

The C5 benchmark problem proposed by the Organisation for Economic Co-operation and Development/Nuclear Energy Agency was modeled to examine the capabilities of Denovo, a three-dimensional (3-D) parallel discrete ordinates (S{sub N}) radiation transport code, for problems with no spatial homogenization. Denovo uses state-of-the-art numerical methods to obtain accurate solutions to the Boltzmann transport equation. Problems were run in parallel on Jaguar, a high-performance supercomputer located at Oak Ridge National Laboratory. Both the two-dimensional (2-D) and 3-D configurations were analyzed, and the results were compared with the reference MCNP Monte Carlo calculations. For an additional comparison, SCALE/KENO-V.a Monte Carlo solutions were also included. In addition, a sensitivity analysis was performed for the optimal angular quadrature and mesh resolution for both the 2-D and 3-D infinite lattices of UO{sub 2} fuel pin cells. Denovo was verified with the C5 problem. The effective multiplication factors, pin powers, and assembly powers were found to be in good agreement with the reference MCNP and SCALE/KENO-V.a Monte Carlo calculations.

RTk/SN Solutions of the Two-Dimensional Multigroup Transport Equations in Hexagonal Geometry

International Nuclear Information System (INIS)

Valle, Edmundo del; Mund, Ernest H.

2004-01-01

This paper describes an extension to the hexagonal geometry of some weakly discontinuous nodal finite element schemes developed by Hennart and del Valle for the two-dimensional discrete ordinates transport equation in quadrangular geometry. The extension is carried out in a way similar to the extension to the hexagonal geometry of nodal element schemes for the diffusion equation using a composite mapping technique suggested by Hennart, Mund, and del Valle. The combination of the weakly discontinuous nodal transport scheme and the composite mapping is new and is detailed in the main section of the paper. The algorithm efficiency is shown numerically through some benchmark calculations on classical problems widely referred to in the literature

An Equation-Type Approach for the Numerical Solution of the Partial Differential Equations Governing Transport Phenomena in Porous Media

KAUST Repository

Sun, Shuyu

2012-06-02

A new technique for the numerical solution of the partial differential equations governing transport phenomena in porous media is introduced. In this technique, the governing equations as depicted from the physics of the problem are used without extra manipulations. In other words, there is no need to reduce the number of governing equations by some sort of mathematical manipulations. This technique enables the separation of the physics part of the problem and the solver part, which makes coding more robust and could be used in several other applications with little or no modifications (e.g., multi-phase flow in porous media). In this method, one abandons the need to construct the coefficient matrix for the pressure equation. Alternatively, the coefficients are automatically generated within the solver routine. We show examples of using this technique to solving several flow problems in porous media.

An Equation-Type Approach for the Numerical Solution of the Partial Differential Equations Governing Transport Phenomena in Porous Media

KAUST Repository

Sun, Shuyu; Salama, Amgad; El-Amin, Mohamed

2012-01-01

A new technique for the numerical solution of the partial differential equations governing transport phenomena in porous media is introduced. In this technique, the governing equations as depicted from the physics of the problem are used without extra manipulations. In other words, there is no need to reduce the number of governing equations by some sort of mathematical manipulations. This technique enables the separation of the physics part of the problem and the solver part, which makes coding more robust and could be used in several other applications with little or no modifications (e.g., multi-phase flow in porous media). In this method, one abandons the need to construct the coefficient matrix for the pressure equation. Alternatively, the coefficients are automatically generated within the solver routine. We show examples of using this technique to solving several flow problems in porous media.

Three-dimensional wave-induced current model equations and radiation stresses

Science.gov (United States)

Xia, Hua-yong

2017-08-01

After the approach by Mellor (2003, 2008), the present paper reports on a repeated effort to derive the equations for three-dimensional wave-induced current. Via the vertical momentum equation and a proper coordinate transformation, the phase-averaged wave dynamic pressure is well treated, and a continuous and depth-dependent radiation stress tensor, rather than the controversial delta Dirac function at the surface shown in Mellor (2008), is provided. Besides, a phase-averaged vertical momentum flux over a sloping bottom is introduced. All the inconsistencies in Mellor (2003, 2008), pointed out by Ardhuin et al. (2008) and Bennis and Ardhuin (2011), are overcome in the presently revised equations. In a test case with a sloping sea bed, as shown in Ardhuin et al. (2008), the wave-driving forces derived in the present equations are in good balance, and no spurious vertical circulation occurs outside the surf zone, indicating that Airy's wave theory and the approach of Mellor (2003, 2008) are applicable for the derivation of the wave-induced current model.

Approximate method for solving the velocity dependent transport equation in a slab lattice

International Nuclear Information System (INIS)

Ferrari, A.

1966-01-01

A method is described that is intended to provide an approximate solution of the transport equation in a medium simulating a water-moderated plate filled reactor core. This medium is constituted by a periodic array of water channels and absorbing plates. The velocity dependent transport equation in slab geometry is included. The computation is performed in a water channel: the absorbing plates are accounted for by the boundary conditions. The scattering of neutrons in water is assumed isotropic, which allows the use of a double Pn approximation to deal with the angular dependence. This method is able to represent the discontinuity of the angular distribution at the channel boundary. The set of equations thus obtained is dependent only on x and v and the coefficients are independent on x. This solution suggests to try solutions involving Legendre polynomials. This scheme leads to a set of equations v dependent only. To obtain an explicit solution, a thermalization model must now be chosen. Using the secondary model of Cadilhac a solution of this set is easy to get. The numerical computations were performed with a particular secondary model, the well-known model of Wigner and Wilkins. (author) [fr

A numerical spectral approach to solve the dislocation density transport equation

International Nuclear Information System (INIS)

Djaka, K S; Taupin, V; Berbenni, S; Fressengeas, C

2015-01-01

A numerical spectral approach is developed to solve in a fast, stable and accurate fashion, the quasi-linear hyperbolic transport equation governing the spatio-temporal evolution of the dislocation density tensor in the mechanics of dislocation fields. The approach relies on using the Fast Fourier Transform algorithm. Low-pass spectral filters are employed to control both the high frequency Gibbs oscillations inherent to the Fourier method and the fast-growing numerical instabilities resulting from the hyperbolic nature of the transport equation. The numerical scheme is validated by comparison with an exact solution in the 1D case corresponding to dislocation dipole annihilation. The expansion and annihilation of dislocation loops in 2D and 3D settings are also produced and compared with finite element approximations. The spectral solutions are shown to be stable, more accurate for low Courant numbers and much less computation time-consuming than the finite element technique based on an explicit Galerkin-least squares scheme. (paper)

A general analytical approach to the one-group, one-dimensional transport equation

International Nuclear Information System (INIS)

Barichello, L.B.; Vilhena, M.T.

1993-01-01

The main feature of the presented approach to solve the neutron transport equation consists in the application of the Laplace transform to the discrete ordinates equations, which yields a linear system of order N to be solved (LTS N method). In this paper this system is solved analytically and the inversion is performed using the Heaviside expansion technique. The general formulation achieved by this procedure is then applied to homogeneous and heterogeneous one-group slab-geometry problems. (orig.) [de

Overview. Department of Environmental and Radiation Transport Physics. Section 6

Energy Technology Data Exchange (ETDEWEB)

Loskiewicz, J. [Institute of Nuclear Physics, Cracow (Poland)

1995-12-31

Research activities in the Department of Environmental and Radiation Transport Physics are carried out by three Laboratories: Laboratory of Environmental Physics, Laboratory of Neutron Transport Physics and Laboratory of Physics and Modeling of Radiation Transport. The researches provided in 1994 cover: tracer transport and flows in porous media, studies on pollution in atmospheric air, physics of molecular phenomena in chromatographic detectors, studies on neutron transport in heterogenous media, studies on evaluation of neutron cross-section in the thermal region, studies on theory and utilization of neural network in data evaluation, numerical modelling of particle cascades for particle accelerator shielding purpose. In this section the description of mentioned activities as well as the information about personnel employed in the Department, papers and reports published in 1994, contribution to conferences and grants is also given.

Overview. Department of Environmental and Radiation Transport Physics. Section 6

Energy Technology Data Exchange (ETDEWEB)

Loskiewicz, J [Institute of Nuclear Physics, Cracow (Poland)

1996-12-31

Research activities in the Department of Environmental and Radiation Transport Physics are carried out by three Laboratories: Laboratory of Environmental Physics, Laboratory of Neutron Transport Physics and Laboratory of Physics and Modeling of Radiation Transport. The researches provided in 1994 cover: tracer transport and flows in porous media, studies on pollution in atmospheric air, physics of molecular phenomena in chromatographic detectors, studies on neutron transport in heterogenous media, studies on evaluation of neutron cross-section in the thermal region, studies on theory and utilization of neural network in data evaluation, numerical modelling of particle cascades for particle accelerator shielding purpose. In this section the description of mentioned activities as well as the information about personnel employed in the Department, papers and reports published in 1994, contribution to conferences and grants is also given.

Survey of radiation protection programmes for transport; Etude des programmes de radioprotection pour les transports de matieres radioactives

Energy Technology Data Exchange (ETDEWEB)

Lizot, M.T.; Perrin, M.L.; Sert, G. [CEA Fontenay-aux-Roses, Inst. de Protection et de Surete Nucleaire, Dept. de Protection et de Surete Nucleaire, 92 (France); Lange, F.; Schwarz, G.; Feet, H.J.; Christ, R. [Gesellschaft fur Anlagen-und Reaktorsicherheit, GRS, mbH, Cologne (Germany); Shaw, K.B.; Hughes, J.S.; Gelder, R. [National Radiological Protection Board (NRPB), Oxon, OX (United Kingdom)

2001-07-01

The survey of radiation protection programmes for transport has been jointly performed by three scientific organisations I.P.S.N. (France), G.R.S. ( Germany), and N.R.P.B. (United kingdom) on behalf of the European Commission and the pertaining documentation summarises the findings and conclusions of the work that was undertaken with the principal objectives to provide guidance on the establishment, implementation and application of radiation protection programmes for the transport of radioactive materials by operators and the assessment and evaluation of such programmes by the competent authority and to review currently existing radiation protection programmes for the transport of radioactive materials. (N.C.)

Some factors affecting radiative heat transport in PWR cores

International Nuclear Information System (INIS)

Hall, A.N.

1989-04-01

This report discusses radiative heat transport in Pressurized Water Reactor cores, using simple models to illustrate basic features of the transport process. Heat transport by conduction and convection is ignored in order to focus attention on the restrictions on radiative heat transport imposed by the geometry of the heat emitting and absorbing structures. The importance of the spacing of the emitting and absorbing structures is emphasised. Steady state temperature distributions are found for models of cores which are uniformly heated by fission product decay. In all of the models, a steady state temperature distribution can only be obtained if the central core temperature is in excess of the melting point of UO 2 . It has recently been reported that the MIMAS computer code, which takes into account radiative heat transport, has been used to model the heat-up of the Three Mile Island-2 reactor core, and the computations indicate that the core could not have reached the melting point of UO 2 at any time or any place. We discuss this result in the light of the calculations presented in this paper. It appears that the predicted stabilisation of the core temperatures at ∼ 2200 0 C may be a consequence of the artificially large spacing between the radial rings employed in the MIMAS code, rather than a result of physical significance. (author)

X-radiation effect on water transport in ascite cells of Ehrlich carcinoma

International Nuclear Information System (INIS)

Barnov, V.A.; Ajvazishvili, M.A.; Kartvelishvili, I.I.; Tushishvili, D.I.

1988-01-01

Effect of local X radiation with doses 0.05 and 0.15 C/kg on water transport in ascitic cells of Erlich carcinoma is studied in rats. To study water transport through cell membranes, tritium mark was used. It is concluded that radiation effect on water transport in cells of Erlich carcinoma may be related to change in ionic permittivity of the membrane, because small changes in transmembrane ion transport affect immediately the osmotic motion of water. 5 refs

Comparison of artificial intelligence methods and empirical equations to estimate daily solar radiation

Science.gov (United States)

Mehdizadeh, Saeid; Behmanesh, Javad; Khalili, Keivan

2016-08-01

In the present research, three artificial intelligence methods including Gene Expression Programming (GEP), Artificial Neural Networks (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) as well as, 48 empirical equations (10, 12 and 26 equations were temperature-based, sunshine-based and meteorological parameters-based, respectively) were used to estimate daily solar radiation in Kerman, Iran in the period of 1992-2009. To develop the GEP, ANN and ANFIS models, depending on the used empirical equations, various combinations of minimum air temperature, maximum air temperature, mean air temperature, extraterrestrial radiation, actual sunshine duration, maximum possible sunshine duration, sunshine duration ratio, relative humidity and precipitation were considered as inputs in the mentioned intelligent methods. To compare the accuracy of empirical equations and intelligent models, root mean square error (RMSE), mean absolute error (MAE), mean absolute relative error (MARE) and determination coefficient (R2) indices were used. The results showed that in general, sunshine-based and meteorological parameters-based scenarios in ANN and ANFIS models presented high accuracy than mentioned empirical equations. Moreover, the most accurate method in the studied region was ANN11 scenario with five inputs. The values of RMSE, MAE, MARE and R2 indices for the mentioned model were 1.850 MJ m-2 day-1, 1.184 MJ m-2 day-1, 9.58% and 0.935, respectively.

1D equation for toroidal momentum transport in a tokamak

International Nuclear Information System (INIS)

Rozhansky, V A; Senichenkov, I Yu

2010-01-01

A 1D equation for toroidal momentum transport is derived for a given set of turbulent transport coefficients. The averaging is performed taking account of the poloidal variation of the toroidal fluxes and is based on the ambipolar condition of the zero net radial current through the flux surface. It is demonstrated that taking account of the Pfirsch-Schlueter fluxes leads to a torque in the toroidal direction which is proportional to the gradient of the ion temperature. This effect is new and has not been discussed before. The boundary condition at the separatrix, which is based on the results of the 2D simulations of the edge plasma, is formulated.

Trade and transport of radiation sources

International Nuclear Information System (INIS)

1996-01-01

The guide specifies the obligations pertaining to the trade in and transport of radiation sources and other matters to be taken into account in safety supervision. It also specifies obligations and procedures relating to transfrontier movements of radioactive waste contained in the EU Council Directive 92/3/Euratom. (7 refs.)

Radiological emergency: road map for radiation accident victim transport; Emergência radiológica: roadmap para o transporte de radioacidentado

Energy Technology Data Exchange (ETDEWEB)

Costa, V.S.G.; Alcantara, Y.P. [Faculdade Casa Branca, SP (Brazil); Lima, C.M.A. [MAXIM Cursos, Rio de Janeiro, RJ (Brazil); Silva, F. C. A. da, E-mail: franciscodasilva13uk@gmail.com [Instituto de Radioproteção e Dosimetria (IRD/CNEN-RJ), Rio de Janeiro, RJ (Brazil)

2017-07-01

During a radiological or nuclear emergency, a number of necessary actions are taken, both within the radiation protection of individuals and the environment, involving many institutions and highly specialized personnel. Among them it is possible to emphasize the air transportation of radiation accident victims.The procedures and measures for the safe transport of these radiation accident victims are generally the responsibility of the armed forces, specifically the Aeronautics, with the action denominated 'Aeromedical Military Evacuation of Radiation Accident Victims'. The experience with the Radiological Accident of Goiânia demonstrated the importance of adequate preparation and response during a radiological emergency and the need for procedures and measures with regard to the transport of radiation victims are clearly defined and clearly presented for the effectiveness of the actions. This work presents the necessary actions for the transport of radiation accident victim during a radiological emergency, through the road map technique, which has been widely used in scientific technical area to facilitate understanding and show the way to be followed to reach the proposed objectives.

Estimated routine radiation doses to transportation workers in alternative spent-fuel transportation systems

International Nuclear Information System (INIS)

Schneider, K.J.; Smith, R.I.; Daling, P.M.; Ross, W.A.; McNair, G.W.

1988-01-01

The federal system for the management of spent fuel and high-level radioactive waste includes the acceptance by the US Department of Energy (DOE) of the spent fuel or waste loaded in casks at the reactor or other waste generators, its transportation to a repository, and its handling and final emplacement in the repository. The DOE plans to implement a transportation system that is safe, secure, efficient, and cost-effective and will meet applicable regulatory safety and security requirements. The DOE commissioned the Pacific Northwest Laboratory (PNL) to develop estimates of the routine radiation doses that would result from the operation of a system postulated using current designs and practices. From that evaluation, PNL identified activities/operations that result in the higher fraction of doses, proposed conceptual alternatives that would effectively reduce such exposures, and evaluated the cost-effectiveness of such alternatives. The study is one of a series used in making overall system design and operational decisions in the development of the DOE's spent-fuel/high-level waste transportation system. This paper contains the highlights from the PNL study of the estimated radiation doses to the transportation workers in a postulated reference transportation system and potential alternatives to that system

High-field transport of electrons and radiative effects using coupled force-balance and Fokker-Planck equations beyond the relaxation-time approximation

International Nuclear Information System (INIS)

Huang, Danhong; Apostolova, T.; Alsing, P.M.; Cardimona, D.A.

2004-01-01

The dynamics of a many-electron system under both dc and infrared fields is separated into a center-of-mass and a relative motion. The first-order force-balance equation is employed for the slow center-of-mass motion of electrons, and the Fokker-Planck equation is used for the ultrafast relative scattering motion of degenerate electrons. This approach allows us to include the anisotropic energy-relaxation process which has been neglected in the energy-balance equation in the past. It also leads us to include the anisotropic coupling to the incident infrared field with different polarizations. Based on this model, the transport of electrons is explored under strong dc and infrared fields by going beyond the relaxation-time approximation. The anisotropic dependence of the electron distribution function on the parallel and perpendicular kinetic energies of electrons is displayed with respect to the dc field direction, and the effect of anisotropic coupling to an incident infrared field with polarizations parallel and perpendicular to the applied dc electric field is shown. The heating of electrons is more accurately described beyond the energy-balance equation with the inclusion of an anisotropic coupling to the infrared field. The drift velocity of electrons is found to increase with the amplitude of the infrared field due to a suppressed momentum-relaxation process (or frictional force) under parallel polarization but decreases with the amplitude due to an enhanced momentum-relaxation process under perpendicular polarization

Numerical solution of the radionuclide transport equation

International Nuclear Information System (INIS)

Hadermann, J.; Roesel, F.

1983-11-01

A numerical solution of the one-dimensional geospheric radionuclide chain transport equation based on the pseudospectral method is developed. The advantages of this approach are flexibility in incorporating space and time dependent migration parameters, arbitrary boundary conditions and solute rock interactions as well as efficiency and reliability. As an application the authors investigate the impact of non-linear sorption isotherms on migration in crystalline rock. It is shown that non-linear sorption, in the present case a Freundlich isotherm, may reduce concentration at the geosphere outlet by orders of magnitude provided the migration time is comparable or larger than the half-life of the nuclide in question. The importance of fixing dispersivity within the continuum approach is stressed. (Auth.)

Steady-state transport equation resolution by particle methods, and numerical results

International Nuclear Information System (INIS)

Mercier, B.

1985-10-01

A method to solve steady-state transport equation has been given. Principles of the method are given. The method is studied in two different cases; estimations given by the theory are compared to numerical results. Results got in 1-D (spherical geometry) and in 2-D (axisymmetric geometry) are given [fr

Tokamak fluidlike equations, with applications to turbulence and transport in H mode discharges

International Nuclear Information System (INIS)

Kim, Y.B.; Biglari, H.; Carreras, B.A.; Diamond, P.H.; Groebner, R.J.; Kwon, O.J.; Spong, D.A.; Callen, J.D.; Chang, Z.; Hollenberg, J.B.; Sundaram, A.K.; Terry, P.W.; Wang, J.F.

1990-01-01

Significant progress has been made in developing tokamak fluidlike equations which are valid in all collisionality regimes in toroidal devices, and their applications to turbulence and transport in tokamaks. The areas highlighted in this paper include: the rigorous derivation of tokamak fluidlike equations via a generalized Chapman-Enskog procedure in various collisionality regimes and on various time scales; their application to collisionless and collisional drift wave models in a sheared slab geometry; applications to neoclassical drift wave turbulence; i.e. neoclassical ion-temperature-gradient-driven turbulence and neoclassical electron-drift-wave turbulence; applications to neoclassical bootstrap-current-driven turbulence; numerical simulation of nonlinear bootstrap-current-driven turbulence and tearing mode turbulence; transport in Hot-Ion H mode discharges. 20 refs., 3 figs

Monte Carlo simulation of neutron transport phenomena

International Nuclear Information System (INIS)

Srinivasan, P.

2009-01-01

Neutron transport is one of the central problems in nuclear reactor related studies and other applied sciences. Some of the major applications of neutron transport include nuclear reactor design and safety, criticality safety of fissile material handling, neutron detector design and development, nuclear medicine, assessment of radiation damage to materials, nuclear well logging, forensic analysis etc. Most reactor and dosimetry studies assume that neutrons diffuse from regions of high to low density just like gaseous molecules diffuse to regions of low concentration or heat flow from high to low temperature regions. However while treatment of gaseous or heat diffusion is quite accurately modeled, treatment of neutron transport as simple diffusion is quite limited. In simple diffusion, the neutron trajectories are irregular, random and zigzag - where as in neutron transport low reaction cross sections (1 barn- 10 -24 cm 2 ) lead to long mean free paths which again depend on the nature and irregularities of the medium. Hence a more accurate representation of the neutron transport evolved based on the Boltzmann equation of kinetic gas theory. In fact the neutron transport equation is a linearized version of the Boltzmann gas equation based on neutron conservation with seven independent variables. The transport equation is difficult to solve except in simple cases amenable to numerical methods. The diffusion (equation) approximation follows from removing the angular dependence of the neutron flux

On the relativistic transport equation for a discontinuity wave of multiplicity one

International Nuclear Information System (INIS)

Giambo, Sebastiano; Palumbo, Annunziata

1980-01-01

In the framework of the theory of the singular hypersurfaces, the transport equation for the amplitude of a discontinuity wave, corresponding to a simple characteristic of a quasi-linear hyperbolic system, is established in the context of special relativity [fr

Electron and ion transport equations in computational weakly-ionized plasmadynamics

International Nuclear Information System (INIS)

Parent, Bernard; Macheret, Sergey O.; Shneider, Mikhail N.

2014-01-01

A new set of ion and electron transport equations is proposed to simulate steady or unsteady quasi-neutral or non-neutral multicomponent weakly-ionized plasmas through the drift–diffusion approximation. The proposed set of equations is advantaged over the conventional one by being considerably less stiff in quasi-neutral regions because it can be integrated in conjunction with a potential equation based on Ohm's law rather than Gauss's law. The present approach is advantaged over previous attempts at recasting the system by being applicable to plasmas with several types of positive ions and negative ions and by not requiring changes to the boundary conditions. Several test cases of plasmas enclosed by dielectrics and of glow discharges between electrodes show that the proposed equations yield the same solution as the standard equations but require 10 to 100 times fewer iterations to reach convergence whenever a quasi-neutral region forms. Further, several grid convergence studies indicate that the present approach exhibits a higher resolution (and hence requires fewer nodes to reach a given level of accuracy) when ambipolar diffusion is present. Because the proposed equations are not intrinsically linked to specific discretization or integration schemes and exhibit substantial advantages with no apparent disadvantage, they are generally recommended as a substitute to the fluid models in which the electric field is obtained from Gauss's law as long as the plasma remains weakly-ionized and unmagnetized

Radiation transport effects in divertor plasmas generated during a tokamak reactor disruption

International Nuclear Information System (INIS)

Peterson, R.R.; MacFarlane, J.J.; Wang, P.

1994-01-01

Vaporization of material from tokamak divertors during disruptions is a critical issue for tokamak reactors from ITER to commercial power plants. Radiation transport from the vaporized material onto the remaining divertor surface plays an important role in the total mass loss to the divertor. Radiation transport in such a vapor is very difficult to calculate in full detail, and this paper quantifies the sensitivity of the divertor mass loss to uncertainties in the radiation transport. Specifically, the paper presents the results of computer simulations of the vaporization of a graphite coated divertor during a tokamak disruption with ITER CDA parameters. The results show that a factor of 100 change in the radiation conductivity changes the mass loss by more than a factor of two

Deterministic methods to solve the integral transport equation in neutronic

International Nuclear Information System (INIS)

Warin, X.

1993-11-01

We present a synthesis of the methods used to solve the integral transport equation in neutronic. This formulation is above all used to compute solutions in 2D in heterogeneous assemblies. Three kinds of methods are described: - the collision probability method; - the interface current method; - the current coupling collision probability method. These methods don't seem to be the most effective in 3D. (author). 9 figs

Method for the determination of the dominant eigenvalue of the neutron transport equation in a slab using fractional derivative

International Nuclear Information System (INIS)

Sperotto, Fabiola Aiub; Segatto, Cynthia Feijo; Zabadal, Jorge

2002-01-01

In this work, we determine the dominant eigenvalue of the one-dimensional neutron transport equation in a slab constructing an integral form for the neutron transport equation which is the expressed in terms of fractional derivative of the angular flux. Equating the fractional derivative of the angular flux to the integrate equation, we determine the unknown order of the fractional derivative comparing the kernel of the integral equation with the one of Riemann-Liouville definition of fractional derivative. Once known the angular flux the dominant eigenvalue is calculated solving a transcendental equation resulting from the application of the boundary conditions. We report the methodology applied, for comparison with available results in literature. (author)

Resolution of the neutron transport equation by massively parallel computer in the Cronos code

International Nuclear Information System (INIS)

Zardini, D.M.

1996-01-01

The feasibility of neutron transport problems parallel resolution by CRONOS code's SN module is here studied. In this report we give the first data about the parallel resolution by angular variable decomposition of the transport equation. Problems about parallel resolution by spatial variable decomposition and memory stage limits are also explained here. (author)

Development of two-group interfacial area transport equation for confined flow-1. Modeling of bubble interactions

International Nuclear Information System (INIS)

Sun, Xiaodong; Kim, Seungjin; Ishii, Mamoru; Beus, Stephen G.

2003-01-01

This paper presents the modeling of bubble interaction mechanisms in the two-group interfacial area transport equation (IATE) for confined gas-liquid two-phase flow. The transport equation is applicable to bubbly, cap-turbulent, and churn-turbulent flow regimes. In the two-group IATE, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 and cap/slug/churn-turbulent bubbles as Group 2. Thus, two sets of equations are used to describe the generation and destruction rates of bubble number density, void fraction, and interfacial area concentration for the two groups of bubbles due to bubble expansion and compression, coalescence and disintegration, and phase change. Five major bubble interaction mechanisms are identified for the gas-liquid two-phase flow of interest, and are analytically modeled as the source/sink terms for the transport equations based on certain assumptions for the confined flow. These models include both intra-group (within a certain group) and inter-group (between two groups) bubble interactions. The comparisons of the prediction by the one-dimensional two-group IATE with experimental data are presented in the second paper of this series. (author)

Coupled force-balance and particle-occupation rate equations for high-field electron transport

International Nuclear Information System (INIS)

Lei, X. L.

2008-01-01

It is pointed out that in the framework of balance-equation approach, the coupled force-balance and particle-occupation rate equations can be used as a complete set of equations to determine the high-field transport of semiconductors in both strong and weak electron-electron interaction limits. We call to attention that the occupation rate equation conserves the total particle number and maintains the energy balance of the relative electron system, and there is no need to introduce any other term in it. The addition of an energy-drift term in the particle-occupation rate equation [Phys. Rev. B 71, 195205 (2005)] is physically inadequate for the violation of the total particle-number conservation and the energy balance. It may lead to a substantial unphysical increase of the total particle number by the application of a dc electric field

Radiation risk assessment for the transport of radioisotopes using KRI-BGM B(U) type container

International Nuclear Information System (INIS)

Cho, Woon-Kap

2008-01-01

The radiation risks were estimated for the transportation of radioisotopes using KRI-BGM transport container. KRI-BGM container was specially designed for transportation of large amount of radioisotopes for industrial or medical applications. The container can carry maximum 370 TBq of solid Ir-192, 29.6 TBq of liquid Mo-99 and 37 TBq of liquid I-131 respectively. For the radiation risk assessment, it was assumed that maximum design activity of those radioisotopes was transported. Transportation route is from Daejeon where radioisotopes are produced to Seoul where radioisotopes are consumed. Transport distance is 200 km including highway and downtown area from Daejeon to Seoul. As the transportation conveyance, an ordinary cargo truck is used exclusively. Radiation risks were estimated for incident free and accident condition of transportation and RADTRAN 5.6 was used as the risk assessment tool. For the risk assessment of radioisotopes transportation, various parameters such as population density around transport route, weather condition, probability of specific accidents such as impact, fire, etc. were considered. From the results of this study, the exclusive transportation of radioisotopes using KRI-BGM transport container by truck showed low radiological risks with manageable safety and health consequences. This paper discusses the methods and results of the radiation risks assessment for the radioisotopes transportation by an ordinary truck and presents the expected radiation risks in person-Sv and latent cancer fatalities. (author)

Integral and Lagrangian simulations of particle and radiation transport in plasma

International Nuclear Information System (INIS)

Christlieb, A J; Hitchon, W N G; Lawler, J E; Lister, G G

2009-01-01

Accurate integral and Lagrangian models of transport in plasmas, in which the models reflect the actual physical behaviour as closely as possible, are presented. These methods are applied to the behaviour of particles and photons in plasmas. First, to show how these types of models arise in a wide range of plasma physics applications, an application to radiation transport in a lighting discharge is given. The radiation transport is solved self-consistently with a model of the discharge to provide what are believed to be very accurate 1D simulations of fluorescent lamps. To extend these integral methods to higher dimensions is computationally very costly. The wide utility of 'treecodes' in solving massive integral problems in plasma physics is discussed, and illustrated in modelling vortex formation in a Penning trap, where a remarkably detailed simulation of vortex formation in the trap is obtained. Extension of treecode methods to other integral problems such as radiation transport is under consideration.

Dynamical equations and transport coefficients for the metals at high pulse electromagnetic fields

International Nuclear Information System (INIS)

Volkov, N B; Chingina, E A; Yalovets, A P

2016-01-01

We offer a metal model suitable for the description of fast electrophysical processes in conductors under influence of powerful electronic and laser radiation of femto- and picosecond duration, and also high-voltage electromagnetic pulses with picosecond front and duration less than 1 ns. The obtained dynamic equations for metal in approximation of one quasineutral liquid are in agreement with the equations received by other authors formerly. New wide-range expressions for the electronic conduction in strong electromagnetic fields are obtained and analyzed. (paper)

Normal scheme for solving the transport equation independently of spatial discretization

International Nuclear Information System (INIS)

Zamonsky, O.M.

1993-01-01

To solve the discrete ordinates neutron transport equation, a general order nodal scheme is used, where nodes are allowed to have different orders of approximation and the whole system reaches a final order distribution. Independence in the election of system discretization and order of approximation is obtained without loss of accuracy. The final equations and the iterative method to reach a converged order solution were implemented in a two-dimensional computer code to solve monoenergetic, isotropic scattering, external source problems. Two benchmark problems were solved using different automatic selection order methods. Results show accurate solutions without spatial discretization, regardless of the initial selection of distribution order. (author)

Numerical Integration of the Transport Equation For Infinite Homogeneous Media

Energy Technology Data Exchange (ETDEWEB)

Haakansson, Rune

1962-01-15

The transport equation for neutrons in infinite homogeneous media is solved by direct numerical integration. Accounts are taken to the anisotropy and the inelastic scattering. The integration has been performed by means of the trapezoidal rule and the length of the energy intervals are constant in lethargy scale. The machine used is a Ferranti Mercury computer. Results are given for water, heavy water, aluminium water mixture and iron-aluminium-water mixture.

Complex eigenvalues for neutron transport equation with quadratically anisotropic scattering

International Nuclear Information System (INIS)

Sjoestrand, N.G.

1981-01-01

Complex eigenvalues for the monoenergetic neutron transport equation in the buckling approximation have been calculated for various combinations of linearly and quadratically anisotropic scattering. The results are discussed in terms of the time-dependent case. Tables are given of complex bucklings for real decay constants and of complex decay constants for real bucklings. The results fit nicely into the pattern of real and purely imaginary eigenvalues obtained earlier. (author)

Solution algorithms for a PN-1 - Equivalent SN angular discretization of the transport equation in one-dimensional spherical coordinates

International Nuclear Information System (INIS)

Warsa, J. S.; Morel, J. E.

2007-01-01

Angular discretizations of the S N transport equation in curvilinear coordinate systems may result in a streaming-plus-removal operator that is dense in the angular variable or that is not lower-triangular. We investigate numerical solution algorithms for such angular discretizations using relationships given by Chandrasekhar to compute the angular derivatives in the one-dimensional S N transport equation in spherical coordinates with Gauss quadrature. This discretization makes the S N transport equation P N-1 - equivalent, but it also makes the sweep operator dense at every spatial point because the N angular derivatives are expressed in terms of the N angular fluxes. To avoid having to invert the sweep operator directly, we must work with the angular fluxes to solve the equations iteratively. We show how we can use approximations to the sweep operator to precondition the full P N-1 equivalent S N equations. We show that these pre-conditioners affect the operator enough such that convergence of a Krylov iterative method improves. (authors)

Application of finite element method in the solution of transport equation

International Nuclear Information System (INIS)

Maiorino, J.R.; Vieira, W.J.

1985-01-01

It is presented the application of finite element method in the solution of second order transport equation (self-adjoint) for the even parity flux. The angular component is treated by expansion in Legendre polinomials uncoupled of the spatial component, which is approached by an expansion in base functions, interpolated in each spatial element. (M.C.K.) [pt

The shielding against radiation produced by powder metallurgy with tungsten copper alloy applied on transport equipment for radio-pharmaceutical products

International Nuclear Information System (INIS)

Cione, Francisco C.; Sene, Frank F.; Souza, Armando C. de; Betini, Evandro G.; Rossi, Jesualdo L.; Rizzuto, Marcia A.

2015-01-01

Safety is mandatory on medicine radiopharmaceutical transportation and dependent on radiation shielding material. The focus of the present work is to minimize the use of harmful materials as lead and depleted uranium usually used in packages transportation. The tungsten-copper composite obtained by powder metallurgy (PM) is non-toxic. In powder metallurgy the density and the porosity of the compacted parts depends basically upon particle size distribution of each component, mixture, compacting pressure and sintering temperature cycle. The tungsten-copper composite, when used for shielding charged particles, X-rays, gamma photons or other photons of lower energy require proper interpretation of the radiation transport phenomena. The radioactive energy reduction varies according to the porosity and density of the materials used as shielding. The main factor for radiation attenuation is the cross section value for tungsten. The motivation research factor is an optimization of the tungsten and cooper composition in order to achieve the best linear absorption coefficient given by equation I (x) = I 0 e (-ux) . Experiments were conducted to quantify the effective radiation shielding properties of tungsten-copper composite produced by PM, varying the cooper amount in the composite. The studied compositions were 15%, 20% and 25% copper in mass. The Compaction pressure was 270 MPa and the sintering atmosphere was in 1.1 atm in N 2 +H 2 . The sintering temperature was 980 deg C for 2 h. The linear absorption coefficient factor was similar either for the green and the sintered compacts, due the amount of porosity did not affect the radiation attenuation. Thus the sintered was meant for size reduction and mechanical properties enhancement. (author)

The shielding against radiation produced by powder metallurgy with tungsten copper alloy applied on transport equipment for radio-pharmaceutical products

Energy Technology Data Exchange (ETDEWEB)

Cione, Francisco C.; Sene, Frank F.; Souza, Armando C. de; Betini, Evandro G.; Rossi, Jesualdo L., E-mail: fceoni@hotmail.com, E-mail: ffsene@hotmail.com, E-mail: armandocirilo@yahoo.com, E-mail: evandrobetini@gmail.com, E-mail: jelrossi@ipen.br [Instituto de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil); Rizzuto, Marcia A., E-mail: marizzutto@if.usp.br [Universidade de Sao Paulo (IF/USP), SP (Brazil). Instituto de Fisica

2015-07-01

Safety is mandatory on medicine radiopharmaceutical transportation and dependent on radiation shielding material. The focus of the present work is to minimize the use of harmful materials as lead and depleted uranium usually used in packages transportation. The tungsten-copper composite obtained by powder metallurgy (PM) is non-toxic. In powder metallurgy the density and the porosity of the compacted parts depends basically upon particle size distribution of each component, mixture, compacting pressure and sintering temperature cycle. The tungsten-copper composite, when used for shielding charged particles, X-rays, gamma photons or other photons of lower energy require proper interpretation of the radiation transport phenomena. The radioactive energy reduction varies according to the porosity and density of the materials used as shielding. The main factor for radiation attenuation is the cross section value for tungsten. The motivation research factor is an optimization of the tungsten and cooper composition in order to achieve the best linear absorption coefficient given by equation I{sub (x)} = I{sub 0}e{sup (-ux)}. Experiments were conducted to quantify the effective radiation shielding properties of tungsten-copper composite produced by PM, varying the cooper amount in the composite. The studied compositions were 15%, 20% and 25% copper in mass. The Compaction pressure was 270 MPa and the sintering atmosphere was in 1.1 atm in N{sub 2}+H{sub 2}. The sintering temperature was 980 deg C for 2 h. The linear absorption coefficient factor was similar either for the green and the sintered compacts, due the amount of porosity did not affect the radiation attenuation. Thus the sintered was meant for size reduction and mechanical properties enhancement. (author)

Fallout radiation protection provided by transportation vehicles

Energy Technology Data Exchange (ETDEWEB)

Burson, Z.G.

1972-10-20

Fallout radiation protection factors (PF's) were estimated for a variety of civilian transportation vehicles using measurements of the natural terrain radiation as a source. The PF values are below 2 in light vehicles, truck beds, or trailers; from 2.5 to 3 in the cabs of heavy trucks and in a railway guard car; and from 3.0 to 3.5 in the engineer's seat of heavy locomotives. This information can be useful in planning the possible movement of personnel from or through areas contaminated either by a wartime incident or a peacetime accident. The information may also be useful for studying the reduction of exposure to the natural terrestrial radiation environment provided by vehicles.

Inelastic Quantum Transport in Superlattices: Success and Failure of the Boltzmann Equation

DEFF Research Database (Denmark)

Wacker, Andreas; Jauho, Antti-Pekka; Rott, Stephan

1999-01-01

the whole held range from linear response to negative differential conductivity. The quantum results are compared with the respective results obtained from a Monte Carlo solution of the Boltzmann equation. Our analysis thus sets the limits of validity for the semiclassical theory in a nonlinear transport...

A numerical solution of the coupled proton-H atom transport equations for the proton aurora

International Nuclear Information System (INIS)

Basu, B.; Jasperse, J.R.; Grossbard, N.J.

1990-01-01

A numerical code has been developed to solve the coupled proton-H atom linear transport equations for the proton aurora. The transport equations have been simplified by using plane-parallel geometry and the forward-scattering approximations only. Otherwise, the equations and their numerical solutions are exact. Results are presented for the particle fluxes and the energy deposition rates, and they are compared with the previous analytical results that were obtained by using additional simplifying approximations. It is found that although the analytical solutions for the particle fluxes differ somewhat from the numerical solutions, the energy deposition rates calculated by the two methods agree to within a few percent. The accurate particle fluxes given by the numerical code are useful for accurate calculation of the characteristic quantities of the proton aurora, such as the ionization rates and the emission rates

Application of synthetic diffusion method in the numerical solution of the equations of neutron transport in slab geometry

International Nuclear Information System (INIS)

Valdes Parra, J.J.

1986-01-01

One of the main problems in reactor physics is to determine the neutron distribution in reactor core, since knowing that, it is possible to calculate the rapidity of occurrence of different nuclear reaction inside the reactor core. Within different theories existing in nuclear reactor physics, is neutron transport the one in which equation who govern the exact behavior of neutronic distribution are developed even inside the proper neutron transport theory, there exist different methods of solution which are approximations to exact solution; still more, with the purpose to reach a more precise solution, the majority of methods have been approached to the obtention of solutions in numerical form with the aim of take the advantages of modern computers, and for this reason a great deal of effort is dedicated to numerical solution of the equations of neutron transport. In agreement with the above mentioned, in this work has been developed a computer program which uses a relatively new techniques known as 'acceleration of synthetic diffusion' which has been applied to solve the neutron transport equation with 'classical schemes of spatial integration' obtaining results with a smaller quantity of interactions, if they compare to done without using such equation (Author)

VU-B radiation inhibits the photosynthetic electron transport chain in chlamydomonas reinhardtii

International Nuclear Information System (INIS)

Cai, W.; Li, X.; Chen, L.

2016-01-01

UV radiation of sunlight is one of harmful factors for earth organisms, especially for photoautotrophs because they require light for energy and biomass production. A number of works have already been done regarding the effects of UV-B radiation at biochemical and molecular level, which showed that UV-B radiation could inhibit photosynthesis activity and reduce photosynthetic electron transport. However quite limited information can accurately make out inhibition site of UV-B radiation on photosynthetic electron transport. In this study, this issue was investigated through measuring oxygen evolution activity, chlorophyll a fluorescence and gene expression in a model unicellular green alga Chlamydomonas reinhardtii. Our results indicated that UV-B radiation could evidently decrease photosynthesis activity and inhibit electron transport by blocking electron transfer process from the first plastoquinone electron acceptors QA to second plastoquinone electron acceptors QB, but not impair electron transfer from the water oxidizing complex to QA. The psbA gene expression was also altered by UV-B radiation, where up-regulation occurred at 2, 4 and 6h after exposure and down-regulation happened at 12 and 24 h after exposure. These results suggested that UV-B could affects D1 protein normal turnover, so there was not enough D1 for binding with QB, which may affect photosynthetic electron transport and photosynthesis activity. (author)

Symbolic math for computation of radiation shielding

International Nuclear Information System (INIS)

Suman, Vitisha; Datta, D.; Sarkar, P.K.; Kushwaha, H.S.

2010-01-01

Radiation transport calculations for shielding studies in the field of accelerator technology often involve intensive numerical computations. Traditionally, radiation transport equation is solved using finite difference scheme or advanced finite element method with respect to specific initial and boundary conditions suitable for the geometry of the problem. All these computations need CPU intensive computer codes for accurate calculation of scalar and angular fluxes. Computation using symbols of the analytical expression representing the transport equation as objects is an enhanced numerical technique in which the computation is completely algorithm and data oriented. Algorithm on the basis of symbolic math architecture is developed using Symbolic math toolbox of MATLAB software. Present paper describes the symbolic math algorithm and its application as a case study in which shielding calculation of rectangular slab geometry is studied for a line source of specific activity. Study of application of symbolic math in this domain evolves a new paradigm compared to the existing computer code such as DORT. (author)

Transport parameter estimation from lymph measurements and the Patlak equation.

Science.gov (United States)

Watson, P D; Wolf, M B

1992-01-01

Two methods of estimating protein transport parameters for plasma-to-lymph transport data are presented. Both use IBM-compatible computers to obtain least-squares parameters for the solvent drag reflection coefficient and the permeability-surface area product using the Patlak equation. A matrix search approach is described, and the speed and convenience of this are compared with a commercially available gradient method. The results from both of these methods were different from those of a method reported by Reed, Townsley, and Taylor [Am. J. Physiol. 257 (Heart Circ. Physiol. 26): H1037-H1041, 1989]. It is shown that the Reed et al. method contains a systematic error. It is also shown that diffusion always plays an important role for transmembrane transport at the exit end of a membrane channel under all conditions of lymph flow rate and that the statement that diffusion becomes zero at high lymph flow rate depends on a mathematical definition of diffusion.

Process and appliance for determining the nature of transported substances by measuring the radiations transmitted

International Nuclear Information System (INIS)

Wykes, J.S.; Surzyn, P.M.; Croke, G.M.; Adsley, Ian.

1980-01-01

The invention relates to a process for determining the nature of a substance transported, comprising the collimation of the radiation of not less than two energies so that they form beams; the irradiation of the matter transported by the beams, the detection of the non-scattered radiations for the two energies at least, after passing in the transported matter, and the deduction of the nature of the transported matter according to the radiations detected. The radiations are collimated by placing a shield around the gamma source (americium 241 or cesium 137). The detector is protected by a shield so that it prevents any significant interference due to the reactions near the surface provoked by those radiations not of the lowest energy, with detection of those radiations of lesser energy. In a variation, a source of relatively higher energy radiations is placed at a distance from the source of relatively lesser energy radiations. The latter have a component taken from natural ionizing radiation and this component is withdrawn to a predetermined calibration [fr

Molecular dynamics studies of transport properties and equation of state of supercritical fluids

Science.gov (United States)

Nwobi, Obika C.

Many chemical propulsion systems operate with one or more of the reactants above the critical point in order to enhance their performance. Most of the computational fluid dynamics (CFD) methods used to predict these flows require accurate information on the transport properties and equation of state at these supercritical conditions. This work involves the determination of transport coefficients and equation of state of supercritical fluids by equilibrium molecular dynamics (MD) simulations on parallel computers using the Green-Kubo formulae and the virial equation of state, respectively. MD involves the solution of equations of motion of a system of molecules that interact with each other through an intermolecular potential. Provided that an accurate potential can be found for the system of interest, MD can be used regardless of the phase and thermodynamic conditions of the substances involved. The MD program uses the effective Lennard-Jones potential, with system sizes of 1000-1200 molecules and, simulations of 2,000,000 time-steps for computing transport coefficients and 200,000 time-steps for pressures. The computer code also uses linked cell lists for efficient sorting of molecules, periodic boundary conditions, and a modified velocity Verlet algorithm for particle displacement. Particle decomposition is used for distributing the molecules to different processors of a parallel computer. Simulations have been carried out on pure argon, nitrogen, oxygen and ethylene at various supercritical conditions, with self-diffusion coefficients, shear viscosity coefficients, thermal conductivity coefficients and pressures computed for most of the conditions. Results compare well with experimental and the National Institute of Standards and Technology (NIST) values. The results show that the number of molecules and the potential cut-off radius have no significant effect on the computed coefficients, while long-time integration is necessary for accurate determination of the

Radiating spheres in general relativity with a mixed transport energy flow

International Nuclear Information System (INIS)

Barreto, W.; Nunez, L.A.

1989-10-01

A seminumeric method by Herrera, Jimenez and Ruggeri is extended to handle the evolution of general relativistic spheres where diffusion and free streaming radiation processes coexist. It is shown when mixed-mode radiation is present a very different hydrodynamic picture emerges from the models previously considered in both radiation limits. Characteristic times for free streaming, hydrodynamics and diffusion processes are considered comparable. Hydrodynamics and radiation are strongly coupled and the particular equation of state of the model emerges as a very important element in the dynamic of the matter distribution. (author). 16 refs, 5 figs

Parallel algorithms for 2-D cylindrical transport equations of Eigenvalue problem

International Nuclear Information System (INIS)

Wei, J.; Yang, S.

2013-01-01

In this paper, aimed at the neutron transport equations of eigenvalue problem under 2-D cylindrical geometry on unstructured grid, the discrete scheme of Sn discrete ordinate and discontinuous finite is built, and the parallel computation for the scheme is realized on MPI systems. Numerical experiments indicate that the designed parallel algorithm can reach perfect speedup, it has good practicality and scalability. (authors)

Description of deeply inelastic collisions in terms of a transport equation

International Nuclear Information System (INIS)

Weidenmueller, H.A.

1977-01-01

A transport equation for deeply inelastic collisions is derived from a random-matrix model for the form factors for inelastic scattering and transfer reactions. The parametrization of these form factors is discussed. Results in one dimension indicate the importance of quantum fluctuations, and limitations of other approaches to the same problem. Results of three dimensions are compared with the data

From analytical solutions of solute transport equations to multidimensional time-domain random walk (TDRW) algorithms

Science.gov (United States)

Bodin, Jacques

2015-03-01

In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

Radiation exposures of workers and the public associated with the transport of radioactive material in Germany

International Nuclear Information System (INIS)

Schwarz, G.; Fett, H.J.; Lange, F.

2004-01-01

Most radioactive material packages transported emit penetrating ionising radiation and radiation exposures of transport workers and the public may occur during their transport. The radiation exposures incurred by transport workers and members of the public can vary significantly depending on a number of factors: most important is the type of radiation emitted (primarily gamma and neutron radiation), the radiation field intensity in the surrounding of a package and conveyance and the duration of exposure to ionising radiation. The information and guidance material on occupational exposures has primarily been derived from a survey and analysis of personal monitoring data provided by a number of commercial transport operators in Germany known as major carrier and handler organisations of fuel cycle and non-fuel cycle material (in terms of the number of pack-ages and the activity carriaged). To some extent advantage was taken of compilations of statistical transport and exposure data collated within other transport safety analysis studies including research projects funded by the European Commission. The exposure data collected cover the time period of the last 4 - 8 years and are most representative for routine transport operations closely related to the movement phase of packaged radioactive material, i.e. receipt, vehicle loading, carriage, in-transit storage, intra-/intermodal transfer, vehicle unloading and delivery at the final destination of loads of radioactive material and packages and the related supervisory and health physics functions. Radiation dose monitoring of members of the public, however, is generally impracticable and, consequently, the information available relies on employing dose assessment models and reflects radiation exposures incurred by hypothetical or critical group individuals of members of the public under normal conditions of transport

Generalized multivariate Fokker-Planck equations derived from kinetic transport theory and linear nonequilibrium thermodynamics

International Nuclear Information System (INIS)

Frank, T.D.

2002-01-01

We study many particle systems in the context of mean field forces, concentration-dependent diffusion coefficients, generalized equilibrium distributions, and quantum statistics. Using kinetic transport theory and linear nonequilibrium thermodynamics we derive for these systems a generalized multivariate Fokker-Planck equation. It is shown that this Fokker-Planck equation describes relaxation processes, has stationary maximum entropy distributions, can have multiple stationary solutions and stationary solutions that differ from Boltzmann distributions

The solution of the multigroup neutron transport equation using spherical harmonics

International Nuclear Information System (INIS)

Fletcher, K.

1981-01-01

A solution of the multi-group neutron transport equation in up to three space dimensions is presented. The flux is expanded in a series of unnormalised spherical harmonics. Using the various recurrence formulae a linked set of first order differential equations is obtained for the moments psisup(g)sub(lm)(r), γsup(g)sub(lm)(r). Terms with odd l are eliminated resulting in a second order system which is solved by two methods. The first is a finite difference formulation using an iterative procedure, secondly, in XYZ and XY geometry a finite element solution is given. Results for a test problem using both methods are exhibited and compared. (orig./RW) [de

The use of non-dimensional representation of the solute transport equations

International Nuclear Information System (INIS)

Laurens, J.-M.

1988-07-01

This report presents the results obtained in a pilot investigation into the use of non-dimensional representations of the solute transport equations, so as to improve the efficiency of the PRA codes used by the DoE and its contractors. A reduced set of parameters was obtained for a single layer transport model. As expected, the response was shown to be highly sensitive on the new parameters. A faster convergence of the system was observed when the sampling technique used was changed to take into account the properties of the new parameters, such that uniform coverage of the reduced parameter hyperspace was achieved. (author)

Finite-difference solution of the space-angle-lethargy-dependent slowing-down transport equation

Energy Technology Data Exchange (ETDEWEB)

Matausek, M V [Boris Kidric Vinca Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)

1972-07-01

A procedure has been developed for solving the slowing-down transport equation for a cylindrically symmetric reactor system. The anisotropy of the resonance neutron flux is treated by the spherical harmonics formalism, which reduces the space-angle-Iethargy-dependent transport equation to a matrix integro-differential equation in space and lethargy. Replacing further the lethargy transfer integral by a finite-difference form, a set of matrix ordinary differential equations is obtained, with lethargy-and space dependent coefficients. If the lethargy pivotal points are chosen dense enough so that the difference correction term can be ignored, this set assumes a lower block triangular form and can be solved directly by forward block substitution. As in each step of the finite-difference procedure a boundary value problem has to be solved for a non-homogeneous system of ordinary differential equations with space-dependent coefficients, application of any standard numerical procedure, for example, the finite-difference method or the method of adjoint equations, is too cumbersome and would make the whole procedure practically inapplicable. A simple and efficient approximation is proposed here, allowing analytical solution for the space dependence of the spherical-harmonics flux moments, and hence the derivation of the recurrence relations between the flux moments at successive lethargy pivotal points. According to the procedure indicated above a computer code has been developed for the CDC -3600 computer, which uses the KEDAK nuclear data file. The space and lethargy distribution of the resonance neutrons can be computed in such a detailed fashion as the neutron cross-sections are known for the reactor materials considered. The computing time is relatively short so that the code can be efficiently used, either autonomously, or as part of some complex modular scheme. Typical results will be presented and discussed in order to prove and illustrate the applicability of the

Interface methods for hybrid Monte Carlo-diffusion radiation-transport simulations

International Nuclear Information System (INIS)

Densmore, Jeffery D.

2006-01-01

Discrete diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Monte Carlo simulations in diffusive media. An important aspect of DDMC is the treatment of interfaces between diffusive regions, where DDMC is used, and transport regions, where standard Monte Carlo is employed. Three previously developed methods exist for treating transport-diffusion interfaces: the Marshak interface method, based on the Marshak boundary condition, the asymptotic interface method, based on the asymptotic diffusion-limit boundary condition, and the Nth-collided source technique, a scheme that allows Monte Carlo particles to undergo several collisions in a diffusive region before DDMC is used. Numerical calculations have shown that each of these interface methods gives reasonable results as part of larger radiation-transport simulations. In this paper, we use both analytic and numerical examples to compare the ability of these three interface techniques to treat simpler, transport-diffusion interface problems outside of a more complex radiation-transport calculation. We find that the asymptotic interface method is accurate regardless of the angular distribution of Monte Carlo particles incident on the interface surface. In contrast, the Marshak boundary condition only produces correct solutions if the incident particles are isotropic. We also show that the Nth-collided source technique has the capacity to yield accurate results if spatial cells are optically small and Monte Carlo particles are allowed to undergo many collisions within a diffusive region before DDMC is employed. These requirements make the Nth-collided source technique impractical for realistic radiation-transport calculations

Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions

International Nuclear Information System (INIS)

Tarvainen, Tanja; Vauhkonen, Marko; Kolehmainen, Ville; Arridge, Simon R; Kaipio, Jari P

2005-01-01

In this paper, a coupled radiative transfer equation and diffusion approximation model is extended for light propagation in turbid medium with low-scattering and non-scattering regions. The light propagation is modelled with the radiative transfer equation in sub-domains in which the assumptions of the diffusion approximation are not valid. The diffusion approximation is used elsewhere in the domain. The two equations are coupled through their boundary conditions and they are solved simultaneously using the finite element method. The streamline diffusion modification is used to avoid the ray-effect problem in the finite element solution of the radiative transfer equation. The proposed method is tested with simulations. The results of the coupled model are compared with the finite element solutions of the radiative transfer equation and the diffusion approximation and with results of Monte Carlo simulation. The results show that the coupled model can be used to describe photon migration in turbid medium with low-scattering and non-scattering regions more accurately than the conventional diffusion model

Low Mach and Peclet number limit for a model of stellar tachocline and upper radiative zones

Directory of Open Access Journals (Sweden)

Donatella Donatelli

2016-09-01

Full Text Available We study a hydrodynamical model describing the motion of internal stellar layers based on compressible Navier-Stokes-Fourier-Poisson system. We suppose that the medium is electrically charged, we include energy exchanges through radiative transfer and we assume that the system is rotating. We analyze the singular limit of this system when the Mach number, the Alfven number, the Peclet number and the Froude number approache zero in a certain way and prove convergence to a 3D incompressible MHD system with a stationary linear transport equation for transport of radiation intensity. Finally, we show that the energy equation reduces to a steady equation for the temperature corrector.

Spherical harmonics solutions of multi-dimensional neutron transport equation by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1977-01-01

A method of solution of a monoenergetic neutron transport equation in P sub(L) approximation is presented for x-y and x-y-z geometries using the finite Fourier transformation. A reactor system is assumed to consist of multiregions in each of which the nuclear cross sections are spatially constant. Since the unknown functions of this method are the spherical harmonics components of the neutron angular flux at the material boundaries alone, the three- and two-dimensional equations are reduced to two- and one-dimensional equations, respectively. The present approach therefore gives fewer unknowns than in the usual series expansion method or in the finite difference method. Some numerical examples are shown for the criticality problem. (auth.)

A linear multiple balance method for discrete ordinates neutron transport equations

International Nuclear Information System (INIS)

Park, Chang Je; Cho, Nam Zin

2000-01-01

A linear multiple balance method (LMB) is developed to provide more accurate and positive solutions for the discrete ordinates neutron transport equations. In this multiple balance approach, one mesh cell is divided into two subcells with quadratic approximation of angular flux distribution. Four multiple balance equations are used to relate center angular flux with average angular flux by Simpson's rule. From the analysis of spatial truncation error, the accuracy of the linear multiple balance scheme is ο(Δ 4 ) whereas that of diamond differencing is ο(Δ 2 ). To accelerate the linear multiple balance method, we also describe a simplified additive angular dependent rebalance factor scheme which combines a modified boundary projection acceleration scheme and the angular dependent rebalance factor acceleration schme. It is demonstrated, via fourier analysis of a simple model problem as well as numerical calculations, that the additive angular dependent rebalance factor acceleration scheme is unconditionally stable with spectral radius < 0.2069c (c being the scattering ration). The numerical results tested so far on slab-geometry discrete ordinates transport problems show that the solution method of linear multiple balance is effective and sufficiently efficient

Radiation Belt Transport Driven by Solar Wind Dynamic Pressure Fluctuations

Science.gov (United States)

Kress, B. T.; Hudson, M. K.; Ukhorskiy, A. Y.; Mueller, H.

2012-12-01

The creation of the Earth's outer zone radiation belts is attributed to earthward transport and adiabatic acceleration of electrons by drift-resonant interactions with electromagnetic fluctuations in the magnetosphere. Three types of radial transport driven by solar wind dynamic pressure fluctuations that have been identified are: (1) radial diffusion [Falthammer, 1965], (2) significant changes in the phase space density radial profile due to a single or few ULF drift-resonant interactions [Ukhorskiy et al., 2006; Degeling et al., 2008], and (3) shock associated injections of radiation belt electrons occurring in less than a drift period [Li et al., 1993]. A progress report will be given on work to fully characterize different forms of radial transport and their effect on the Earth's radiation belts. The work is being carried out by computing test-particle trajectories in electric and magnetic fields from a simple analytic ULF field model and from global MHD simulations of the magnetosphere. Degeling, A. W., L. G. Ozeke, R. Rankin, I. R. Mann, and K. Kabin (2008), Drift resonant generation of peaked relativistic electron distributions by Pc 5 ULF waves, textit{J. Geophys. Res., 113}, A02208, doi:10.1029/2007JA012411. Fälthammar, C.-G. (1965), Effects of Time-Dependent Electric Fields on Geomagnetically Trapped Radiation, J. Geophys. Res., 70(11), 2503-2516, doi:10.1029/JZ070i011p02503. Li, X., I. Roth, M. Temerin, J. R. Wygant, M. K. Hudson, and J. B. Blake (1993), Simulation of the prompt energization and transport of radiation belt particles during the March 24, 1991 SSC, textit{Geophys. Res. Lett., 20}(22), 2423-2426, doi:10.1029/93GL02701. Ukhorskiy, A. Y., B. J. Anderson, K. Takahashi, and N. A. Tsyganenko (2006), Impact of ULF oscillations in solar wind dynamic pressure on the outer radiation belt electrons, textit{Geophys. Res. Lett., 33}(6), L06111, doi:10.1029/2005GL024380.

On the history of a stochastic ansatz for solving the transport equation

International Nuclear Information System (INIS)

Williams, M.M.R.

2010-01-01

A very useful approximate tool for understanding the role of random material properties on solutions of the transport equation is described and its historical derivation given. The development of this stochastic tool, from its introduction by Randall, to its use in describing current problems involving dichotomic or pseudo-dichotomic Markov processes is discussed.

Determination of a closed-form solution for the multidimensional transport equation using a fractional derivative

International Nuclear Information System (INIS)

Zabadal, J.; Vilhena, M.T.; Segatto, C.F.; Pazos, R.P.Ruben Panta.

2002-01-01

In this work we construct a closed-form solution for the multidimensional transport equation rewritten in integral form which is expressed in terms of a fractional derivative of the angular flux. We determine the unknown order of the fractional derivative comparing the kernel of the integral equation with the one of the Riemann-Liouville definition of fractional derivative. We report numerical simulations

Determination of a closed-form solution for the multidimensional transport equation using a fractional derivative

Energy Technology Data Exchange (ETDEWEB)

Zabadal, J. E-mail: jorge.zabadal@ufrgs.br; Vilhena, M.T. E-mail: vilhena@mat.ufrgs.br; Segatto, C.F. E-mail: cynthia@mat.ufrgs.br; Pazos, R.P.Ruben Panta. E-mail: rpp@mat.pucrgs.br

2002-07-01

In this work we construct a closed-form solution for the multidimensional transport equation rewritten in integral form which is expressed in terms of a fractional derivative of the angular flux. We determine the unknown order of the fractional derivative comparing the kernel of the integral equation with the one of the Riemann-Liouville definition of fractional derivative. We report numerical simulations.

Approximate solution to neutron transport equation with linear anisotropic scattering

International Nuclear Information System (INIS)

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

1983-01-01

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

Modelling uncertainties in the diffusion-advection equation for radon transport in soil using interval arithmetic.

Science.gov (United States)

Chakraverty, S; Sahoo, B K; Rao, T D; Karunakar, P; Sapra, B K

2018-02-01

Modelling radon transport in the earth crust is a useful tool to investigate the changes in the geo-physical processes prior to earthquake event. Radon transport is modeled generally through the deterministic advection-diffusion equation. However, in order to determine the magnitudes of parameters governing these processes from experimental measurements, it is necessary to investigate the role of uncertainties in these parameters. Present paper investigates this aspect by combining the concept of interval uncertainties in transport parameters such as soil diffusivity, advection velocity etc, occurring in the radon transport equation as applied to soil matrix. The predictions made with interval arithmetic have been compared and discussed with the results of classical deterministic model. The practical applicability of the model is demonstrated through a case study involving radon flux measurements at the soil surface with an accumulator deployed in steady-state mode. It is possible to detect the presence of very low levels of advection processes by applying uncertainty bounds on the variations in the observed concentration data in the accumulator. The results are further discussed. Copyright © 2017 Elsevier Ltd. All rights reserved.

Coupled heat transfer in high temperature transporting system with semitransparent/opaque material

International Nuclear Information System (INIS)

Du Shenghua; Xia Xinjin

2010-01-01

The heat transfer model of the aerodynamic heating coupled with radiative cooling was developed. The thermal protect system includes the higher heat flux region with high temperature semitransparent material, the heat transporting channel and the lower heat flux region with metal. The control volume method was combined with the Monte Carlo method to calculate the coupled heat transfer of the transporting system, and the thermal equilibrium equation for the transporting channel was solved simultaneously. The effect of the aeroheating flux radio, the area ratio of radiative surfaces, the convective heat transfer coefficient of the heat transporting channel on the radiative surface temperature and the fluid temperature in the heat transporting channel were analyzed. The effect of radiation and conduction in the semitransparent material was discussed. The result shows that to increase the convective heat transfer coefficient in heat flux channel can enhance the heat transporting ability of the system, but the main parameter to effect on the temperature of the heat transporting system is the area ratio of radiative surfaces. (authors)

Radiation exposures of workers resulting from the transport of gamma radiography sources in Germany

International Nuclear Information System (INIS)

Sentuc, F.N.; Schwarz, G.

2006-01-01

Gamma radiation sources are widely used for industrial purposes e.g. for non-destructive material testing. Many of these sources are permanently installed at a facility within instruments e.g. for level or thickness gauging. Other radioactive sources are implemented in portable devices for industrial gamma radiography which have to be carried to the various remote usage sites. In Germany, approximately 20 000 - 25 000 shipments of gamma radiography sources are proceeding annually on public transport routes. Since routine radiation monitoring programmes do not permit task-specific determination of occupational doses e.g. doses incurred during the movement phase and handling related doses, work has been carried out with the objective to determine the radiation exposures of the personnel attributable to transportation. For this purpose, a survey was launched in 2005 collecting data about e.g. the number and conditions of transports, the activity and type of transported radiation sources and the radiation level within the driver's cab to allow a dose assessment to be made for transport workers. The results of this survey covering the most important companies for gamma radiography services in Germany are presented in this paper. (authors)

Chemical and kinetic equilibrations via radiative parton transport

International Nuclear Information System (INIS)

Zhang Bin; Wortman, Warner A

2011-01-01

A hot and dense partonic system can be produced in the early stage of a relativistic heavy ion collision. How it equilibrates is important for the extraction of Quark-Gluon Plasma properties. We study the chemical and kinetic equilibrations of the Quark-Gluon Plasma using a radiative transport model. Thermal and Color-Glass-Condensate motivated initial conditions are used. We observe that screened parton interactions always lead to partial pressure isotropization. Different initial pressure anisotropies result in the same asymptotic evolution. Comparison of evolutions with and without radiative processes shows that chemical equilibration interacts with kinetic equilibration and radiative processes can contribute significantly to pressure isotropization.

Factors affecting radiation doses from dedicated rail transport of spent reactor fuel

International Nuclear Information System (INIS)

Martin, J.E.

1988-01-01

This paper reports there are two exposure control concerns associated with the shipment of spent reactor fuel in dedicated trains -- compliance with transportation regulations for maximum allowable radiation levels, and minimizing the dose received by the general public. This article examines the methods used to calculate the dose equivalent rates alongside stationary (transport regulations) and moving trains (public exposure) of various lengths. The factors examined include the source term, the effect of overlapping radiation fields, the speed of the train, and the location of the population relative to the train. Trains made up of series of cars that individually meet transport regulations can, as a whole, exceed transport vehicle dose equivalent rate limits by up to 23% due to overlapping radiation fields. For moving trains and the worst case analyzed -- a person located 20 feet from the tracks and a train speed of 5 mph --- 141 rail cars would have to pass by to deliver a dose equivalent of 1 mrem

Simulation of neutron transport equation using parallel Monte Carlo for deep penetration problems

International Nuclear Information System (INIS)

Bekar, K. K.; Tombakoglu, M.; Soekmen, C. N.

2001-01-01

Neutron transport equation is simulated using parallel Monte Carlo method for deep penetration neutron transport problem. Monte Carlo simulation is parallelized by using three different techniques; direct parallelization, domain decomposition and domain decomposition with load balancing, which are used with PVM (Parallel Virtual Machine) software on LAN (Local Area Network). The results of parallel simulation are given for various model problems. The performances of the parallelization techniques are compared with each other. Moreover, the effects of variance reduction techniques on parallelization are discussed

Higher-fidelity yet efficient modeling of radiation energy transport through three-dimensional clouds

International Nuclear Information System (INIS)

Hall, M.L.; Davis, A.B.

2005-01-01

Accurate modeling of radiative energy transport through cloudy atmospheres is necessary for both climate modeling with GCMs (Global Climate Models) and remote sensing. Previous modeling efforts have taken advantage of extreme aspect ratios (cells that are very wide horizontally) by assuming a 1-D treatment vertically - the Independent Column Approximation (ICA). Recent attempts to resolve radiation transport through the clouds have drastically changed the aspect ratios of the cells, moving them closer to unity, such that the ICA model is no longer valid. We aim to provide a higher-fidelity atmospheric radiation transport model which increases accuracy while maintaining efficiency. To that end, this paper describes the development of an efficient 3-D-capable radiation code that can be easily integrated into cloud resolving models as an alternative to the resident 1-D model. Applications to test cases from the Intercomparison of 3-D Radiation Codes (I3RC) protocol are shown

Exact solutions of Fisher and Burgers equations with finite transport memory

International Nuclear Information System (INIS)

Kar, Sandip; Banik, Suman Kumar; Ray, Deb Shankar

2003-01-01

The Fisher and Burgers equations with finite memory transport, describing reaction-diffusion and convection-diffusion processes, respectively have recently attracted a lot of attention in the context of chemical kinetics, mathematical biology and turbulence. We show here that they admit exact solutions. While the speed of the travelling wavefront is dependent on the relaxation time in the Fisher equation, memory effects significantly smoothen out the shock wave nature of the Burgers solution, without any influence on the corresponding wave speed. We numerically analyse the ansatz for the exact solution and show that for the reaction-diffusion system the strength of the reaction term must be moderate enough not to exceed a critical limit to allow a travelling wave solution to exist for appreciable finite memory effect

Exact solutions of Fisher and Burgers equations with finite transport memory

CERN Document Server

Kar, S; Ray, D S

2003-01-01

The Fisher and Burgers equations with finite memory transport, describing reaction-diffusion and convection-diffusion processes, respectively have recently attracted a lot of attention in the context of chemical kinetics, mathematical biology and turbulence. We show here that they admit exact solutions. While the speed of the travelling wavefront is dependent on the relaxation time in the Fisher equation, memory effects significantly smoothen out the shock wave nature of the Burgers solution, without any influence on the corresponding wave speed. We numerically analyse the ansatz for the exact solution and show that for the reaction-diffusion system the strength of the reaction term must be moderate enough not to exceed a critical limit to allow a travelling wave solution to exist for appreciable finite memory effect.

Modeling strategy of the source and sink terms in the two-group interfacial area transport equation

International Nuclear Information System (INIS)

Ishii, Mamoru; Sun Xiaodong; Kim, Seungjin

2003-01-01

This paper presents the general strategy for modeling the source and sink terms in the two-group interfacial area transport equation. The two-group transport equation is applicable in bubbly, cap bubbly, slug, and churn-turbulent flow regimes to predict the change of the interfacial area concentration. This dynamic approach has an advantage of flow regime-independence over the conventional empirical correlation approach for the interfacial area concentration in the applications with the two-fluid model. In the two-group interfacial area transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 and cap/slug/churn-turbulent bubbles as Group 2. Thus, two sets of equations are used to describe the generation and destruction rates of bubble number density, void fraction, and interfacial area concentration for the two groups of bubbles due to bubble expansion and compression, coalescence and disintegration, and phase change. Based upon a detailed literature review of the research on the bubble interactions, five major bubble interaction mechanisms are identified for the gas-liquid two-phase flow of interest. A systematic integral approach, in which the significant variations of bubble volume and shape are accounted for, is suggested for the modeling of two-group bubble interactions. To obtain analytical forms for the various bubble interactions, a simplification is made for the bubble number density distribution function

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

International Nuclear Information System (INIS)

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

2007-01-01

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

Exact solutions of the population balance equation including particle transport, using group analysis

Science.gov (United States)

Lin, Fubiao; Meleshko, Sergey V.; Flood, Adrian E.

2018-06-01

The population balance equation (PBE) has received an unprecedented amount of attention in recent years from both academics and industrial practitioners because of its long history, widespread use in engineering, and applicability to a wide variety of particulate and discrete-phase processes. However it is typically impossible to obtain analytical solutions, although in almost every case a numerical solution of the PBEs can be obtained. In this article, the symmetries of PBEs with homogeneous coagulation kernels involving aggregation, breakage and growth processes and particle transport in one dimension are found by direct solving the determining equations. Using the optimal system of one and two-dimensional subalgebras, all invariant solutions and reduced equations are obtained. In particular, an explicit analytical physical solution is also presented.

Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

Science.gov (United States)

Ancey, C.; Bohorquez, P.; Heyman, J.

2015-12-01

The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due

Transport analysis of high radiation and high density plasmas in the ASDEX Upgrade tokamak

Directory of Open Access Journals (Sweden)

Casali L.

2014-01-01

Full Text Available Future fusion reactors, foreseen in the “European road map” such as DEMO, will operate under more demanding conditions compared to present devices. They will require high divertor and core radiation by impurity seeding to reduce heat loads on divertor target plates. In addition, DEMO will have to work at high core densities to reach adequate fusion performance. The performance of fusion reactors depends on three essential parameters: temperature, density and energy confinement time. The latter characterizes the loss rate due to both radiation and transport processes. The DEMO foreseen scenarios described above were not investigated so far, but are now addressed at the ASDEX Upgrade tokamak. In this work we present the transport analysis of such scenarios. Plasma with high radiation by impurity seeding: transport analysis taking into account the radiation distribution shows no change in transport during impurity seeding. The observed confinement improvement is an effect of higher pedestal temperatures which extend to the core via stiffness. A non coronal radiation model was developed and compared to the bolometric measurements in order to provide a reliable radiation profile for transport calculations. High density plasmas with pellets: the analysis of kinetic profiles reveals a transient phase at the start of the pellet fuelling due to a slower density build up compared to the temperature decrease. The low particle diffusion can explain the confinement behaviour.

To the development of numerical methods in problems of radiation transport

International Nuclear Information System (INIS)

Germogenova, T.A.

1990-01-01

Review of studies on the development of numerical methods and the discrete ordinate method in particular, used for solution of radiation protection physics problems is given. Consideration is given to the problems, which arise when calculating fields of penetrating radiation and when studying processes of charged-particle transport and cascade processes, generated by high-energy primary radiation

Fluctuation theory for radiative transfer in random media

International Nuclear Information System (INIS)

Bal, Guillaume; Jing Wenjia

2011-01-01

We consider the effect of small scale random fluctuations of the constitutive coefficients on boundary measurements of solutions to radiative transfer equations. As the correlation length of the random oscillations tends to zero, the transport solution is well approximated by a deterministic, averaged, solution. In this paper, we analyze the random fluctuations to the averaged solution, which may be interpreted as a central limit correction to homogenization. With the inverse transport problem in mind, we characterize the random structure of the singular components of the transport measurement operator. In regimes of moderate scattering, such components provide stable reconstructions of the constitutive parameters in the transport equation. We show that the random fluctuations strongly depend on the decorrelation properties of the random medium.

Measuring the contour of a wavefront using the Irradiance Transport Equation (ITE)

Science.gov (United States)

Castillo-Rodríguez, Luis; Granados-Agustín, Fermín; Fernández-Guasti, Manuel; Cornejo-Rodríguez, Alejandro

2006-01-01

The Irradiance Transport Equation (ITE), found by Teague, had been used in optics with different applications. One of the field where had been used is in optical testing, for example, with the method developed by Takeda. In this paper following the idea of using different optical and mathematical analysis method, theorical and experimental results are presented.

Evaluation of dose equivalent rate distribution in JCO critical accident by radiation transport calculation

CERN Document Server

Sakamoto, Y

2002-01-01

In the prevention of nuclear disaster, there needs the information on the dose equivalent rate distribution inside and outside the site, and energy spectra. The three dimensional radiation transport calculation code is a useful tool for the site specific detailed analysis with the consideration of facility structures. It is important in the prediction of individual doses in the future countermeasure that the reliability of the evaluation methods of dose equivalent rate distribution and energy spectra by using of Monte Carlo radiation transport calculation code, and the factors which influence the dose equivalent rate distribution outside the site are confirmed. The reliability of radiation transport calculation code and the influence factors of dose equivalent rate distribution were examined through the analyses of critical accident at JCO's uranium processing plant occurred on September 30, 1999. The radiation transport calculations including the burn-up calculations were done by using of the structural info...

An extended step characteristic method for solving the transport equation in general geometries

International Nuclear Information System (INIS)

DeHart, M.D.; Pevey, R.E.; Parish, T.A.

1994-01-01

A method for applying the discrete ordinates method to solve the Boltzmann transport equation on arbitrary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the geometrical shape of a mesh element characteristic of a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. By using the method developed here, a general two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons. Results for a number of test problems have been compared with solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well as numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN-II computer programs

The use of Monte Carlo radiation transport codes in radiation physics and dosimetry

CERN Multimedia

CERN. Geneva; Ferrari, Alfredo; Silari, Marco

2006-01-01

Transport and interaction of electromagnetic radiation Interaction models and simulation schemes implemented in modern Monte Carlo codes for the simulation of coupled electron-photon transport will be briefly reviewed. In these codes, photon transport is simulated by using the detailed scheme, i.e., interaction by interaction. Detailed simulation is easy to implement, and the reliability of the results is only limited by the accuracy of the adopted cross sections. Simulations of electron and positron transport are more difficult, because these particles undergo a large number of interactions in the course of their slowing down. Different schemes for simulating electron transport will be discussed. Condensed algorithms, which rely on multiple-scattering theories, are comparatively fast, but less accurate than mixed algorithms, in which hard interactions (with energy loss or angular deflection larger than certain cut-off values) are simulated individually. The reliability, and limitations, of electron-interacti...

Real time quantitative phase microscopy based on single-shot transport of intensity equation (ssTIE) method

Science.gov (United States)

Yu, Wei; Tian, Xiaolin; He, Xiaoliang; Song, Xiaojun; Xue, Liang; Liu, Cheng; Wang, Shouyu

2016-08-01

Microscopy based on transport of intensity equation provides quantitative phase distributions which opens another perspective for cellular observations. However, it requires multi-focal image capturing while mechanical and electrical scanning limits its real time capacity in sample detections. Here, in order to break through this restriction, real time quantitative phase microscopy based on single-shot transport of the intensity equation method is proposed. A programmed phase mask is designed to realize simultaneous multi-focal image recording without any scanning; thus, phase distributions can be quantitatively retrieved in real time. It is believed the proposed method can be potentially applied in various biological and medical applications, especially for live cell imaging.

Transport equation theory of electron backscattering and x-ray production

International Nuclear Information System (INIS)

Fathers, D.J.; Rez, P.

1978-02-01

A transport equation theory of electron backscattering and x ray production is derived and applied to energy dissipation of 30-KeV electrons for copper as a function of depth and to the energy distribution of backscattered electrons for copper, aluminum, and gold. These results are plotted and compared with experiment. Plots for variations of backscattering with atomic number and with angle of incidence, and polar plots of backscattering for 30-keV electrons at normal incidence are also presented. 10 references, seven figures

On discontinuous Galerkin and discrete ordinates approximations for neutron transport equation and the critical eigenvalue

International Nuclear Information System (INIS)

Asadzadeh, M.; Thevenot, L.

2010-01-01

The objective of this paper is to give a mathematical framework for a fully discrete numerical approach for the study of the neutron transport equation in a cylindrical domain (container model,). More specifically, we consider the discontinuous Galerkin (D G) finite element method for spatial approximation of the mono-energetic, critical neutron transport equation in an infinite cylindrical domain ??in R3 with a polygonal convex cross-section ? The velocity discretization relies on a special quadrature rule developed to give optimal estimates in discrete ordinate parameters compatible with the quasi-uniform spatial mesh. We use interpolation spaces and derive optimal error estimates, up to maximal available regularity, for the fully discrete scalar flux. Finally we employ a duality argument and prove superconvergence estimates for the critical eigenvalue.

On the Solution of the Neutron Transport Equation

Energy Technology Data Exchange (ETDEWEB)

Depken, S

1962-12-15

The neutron transport equation has occupied the attention of many authors since Placzek, Wick and others made their first attempts to solve it, Even in the simple case of energy independent cross-sections, and disregarding the motion of the scattering nucleons, it is difficult to find a solution in an analytical form which is easily surveyable and fitted for numerical calculations. In Part I of this paper some new viewpoints will be introduced which enable the solution to be presented in its simplest possible form. Part II is devoted to an investigation of some functions introduced in Part I. In Part III the results are applied to the case of large energy lethargy, and the validity of derived formulas is discussed.

FMCEIR: a Monte Carlo program for solving the stationary neutron and gamma transport equation

International Nuclear Information System (INIS)

Taormina, A.

1978-05-01

FMCEIR is a three-dimensional Monte Carlo program for solving the stationary neutron and gamma transport equation. It is used to study the problem of neutron and gamma streaming in the GCFR and HHT reactor channels. (G.T.H.)

Pure radiation in space-time models that admit integration of the eikonal equation by the separation of variables method

Science.gov (United States)

Osetrin, Evgeny; Osetrin, Konstantin

2017-11-01

We consider space-time models with pure radiation, which admit integration of the eikonal equation by the method of separation of variables. For all types of these models, the equations of the energy-momentum conservation law are integrated. The resulting form of metric, energy density, and wave vectors of radiation as functions of metric for all types of spaces under consideration is presented. The solutions obtained can be used for any metric theories of gravitation.

Computation of the radiation Q of dielectric-loaded electrically small antennas in integral equation formulations

DEFF Research Database (Denmark)

Kim, Oleksiy S.

2016-01-01

A new technique for estimating the impedance frequency bandwidth of electrically small antennas loaded with magneto-dielectric material from a single-frequency simulation in a surface integral equation solver is presented. The estimate is based on the inverse of the radiation Q computed using newly...... derived expressions for the stored energy and the radiated power of arbitrary coupled electric and magnetic currents in free space....

Activities of the Radiation Shielding Information Center and a report on codes/data for high energy radiation transport

International Nuclear Information System (INIS)

Roussin, R.W.

1993-01-01

From the very early days in its history Radiation Shielding Information Center (RSIC) has been involved with high energy radiation transport. The National Aeronautics and Space Administration was an early sponsor of RSIC until the completion of the Apollo Moon Exploration Program. In addition, the intranuclear cascade work of Bertini at Oak Ridge National Laboratory provided valuable resources which were made available through RSIC. Over the years, RSIC has had interactions with many of the developers of high energy radiation transport computing technology and data libraries and has been able to collect and disseminate this technology. The current status of this technology will be reviewed and prospects for new advancements will be examined

Edge turbulence and transport: Text and ATF modeling

International Nuclear Information System (INIS)

Ritz, C.P.; Rhodes, T.L.; Lin, H.; Rowan, W.L.; Bengtson, R.; Wootton, A.J.; Diamond, P.H.; Ware, A.S.; Thayer, D.R.

1990-01-01

We present experimental results on edge turbulence and transport from the tokamak TEXT and the torsatron ATF. The measured electrostatic fluctuations can explain the edge transport of particles and energy. Certain drive (radiation) and stabilizing (velocity shear) terms are suggested by the results. The experimental fluctuation levels and spectral widths can be reproduced by considering the nonlinear evolution of the reduced MHD equations, incorporating a thermal drive from line radiation. In the tokamak limit (with toroidal electric field) the model corresponds to the resistivity gradient mode, while in the currentless torsatron or stellarator limit it corresponds to a thermally driven drift wave

Education and Training in Radiation, Transport and Waste Safety Newsletter, No. 2c, May 2013

International Nuclear Information System (INIS)

2013-05-01

The IAEA Strategic Approach to Education and Training in Radiation, Transport and Waste Safety (2011-2020) provides a framework for establishing a sustainable education and training infrastructure in Member States that addresses national needs for building and maintaining competence in radiation, transport and waste safety that is consistent with IAEA Safety Standards. For this purpose, IAEA's General Conference has encouraged Member States to develop a national strategy for education and training, underlining the fundamental importance of sustainable programmes for building competence in radiation, transport and waste safety, as a key component of safety infrastructure. Furthermore Member States that receive assistance from IAEA are obliged to apply IAEA Safety Standards which require, inter alia, governments to establish a national policy and strategy for safety, including provisions for acquiring and maintaining the necessary competence nationally for ensuring safety. IAEA's Division of Radiation, Transport and Waste Safety is assisting Member States to develop their own national strategies in Europe via the Regional Project RER/9/109 on ''Strengthening Education and training Infrastructure, and Building Competence in Radiation Safety'', which includes, inter alia, Regional Workshops on National Strategies for education and training in radiation transport and waste safety. IAEA's Regional Training Centres (RTCs) in Greece and Belarus are key partners in the European region.

Education and Training in Radiation, Transport and Waste Safety Newsletter, No. 2d, June 2013

International Nuclear Information System (INIS)

2013-06-01

The IAEA Strategic Approach to Education and Training in Radiation, Transport and Waste Safety (2011-2020) provides a framework for establishing a sustainable education and training infrastructure in Member States that addresses national needs for building and maintaining competence in radiation, transport and waste safety that is consistent with IAEA Safety Standards. For this purpose, IAEA's General Conference has encouraged Member States to develop a national strategy for education and training, underlining the fundamental importance of sustainable programmes for building competence in radiation, transport and waste safety, as a key component of safety infrastructure. Furthermore Member States that receive assistance from IAEA are obliged to apply IAEA Safety Standards which require, inter alia, governments to establish a national policy and strategy for safety, including provisions for acquiring and maintaining the necessary competence nationally for ensuring safety. IAEA's Division of Radiation, Transport and Waste Safety is assisting Member States to develop their own national strategies in Latin America via the Regional Project RLA/9/070 on ''Strengthening Education and training Infrastructure, and Building Competence in Radiation Safety'', which includes, inter alia, Regional Workshops on National Strategies for education and training in radiation transport and waste safety. IAEA's Regional Training Centres (RTCs) in Argentina and Brazil are key partners in the Latin-American region.

Optimal calculational schemes for solving multigroup photon transport problem

International Nuclear Information System (INIS)

Dubinin, A.A.; Kurachenko, Yu.A.

1987-01-01

A scheme of complex algorithm for solving multigroup equation of radiation transport is suggested. The algorithm is based on using the method of successive collisions, the method of forward scattering and the spherical harmonics method, and is realized in the FORAP program (FORTRAN, BESM-6 computer). As an example the results of calculating reactor photon transport in water are presented. The considered algorithm being modified may be used for solving neutron transport problems

Monte Carlo method in radiation transport problems

International Nuclear Information System (INIS)

Dejonghe, G.; Nimal, J.C.; Vergnaud, T.

1986-11-01

In neutral radiation transport problems (neutrons, photons), two values are important: the flux in the phase space and the density of particles. To solve the problem with Monte Carlo method leads to, among other things, build a statistical process (called the play) and to provide a numerical value to a variable x (this attribution is called score). Sampling techniques are presented. Play biasing necessity is proved. A biased simulation is made. At last, the current developments (rewriting of programs for instance) are presented due to several reasons: two of them are the vectorial calculation apparition and the photon and neutron transport in vacancy media [fr

A retrospective and prospective survey of three-dimensional transport calculations

International Nuclear Information System (INIS)

Nakahara, Yasuaki

1985-01-01

A retrospective survey is made on the three-dimensional radiation transport calculations. Introduction is given to computer codes based on the distinctive numerical methods such as the Monte Carlo, Direct Integration, Ssub(n) and Finite Element Methods to solve the three-dimensional transport equations. Prospective discussions are made on pros and cons of these methods. (author)

Fresnel Lens Solar Concentrator Design Based on Geometric Optics and Blackbody Radiation Equations

Science.gov (United States)

Watson, Michael D.; Jayroe, Robert, Jr.

1999-01-01

Fresnel lenses have been used for years as solar concentrators in a variety of applications. Several variables effect the final design of these lenses including: lens diameter, image spot distance from the lens, and bandwidth focused in the image spot. Defining the image spot as the geometrical optics circle of least confusion and applying blackbody radiation equations the spot energy distribution can be determined. These equations are used to design a fresnel lens to produce maximum flux for a given spot size, lens diameter, and image distance. This approach results in significant increases in solar efficiency over traditional single wavelength designs.

Equations of motion for a radiating charged particle in electromagnetic fields on curved spacetime

International Nuclear Information System (INIS)

Prasanna, A.R.

1982-11-01

In this note we present the equations of motion for a radiating charged particle in the framework of general relativity and give a formal procedure of solving the system numerically using iterations, when the motion is confined to the equatorial plane. (author)

Coupling of discrete ordinates methods by transmission of boundary conditions in solving the neutron transport equation in slab geometry; Couplage de discretisations aux ordonnees discretes d`equations de transport 1D par passage de conditions frontieres

Energy Technology Data Exchange (ETDEWEB)

Bal, G. [Departement MMN, Service IMA, Direction des Etudes et Recherches, Electricite de France (EDF), 92 - Clamart (France)

1995-10-01

Neutron transport in nuclear reactors is quite well modelled by the linear Boltzmann transport equation. Its solution is relatively easy, but unfortunately too expensive to achieve whole core computations. Thus, we have to simplify it, for example by homogenizing some physical characteristics. However, the solution may then be inaccurate. Moreover, in strongly homogeneous areas, the error may be too big. Then we would like to deal with such an inconvenient by solving the equation accurately on this area, but more coarsely away from it, so that the computation is not too expensive. This problem is the subject of a thesis. We present here some results obtained for slab geometry. The couplings between the fine and coarse discretization regions could be conceived in a number of approaches. Here, we only deal with the coupling at crossing the interface between two sub-domains. In the first section, we present the coupling of discrete ordinate methods for solving the homogeneous, isotropic and mono-kinetic equation. Coupling operators are defined and shown to be optimal. The second and the third sections are devoted to an extension of the previous results when the equation is non-homogeneous, anisotropic and multigroup (under some restrictive assumptions). Some numerical results are given in the case of isotropic and mono-kinetic equations. (author) 15 refs.

Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method

Energy Technology Data Exchange (ETDEWEB)

Le Hardy, D. [Université de Nantes, LTN UMR CNRS 6607 (France); Favennec, Y., E-mail: yann.favennec@univ-nantes.fr [Université de Nantes, LTN UMR CNRS 6607 (France); Rousseau, B. [Université de Nantes, LTN UMR CNRS 6607 (France); Hecht, F. [Sorbonne Universités, UPMC Université Paris 06, UMR 7598, inria de Paris, Laboratoire Jacques-Louis Lions, F-75005, Paris (France)

2017-04-01

The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken into account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.

A practical nonlocal model for heat transport in magnetized laser plasmas

International Nuclear Information System (INIS)

Nicolaie, Ph.D.; Feugeas, J.-L.A.; Schurtz, G.P.

2006-01-01

A model of nonlocal transport for multidimensional radiation magnetohydrodynamics codes is presented. In laser produced plasmas, it is now believed that the heat transport can be strongly modified by the nonlocal nature of the electron conduction. Other mechanisms, such as self-generated magnetic fields, may also affect the heat transport. The model described in this work, based on simplified Fokker-Planck equations aims at extending the model of G. Schurtz, Ph. Nicolaie, and M. Busquet [Phys. Plasmas 7, 4238 (2000)] to magnetized plasmas. A complete system of nonlocal equations is derived from kinetic equations with self-consistent electric and magnetic fields. These equations are analyzed and simplified in order to be implemented into large laser fusion codes and coupled to other relevant physics. The model is applied to two laser configurations that demonstrate the main features of the model and point out the nonlocal Righi-Leduc effect in a multidimensional case

Revisiting Wiedemann-Franz law through Boltzmann transport equations and ab-initio density functional theory

Science.gov (United States)

Nag, Abhinav; Kumari, Anuja; Kumar, Jagdish

2018-05-01

We have investigated structural, electronic and transport properties of the alkali metals using ab-initio density functional theory. The electron energy dispersions are found parabolic free electron like which is expected for alkali metals. The lattice constants for all the studied metals are also in good agreement within 98% with experiments. We have further computed their transport properties using semi-classical Boltzmann transport equations with special focus on electrical and thermal conductivity. Our objective was to obtain Wiedemann-Franz law and hence Lorenz number. The motivation to do these calculations is to see that how the incorporation of different interactions such as electron-lattice, electron-electron interaction affect the Wiedeman-Franz law. By solving Boltzmann transport equations, we have obtained electrical conductivity (σ/τ) and thermal conductivity (κ0 /τ) at different temperatures and then calculated Lorenz number using L = κ0 /(σT). The obtained value of Lorenz number has been found to match with value derived for free electron Fermi gas 2.44× 10-8 WΩK-2. Our results prove that the Wiedemann-Franz law as derived for free electron gas does not change much for alkali metals, even when one incorporates interaction of electrons with atomic nuclei and other electrons. However, at lower temperatures, the Lorenz number, was found to be deviating from its theoretical value.

Radiation Shielding Information Center: a source of computer codes and data for fusion neutronics studies

International Nuclear Information System (INIS)

McGill, B.L.; Roussin, R.W.; Trubey, D.K.; Maskewitz, B.F.

1980-01-01

The Radiation Shielding Information Center (RSIC), established in 1962 to collect, package, analyze, and disseminate information, computer codes, and data in the area of radiation transport related to fission, is now being utilized to support fusion neutronics technology. The major activities include: (1) answering technical inquiries on radiation transport problems, (2) collecting, packaging, testing, and disseminating computing technology and data libraries, and (3) reviewing literature and operating a computer-based information retrieval system containing material pertinent to radiation transport analysis. The computer codes emphasize methods for solving the Boltzmann equation such as the discrete ordinates and Monte Carlo techniques, both of which are widely used in fusion neutronics. The data packages include multigroup coupled neutron-gamma-ray cross sections and kerma coefficients, other nuclear data, and radiation transport benchmark problem results

Radiation safety of crew and passengers of air transportation in civil aviation. Provisional standards

Science.gov (United States)

Aksenov, A. F.; Burnazyan, A. I.

1985-01-01

The purpose and application of the provisional standards for radiation safety of crew and passengers in civil aviation are given. The radiation effect of cosmic radiation in flight on civil aviation air transport is described. Standard levels of radiation and conditions of radiation safety are discussed.

Radiation transport in high-level waste form

International Nuclear Information System (INIS)

Arakali, V.S.; Barnes, S.M.

1992-01-01

The waste form selected for vitrifying high-level nuclear waste stored in underground tanks at West Valley, NY is borosilicate glass. The maximum radiation level at the surface of a canister filled with the high-level waste form is prescribed by repository design criteria for handling and disposition of the vitrified waste. This paper presents an evaluation of the radiation transport characteristics for the vitreous waste form expected to be produced at West Valley and the resulting neutron and gamma dose rates. The maximum gamma and neutron dose rates are estimated to be less than 7500 R/h and 10 mRem/h respectively at the surface of a West Valley canister filled with borosilicate waste glass

Deterministic methods in radiation transport. A compilation of papers presented February 4--5, 1992

Energy Technology Data Exchange (ETDEWEB)