FEM-2D, 2-D MultiGroup Diffusion in X-Y Geometry
1 - Nature of physical problem solved: FEM-2D solves the two-dimensional diffusion equation in x-y geometry. This is done by the finite elements method. 2 - Method of solution: FEM-2D uses triangular elements with first and second order Lagrange approximations. The systems equations are formulated in multigroup form and solved by Cholesky procedure which operates only on nonzero elements. Various acceleration techniques are available for the outer iteration. Fluxes along various lines and rates in arbitrary zones may be output. 3 - Restrictions on the complexity of the problem: The code uses variable dimensioning. Thus, the problem size is restricted by the largest array which usually is the systems matrix. Fluxes of all groups are kept in memory. This might become another restrictive data set for a large number of groups. The validity of the results is restricted by the approximations used. FEM-2D requires a finite element net which allows the approximation of fluxes by at most parabolas. The node distribution should be more dense in areas of heavy flux changes (near absorbers or the reflector)
Highlights: ► The multi-group IDE-NDK was solved numerically in 2D-Cartesian geometry. ► The progressive basic polynomial (BPn) methods showed no numerical oscillations. ► The BP2 algorithm showed good accuracy and efficiency. -- Abstract: The multi-group time-integro-differential equations of the neutron diffusion kinetics (IDE-NDK) was solved numerically in 2D Cartesian geometry with the use of the basic-progressive polynomial approximation (BPn). Two applications were computed: a ramp, and an instantaneous change of the thermal removal macroscopic cross sections of the driver material of the 2D-TWGL benchmark problems. The BP2 algorithm showed good accuracy when compared with the results of other codes. BPn did not show the undesirable oscillations that appeared in other codes.
VARI-QUIR-3, 2-D Multigroup Steady-State Neutron Diffusion in X-Y R-Z or R-Theta Geometry
1 - Nature of physical problem solved: The steady-state, multigroup, two-dimensional neutron diffusion equations are solved in x-y, r-z, and r-theta geometry. 2 - Method of solution: A Gauss-Seidel type of solution with inner and outer iterations is used. The source is held constant during the inner iterations
1 - Description of program or function: DIF3D solves multigroup diffusion theory eigenvalue, adjoint, fixed source and criticality (concentration search) problems in 1-, 2- and 3-space dimensions for orthogonal (rectangular or cylindrical), triangular and hexagonal geometries. Anisotropic diffusion coefficients are permitted. Flux and power density maps by mesh cell and region-wise balance integrals are provided. Although primarily designed for fast reactor problems, up-scattering and internal black boundary conditions are also treated. The DIF3D8.0/VARIANT8.0 release differs from the previous DIF3D7.0 release in that it includes a significantly expanded set of solution techniques using variational nodal methods. DIF3D's nodal option solves the multigroup steady state neutron diffusion equation in two- and three-dimensional hexagonal and cartesian geometries and solves the transport equation in two-and three-dimensional cartesian geometries. Eigenvalue, adjoint, fixed source and criticality (concentration) search problems are permitted as are anisotropic diffusion coefficients. Flux and power density maps by mesh cell and region-wise balance integrals are provided. Although primarily designed for fast reactor problems, up-scattering and for finite difference option only internal black boundary conditions are also treated. VARIANT solves the multigroup steady-state neutron diffusion and transport equations in two- and three-dimensional Cartesian and hexagonal geometries using variational nodal methods. The transport approximations involve complete spherical harmonic expansions up to order P5. Eigenvalue, adjoint, fixed source, gamma heating, and criticality (concentration) search problems are permitted. Anisotropic scattering is treated, and although primarily designed for fast reactor problems, up-scattering options are also included. Related and Auxiliary Programs: DIF3D reads and writes the standard interface files specified by the Committee on Computer Code
Three-dimensional multigroup diffusion code ANDEX based on nodal method for cartesian geometry
An analytic polynomial nodal method using partial currents has been derived for the solution of multigroup neutron diffusion equations in three-dimensional (3-D) cartesian geometry. This method is characterized by expressing the source and leakage terms in an auxiliary 1-D diffusion equation by quadratic polynomials and solving it analytically. Based on this method, we have developed a 3-D multigroup diffusion code ANDEX, and applied to 2-D LWR and 3-D FBR models. The results of keff, power distributions and computing time have been compared with those of finite difference method calculations. (author)
Second order time evolution of the multigroup diffusion and P1 equations for radiation transport
Highlights: → An existing multigroup transport algorithm is extended to be second-order in time. → A new algorithm is presented that does not require a grey acceleration solution. → The two algorithms are tested with 2D, multi-material problems. → The two algorithms have comparable computational requirements. - Abstract: An existing solution method for solving the multigroup radiation equations, linear multifrequency-grey acceleration, is here extended to be second order in time. This method works for simple diffusion and for flux-limited diffusion, with or without material conduction. A new method is developed that does not require the solution of an averaged grey transport equation. It is effective solving both the diffusion and P1 forms of the transport equation. Two dimensional, multi-material test problems are used to compare the solution methods.
Development and validation of Apros multigroup nodal diffusion model
Rintala, Antti
2015-01-01
The development of a steady state and transient multigroup nodal diffusion model for process simulation software Apros was continued and the models were validated. The initial implementation of the model was performed in 2009 and it has not been under continuous development afterwards. Some errors in the steady state model were corrected. The transient model was found to be incorrect. The solution method of the transient model was derived, and the program code not common with the steady s...
FINELM: a multigroup finite element diffusion code
FINELM is a FORTRAN IV program to solve the Neutron Diffusion Equation in X-Y, R-Z, R-theta, X-Y-Z and R-theta-Z geometries using the method of Finite Elements. Lagrangian elements of linear or higher degree to approximate the spacial flux distribution have been provided. The method of dissections, coarse mesh rebalancing and Chebyshev acceleration techniques are available. Simple user defined input is achieved through extensive input subroutines. The input preparation is described followed by a program structure description. Sample test cases are provided. (Auth.)
Multigroup finite element-boundary element method for neutron diffusion
Full text: The finite element method (FEM) is an efficient method used for the solution of partial differential equations (PDE's) of engineering physics due to its symmetric, sparse and positive-definite coefficient matrix. FEM has been successfully applied for the solution of multigroup neutron transport and diffusion equations since 1970's. The boundary element method (BEM), on the other hand, is a newer method and is unique among the numerical methods used for the solution of PDE's with its property of confining the unknowns only to the boundaries of homogeneous regions, thus, greatly reducing matrix dimensions. The first application of BEM to the neutron diffusion equation (NDE) dates back to 1985 and many researchers are currently working in this area. Although BEM is known to have the desirable property of being an internal-mesh free method, this advantage is lost in some of its application to the NDE due to the existence of fission source volume integrals in fissionable regions unless domain-decomposition methods are used. To exploit the favorable properties of both FEM and BEM, a hybrid FE/BE method has been recently proposed for reflected systems treated by one or two-group diffusion theories in a recent paper co-authored by the first author. In this work, the hybrid FE/BE method for reflected systems is generalized to multigroup diffusion theory. The core is treated by FEM to preserve the high accuracy of FEM in such neutron-producing regions. Using a boundary integral equation formerly proposed by the second author, BEM, is utilized for the discretization of the reflector, thus, eliminating the internal mesh completely for this nonfissionable region. The multigroup FE/BE method has been implemented in our recently developed FORTRAN program. The program is validated by comparison of the calculated effective multiplication factor and the group fluxes with their analytical counterparts for a two-group reflected system. Comparison of these results and
SCALE 6 computes problem-dependent multigroup (MG) cross sections through a combination of the conventional Bondarenko shielding-factor method and a deterministic pointwise (PW) transport calculation of the fine-structure spectra in the resolved resonance and thermal energy ranges. The PW calculation is performed by the CENTRM code using a 1-D cylindrical Wigner-Seitz model with the white boundary condition instead of the real rectangular cell shape to represent a lattice unit cell. The pointwise fluxes computed by CENTRM are not exact because a 1-D model is used for the transport calculation, which introduces discrepancies in the MG self-shielded cross sections, resulting in some deviation in the eigenvalue. In order to solve this problem, the method of characteristics (MOC) has been applied to enable the CENTRM PW transport calculation for a 2-D square pin cell. The computation results show that the new BONAMI/CENTRM-MOC procedure produces very precise self-shielded cross sections compared to MCNP reaction rates.
A code called COMESH based on corner mesh finite difference scheme has been developed to solve multigroup diffusion theory equations. One can solve 1-D, 2-D or 3-D problems in Cartesian geometry and 1-D (r) or 2-D (r-z) problem in cylindrical geometry. On external boundary one can use either homogeneous Dirichlet (θ-specified) or Neumann (∇θ specified) type boundary conditions or a linear combination of the two. Internal boundaries for control absorber simulations are also tackled by COMESH. Many an acceleration schemes like successive line over-relaxation, two parameter Chebyschev acceleration for fission source, generalised coarse mesh rebalancing etc., render the code COMESH a very fast one for estimating eigenvalue and flux/power profiles in any type of reactor core configuration. 6 refs. (author)
The subject is divided in two parts: In the first part a nodal method has been worked out to solve the steady state multigroup diffusion equation. This method belongs to the same set of nodal methods currently used to calculate the exact fission powers and neutron fluxes in a very short computing time. It has been tested on a two dimensional idealized reactors. The effective multiplication factor and the fission powers for each fuel element have been calculated. The second part consists in studying and mastering the multigroup diffusion code DAHRA - a reduced version of DIANE - a two dimensional code using finite difference method
1 - Description of program or function: PARTISN (Parallel, Time-Dependent SN) is the evolutionary successor to CCC-0547/DANTSYS. User input and cross section formats are very similar to that of DANTSYS. The linear Boltzmann transport equation is solved for neutral particles using the deterministic (SN) method. Both the static (fixed source or eigenvalue) and time-dependent forms of the transport equation are solved in forward or adjoint mode. Vacuum, reflective, periodic, white, or inhomogeneous boundary conditions are solved. General anisotropic scattering and inhomogeneous sources are permitted. PARTISN solves the transport equation on orthogonal (single level or block-structured AMR) grids in 1-D (slab, two-angle slab, cylindrical, or spherical), 2-D (X-Y, R-Z, or R-T) and 3-D (X-Y-Z or R-Z-T) geometries. 2 - Methods:PARTISN numerically solves the multigroup form of the neutral-particle Boltzmann transport equation. The discrete-ordinates form of approximation is used for treating the angular variation of the particle distribution. For curvilinear geometries, diamond differencing is used for angular discretization. The spatial discretizations may be either low-order (diamond difference or Adaptive Weighted Diamond Difference (AWDD)) or higher-order (linear discontinuous or exponential discontinuous). Negative fluxes are eliminated by a local set-to-zero-and-correct algorithm for the diamond case (DD/STZ). Time differencing is Crank-Nicholson (diamond), also with a set-to-zero fix-up scheme. Both inner and outer iterations can be accelerated using the diffusion synthetic acceleration method, or transport synthetic acceleration can be used to accelerate the inner iterations. The diffusion solver uses either the conjugate gradient or multigrid method. Chebyshev acceleration of the fission source is used. The angular source terms may be treated either via standard PN expansions or Galerkin scattering. An option is provided for strictly positive scattering sources
FINELM: a multigroup finite element diffusion code. Part I
The author presents a two dimensional code for multigroup diffusion using the finite element method. It was realized that the extensive connectivity which contributes significantly to the accuracy, results in a matrix which, although symmetric and positive definite, is wide band and possesses an irregular profile. Hence, it was decided to introduce sparsity techniques into the code. The introduction of the R-Z geometry lead to a great deal of changes in the code since the rotational invariance of the removal matrices in X-Y geometry did not carry over in R-Z geometry. Rectangular elements were introduced to remedy the inability of the triangles to model essentially one dimensional problems such as slab geometry. The matter is discussed briefly in the text in the section on benchmark problems. This report is restricted to the general theory of the triangular elements and to the sparsity techniques viz. incomplete disections. The latter makes the size of the problem that can be handled independent of core memory and dependent only on disc storage capacity which is virtually unlimited. (Auth.)
Highlights: ► We develop a 2-D, multigroup neutron/adjoint diffusion computer code based on GFEM. ► The spatial discretization is performed using unstructured triangle elements. ► Multiplication factor, flux/adjoint and power distribution are outputs of the code. ► Sensitivity analysis to the number, arrangement and size of elements is performed. ► We proved that the developed code is a reliable tool to solve diffusion equation. -- Abstract: Various methods for solving the forward/adjoint equation in hexagonal and rectangular geometries are known in the literatures. In this paper, the solution of multigroup forward/adjoint equation using Finite Element Method (FEM) for hexagonal and rectangular reactor cores is reported. The spatial discretization of equations is based on Galerkin FEM (GFEM) using unstructured triangle elements. Calculations are performed for both linear and quadratic approximations of the shape function; based on which results are compared. Using power iteration method for the forward and adjoint calculations, the forward and adjoint fluxes with the corresponding eigenvalues are obtained. The results are then benchmarked against the valid results for IAEA-2D, BIBLIS-2D and IAEA-PWR benchmark problems. Convergence rate of GFEM in linear and quadratic approximations of the shape function are calculated and results are quantitatively compared. A sensitivity analysis of the calculations to the number and arrangement of elements has been performed.
Highlights: → Coupled neutron and gamma transport is considered in the multigroup diffusion approximation. → The model accommodates fission, up- and down-scattering and common neutron-gamma interactions. → The exact solution to the diffusion equation in a heterogeneous media of any number of regions is found. → The solution is shown to parallel the one-group case in a homogeneous medium. → The discussion concludes with a heterogeneous, 2 fuel-plate 93.2% enriched reactor fuel benchmark demonstration. - Abstract: The angular flux for the 'rod model' describing coupled neutron/gamma (n, γ) diffusion has a particularly straightforward analytical representation when viewed from the perspective of a one-group homogeneous medium. Cast in the form of matrix functions of a diagonalizable matrix, the solution to the multigroup equations in heterogeneous media is greatly simplified. We shall show exactly how the one-group homogeneous medium solution leads to the multigroup solution.
Multigroup neutron transport equation in the diffusion and P1 approximation
Investigations of the properties of the multigroup transport operator, width and without delayed neutrons in the diffusion and P1 approximation, is performed using Keldis's theory of operator families as well as a technique . recently used for investigations into the properties of the general linearized Boltzmann operator. It is shown that in the case without delayed neutrons, multigroup transport operator in the diffusion and P1 approximation possesses a complete set of generalized eigenvectors. A formal solution to the initial value problem is also given. (author)
SIXTUS-2. A two dimensional multigroup diffusion theory code in hexagonal geometry. Pt. 1
A new algorithm for solving the 2-dimensional multigroup diffusion equations in hexagonal geometry is described. It is based on three novel ideas: analytic intranodal solutions, use of the group irreducible representations and an explicit scheme for solving the response matrix equations. The resulting computer code SIXTUS-2 has been found to be very accurate and effective. (Auth.)
The Analytic Coarse-Mesh Finite-Difference method is developed in detail for multi-group and multi-dimensional diffusion calculations, including the general and particular modal solutions in the complex space for any number of groups. For rectangular multidimensional geometries, the Chao's generalized relations with transverse integration provide a high-order approximation of the ACMFD method, where all energy groups are coupled by matrix-vector FD relations and the errors are limited to the ones incurred by the interpolation of the transverse interface currents, in a non-linear iterative scheme. The implementation of the method in a multigroup 3D rectangular geometry nodal solver called ANDES is discussed, pointing out the encapsulation achieved for integration of the solver as an optional module within larger code systems. The performance of the ANDES solver in 3D rectangular (X-Y-Z) geometry and multi-groups is verified by its application to several 2D-3D model and international benchmarks (NEA-OECD), with given diffusion cross section sets in few-groups (2 to 8). The extensive verification, always required for new methods and codes, shows a quite fast convergence of ANDES in both the eigenvalue and transverse leakage iteration loops and with the nodal coarse-mesh size, allowing to reach the conclusion that quite high accuracy is achieved with rather large nodes, one node or four nodes per PWR fuel assembly, as compared with reference solutions obtained with fine-mesh finite-difference diffusion calculations using mesh sizes 64 to 128 times smaller than the ANDES nodes. (authors)
Three-dimensional h-adaptivity for the multigroup neutron diffusion equations
Wang, Yaqi
2009-04-01
Adaptive mesh refinement (AMR) has been shown to allow solving partial differential equations to significantly higher accuracy at reduced numerical cost. This paper presents a state-of-the-art AMR algorithm applied to the multigroup neutron diffusion equation for reactor applications. In order to follow the physics closely, energy group-dependent meshes are employed. We present a novel algorithm for assembling the terms coupling shape functions from different meshes and show how it can be made efficient by deriving all meshes from a common coarse mesh by hierarchic refinement. Our methods are formulated using conforming finite elements of any order, for any number of energy groups. The spatial error distribution is assessed with a generalization of an error estimator originally derived for the Poisson equation. Our implementation of this algorithm is based on the widely used Open Source adaptive finite element library deal.II and is made available as part of this library\\'s extensively documented tutorial. We illustrate our methods with results for 2-D and 3-D reactor simulations using 2 and 7 energy groups, and using conforming finite elements of polynomial degree up to 6. © 2008 Elsevier Ltd. All rights reserved.
Tredit A 3-D multigroup diffusion theory simulator for hexagonal fuel assembly cores
A multigroup 3-D reactor core simulator based on neutron diffusion theory, called TREDIT has been developed for Light Water Reactors (LWRs). It considers triangle shaped meshes in X-Y plane and variable mesh spacing in Z-direction. Thus it is especially suited for designing and analysing LWR cores with hexagonal fuel assemblied like the Russian WWER reactors. When fuel assembly cross-sections in multigroup form are input as fitted constants, the computer code TREDIT can build up core burnup distribution with power distribution computed for initial reactor conditions. The results of this code have been compared with another diffusion theory based code and found satisfactory. Xenon feedback effects on core power distribution are demonstrated. (author)
A multigroup diffusion theory code, TRIHEX-3D, has been developed for hexagonal lattice core analyses. For 2-D problems one can use hexagonal or triangular centre-mesh finite difference (FD) schemes. The geometrical description of the problem is for hexagonal geometry only. Subdivision of each hexagon into uniform triangles is facilitated by a built-in auto-triangularisati on procedure. One can analyse any symmetric part of the core or the whole core as well. Reflective (30deg, 60deg, 90deg, 120deg and 180deg) and rotational (60deg, 120deg and 180deg) symmetry boundary conditions are allowed. For 3-D problems one can use a direct 3-D FDM or an axial flux synthesis method. TRIHEX-3D can be used for the core design problems of VVER type of hexagonal lattice cores. The code has been validated against a LMFBR SNR-300 benchmark problem. (author). 8 tabs., 9 figs., 9 refs., 5 appendixes
Cassandre : a two-dimensional multigroup diffusion code for reactor transient analysis
CASSANDRE is a two-dimensional (x-y or r-z) finite element neutronics code with thermohydraulics feedback for reactor dynamics prior to the disassembly phase. It uses the multigroup neutron diffusion theory. Its main characteristics are the use of a generalized quasistatic model, the use of a flexible multigroup point-kinetics algorithm allowing for spectral matching and the use of a finite element description. The code was conceived in order to be coupled with any thermohydraulics module, although thermohydraulics feedback is only considered in r-z geometry. In steady state criticality search is possible either by control rod insertion or by homogeneous poisoning of the coolant. This report describes the main characterstics of the code structure and provides all the information needed to use the code. (Author)
FINELM: a multigroup finite element diffusion code. III
The authors describe the formalism of the finite element for r-theta geometry. The treatment of a four sided element with two circular arcs and two radial sides is presented. At the centre of the disc this element is collapsed into a three sided element by reducing the inner arc length to zero. The singularity of the leakage term of such an element at r=0 is described. The modelling of control and safety rods by introducing boundary conditions interior to the reactor is presented. This has the effect of converting the diffusion region from a simply connected to a multiply connected region. Dirichlet conditions with prescribed flux values zero are imposed on nodes in the interior of the non diffusion zones in order to decouple these nodes from the rest. The method is tested by calculating the effectiveness of control and safety rods for a 500 MW Th high temperature reactor. The results are compared with those obtained with DIFGEN using x-y geometry. The DIFGEN results and the problem data are by courtsey of Hochtemperatur Reaktor Bau AG, Mannheim. (Auth.)
Development of a three-dimensional multigroup nodal diffusion code for the LMR
STEP is a three-dimensional multigroup nodal diffusion code for the neutronics analysis of the LMR core and accepts microscopic cross section data. Material cross sections are obtained by summing the product of atom densities and microscopic cross sections over all isotopes comprising the material. STEP contains a thermal-hydraulics module which enables feedback effects from both fuel temperature and coolant temperature changes. Numerical results of the STEP code over the KALIMER core (392 MWt) agree well with those of DIF-3D. And it has been observed that the thermal-hydraulics module is working properly
An effective method of solving the multigroup diffusion problem in hexagonal geometry. Part I
An effective method of solving two-dimensional multigroup diffusion equations in hexagonal geometry is described. The method is based on the following two ideas: nodal approach, and expansion of one-dimensional neutron fluxes inside the node into polynomials up to the third order. The resulting relations for the interface-averaged partial currents, node-averaged fluxes and flux moments are used in computer code NEHEX. The code was found to be an accurate and effective computational tool. Its description and validation against reference benchmark problems will be published as Part II of this report. (author) 1 fig., 1 tab., 9 refs
Simulate-HEX - The multi-group diffusion equation in hexagonal-z geometry
The multigroup diffusion equation is solved for the hexagonal-z geometry by dividing each hexagon into 6 triangles. In each triangle, the Fourier solution of the wave equation is approximated by 8 plane waves to describe the intra-nodal flux accurately. In the end an efficient Finite Difference like equation is obtained. The coefficients of this equation depend on the flux solution itself and they are updated once per power/void iteration. A numerical example demonstrates the high accuracy of the method. (authors)
FEM-BABEL, 3-D Multigroup Neutron Diffusion by Galerkin Method
1 - Nature of the physical problem solved: This program computes the three-dimensional multigroup neutron diffusion equation using the finite element method. 2 - Method of solution: The equation is solved using a solution algorithm based on a Galerkin-type scheme. Prism and box-shaped finite elements are used. The resulting equation system is solved using the successive over-relaxation method and the inner iterations are accelerated by a coarse mesh re-balancing technique. 3 - Restrictions on the complexity of the problem: Any down-scattering of neutrons is allowed but up-scattering and region-dependent fission spectra are not permitted
The good features of the Analytic Function Expansion Nodal (AFEN) method are utilized to develop a practical scheme for the multigroup diffusion problems, in combination with the polynomial expansion nodal (PEN) method. The thermal group fluxes exhibiting strong gradients are solved by the AFEN method, while the fast group fluxes that are smoother than the thermal group fluxes are solved by the PEN method. The scheme is developed for cores of rectangular and hexagonal geometries. In particular, to model the fast group fluxes in the hexagonal geometry by the PEN method, a polynomial function set which shows good performance in accuracy and numerical stability is derived, in premiere. (author)
Converged accelerated finite difference scheme for the multigroup neutron diffusion equation
Computer codes involving neutron transport theory for nuclear engineering applications always require verification to assess improvement. Generally, analytical and semi-analytical benchmarks are desirable, since they are capable of high precision solutions to provide accurate standards of comparison. However, these benchmarks often involve relatively simple problems, usually assuming a certain degree of abstract modeling. In the present work, we show how semi-analytical equivalent benchmarks can be numerically generated using convergence acceleration. Specifically, we investigate the error behavior of a 1D spatial finite difference scheme for the multigroup (MG) steady-state neutron diffusion equation in plane geometry. Since solutions depending on subsequent discretization can be envisioned as terms of an infinite sequence converging to the true solution, extrapolation methods can accelerate an iterative process to obtain the limit before numerical instability sets in. The obtained results have been compared to the analytical solution to the 1D multigroup diffusion equation when available, using FORTRAN as the computational language. Finally, a slowing down problem has been solved using a cascading source update, showing how a finite difference scheme performs for ultra-fine groups (104 groups) in a reasonable computational time using convergence acceleration. (authors)
Nonlinear diffusion acceleration (NDA) can improve the performance of a neutron transport solver significantly especially for the multigroup eigenvalue problems. The high-order transport equation and the transport-corrected low-order diffusion equation form a nonlinear system in NDA, which can be solved via a Picard iteration. The consistency of the correction of the low-order equation is important to ensure the stabilization and effectiveness of the iteration. It also makes the low-order equation preserve the scalar flux of the high-order equation. In this paper, the consistent correction for a particular discretization scheme, self-adjoint angular flux (SAAF) formulation with discrete ordinates method (SN) and continuous finite element method (CFEM) is proposed for the multigroup neutron transport equation. Equations with the anisotropic scatterings and a void treatment are included. The Picard iteration with this scheme has been implemented and tested with RattleSNake, a MOOSE-based application at INL. Convergence results are presented. (authors)
Most of the neutron diffusion codes use numerical methods giving accurate results in structured meshes. However, the application of these methods in unstructured meshes to deal with complex geometries is not straightforward and it may cause problems of stability and convergence of the solution. By contrast, the Finite Volume Method (FVM) is easily applied to unstructured meshes and is typically used in the transport equations due to the conservation of the transported quantity within the volume. In this paper, the FVM algorithm implemented in the ARB Partial Differential Equations Solver has been used to discretize the multigroup neutron diffusion equation to obtain the matrices of the generalized eigenvalue problem, which has been solved by means of the SLEPc library. Nevertheless, these matrices could be large for fine meshes and the eigenvalue problem resolution could require a high calculation time. Therefore, a transformation of the generalized eigenvalue problem into a standard one is performed in order to reduce the calculation time. (author)
FEM-RZ, 2-D Multigroup Neutron Transport in R-Z Geometry, Eigenvalue and Fixed Source Problems
1 - Nature of the physical problem solved: FEM-RZ is a computer program for solving multi-group neutron transport problems in two-dimensional cylindrical (r,z) geometry. It can solve not only eigenvalue problems but also other problems, such as fixed source problems. 2 - Method of solution: The method of higher order finite elements is used for the spatial variables. It is based on the discontinuous method with Galerkin-type scheme. The discrete ordinate Sn method is used for the angular variables. 3 - Restrictions on the complexity of the problem: No restrictions except for computer size
AIRDIF, Neutron and Gamma Doses from Nuclear Explosion by 2-D Air Diffusion
1 - Description of problem or function: AIRDIF is a two-dimensional atmospheric radiation diffusion code designed to calculate neutron and gamma doses in the environment of a nuclear explosion. It calculates radiation fluxes in one-dimensional homogeneous air, or two-dimensional variable density air. The results are limited by the assumptions inherent in diffusion theory: the region of interest must be large compared to the radiation mean free path, the spatial flux gradients must not be steep, flux varies linearly with the cosine of the direction angle. The code requires as input data neutron and gamma source spectra, coupled neutron-gamma multigroup cross sections, and, for two- dimensional problems, a set of mass integral scaling (MIS) coefficients. These latter are calculated from an AIRDIF output flux file for a one-dimensional problem by the auxiliary program MISFIT, using a least squares fitting technique to Murphy's radiation transmission equation. MISFIT can also be used to calculate one- dimensional MIS doses. The MIS coefficients and doses can be input to AIRDIF, in two- dimensional mode to calculate 2-D fluxes, doses and K-factors (the ratio of 2-D to 1-D dose). Alternatively the 2-D doses and K-factors may be computed using the output 2-D flux file of a previous AIRDIF run using the auxiliary program DOSCOMP. 2 - Method of solution: Un-collided particle flux is determined from an analytic expression describing exponential attenuation with distance. Diffusion theory is used for the flux, using un-collided flux as a source term. A central collided differencing technique is used to reduce the diffusion equation to a matrix equation, which is solved by the Successive Line Over-relaxation (SLOR) method. Total flux is calculated as the sum of collided and un-collided components. To maintain a mesh interval which has the same relationship to mean free path at all heights, an expanding non-orthogonal coordinate system is used. In homogeneous air this system
In this work we developed a software to model and generate results in tables and graphs of one-dimensional neutron transport problems in multi-group formulation of energy. The numerical method we use to solve the problem of neutron diffusion is analytic, thus eliminating the truncation errors that appear in classical numerical methods, e.g., the method of finite differences. This numerical analytical method increases the computational efficiency, since they are not refined spatial discretization necessary because for any spatial discretization grids used, the numerical result generated for the same point of the domain remains unchanged unless the rounding errors of computational finite arithmetic. We chose to develop a computational application in MatLab platform for numerical computation and program interface is simple and easy with knobs. We consider important to model this neutron transport problem with a fixed source in the context of shielding calculations of radiation that protects the biosphere, and could be sensitive to ionizing radiation
Lozano Montero, Juan Andrés; García Herranz, Nuria; Ahnert Iglesias, Carolina; Aragonés Beltrán, José María
2008-01-01
In this work we address the development and implementation of the analytic coarse-mesh finite-difference (ACMFD) method in a nodal neutron diffusion solver called ANDES. The first version of the solver is implemented in any number of neutron energy groups, and in 3D Cartesian geometries; thus it mainly addresses PWR and BWR core simulations. The details about the generalization to multigroups and 3D, as well as the implementation of the method are given. The transverse integration procedure i...
An extended version of Hassitt's one-dimension Multi-group diffusion programme has been prepared which allows for a maximum of twenty-two energy groups rather than sixteen. It also permits the use of drum storage by programme and data up to the full machine capacity of 1024 sectors, rather than 478 sectors. Some minor corrections have been made, A binary tape of an 830-sector version has been prepared (Winfrith P.5272). (author)
The fine mesh diffusion formulation is extended to deal with multigroup 3-D problems in rectangular geometries. The formulation includes interface discontinuity factors per cell type, pre-calculated from transport solutions. The iterative scheme, aiming to an efficient parallel implementation in memory distributed multi-processors, is based on domain decomposition in the 4 possible sets of 4 neighbor quarters of assemblies. The alternate dissections achieve convergence to the exact boundary conditions, while attenuating high frequency noise. Whole core convergence is accelerated in the long wavelength effects by a consistent high-order analytical nodal solution performed by the ANDES solver. A neutronics - thermal-hydraulics iterative scheme is also developed to compute best estimate results, by coupling at the detailed cell-subchannel scale the COBAYA3 code with several TH subchannel codes. The numerical performance and convergence rates are verified by computing pin-cell scale solutions for the OECD/NEA/USNRC PWR MOX/UO2 Core Transient Benchmark in 8 energy groups and heterogeneous assemblies. The cell-subchannel scale neutronics and thermal-hydraulics coupling, allows the verification of the effects of the detailed TH feedbacks on cross-sections and, thus, on fuel pin powers, calculated here for a 3D color-set of two different fuel types of the previous benchmark, using COBAYA3 and COBRA-3C. (authors)
Multigroup radiation hydrodynamics with flux-limited diffusion and adaptive mesh refinement
González, Matthias; Commerçon, Benoît; Masson, Jacques
2015-01-01
Radiative transfer plays a key role in the star formation process. Due to a high computational cost, radiation-hydrodynamics simulations performed up to now have mainly been carried out in the grey approximation. In recent years, multi-frequency radiation-hydrodynamics models have started to emerge, in an attempt to better account for the large variations of opacities as a function of frequency. We wish to develop an efficient multigroup algorithm for the adaptive mesh refinement code RAMSES which is suited to heavy proto-stellar collapse calculations. Due to prohibitive timestep constraints of an explicit radiative transfer method, we constructed a time-implicit solver based on a stabilised bi-conjugate gradient algorithm, and implemented it in RAMSES under the flux-limited diffusion approximation. We present a series of tests which demonstrate the high performance of our scheme in dealing with frequency-dependent radiation-hydrodynamic flows. We also present a preliminary simulation of a three-dimensional p...
Tønning, Erik; Polders, Daniel; Callaghan, Paul T.; Engelsen, Søren B.
2007-09-01
This paper demonstrates how the multi-linear PARAFAC model can with advantage be used to decompose 2D diffusion-relaxation correlation NMR spectra prior to 2D-Laplace inversion to the T2- D domain. The decomposition is advantageous for better interpretation of the complex correlation maps as well as for the quantification of extracted T2- D components. To demonstrate the new method seventeen mixtures of wheat flour, starch, gluten, oil and water were prepared and measured with a 300 MHz nuclear magnetic resonance (NMR) spectrometer using a pulsed gradient stimulated echo (PGSTE) pulse sequence followed by a Carr-Purcell-Meiboom-Gill (CPMG) pulse echo train. By varying the gradient strength, 2D diffusion-relaxation data were recorded for each sample. From these double exponentially decaying relaxation data the PARAFAC algorithm extracted two unique diffusion-relaxation components, explaining 99.8% of the variation in the data set. These two components were subsequently transformed to the T2- D domain using 2D-inverse Laplace transformation and quantitatively assigned to the oil and water components of the samples. The oil component was one distinct distribution with peak intensity at D = 3 × 10 -12 m 2 s -1 and T2 = 180 ms. The water component consisted of two broad populations of water molecules with diffusion coefficients and relaxation times centered around correlation pairs: D = 10 -9 m 2 s -1, T2 = 10 ms and D = 3 × 10 -13 m 2 s -1, T2 = 13 ms. Small spurious peaks observed in the inverse Laplace transformation of original complex data were effectively filtered by the PARAFAC decomposition and thus considered artefacts from the complex Laplace transformation. The oil-to-water ratio determined by PARAFAC followed by 2D-Laplace inversion was perfectly correlated with known oil-to-water ratio of the samples. The new method of using PARAFAC prior to the 2D-Laplace inversion proved to have superior potential in analysis of diffusion-relaxation spectra, as it
Shestakov, A I; Offner, S R
2007-03-02
We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate 'level-solve' packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation ({Psi}tc). We analyze the magnitude of the {Psi}tc parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichet boundary data at the coarse-fine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the sync-solve (SS), is required in order to enforce conservation. The MGD SS reduces to an elliptic solve on a combined grid for a system of G equations, where G is the number of groups. We adapt the 'partial temperature' scheme for the SS; hence, we reuse the infrastructure developed for scalar equations. Results are presented. We consider a multigroup test problem with a known analytic solution. We demonstrate utility of {Psi}tc by running with increasingly larger timesteps. Lastly, we simulate the sudden release of energy Y inside an Al sphere (r = 15 cm) suspended in air at STP. For Y = 11 kT, we find that gray radiation diffusion and MGD produce similar results. However, if Y = 1 MT, the two packages yield different results. Our large Y simulation contradicts a long-standing theory
Approximate Lie group analysis and solutions of 2D nonlinear diffusion-convection equations
Approximate Lie symmetries of the (2+1)-dimensional nonlinear diffusion equation with a small convection are completely classified. It is known that the invariance principle furnishes a systematic method of solving initial-value problems. The solutions of instantaneous source type of the 2D diffusion-convection equation are obtained for the case of power-law diffusivity, using a symmetry reduction
The objective of this work is to obtain an analytical solution of the neutron diffusion kinetic equation in one-dimensional cartesian geometry, to monoenergetic and multigroup problems. These equations are of the type stiff, due to large differences in the orders of magnitude of the time scales of the physical phenomena involved, which make them difficult to solve. The basic idea of the proposed method is applying the spectral expansion in the scalar flux and in the precursor concentration, taking moments and solving the resulting matrix problem by the Laplace transform technique. Bearing in mind that the equation for the precursor concentration is a first order linear differential equation in the time variable, to enable the application of the spectral method we introduce a fictitious diffusion term multiplied by a positive value which tends to zero. This procedure opened the possibility to find an analytical solution to the problem studied. We report numerical simulations and analysis of the results obtained with the precision controlled by the truncation order of the series. (author)
Prinsloo, Rian Hendrik
2006-01-01
Nodal diffusion methods have been used extensively in nuclear reactor calculations specifically for their performance advantage, but also their superior accuracy. In this work a nodal diffusion method is developed for three-dimensional cylindrical geometry. Recent developments in the Pebble Bed Modular Reactor (PBMR) project have sparked renewed interest in the application of different modelling methods to its design, and naturally included in this effort is a nodal method for ...
Today, we can use a computer cluster consist of a few hundreds CPUs with reasonable budget. Such computer system enables us to do detailed modeling of reactor core. The detailed modeling will improve the safety and the economics of a nuclear reactor by eliminating un-necessary conservatism or missing consideration. To take advantage of such a cluster computer, efficient parallel algorithms must be developed. Mechanical structure analysis community has studied the domain decomposition method to solve the stress-strain equation using the finite element methods. One of the most successful domain decomposition method in terms of robustness is FETI-DP. We have modified the original FETI-DP to solve the eigenvalue problem for the multi-group diffusion problem in previous study. In this study, we report the result of recent modification to handle the three-dimensional subdomain partitioning, and the sub-domain multi-group problem. Modified FETI-DP algorithm has been successfully applied for the eigenvalue problem of multi-group neutron diffusion equation. The overall CPU time is decreasing as number of sub-domains (partitions) is increasing. However, there may be a limit in decrement due to increment of the number of primal points will increase the CPU time spent by the solution of the global equation. Even distribution of computational load (criterion a) is important to achieve fast computation. The subdomain partition can be effectively performed using suitable graph theory partition package such as MeTIS
Benchmarking with the multigroup diffusion high-order response matrix method
The benchmarking capabilities of the high-order response matrix eigenvalue method, which was developed more than a decade ago, are demonstrated by means of the numerical analysis of a variety of two-dimensional Cartesian geometry light-water reactor test problems. These problems are typical of those generally used for the benchmarking of coarse-mesh (nodal) diffusion methods and the numerical results show that the high-order response matrix eigenvalue method is well suited to be used as an alternative to fine-mesh finite-difference and refined mesh nodal methods for the purpose of generating reference solutions to such problems. (author)
In this work we address the development and implementation of the analytic coarse-mesh finite-difference (ACMFD) method in a nodal neutron diffusion solver called ANDES. The first version of the solver is implemented in any number of neutron energy groups, and in 3D Cartesian geometries; thus it mainly addresses PWR and BWR core simulations. The details about the generalization to multigroups and 3D, as well as the implementation of the method are given. The transverse integration procedure is the scheme chosen to extend the ACMFD formulation to multidimensional problems. The role of the transverse leakage treatment in the accuracy of the nodal solutions is analyzed in detail: the involved assumptions, the limitations of the method in terms of nodal width, the alternative approaches to implement the transverse leakage terms in nodal methods - implicit or explicit -, and the error assessment due to transverse integration. A new approach for solving the control rod 'cusping' problem, based on the direct application of the ACMFD method, is also developed and implemented in ANDES. The solver architecture turns ANDES into an user-friendly, modular and easily linkable tool, as required to be integrated into common software platforms for multi-scale and multi-physics simulations. ANDES can be used either as a stand-alone nodal code or as a solver to accelerate the convergence of whole core pin-by-pin code systems. The verification and performance of the solver are demonstrated using both proof-of-principle test cases and well-referenced international benchmarks
Development of 3D multi-group neutron diffusion code for hexagonal geometry
Based on the theory of new flux expansion nodal method to solve the neutron diffusion equations, the intra-nodal fluence rate distribution was expanded in a series of analytic basic functions for each group. In order to improve the accuracy of calculation result, continuities of neutron fluence rate and current were utilized across the nodal surfaces. According to the boundary conditions, the iteration method was adopted to solve the diffusion equation, where inner iteration speedup method is Gauss-Seidel method and outer is Lyusternik-Wagner. A new speedup method (one-outer-iteration and multi-inner-iteration method) was proposed according to the characteristic that the convergence speed of multiplication factor is faster than that of neutron fluence rate and the update of inner iteration matrix is slow. Based on the proposed model, the code HANDF-D was developed and tested by 3D two-group vver440 benchmark, experiment 2 of HFETR, 3D four-group thermal reactor benchmark, and 3D seven-group fast reactor benchmark. The numerical results show that HANDF-D can predict accurately the multiplication factor and nodal powers. (authors)
Quantum Diffusion on Molecular Tubes: Universal Scaling of the 1D to 2D Transition
Chuang, Chern; Lee, Chee Kong; Moix, Jeremy M.; Knoester, Jasper; Cao, Jianshu
2016-05-01
The transport properties of disordered systems are known to depend critically on dimensionality. We study the diffusion coefficient of a quantum particle confined to a lattice on the surface of a tube, where it scales between the 1D and 2D limits. It is found that the scaling relation is universal and independent of the temperature, disorder, and noise parameters, and the essential order parameter is the ratio between the localization length in 2D and the circumference of the tube. Phenomenological and quantitative expressions for transport properties as functions of disorder and noise are obtained and applied to real systems: In the natural chlorosomes found in light-harvesting bacteria the exciton transfer dynamics is predicted to be in the 2D limit, whereas a family of synthetic molecular aggregates is found to be in the homogeneous limit and is independent of dimensionality.
A variational nodal expansion method for the solution of multigroup neutron diffusion equations
An accurate neutronics analysis method is needed for light water reactor core monitoring systems to efficiently operate the core with a smaller margin to limiting parameters. It is also required in in-core fuel management systems to optimize the core loading patterns, and the fuel designs with a higher reliability. When mixed oxide fuel or much higher burnup fuel is used, a new higher order nodal method seems necessary to introduce. Based on these considerations, a new nodal diffusion method for the neutronics analysis of light water reactor cores has been developed. The method is based on an approximation of neutron fluxes by expanding them with a set of functions defined within a node. The expansion coefficients are determined in such a way that the solution becomes the most accurate approximation to the exact solution by utilizing the variational principle. The expansion functions are obtained only from single assembly diffusion calculations. The present method includes no homogenization procedure, and the assembly heterogeneity effect on neutron fluxes is taken into account in a consistent way. The intra-nodal pin-power distribution can also be determined in a consistent way with high accuracy. The present method was implemented in a two-dimensional nodal code, and tested for benchmark cases. The results proved that the accuracy of the present method was excellent. The root mean square errors of both nodal powers and nodal maximum pin powers were observed to be less than 1%. The computing time of the code was measured to be about 3% of the reference, fine-mesh calculation. A three-dimensional version is currently being developed, and since the heterogeneity effect is of less importance in axial direction, a more efficient calculation method can be adopted for the axial solution of the neutron flux. The new method can be used as a ''plug-in'' module to existing core simulators to increase the accuracy of the neutronics part of existing core models, including the
2 D patterns of soil gas diffusivity , soil respiration, and methane oxidation in a soil profile
Maier, Martin; Schack-Kirchner, Helmer; Lang, Friederike
2015-04-01
The apparent gas diffusion coefficient in soil (DS) is an important parameter describing soil aeration, which makes it a key parameter for root growth and gas production and consumption. Horizontal homogeneity in soil profiles is assumed in most studies for soil properties - including DS. This assumption, however, is not valid, even in apparently homogeneous soils, as we know from studies using destructive sampling methods. Using destructive methods may allow catching a glimpse, but a large uncertainty remains, since locations between the sampling positions cannot be analyzed, and measurements cannot be repeated. We developed a new method to determine in situ the apparent soil gas diffusion coefficient in order to examine 2 D pattern of DS and methane oxidation in a soil profile. Different tracer gases (SF6, CF4, C2H6) were injected continuously into the subsoil and measured at several locations in the soil profile. These data allow for modelling inversely the 2 D patterns of DS using Finite Element Modeling. The 2D DS patterns were then combined with naturally occurring CH4 and CO2 concentrations sampled at the same locations to derive the 2D pattern of soil respiration and methane oxidation in the soil profile. We show that methane oxidation and soil respiration zones shift within the soil profile while the gas fluxes at the surface remain rather stable during a the 3 week campaign.
HEXPEDITE: A net current multigroup nodal diffusion method for hexagonal-z geometry
The feasibility of a nodal diffusion algorithm for hexagonal cores was first demonstrated by Duracz and by Lawrence. They implemented a polynomial method with partial currents for internode coupling. Following them, several authors introduced variants of the expansion technique. Wagner developed an analytical method; however, like all previous authors, he still used partial currents for internode coupling and a response matrix solution approach. Very recently, another polynomial model with net currents expressed in terms of transverse-integrated fluxes and a nodal integral method based on coordinate transformations were presented. A transformation-group method was also introduced. In this paper, a hexagonal-z method similar in approach to that of the Cartesian geometry ILLICO is presented. The new method uses an analytical solution of the transverse-integrated equations, net currents for internode coupling, and a global coupling solution scheme different from that of the methods discussed earlier. An extension that treats explicitly the in-node spatial dependence of cross sections is also introduced
Al-Chalabi, Rifat M. Khalil
1997-09-01
Development of an improvement to the computational efficiency of the existing nested iterative solution strategy of the Nodal Exapansion Method (NEM) nodal based neutron diffusion code NESTLE is presented. The improvement in the solution strategy is the result of developing a multilevel acceleration scheme that does not suffer from the numerical stalling associated with a number of iterative solution methods. The acceleration scheme is based on the multigrid method, which is specifically adapted for incorporation into the NEM nonlinear iterative strategy. This scheme optimizes the computational interplay between the spatial discretization and the NEM nonlinear iterative solution process through the use of the multigrid method. The combination of the NEM nodal method, calculation of the homogenized, neutron nodal balance coefficients (i.e. restriction operator), efficient underlying smoothing algorithm (power method of NESTLE), and the finer mesh reconstruction algorithm (i.e. prolongation operator), all operating on a sequence of coarser spatial nodes, constitutes the multilevel acceleration scheme employed in this research. Two implementations of the multigrid method into the NESTLE code were examined; the Imbedded NEM Strategy and the Imbedded CMFD Strategy. The main difference in implementation between the two methods is that in the Imbedded NEM Strategy, the NEM solution is required at every MG level. Numerical tests have shown that the Imbedded NEM Strategy suffers from divergence at coarse- grid levels, hence all the results for the different benchmarks presented here were obtained using the Imbedded CMFD Strategy. The novelties in the developed MG method are as follows: the formulation of the restriction and prolongation operators, and the selection of the relaxation method. The restriction operator utilizes a variation of the reactor physics, consistent homogenization technique. The prolongation operator is based upon a variant of the pin power
The report documents the computer code block VENTURE designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P1) in up to three-dimensional geometry. It uses and generates interface data files adopted in the cooperative effort sponsored by the Reactor Physics Branch of the Division of Reactor Research and Development of the Energy Research and Development Administration. Several different data handling procedures have been incorporated to provide considerable flexibility; it is possible to solve a wide variety of problems on a variety of computer configurations relatively efficiently
In the present contribution we discuss the solution of the two-dimensional multi-group neutron kinetic equation in cylindrical geometry. The solution is obtained in analytical representation. To this end the scalar flux is extended in terms of the eigenfunctions associated to the respective problem in Cartesian geometry. Taking moments and using orthogonality properties of the eigenfunctions we get a matrix differential equation for the expansion coefficients which has a known solution. We apply this methodology for the neutron kinetic diffusion equation and show numerical results for two-energy groups. (author)
This report presents the HEXAGA-III-programme solving multi-group time-independent real and/or adjoint neutron diffusion equations for three-dimensional-triangular-z-geometry. The method of solution is based on the AGA two-sweep iterative method belonging to the family of factorization techniques. An arbitrary neutron scattering model is permitted. The report written for users provides the description of the programme input and output and the use of HEXAGA-III is illustrated by a sample reactor problem. (orig.)
The computer code block VENTURE, designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P1) in up to three-dimensional geometry is described. A variety of types of problems may be solved: the usual eigenvalue problem, a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations, or an indirect criticality search on nuclide concentrations, or on dimensions. First-order perturbation analysis capability is available at the macroscopic cross section level
Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.
1977-11-01
The report documents the computer code block VENTURE designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P/sub 1/) in up to three-dimensional geometry. It uses and generates interface data files adopted in the cooperative effort sponsored by the Reactor Physics Branch of the Division of Reactor Research and Development of the Energy Research and Development Administration. Several different data handling procedures have been incorporated to provide considerable flexibility; it is possible to solve a wide variety of problems on a variety of computer configurations relatively efficiently.
Oliveira, F.R.; Vilhena, Marco T.; Bodmann, B.E.J., E-mail: fernando.rodrigues@ufrgs.br, E-mail: bardo.bodmann@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil); Carvalho, F., E-mail: fernando@nuclear.ufrj.br [Coordenacao dos Cursos de Pos-Graduacao em Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Institute Alberto Luiz Coimbra
2015-07-01
In the present contribution we discuss the solution of the two-dimensional multi-group neutron kinetic equation in cylindrical geometry. The solution is obtained in analytical representation. To this end the scalar flux is extended in terms of the eigenfunctions associated to the respective problem in Cartesian geometry. Taking moments and using orthogonality properties of the eigenfunctions we get a matrix differential equation for the expansion coefficients which has a known solution. We apply this methodology for the neutron kinetic diffusion equation and show numerical results for two-energy groups. (author)
A 3D multigroup transport kinetics code in hexagonal geometry for fast reactor transient analysis
A description of the 3D multigroup diffusion/transport kinetics code HEXNODYN is given and numerical results are reported. HEXNODYN couples time integration by the quasi-static method with space integration by HEXNOD's analytic (diffusion option) or discrete ordinates (transport option) nodal method. An equivalent hexagonal version of the KfK rod ejection problem has been set up to validate the diffusion option by comparison with available 2D diffusion codes. The transport option has been validated by comparison with the diffusion option. Numerical results indicate that the diffusion option may be considered as fully validated while the transport version is at least internally consistent
A Module for Radiation Hydrodynamic Calculations With ZEUS-2D Using Flux-Limited Diffusion
Turner, N J
2001-01-01
A module for the ZEUS-2D code is described which may be used to solve the equations of radiation hydrodynamics to order unity in v/c, in the flux-limited diffusion (FLD) approximation. In this approximation, the tensor Eddington factor f which closes the radiation moment equations is chosen to be an empirical function of radiation energy density. This is easier to implement and faster than full-transport techniques, in which f is computed by solving the transfer equation. However, FLD is less accurate when the flux has a component perpendicular to the gradient in radiation energy density, and in optically thin regions when the radiation field depends strongly on angle. The material component of the fluid is here assumed to be in local thermodynamic equilibrium. The energy equations are operator-split, with transport terms, radiation diffusion term, and other source terms evolved separately. Transport terms are applied using the same consistent transport algorithm as in ZEUS-2D. The radiation diffusion term is...
3D hydrodynamic interactions lead to divergences in 2D diffusion
We investigate the influence of 3D hydrodynamic interactions on confined colloidal suspensions, where only the colloids are restricted to one or two dimensions. In the absence of static interactions among the colloids, i.e., an ideal gas of colloidal particles with a finite hydrodynamic radius, we find a divergent collective diffusion coefficient. The origin of the divergence is traced back to the dimensional mismatch of 3D hydrodynamic interactions and the colloidal particles moving only in 1D or 2D. Our results from theory are confirmed by Stokesian dynamics simulations and supported by light scattering observational data for particles at a fluid interface. (paper)
3D hydrodynamic interactions lead to divergences in 2D diffusion.
Bleibel, Johannes; Domínguez, Alvaro; Oettel, Martin
2015-05-20
We investigate the influence of 3D hydrodynamic interactions on confined colloidal suspensions, where only the colloids are restricted to one or two dimensions. In the absence of static interactions among the colloids, i.e., an ideal gas of colloidal particles with a finite hydrodynamic radius, we find a divergent collective diffusion coefficient. The origin of the divergence is traced back to the dimensional mismatch of 3D hydrodynamic interactions and the colloidal particles moving only in 1D or 2D. Our results from theory are confirmed by Stokesian dynamics simulations and supported by light scattering observational data for particles at a fluid interface. PMID:25923320
3D hydrodynamic interactions lead to divergences in 2D diffusion
Bleibel, Johannes; Domínguez, Alvaro; Oettel, Martin
2015-05-01
We investigate the influence of 3D hydrodynamic interactions on confined colloidal suspensions, where only the colloids are restricted to one or two dimensions. In the absence of static interactions among the colloids, i.e., an ideal gas of colloidal particles with a finite hydrodynamic radius, we find a divergent collective diffusion coefficient. The origin of the divergence is traced back to the dimensional mismatch of 3D hydrodynamic interactions and the colloidal particles moving only in 1D or 2D. Our results from theory are confirmed by Stokesian dynamics simulations and supported by light scattering observational data for particles at a fluid interface.
The multi-group integro-differential equations of the neutron diffusion kinetics (IDE-NDK) was presented and solved numerically in multi-slab geometry with the use of the progressive polynomial approximation. Four applications were computed: a positive ramp, a negative ramp, a sinusoidal and an instantaneous change of thermal macroscopic cross-sections in an 120 slab-nuclear reactor for a 2 prompt-group model. The results showed good accuracy for the developed non-iterative algorithms. It was shown the advantage of using the IDE-NDK over the traditional partial differential equations of the neutron diffusion kinetics from an accuracy point of view. Finite difference algorithms were also developed to obtain initial conditions and to make desired comparisons.
A New 2D-Advection-Diffusion Model Simulating Trace Gas Distributions in the Lowermost Stratosphere
Hegglin, M. I.; Brunner, D.; Peter, T.; Wirth, V.; Fischer, H.; Hoor, P.
2004-12-01
Tracer distributions in the lowermost stratosphere are affected by both, transport (advective and non-advective) and in situ sources and sinks. They influence ozone photochemistry, radiative forcing, and heating budgets. In-situ measurements of long-lived species during eight measurement campaigns revealed relatively simple behavior of the tracers in the lowermost stratosphere when represented in an equivalent-latitude versus potential temperature framework. We here present a new 2D-advection-diffusion model that simulates the main transport pathways influencing the tracer distributions in the lowermost stratosphere. The model includes slow diabatic descent of aged stratospheric air and vertical and/or horizontal diffusion across the tropopause and within the lowermost stratosphere. The diffusion coefficients used in the model represent the combined effects of different processes with the potential of mixing tropospheric air into the lowermost stratosphere such as breaking Rossby and gravity waves, deep convection penetrating the tropopause, turbulent diffusion, radiatively driven upwelling etc. They were specified by matching model simulations to observed distributions of long-lived trace gases such as CO and N2O obtained during the project SPURT. The seasonally conducted campaigns allow us to study the seasonal dependency of the diffusion coefficients. Despite its simplicity the model yields a surprisingly good description of the small scale features of the measurements and in particular of the observed tracer gradients at the tropopause. The correlation coefficients between modeled and measured trace gas distributions were up to 0.95. Moreover, mixing across isentropes appears to be more important than mixing across surfaces of constant equivalent latitude (or PV). With the aid of the model, the distribution of the fraction of tropospheric air in the lowermost stratosphere can be determined.
The energy spectra of fast and thermal neutrons from fission reactions in the FZJ code TINTE are modelled by two broad energy groups. Present demands for increased numerical accuracy led to the question of how precise the 2-group approximation is compared to a multi-group model. Therefore a new simulation program called MGT (Multi Group TINTE) has recently been developed which is able to handle up to 43 energy groups. Furthermore, an internal spectrum calculation for the determination of cross-sections can be performed for each time step and location within the reactor. In this study the multi-group energy models are compared to former calculations with only two energy groups. Different scenarios (normal operation and design-basis accidents) have been defined for a high temperature pebble bed reactor design with annular core. The effect of an increasing number of energy groups on safety-related parameters like the fuel and coolant temperature, the nuclear heat source or the xenon concentration is studied. It has been found that for the studied scenarios the use of up to 8 energy groups is a good trade-off between precision and a tolerable amount of computing time. (orig.)
Methodology for 3-D calculation analysis of nuclear reactor cell with axial symmetry and finite mesh step is described. This methodology is based on the axial leakage calculation analysis method that has been developed for nuclear reactor with closed lattice like VVER-type. The trial functions that are used at full core level of nuclear reactor calculation analysis are defined. Connection between core reactor equation and the definition of trial functions is given. Importance of different trial functions from the point of view the full reactor core calculation is analyzed. If we deal with the case when reactor has strong neutron flux gradients caused with regularization rods it is important to take into account the influence of neutron spectrum into axial leakage. So this paper focuses upon just multi-group approach to obtain matrixes that are defined with trial functions values and with boundary conditions. Previous numerical results of comparison of the matrixes elements analytically obtained and matrix elements obtained with described methodology are given. Analytical expressions for two-group matrix elements are considered as verification results for multi-group numerical scheme. (authors)
A modular computer code system called FEMSYN has been developed to solve the multigroup diffusion theory equations. The various methods that are incorporated in FEMSYN are (i) finite difference method (FDM) (ii) finite element method (FEM) and (iii) single channel flux synthesis method (SCFS). These methods are described in detail in parts II, III and IV of the present report. In this report, a comparison of the accuracy and the speed of different methods of solution for some benchmark problems are reported. The input preparation and listing of sample input and output are included in the Appendices. The code FEMSYN has been used to solve a wide variety of reactor core problems. It can be used for both LWR and PHWR applications. (author)
Ceolin, C.; Schramm, M.; Vilhena, M.T.; Bodmann, B.E.J., E-mail: celina.ceolin@gmail.com, E-mail: marceloschramm@hotmail.com, E-mail: vilhena@pq.cnpq.br, E-mail: bardo.bodmann@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica
2013-07-01
In this work the authors solved the steady state neutron diffusion equation for a multi-layer slab assuming the multi-group energy model. The method to solve the equation system is based on a expansion in Taylor Series, which was proven to be useful in [1] [2] [3]. The results obtained can be used as initial condition for neutron space kinetics problems. The neutron scalar flux was expanded in a power series, and the coefficients were found by using the ordinary differential equation and the boundary and interface conditions. The effective multiplication factor k was evaluated using the power method [4]. We divided the domain into several slabs to guarantee the convergence with a low truncation order. We present the formalism together with some numerical simulations. (author)
Ceolin, Celina; Schramm, Marcelo; Bodmann, Bardo Ernst Josef; Vilhena, Marco Tullio Mena Barreto de [Universidade Federal do Rio Grande do Sul, Porto Alegre (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Bogado Leite, Sergio de Queiroz [Comissao Nacional de Energia Nuclear, Rio de Janeiro (Brazil)
2014-11-15
In this work the authors solved the steady state neutron diffusion equation for a multi-layer slab assuming the multi-group energy model. The method to solve the equation system is based on an expansion in Taylor Series resulting in an analytical expression. The results obtained can be used as initial condition for neutron space kinetics problems. The neutron scalar flux was expanded in a power series, and the coefficients were found by using the ordinary differential equation and the boundary and interface conditions. The effective multiplication factor k was evaluated using the power method. We divided the domain into several slabs to guarantee the convergence with a low truncation order. We present the formalism together with some numerical simulations.
2D BEM modeling of a singular thermal diffusion free boundary problem with phase change
Nikolayev, Vadim
2016-01-01
We report a 2D Boundary Element Method (BEM) modeling of the thermal diffusion-controlled growth of a vapor bubble attached to a heating surface during saturated pool boiling. The transient heat conduction problem is solved in a liquid that surrounds a bubble with a free boundary and in a semi-infinite solid heater. The heat generated homogeneously in the heater causes evaporation, i. e. the bubble growth. A singularity exists at the point of the triple (liquid-vapor-solid) contact. At high system pressure the bubble is assumed to grow slowly, its shape being defined by the surface tension and the vapor recoil force, a force coming from the liquid evaporating into the bubble. It is shown that at some typical time the dry spot under the bubble begins to grow rapidly under the action of the vapor recoil. Such a bubble can eventually spread into a vapor film that can separate the liquid from the heater, thus triggering the boiling crisis (Critical Heat Flux phenomenon).
More accurate modelling of physical phenomena involved in present and future nuclear reactors requires a multi-scale and multi-physics approach. This challenge can be accomplished by the coupling of best-estimate core-physics, thermal-hydraulics and multi-physics solvers. In order to make viable that coupling, the current trends in reactor simulations are along the development of a new generation of tools based on user-friendly, modular, easily linkable, faster and more accurate codes to be integrated in common platforms. These premises are in the origin of the NURESIM Integrated Project within the 6. European Framework Program, which is envisaged to provide the initial step towards a Common European Standard Software Platform for nuclear reactors simulations. In the frame of this project and to reach the above-mentioned goals, a 3-D multigroup nodal solver for neutron diffusion calculations called ANDES (Analytic Nodal Diffusion Equation Solver) has been developed and tested in-depth in this Thesis. ANDES solves the steady-state and time-dependent neutron diffusion equation in three-dimensions and any number of energy groups, utilizing the Analytic Coarse-Mesh Finite-Difference (ACMFD) scheme to yield the nodal coupling equations. It can be applied to both Cartesian and triangular-Z geometries, so that simulations of LWR as well as VVER, HTR and fast reactors can be performed. The solver has been implemented in a fully encapsulated way, enabling it as a module to be readily integrated in other codes and platforms. In fact, it can be used either as a stand-alone nodal code or as a solver to accelerate the convergence of whole core pin-by-pin code systems. Verification of performance has shown that ANDES is a code with high order definition for whole core realistic nodal simulations. In this paper, the methodology developed and involved in ANDES is presented. (authors)
On symmetry groups of a 2D nonlinear diffusion equation with source
Radica Cimpoiasu
2015-04-01
Symmetry analysis of a 2D nonlinear evolutionary equation with mixed spatial derivative and general source term involving the dependent variable and its spatial derivatives is performed. The source terms for which the equation admits nontrivial Lie symmetries are identified for two different forms of the symmetry operator. In one of these cases, the symmetries do not depend on the form of nonlinearities and in the other case, nonlinearities of power, exponential and trigonometric forms are considered. There are no supplementary nonclassical symmetries for the investigated equation. The results reported here generalize the previous results on the 2D heat equation and the 2D Ricci model.
The four group, 2D and 3D hexagonal geometry HTGR benchmark problems and a 2D hexagonal geometry PWR (WWER) benchmark problem have been solved by using the finite element diffusion code DIFGEN. The hexagons (or hexagonal prisms) were subdivided into first order or second order triangles or quadrilaterals (or triangular or quadrilateral prisms). In the 2D HTGR case of the number of the inserted absorber rods was also varied (7, 6, 0 or 37 rods). The calculational results are in a good agreement with the results of other calculations. The larger systematic series of DIFGEN calculations have given a quantitative picture on the convergence properties of various finite element modellings of hexagonal grids in DIFGEN. (orig.)
Hernandez-Charpak, J.; Hoogeboom-Pot, K.; Anderson, E.; Murnane, M.; Kapteyn, H.; Nardi, D.
2014-03-01
How is thermal transport affected by spatial confinement in nanoscale systems? In past work we and others demonstrated that the Fourier Law of heat diffusion fails for length scales smaller than the mean free path of the energy carriers in a material. Here we probe how the transition from macroscopic diffusive behavior of phonons through the quasi-ballistic regime is different for 1D and 2D nano-confined hot spots. We study a series of periodic nickel lines (1D) and dots (2D) with linewidths varying from 750 to 30 nm deposited on both sapphire and silicon substrates. The thermal relaxation of these femtosecond-laser-excited nanostructures is monitored by the diffraction of extreme ultraviolet (EUV) light obtained from tabletop high harmonic generation. The short wavelength of EUV light, combined with the coherence and ultrashort pulses of high harmonic sources, provides a unique and powerful probe for nanostructured materials on their intrinsic length and time scales. The relaxation dynamics are linked to an effective thermal boundary resistivity with the assistance of multi-physics finite element analysis to quantify the stronger deviation from macroscopic diffusive behavior as a function of nanostructure linewidth in 2D hot spots compared to 1D. This work was supported by SRC Contract 2012-OJ-2304, by NSF Award No.: DGE 1144083, and used facilities provided by the NSF Engineering Research Center in EUV Science and Technology.
CHOLESK, Diffusion Calculation with 2-D Source in X-Y or R-Z Geometry
1 - Description of problem or function: Solution of the diffusion equation with source in two-dimensional geometries x-y or r-z. 2 - Method of solution: The finite-element method of Ritz-Galerkin is applied
Ferizi, Uran; Schneider, Torben; Alipoor, Mohammad; Eufracio, Odin; Fick, Rutger H J; Deriche, Rachid; Nilsson, Markus; Loya-Olivas, Ana K; Rivera, Mariano; Poot, Dirk H J; Ramirez-Manzanares, Alonso; Marroquin, Jose L; Rokem, Ariel; Pötter, Christian; Dougherty, Robert F; Sakaie, Ken; Wheeler-Kingshott, Claudia; Warfield, Simon K; Witzel, Thomas; Wald, Lawrence L; Raya, José G; Alexander, Daniel C
2016-01-01
A large number of mathematical models have been proposed to describe the measured signal in diffusion-weighted (DW) magnetic resonance imaging (MRI) and infer properties about the white matter microstructure. However, a head-to-head comparison of DW-MRI models is critically missing in the field. To address this deficiency, we organized the "White Matter Modeling Challenge" during the International Symposium on Biomedical Imaging (ISBI) 2015 conference. This competition aimed at identifying the DW-MRI models that best predict unseen DW data. in vivo DW-MRI data was acquired on the Connectom scanner at the A.A.Martinos Center (Massachusetts General Hospital) using gradients strength of up to 300 mT/m and a broad set of diffusion times. We focused on assessing the DW signal prediction in two regions: the genu in the corpus callosum, where the fibres are relatively straight and parallel, and the fornix, where the configuration of fibres is more complex. The challenge participants had access to three-quarters of t...
Iterative 2-D/1-D methods for the 3-D neutron diffusion calculation
To remedy the problems arising from assembly homogenization and de-homogenization, several efforts have been made to solve directly the heterogeneous problem with a fine mesh and to reduce the computational burden by coupling 2-D planar with 1-D axial solutions using a Transverse Leakage (TL) coupling. However, the potential for a numerical instability at a small axial mesh size has been observed. Lee et al. showed that one of the two existing methods, method A, is mathematically unstable at a small mesh size while the other, method B, is always stable. They also proposed a new method for a 2-D/1-D coupling, method C, and they showed that it is always stable and it provides the best performance in terms of the convergence rate. In this paper another algorithm, method D, is proposed and its stability is also investigated
A New 2D-Transport, 1D-Diffusion Approximation of the Boltzmann Transport equation
Larsen, Edward
2013-06-17
The work performed in this project consisted of the derivation, implementation, and testing of a new, computationally advantageous approximation to the 3D Boltz- mann transport equation. The solution of the Boltzmann equation is the neutron flux in nuclear reactor cores and shields, but solving this equation is difficult and costly. The new “2D/1D” approximation takes advantage of a special geometric feature of typical 3D reactors to approximate the neutron transport physics in a specific (ax- ial) direction, but not in the other two (radial) directions. The resulting equation is much less expensive to solve computationally, and its solutions are expected to be sufficiently accurate for many practical problems. In this project we formulated the new equation, discretized it using standard methods, developed a stable itera- tion scheme for solving the equation, implemented the new numerical scheme in the MPACT code, and tested the method on several realistic problems. All the hoped- for features of this new approximation were seen. For large, difficult problems, the resulting 2D/1D solution is highly accurate, and is calculated about 100 times faster than a 3D discrete ordinates simulation.
Measurement of turbulent diffusivity of both gas and liquid phases in quasi-2D two-phase flow
The turbulent diffusion process has been studied experimentally by observing a tracer plume emitted continuously from a line source in a uniform, quasi-2D two-phase flow. The test section was a vertical, relatively narrow, concentric annular channel consisting of two large pipes. Air and water were used as the working fluids, and methane and acid organge II were used as tracers for the respective phases. Measurements of local, time-averaged tracer concentrations were made by means of a sampling method and image processing for bubbly flows and churn flows, and the turbulent diffusivity, the coefficient of turbulent diffusion, was determined from the concentration distributions measured. The diffusivities for the gas and liquid phases, εDG and εDL respectively, are presented and compared with each other in this paper. When a flow is bubbly, εDG is close to or slightly smaller than εDL. In a churn flow, on the contrary, εDG is much greater than εDL. Regarding bubbly flow, a plausible model on turbulent diffusivity of the liquid phase is presented and examined by the present data. (orig.)
An Asymptotic Analysis of a 2-D Model of Dynamically Active Compartments Coupled by Bulk Diffusion
Gou, J.; Ward, M. J.
2016-04-01
A class of coupled cell-bulk ODE-PDE models is formulated and analyzed in a two-dimensional domain, which is relevant to studying quorum-sensing behavior on thin substrates. In this model, spatially segregated dynamically active signaling cells of a common small radius ɛ ≪ 1 are coupled through a passive bulk diffusion field. For this coupled system, the method of matched asymptotic expansions is used to construct steady-state solutions and to formulate a spectral problem that characterizes the linear stability properties of the steady-state solutions, with the aim of predicting whether temporal oscillations can be triggered by the cell-bulk coupling. Phase diagrams in parameter space where such collective oscillations can occur, as obtained from our linear stability analysis, are illustrated for two specific choices of the intracellular kinetics. In the limit of very large bulk diffusion, it is shown that solutions to the ODE-PDE cell-bulk system can be approximated by a finite-dimensional dynamical system. This limiting system is studied both analytically, using a linear stability analysis and, globally, using numerical bifurcation software. For one illustrative example of the theory, it is shown that when the number of cells exceeds some critical number, i.e., when a quorum is attained, the passive bulk diffusion field can trigger oscillations through a Hopf bifurcation that would otherwise not occur without the coupling. Moreover, for two specific models for the intracellular dynamics, we show that there are rather wide regions in parameter space where these triggered oscillations are synchronous in nature. Unless the bulk diffusivity is asymptotically large, it is shown that a diffusion-sensing behavior is possible whereby more clustered spatial configurations of cells inside the domain lead to larger regions in parameter space where synchronous collective oscillations between the small cells can occur. Finally, the linear stability analysis for these cell
An Asymptotic Analysis of a 2-D Model of Dynamically Active Compartments Coupled by Bulk Diffusion
Gou, J.; Ward, M. J.
2016-08-01
A class of coupled cell-bulk ODE-PDE models is formulated and analyzed in a two-dimensional domain, which is relevant to studying quorum-sensing behavior on thin substrates. In this model, spatially segregated dynamically active signaling cells of a common small radius ɛ ≪ 1 are coupled through a passive bulk diffusion field. For this coupled system, the method of matched asymptotic expansions is used to construct steady-state solutions and to formulate a spectral problem that characterizes the linear stability properties of the steady-state solutions, with the aim of predicting whether temporal oscillations can be triggered by the cell-bulk coupling. Phase diagrams in parameter space where such collective oscillations can occur, as obtained from our linear stability analysis, are illustrated for two specific choices of the intracellular kinetics. In the limit of very large bulk diffusion, it is shown that solutions to the ODE-PDE cell-bulk system can be approximated by a finite-dimensional dynamical system. This limiting system is studied both analytically, using a linear stability analysis and, globally, using numerical bifurcation software. For one illustrative example of the theory, it is shown that when the number of cells exceeds some critical number, i.e., when a quorum is attained, the passive bulk diffusion field can trigger oscillations through a Hopf bifurcation that would otherwise not occur without the coupling. Moreover, for two specific models for the intracellular dynamics, we show that there are rather wide regions in parameter space where these triggered oscillations are synchronous in nature. Unless the bulk diffusivity is asymptotically large, it is shown that a diffusion-sensing behavior is possible whereby more clustered spatial configurations of cells inside the domain lead to larger regions in parameter space where synchronous collective oscillations between the small cells can occur. Finally, the linear stability analysis for these cell
Katyal, Vini
2012-01-01
This paper focuses on fruit defect detection and glare removal using morphological operations, Glare removal can be considered as an important preprocessing step as uneven lighting may introduce it in images, which hamper the results produced through segmentation by Gabor filters .The problem of glare in images is very pronounced sometimes due to the unusual reflectance from the camera sensor or stray light entering, this method counteracts this problem and makes the defect detection much more pronounced. Anisotropic diffusion is used for further smoothening of the images and removing the high energy regions in an image for better defect detection and makes the defects more retrievable. Our algorithm is robust and scalable the employability of a particular mask for glare removal has been checked and proved useful for counteracting.this problem, anisotropic diffusion further enhances the defects with its use further Optimal Gabor filter at various orientations is used for defect detection.
Selected neutron reaction nuclear data libraries and photon-atomic interaction cross section libraries for elements of interest to the IAEA's program on Fusion Evaluated Nuclear Data Library (FENDL) have been processed into MATXSR format using the NJOY system on the VAX4000 computer of the IAEA. This document lists the resulting multigroup data libraries. All the multigroup data generated are available cost-free upon request from the IAEA Nuclear Data Section. (author). 9 refs
3D coarse mesh NEM embedded with 2D fine mesh NDOM for PWR core analysis - 032
The paper describes an algorithm of 3D multi-group coarse mesh Nodal Expansion Method (NEM) embedded with 2D multi-group fine mesh Nodal Discrete Ordinate Method (NDOM). The main idea of the algorithm is to substitute the radial part of 3D NEM inner iteration, which is based on coarse mesh diffusion theory, with 2D NDOM inner iteration, which is based on transport theory. Taking advantages of both NEM and NDOM, the algorithm efficiently models the heterogeneous pin-by-pin layout in radial planes of PWR core and overcomes the challenges of computer memory and computation time, which are inherent bottlenecks of 3D fine mesh discrete ordinate method (Sn). 2 prototype codes MGNSNM and MGNEM are developed, which are based on 2D multi-group NDOM and 3D multi-group NEM respectively; the final computer code HANWIND is integrated based on the above 2 prototype codes. Numerical experiments on benchmark problem OECD/NEA-2D C5G7MOX and a self-established benchmark problem of 2-loop PWR 3D core are summarized in the paper. (authors)
Highlights: • New type of multi-level rebalancing approach for nodal transport. • Generally improved and more mesh-independent convergence behavior. • Importance for intended regime of 3D pin-by-pin core computations. - Abstract: A new multi-level surface rebalancing (MLSR) approach has been developed, aimed at enabling an improved non-linear acceleration of nodal flux iteration convergence in 3D steady-state and transient reactor simulation. This development is meant specifically for anticipating computational needs for solving envisaged multi-group diffusion-like SPN calculations with enhanced mesh resolution (i.e. 3D multi-box up to 3D pin-by-pin grid). For the latter grid refinement regime, the previously available multi-level coarse mesh rebalancing (MLCMR) strategy has been observed to become increasingly inefficient with increasing 3D mesh resolution. Furthermore, for very fine 3D grids that feature a very fine axial mesh as well, non-convergence phenomena have been observed to emerge. In the verifications pursued up to now, these problems have been resolved by the new approach. The novelty arises from taking the interface current balance equations defined over all Cartesian box edges, instead of the nodal volume-integrated process-rate balance equation, as an appropriate restriction basis for setting up multi-level acceleration of fine grid interface current iterations. The new restriction strategy calls for the use of a newly derived set of adjoint spectral equations that are needed for computing a limited set of spectral response vectors per node. This enables a straightforward determination of group-condensed interface current spectral coupling operators that are of crucial relevance in the new rebalancing setup. Another novelty in the approach is a new variational method for computing the neutronic eigenvalue. Within this context, the latter is treated as a control parameter for driving another, newly defined and numerically more fundamental
Discontinuous diffusion synthetic acceleration for Sn transport on 2D arbitrary polygonal meshes
In this paper, a Diffusion Synthetic Acceleration (DSA) technique applied to the Sn radiation transport equation is developed using Piece-Wise Linear Discontinuous (PWLD) finite elements on arbitrary polygonal grids. The discretization of the DSA equations employs an Interior Penalty technique, as is classically done for the stabilization of the diffusion equation using discontinuous finite element approximations. The penalty method yields a system of linear equations that is Symmetric Positive Definite (SPD). Thus, solution techniques such as Preconditioned Conjugate Gradient (PCG) can be effectively employed. Algebraic MultiGrid (AMG) and Symmetric Gauss–Seidel (SGS) are employed as conjugate gradient preconditioners for the DSA system. AMG is shown to be significantly more efficient than SGS. Fourier analyses are carried out and we show that this discontinuous finite element DSA scheme is always stable and effective at reducing the spectral radius for iterative transport solves, even for grids with high-aspect ratio cells. Numerical results are presented for different grid types: quadrilateral, hexagonal, and polygonal grids as well as grids with local mesh adaptivity
2D coherent charge transport in highly ordered conducting polymers doped by solid state diffusion
Kang, Keehoon; Watanabe, Shun; Broch, Katharina; Sepe, Alessandro; Brown, Adam; Nasrallah, Iyad; Nikolka, Mark; Fei, Zhuping; Heeney, Martin; Matsumoto, Daisuke; Marumoto, Kazuhiro; Tanaka, Hisaaki; Kuroda, Shin-Ichi; Sirringhaus, Henning
2016-08-01
Doping is one of the most important methods to control charge carrier concentration in semiconductors. Ideally, the introduction of dopants should not perturb the ordered microstructure of the semiconducting host. In some systems, such as modulation-doped inorganic semiconductors or molecular charge transfer crystals, this can be achieved by spatially separating the dopants from the charge transport pathways. However, in conducting polymers, dopants tend to be randomly distributed within the conjugated polymer, and as a result the transport properties are strongly affected by the resulting structural and electronic disorder. Here, we show that in the highly ordered lamellar microstructure of a regioregular thiophene-based conjugated polymer, a small-molecule p-type dopant can be incorporated by solid state diffusion into the layers of solubilizing side chains without disrupting the conjugated layers. In contrast to more disordered systems, this allows us to observe coherent, free-electron-like charge transport properties, including a nearly ideal Hall effect in a wide temperature range, a positive magnetoconductance due to weak localization and the Pauli paramagnetic spin susceptibility.
We report developments of the kinetic Monte Carlo (KMC) method with improved accuracy and increased versatility for the description of atomic diffusivity on metal surfaces. The on-lattice constraint built into our recently proposed self-learning KMC (SLKMC) (Trushin et al 2005 Phys. Rev. B 72 115401) is released, leaving atoms free to occupy 'off-lattice' positions to accommodate several processes responsible for small-cluster diffusion, periphery atom motion and heteroepitaxial growth. This technique combines the ideas embedded in the SLKMC method with a new pattern-recognition scheme fitted to an off-lattice model in which relative atomic positions are used to characterize and store configurations. Application of a combination of the 'drag' and the repulsive bias potential (RBP) methods for saddle point searches allows the treatment of concerted cluster, and multiple- and single-atom, motions on an equal footing. This tandem approach has helped reveal several new atomic mechanisms which contribute to cluster migration. We present applications of this off-lattice SLKMC to the diffusion of 2D islands of Cu (containing 2-30 atoms) on Cu and Ag(111), using the interatomic potential from the embedded-atom method. For the hetero-system Cu/Ag(111), this technique has uncovered mechanisms involving concerted motions such as shear, breathing and commensurate-incommensurate occupancies. Although the technique introduces complexities in storage and retrieval, it does not introduce noticeable extra computational cost.
Simulation of Ultra-Small MOSFETs Using a 2-D Quantum-Corrected Drift-Diffusion Model
Biegal, Bryan A.; Rafferty, Connor S.; Yu, Zhiping; Ancona, Mario G.; Dutton, Robert W.; Saini, Subhash (Technical Monitor)
1998-01-01
The continued down-scaling of electronic devices, in particular the commercially dominant MOSFET, will force a fundamental change in the process of new electronics technology development in the next five to ten years. The cost of developing new technology generations is soaring along with the price of new fabrication facilities, even as competitive pressure intensifies to bring this new technology to market faster than ever before. To reduce cost and time to market, device simulation must become a more fundamental, indeed dominant, part of the technology development cycle. In order to produce these benefits, simulation accuracy must improve markedly. At the same time, device physics will become more complex, with the rapid increase in various small-geometry and quantum effects. This work describes both an approach to device simulator development and a physical model which advance the effort to meet the tremendous electronic device simulation challenge described above. The device simulation approach is to specify the physical model at a high level to a general-purpose (but highly efficient) partial differential equation solver (in this case PROPHET, developed by Lucent Technologies), which then simulates the model in 1-D, 2-D, or 3-D for a specified device and test regime. This approach allows for the rapid investigation of a wide range of device models and effects, which is certainly essential for device simulation to catch up with, and then stay ahead of, electronic device technology of the present and future. The physical device model used in this work is the density-gradient (DG) quantum correction to the drift-diffusion model [Ancona, Phys. Rev. B 35(5), 7959 (1987)]. This model adds tunneling and quantum smoothing of carrier density profiles to the drift-diffusion model. We used the DG model in 1-D and 2-D (for the first time) to simulate both bipolar and unipolar devices. Simulations of heavily-doped, short-base diodes indicated that the DG quantum
D3D and D3E, branches of a computer program, solve two- and three-dimensional real and ajoint stationary multigroup neutron diffusion equations by approximating the differential equations by finite difference equations. The discrete grid is a mesh edged one, so that the neutron fluxes are calculated on surfaces separating zones to which different physical conditions apply. Different options allow to treat homogeneous, i.e. eigenvalue problems as well as inhomogeneous, i.e. external source driven problems. The linear algebraic system of the difference equations is solved by the outer and inner iterations method. An outer iteration of the homogeneous problem is the power iteration with the fission source, whereas the outer iteration of the inhomogeneous problem is an iteration with the fission source. Within the process of an outer iteration the group fluxes are determined by inner iterations, either via block overrelaxation or a method of conjugate gradients. (orig./HP)
Huang, Aimin
2014-01-01
Global well-posedness of strong solutions and existence of the global attractor to the initial and boundary value problem of 2D Boussinesq system in a periodic channel with non-homogeneous boundary conditions for the temperature and viscosity and thermal diffusivity depending on the temperature are proved.
The Suppression of Energy Discretization Errors in Multigroup Transport Calculations
Larsen, Edward
2013-06-17
The Objective of this project is to develop, implement, and test new deterministric methods to solve, as efficiently as possible, multigroup neutron transport problems having an extremely large number of groups. Our approach was to (i) use the standard CMFD method to "coarsen" the space-angle grid, yielding a multigroup diffusion equation, and (ii) use a new multigrid-in-space-and-energy technique to efficiently solve the multigroup diffusion problem. The overall strategy of (i) how to coarsen the spatial and energy grids, and (ii) how to navigate through the various grids, has the goal of minimizing the overall computational effort. This approach yields not only the fine-grid solution, but also coarse-group flux-weighted cross sections that can be used for other related problems.
The Suppression of Energy Discretization Errors in Multigroup Transport Calculations
The Objective of this project is to develop, implement, and test new deterministric methods to solve, as efficiently as possible, multigroup neutron transport problems having an extremely large number of groups. Our approach was to (i) use the standard CMFD method to 'coarsen' the space-angle grid, yielding a multigroup diffusion equation, and (ii) use a new multigrid-in-space-and-energy technique to efficiently solve the multigroup diffusion problem. The overall strategy of (i) how to coarsen the spatial an energy grids, and (ii) how to navigate through the various grids, has the goal of minimizing the overall computational effort. This approach yields not only the fine-grid solution, but also coarse-group flux-weighted cross sections that can be used for other related problems.
Noguchi, Naoki; Kubo, Tomoaki; Durham, William B.; Kagi, Hiroyuki; Shimizu, Ichiko
2016-08-01
We have developed a high-resolution technique based on micro Raman spectroscopy to measure hydrogen isotope diffusion profiles in ice Ih. The calibration curve for quantitative analysis of deuterium in ice Ih was constructed using micro Raman spectroscopy. Diffusion experiments using diffusion couples composed of dense polycrystalline H2O and D2O ice were carried out under a gas confining pressure of 100 MPa (to suppress micro-fracturing and pore formation) at temperatures from 235 K to 245 K and diffusion times from 0.2 to 94 hours. Two-dimensional deuterium profiles across the diffusion couples were determined by Raman imaging. The location of small spots of frost from room air could be detected from the shapes of the Raman bands of OH and OD stretching modes, which change because of the effect of the molar ratio of deuterium on the molecular coupling interaction. We emphasize the validity for screening the impurities utilizing the coupling interaction. Some recrystallization and grain boundary migration occurred in recovered diffusion couples, but analysis of two-dimensional diffusion profiles of regions not affected by grain boundary migration allowed us to measure a volume diffusivity for ice at 100 MPa of (2.8 ± 0.4) ×10-3exp[ -57.0±15.4kJ/mol/RT ] m2 /s (R is the gas constant, T is temperature). Based on ambient pressure diffusivity measurements by others, this value indicates a high (negative) activation volume for volume diffusivity of -29.5 cm3/mol or more. We can also constrain the value of grain boundary diffusivity in ice at 100 MPa to be <104 that of volume diffusivity.
2D hybrid simulations of super-diffusion at the magnetopause driven by Kelvin-Helmholtz instability
Cowee, Misa M [Los Alamos National Laboratory; Winske, Dan [Los Alamos National Laboratory; Gary, S Peter [Los Alamos National Laboratory
2009-01-01
This manuscript describes the self-consistent simulation of diffusion at the magnetopause driven by Kelvin-Helmholtz (KH) instability. Two-dimensional hybrid (kinetic ions, fluid electrons) simulations of the most KH-unstable configuration where the shear flow is oriented perpendicular to the uniform magnetic field are carried out. The motion of the simulation particles are tracked during the run and their mean-square displacement normal to the magnetopause is calculated from which diffusion coefficients are determined. The diffusion coefficients are found to be time dependent, with D{sub x} {proportional_to} t{sup {alpha}}, where {alpha} > 1. Additionally, the probability distribution functions (PDF) of the 'jump lengths' the particles make over time are found to be non-gaussian. Such time-dependent diffusion coefficients and non-gaussian PDF's have been associated with so-called 'super-diffusion', in which diffusive mixing of particles is enhanced over classical diffusion. The results indicate that while turbulence associated with the break-down of vortices contributes to this enhanced diffusion, it is the growth of large-scale, coherent vortices is the more important process in facilitating it.
Tzannis, A.P.; Beaud, P.; Frey, H.M.; Gerber, T.; Mischler, B.; Radi, P.P. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1997-06-01
Resonant Holographic Interferometry is a method based on the anomalous dispersion of light having a frequency close to an electronic transition of a molecule. We propose a novel single-laser, two-colour setup for recording resonant holograms and apply it to 2D species concentration measurements. The second colour is generated by optical phase-conjugation from Stimulated Brillouin scattering in a cell. Phase-Conjugate Resonant Holographic Interferometry (PCRHI) is demonstrated in a 2D NH{sub 3}/O{sub 2} flame yielding interferograms that contain information on the NH radical distribution in the flame. Experimental results are quantified by applying a numerical computation of the Voigt profiles. (author) 1 fig., 3 refs.
Larios, Adam; Titi, Edriss S
2010-01-01
We establish global existence and uniqueness theorems for the two-dimensional non-diffusive Boussinesq system with viscosity only in the horizontal direction, which arises in Ocean dynamics. This work improves the global well-posedness results established recently by R. Danchin and M. Paicu for the Boussinesq system with anisotropic viscosity and zero diffusion. Although we follow some of their ideas, in proving the uniqueness result, we have used an alternative approach by writing the transported temperature (density) as $\\theta = \\Delta\\xi$ and adapting the techniques of V. Yudovich for the 2D incompressible Euler equations. This new idea allows us to establish uniqueness results with fewer assumptions on the initial data for the transported quantity $\\theta$. Furthermore, this new technique allows us to establish uniqueness results without having to resort to the paraproduct calculus of J. Bony. We also propose an inviscid $\\alpha$-regularization for the two-dimensional inviscid, non-diffusive Boussinesq s...
We have analyzed the 2D convective motion of coherent structures, which is associated with plasma blobs, under attached and detached plasma conditions of a linear divertor simulator, NAGDIS-II. Data analysis of probes and a fast-imaging camera by spatio-temporal correlation with three decomposition and proper orthogonal decomposition (POD) was carried out to determine the basic properties of coherent structures detached from a bulk plasma column. Under the attached plasma condition, the spatio-temporal correlation with three decomposition based on the probe measurement showed that two types of coherent structures with different sizes detached from the bulk plasma and the azimuthally localized structure radially propagated faster than the larger structure. Under the detached plasma condition, movies taken by the fast-imaging camera clearly showed the dynamics of a 2D spiral structure at peripheral regions of the bulk plasma; this dynamics caused the broadening of the plasma profile. The POD method was used for the data processing of the movies to obtain low-dimensional mode shapes. It was found that the m=1 and m=2 ring-shaped coherent structures were dominant. Comparison between the POD analysis of both the movie and the probe data suggested that the coherent structure could be detached from the bulk plasma mainly associated with the m=2 fluctuation. This phenomena could play an important role in the reduction of the particle and heat flux as well as the plasma recombination processes in plasma detachment (copyright 2010 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Chris J. Conklin
2016-01-01
Full Text Available Magnetic resonance based diffusion imaging has been gaining more utility and clinical relevance over the past decade. Using conventional echo planar techniques, it is possible to acquire and characterize water diffusion within the central nervous system (CNS; namely in the form of Diffusion Weighted Imaging (DWI and Diffusion Tensor Imaging (DTI. While each modality provides valuable clinical information in terms of the presence of diffusion and its directionality, both techniques are limited to assuming an ideal Gaussian distribution for water displacement with no intermolecular interactions. This assumption neglects pathological processes that are not Gaussian therefore reducing the amount of potentially clinically relevant information. Additions to the Gaussian distribution measured by the excess kurtosis, or peakedness, of the probabilistic model provide a better understanding of the underlying cellular structure. The objective of this work is to provide mathematical and experimental evidence that Diffusion Kurtosis Imaging (DKI can offer additional information about the micromolecular environment of the pediatric spinal cord. This is accomplished by a more thorough characterization of the nature of random water displacement within the cord. A novel DKI imaging sequence based on a tilted 2D spatially selective radio frequency pulse providing reduced field of view (FOV imaging was developed, implemented, and optimized on a 3 Tesla MRI scanner, and tested on pediatric subjects (healthy subjects: 15; patients with spinal cord injury (SCI:5. Software was developed and validated for post processing of the DKI images and estimation of the tensor parameters. The results show statistically significant differences in mean kurtosis (p < 0.01 and radial kurtosis (p < 0.01 between healthy subjects and subjects with SCI. DKI provides incremental and novel information over conventional diffusion acquisitions when coupled with higher order estimation
Conklin, Chris J; Middleton, Devon M; Alizadeh, Mahdi; Finsterbusch, Jürgen; Raunig, David L; Faro, Scott H; Shah, Pallav; Krisa, Laura; Sinko, Rebecca; Delalic, Joan Z; Mulcahey, M J; Mohamed, Feroze B
2016-01-01
Magnetic resonance based diffusion imaging has been gaining more utility and clinical relevance over the past decade. Using conventional echo planar techniques, it is possible to acquire and characterize water diffusion within the central nervous system (CNS); namely in the form of Diffusion Weighted Imaging (DWI) and Diffusion Tensor Imaging (DTI). While each modality provides valuable clinical information in terms of the presence of diffusion and its directionality, both techniques are limited to assuming an ideal Gaussian distribution for water displacement with no intermolecular interactions. This assumption neglects pathological processes that are not Gaussian therefore reducing the amount of potentially clinically relevant information. Additions to the Gaussian distribution measured by the excess kurtosis, or peakedness, of the probabilistic model provide a better understanding of the underlying cellular structure. The objective of this work is to provide mathematical and experimental evidence that Diffusion Kurtosis Imaging (DKI) can offer additional information about the micromolecular environment of the pediatric spinal cord. This is accomplished by a more thorough characterization of the nature of random water displacement within the cord. A novel DKI imaging sequence based on a tilted 2D spatially selective radio frequency pulse providing reduced field of view (FOV) imaging was developed, implemented, and optimized on a 3 Tesla MRI scanner, and tested on pediatric subjects (healthy subjects: 15; patients with spinal cord injury (SCI):5). Software was developed and validated for post processing of the DKI images and estimation of the tensor parameters. The results show statistically significant differences in mean kurtosis (p < 0.01) and radial kurtosis (p < 0.01) between healthy subjects and subjects with SCI. DKI provides incremental and novel information over conventional diffusion acquisitions when coupled with higher order estimation algorithms
In this work, we treat spin-selective recombination of a geminate radical pair (RP) in a spherical “microreactor,” i.e., of a RP confined in a micelle, vesicle, or liposome. We consider the microreactor model proposed earlier, in which one of the radicals is located at the center of the micelle and the other one undergoes three-dimensional diffusion inside the micelle. In addition, we suggest a two-dimensional model, in which one of the radicals is located at the “pole” of the sphere, while the other one diffuses on the spherical surface. For this model, we have obtained a general analytical expression for the RP recombination yield in terms of the free Green function of two-dimensional diffusion motion. In turn, this Green function is expressed via the Legendre functions and thus takes account of diffusion over a restricted spherical surface and its curvature. The obtained expression allows one to calculate the RP recombination efficiency at an arbitrary magnetic field strength. We performed a comparison of the two models taking the same geometric parameters (i.e., the microreactor radius and the closest approach distance of the radicals), chemical reactivity, magnetic interactions in the RP and diffusion coefficient. Significant difference between the predictions of the two models is found, which is thus originating solely from the dimensionality effect: for different dimensionality of space, the statistics of diffusional contacts of radicals becomes different altering the reaction yield. We have calculated the magnetic field dependence of the RP reaction yield and chemically induced dynamic nuclear polarization of the reaction products at different sizes of the microreactor, exchange interaction, and spin relaxation rates. Interestingly, due to the intricate interplay of diffusional contacts of reactants and spin dynamics, the dependence of the reaction yield on the microreactor radius is non-monotonous. Our results are of importance for (i) interpreting
Ivanov, Konstantin L., E-mail: ivanov@tomo.nsc.ru; Lukzen, Nikita N. [International Tomography Center, Siberian Branch, Russian Academy of Sciences, Institutskaya St. 3a, Novosibirsk 630090 (Russian Federation); Novosibirsk State University, Pirogova St. 2, Novosibirsk 630090 (Russian Federation); Sadovsky, Vladimir M. [Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Akademgorodok 50/44, Krasnoyarsk 660036 (Russian Federation)
2015-08-28
In this work, we treat spin-selective recombination of a geminate radical pair (RP) in a spherical “microreactor,” i.e., of a RP confined in a micelle, vesicle, or liposome. We consider the microreactor model proposed earlier, in which one of the radicals is located at the center of the micelle and the other one undergoes three-dimensional diffusion inside the micelle. In addition, we suggest a two-dimensional model, in which one of the radicals is located at the “pole” of the sphere, while the other one diffuses on the spherical surface. For this model, we have obtained a general analytical expression for the RP recombination yield in terms of the free Green function of two-dimensional diffusion motion. In turn, this Green function is expressed via the Legendre functions and thus takes account of diffusion over a restricted spherical surface and its curvature. The obtained expression allows one to calculate the RP recombination efficiency at an arbitrary magnetic field strength. We performed a comparison of the two models taking the same geometric parameters (i.e., the microreactor radius and the closest approach distance of the radicals), chemical reactivity, magnetic interactions in the RP and diffusion coefficient. Significant difference between the predictions of the two models is found, which is thus originating solely from the dimensionality effect: for different dimensionality of space, the statistics of diffusional contacts of radicals becomes different altering the reaction yield. We have calculated the magnetic field dependence of the RP reaction yield and chemically induced dynamic nuclear polarization of the reaction products at different sizes of the microreactor, exchange interaction, and spin relaxation rates. Interestingly, due to the intricate interplay of diffusional contacts of reactants and spin dynamics, the dependence of the reaction yield on the microreactor radius is non-monotonous. Our results are of importance for (i) interpreting
Ivanov, Konstantin L.; Sadovsky, Vladimir M.; Lukzen, Nikita N.
2015-08-01
In this work, we treat spin-selective recombination of a geminate radical pair (RP) in a spherical "microreactor," i.e., of a RP confined in a micelle, vesicle, or liposome. We consider the microreactor model proposed earlier, in which one of the radicals is located at the center of the micelle and the other one undergoes three-dimensional diffusion inside the micelle. In addition, we suggest a two-dimensional model, in which one of the radicals is located at the "pole" of the sphere, while the other one diffuses on the spherical surface. For this model, we have obtained a general analytical expression for the RP recombination yield in terms of the free Green function of two-dimensional diffusion motion. In turn, this Green function is expressed via the Legendre functions and thus takes account of diffusion over a restricted spherical surface and its curvature. The obtained expression allows one to calculate the RP recombination efficiency at an arbitrary magnetic field strength. We performed a comparison of the two models taking the same geometric parameters (i.e., the microreactor radius and the closest approach distance of the radicals), chemical reactivity, magnetic interactions in the RP and diffusion coefficient. Significant difference between the predictions of the two models is found, which is thus originating solely from the dimensionality effect: for different dimensionality of space, the statistics of diffusional contacts of radicals becomes different altering the reaction yield. We have calculated the magnetic field dependence of the RP reaction yield and chemically induced dynamic nuclear polarization of the reaction products at different sizes of the microreactor, exchange interaction, and spin relaxation rates. Interestingly, due to the intricate interplay of diffusional contacts of reactants and spin dynamics, the dependence of the reaction yield on the microreactor radius is non-monotonous. Our results are of importance for (i) interpreting
Numerical method for a 2D drift diffusion model arising in strained n-type MOSFET device
BENSEGUENI RACHIDA; LATRECHE SAIDA
2016-06-01
This paper reports the calculation of electron transport in metal oxide semiconductor field effects transistors (MOSFETs) with biaxially tensile strained silicon channel. The calculation is formulated based on two-dimensional drift diffusion model (DDM) including strain effects. The carrier mobility dependence on the lateral and vertical electric field model is especially consideredin the formulation. By using the model presented here, numerical method based on finite difference approach is performed. The obtained results show that the presence of biaxially tensile strain enhances the current in the devices.
Petersen, Claudio Z. [Universidade Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Bodmann, Bardo E.J.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-graduacao em Engenharia Mecanica; Barros, Ricardo C. [Universidade do Estado do Rio de Janeiro, Nova Friburgo, RJ (Brazil). Inst. Politecnico
2014-12-15
In the present work we solve in analytical representation the three dimensional neutron kinetic diffusion problem in rectangular Cartesian geometry for homogeneous and bounded domains for any number of energy groups and precursor concentrations. The solution in analytical representation is constructed using a hierarchical procedure, i.e. the original problem is reduced to a problem previously solved by the authors making use of a combination of the spectral method and a recursive decomposition approach. Time dependent absorption cross sections of the thermal energy group are considered with step, ramp and Chebyshev polynomial variations. For these three cases, we present numerical results and discuss convergence properties and compare our results to those available in the literature.
SCORE-4, 2-D Removal Diffusion in X-Y or R-Z Geometry for Rectangular Shields
1 - Nature of physical problem solved: The neutron flux is calculated for a shield made up of rectangular regions. The geometry is either x-y or r-z. 2 - Method of solution: Removal fluxes and sources throughout the shield regions are calculated from a given reactor core power distribution using a point kernel method. The diffusion neutron fluxes are obtained from the removal source distribution using an iterative Method of solution. 3 - Restrictions on the complexity of the problem: The amount of fast core required for the program depends on the size of shield being calculated. For example, a 100 by 100 mesh shielding calculation would require approximately 300 k bytes. Larger problems could be solved by increasing the fast storage requirements
2D coherent charge transport in highly ordered conducting polymers doped by solid state diffusion.
Kang, Keehoon; Watanabe, Shun; Broch, Katharina; Sepe, Alessandro; Brown, Adam; Nasrallah, Iyad; Nikolka, Mark; Fei, Zhuping; Heeney, Martin; Matsumoto, Daisuke; Marumoto, Kazuhiro; Tanaka, Hisaaki; Kuroda, Shin-Ichi; Sirringhaus, Henning
2016-08-01
Doping is one of the most important methods to control charge carrier concentration in semiconductors. Ideally, the introduction of dopants should not perturb the ordered microstructure of the semiconducting host. In some systems, such as modulation-doped inorganic semiconductors or molecular charge transfer crystals, this can be achieved by spatially separating the dopants from the charge transport pathways. However, in conducting polymers, dopants tend to be randomly distributed within the conjugated polymer, and as a result the transport properties are strongly affected by the resulting structural and electronic disorder. Here, we show that in the highly ordered lamellar microstructure of a regioregular thiophene-based conjugated polymer, a small-molecule p-type dopant can be incorporated by solid state diffusion into the layers of solubilizing side chains without disrupting the conjugated layers. In contrast to more disordered systems, this allows us to observe coherent, free-electron-like charge transport properties, including a nearly ideal Hall effect in a wide temperature range, a positive magnetoconductance due to weak localization and the Pauli paramagnetic spin susceptibility. PMID:27159015
HEXNOD23, 2-D, 3-D Coarse Mesh Solution of Steady State Diffusion Equation in Hexagonal Geometry
1 - Description of program or function: Two- or three dimensional coarse mesh solution of steady state two group neutron diffusion equation in arrays of regular hexagons or hexagonal subassemblies. 2 - Method of solution: The neutron flux in a hexagonal node is expanded in a series of Bessel functions in the hexagonal plane. Polynomials up to the 4. order are used for the approximation of neutron flux in axial direction of three dimensional cases. Resulting relations between node averaged fluxes and mean partial currents of node faces in connection with the neutron balance of nodes are used to calculate the eigenvalue Keff, mean fluxes and mean powers of nodes. The iterations process is divided into inner and outer iterations. The iterations are accelerated by Ljusternik and Tschebyscheff extrapolation schemes. The power densities in the nodes and subassembly powers are computed for given reactor power in three dimensional cases. 30 degree reflectional, 60 and 120 degree rotational core symmetry and the whole core can be treated. 3 - Restrictions on the complexity of the problem: If the problem size designated by LIAR and LRAR exceeds 3000 and 50000 respectively, the lengths of the working array MIAR and MRAR in the main program can be increased. External sources are not permitted
The multigroup neutronics model of NuStar's 3D core code EGRET
As a key component of NuStar's core analysis system for PWR application, EGRET is designed to perform steady-state coupled neutronic/hydraulic analysis of PWRs. This paper presents EGRET's unique 3D nodal diffusion model and 2D pin power reconstruction (PPR) model. Unlike the practice in most of today's production codes that iteratively solves the global 3D coarse-mesh problem and the local axially 1D fine-mesh problem to handle the axial heterogeneity within a node caused by fuel grid and partially-inserted control rod, EGRET resolves the issue by inventing a new nodal technology and introducing the adaptive meshing technique to follow the movement of control rod tip. The new nodal method employs fine-mesh heterogeneous calculation with coarse-mesh transverse coupling such that the axial heterogeneous nodes can be explicitly modeled in exact geometry and directly incorporated into the scheme of transversely coupled coarse-mesh nodal methods. Each axial channel can have its own fine-mesh division without the need of dividing the whole core into radially coupled fine-meshes. There is no need to do 1D fine-mesh and 3D coarse-mesh iteration either. While for the PPR model, EGRET adopts a group-decoupled direct fitting method, which avoids both the complication of constructing 2D analytic multigroup flux solution and any group-coupled iteration. Another unique feature of the PPR model is that it fully utilizes all the information available from 3D core calculation into the downstream PPR process. Particularly, for the first time, the 1D profiles of transversely-integrated fluxes are utilized as the additional conditions to reconstruct pin power. Numerical results of series of benchmark problems verify the good performance of EGRET's unique multi-group neutronics model. (author)
Maryam Mobed-Miremadi
2014-12-01
Full Text Available Hollow alginate microfibers (od = 1.3 mm, id = 0.9 mm, th = 400 µm, L = 3.5 cm comprised of 2% (w/v medium molecular weight alginate cross-linked with 0.9 M CaCl2 were fabricated to model outward diffusion capture by 2D fluorescent microscopy. A two-fold comparison of diffusivity determination based on real-time diffusion of Fluorescein isothiocyanate molecular weight (FITC MW markers was conducted using a proposed Fickian-based approach in conjunction with a previously established numerical model developed based on spectrophotometric data. Computed empirical/numerical (Dempiricial/Dnumerical diffusivities characterized by small standard deviations for the 4-, 70- and 500-kDa markers expressed in m2/s are (1.06 × 10−9 ± 1.96 × 10−10/(2.03 × 10−11, (5.89 × 10−11 ± 2.83 × 10−12/(4.6 × 10−12 and (4.89 × 10−12 ± 3.94 × 10−13/(1.27 × 10−12, respectively, with the discrimination between the computation techniques narrowing down as a function of MW. The use of the numerical approach is recommended for fluorescence-based measurements as the standard computational method for effective diffusivity determination until capture rates (minimum 12 fps for the 4-kDa marker and the use of linear instead of polynomial interpolating functions to model temporal intensity gradients have been proven to minimize the extent of systematic errors associated with the proposed empirical method.
A multigroup treatment of radiation transport
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)
The purpose of our study was to evaluate the use of 2D-selective, parallel-transmit excitation magnetic resonance imaging (MRI) for diffusion-weighted echo-planar imaging (pTX-EPI) of the prostate, and to compare it to conventional, single-shot EPI (c-EPI). The MRI examinations of 35 patients were evaluated in this prospective study. PTX-EPI was performed with a TX-acceleration factor of 1.7 and a field of view (FOV) of 150 x 90 mm2, whereas c-EPI used a full FOV of 380 x 297 mm2. Two readers evaluated three different aspects of image quality on 5-point Likert scales. To quantify distortion artefacts, maximum diameters and prostate volume were determined for both techniques and compared to T2-weighted imaging. The zoomed pTX-EPI was superior to c-EPI with respect to overall image quality (3.39 ± 0.62 vs 2.45 ± 0.67) and anatomic differentiability (3.29 ± 0.65 vs 2.41 ± 0.65), each with p 0.05). Zoomed pTX-EPI leads to substantial improvements in diffusion-weighted imaging (DWI) of the prostate with respect to different aspects of image quality and severity of artefacts. (orig.)
Thierfelder, Kolja M.; Scherr, Michael K.; Weiss, Jakob; Mueller-Lisse, Ullrich G.; Theisen, Daniel [Ludwig-Maximilians-University Hospital Munich, Institute for Clinical Radiology, Munich (Germany); Notohamiprodjo, Mike; Nikolaou, Konstantin [Ludwig-Maximilians-University Hospital Munich, Institute for Clinical Radiology, Munich (Germany); University Hospital Tuebingen, Department of Diagnostic and Interventional Radiology, Tuebingen (Germany); Dietrich, Olaf [Ludwig-Maximilians-University Hospital Munich, Josef Lissner Laboratory for Biomedical Imaging, Institute for Clinical Radiology, Munich (Germany); Pfeuffer, Josef [Siemens Healthcare, Application Development, Erlangen (Germany)
2014-12-15
The purpose of our study was to evaluate the use of 2D-selective, parallel-transmit excitation magnetic resonance imaging (MRI) for diffusion-weighted echo-planar imaging (pTX-EPI) of the prostate, and to compare it to conventional, single-shot EPI (c-EPI). The MRI examinations of 35 patients were evaluated in this prospective study. PTX-EPI was performed with a TX-acceleration factor of 1.7 and a field of view (FOV) of 150 x 90 mm{sup 2}, whereas c-EPI used a full FOV of 380 x 297 mm{sup 2}. Two readers evaluated three different aspects of image quality on 5-point Likert scales. To quantify distortion artefacts, maximum diameters and prostate volume were determined for both techniques and compared to T2-weighted imaging. The zoomed pTX-EPI was superior to c-EPI with respect to overall image quality (3.39 ± 0.62 vs 2.45 ± 0.67) and anatomic differentiability (3.29 ± 0.65 vs 2.41 ± 0.65), each with p < 0.0001. Artefacts were significantly less severe in pTX-EPI (0.93 ± 0.73 vs 1.49 ± 1.08), p < 0.001. The quantitative analysis yielded a higher agreement of pTX-EPI with T2-weighted imaging than c-EPI with respect to coronal (ICCs: 0.95 vs 0.93) and sagittal (0.86 vs 0.73) diameters as well as prostate volume (0.94 vs 0.92). Apparent diffusion coefficient (ADC) values did not differ significantly between the two techniques (p > 0.05). Zoomed pTX-EPI leads to substantial improvements in diffusion-weighted imaging (DWI) of the prostate with respect to different aspects of image quality and severity of artefacts. (orig.)
Gao, Longfei
2015-01-01
In this paper, we combine the Alternating Direction Implicit (ADI) algorithm with the concept of preconditioning and apply it to linear systems discretized from the 2D steady-state diffusion equations with orthotropic heterogeneous coefficients by the finite element method assuming tensor product basis functions. Specifically, we adopt the compound iteration idea and use ADI iterations as the preconditioner for the outside Krylov subspace method that is used to solve the preconditioned linear system. An efficient algorithm to perform each ADI iteration is crucial to the efficiency of the overall iterative scheme. We exploit the Kronecker product structure in the matrices, inherited from the tensor product basis functions, to achieve high efficiency in each ADI iteration. Meanwhile, in order to reduce the number of Krylov subspace iterations, we incorporate partially the coefficient information into the preconditioner by exploiting the local support property of the finite element basis functions. Numerical results demonstrated the efficiency and quality of the proposed preconditioner. © 2014 Elsevier B.V. All rights reserved.
Procedure to Generate the MPACT Multigroup Library
The CASL neutronics simulator MPACT is under development for the neutronics and T-H coupled simulation for the light water reactor. The objective of this document is focused on reviewing the current procedure to generate the MPACT multigroup library. Detailed methodologies and procedures are included in this document for further discussion to improve the MPACT multigroup library.
Procedure to Generate the MPACT Multigroup Library
Kim, Kang Seog [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2015-12-17
The CASL neutronics simulator MPACT is under development for the neutronics and T-H coupled simulation for the light water reactor. The objective of this document is focused on reviewing the current procedure to generate the MPACT multigroup library. Detailed methodologies and procedures are included in this document for further discussion to improve the MPACT multigroup library.
Current theories for approximating the effects of stochastic media on radiation transport assume very limited physics such as one dimension, constant grey opacities, and no material energy balance equation. When applied to more complex physical problems, the standard theory fails to match the results from direct numerical simulations. This work presents the first direct numerical simulations of multigroup radiation transport coupled to a material temperature equation in a 2D stochastic medium that are compared to closures proposed by various authors. After extending it from grey to multigroup physics, one closure that is not commonly used successfully models the results in dilute systems where one material comprises less than 5% of the total. This closure is more accurate for related grey transport problems than it is for the multigroup problem. When the specific heats are material- and temperature-dependent, it is much more difficult to fit the direct numerical solutions with an approximate closure.
The spatial eigenfunction expansion method is used to solve the multigroup time-dependent diffusion equation when the absorption cross-section in the thermal group is a function of time. An expression for the multi region reactor transfer function is obtained. Some numerical results for two energy groups are also presented. (author)
A discretization of the multigroup PN radiative transfer equation on general meshes
Hermeline, F.
2016-05-01
We propose and study a finite volume method of discrete duality type for discretizing the multigroup PN approximation of radiative transfer equation on general meshes. This method is second order-accurate on a very large variety of meshes, stable under a Courant-Friedrichs-Lewy condition and it preserves naturally the diffusion asymptotic limit.
Multi-group SP3 approximation for simulation of a three-dimensional PWR rod ejection accident
Highlights: • The multi-group SP3 method developed and implemented in PARCS for the MOX analysis. • The verifications were performed in 2D and 3D, 2G and MG, diffusion and transport, with and without feedback. • All results show consistency with the reference results obtained from the ANL PN transport code VARIANT for steady-state and transport calculations. • It was found that the SP3 angular approximation captures sufficient transport effects for both steady-state and transient, and provides essentially the same results as the VARIANT P5 method. • From the transient results of the full-core problem, it was noted that MG is more conservative than 2G, and P1 is more conservative than SP3. - Abstract: Previous researchers have shown that the simplified P3 (SP3) approximation is capable of providing sufficiently high accuracy for both static and transient simulations for reactor core analysis with considerably less computational expense than higher order transport methods such as the discrete ordinate or the full spherical harmonics methods. The objective of this paper is to provide a consistent comparison of two-group (2G) and multi-group (MG) diffusion and SP3 transport for rod ejection accident (REA) in a practical light water reactor (LWR) problem. The analysis is performed on two numerical benchmarks, a 3 × 3 assembly mini-core and a full pressurized water reactor (PWR) core. The calculations were performed using pin homogenized and assembly homogenized cross sections for a series of benchmarks of increasing difficulty, in two-dimensional (2D) and three-dimensional (3D), 2G and MG, diffusion and transport, as well as with and without feedback. All results show consistency with the reference results obtained from higher-order methods. It is demonstrated that the analyzed problems show small group-homogenization effects, but relatively significant transport effects which are satisfactorily addressed by the SP3 transport method. The sensitivity tests
LWR fuel reactivity depletion verification using 2D full-core MOC and flux map data
Experimental quantification of PWR fuel reactivity (k-infinity) burnup decrement biases and uncertainties using in-core flux map data from operating power reactors has previously been conducted employing analytical methods to systematically determine experimental fuel reactivities that best match measured fission rate distributions. This optimal core reactivity distribution that best matches the measured fission rate distribution is assumed to be associated with the true fuel reactivity distribution. Some parties have questioned whether fortuitous cancellation of errors between various approximations inherent in the 3D nodal diffusion core analysis models might have caused reactivity decrement biases and uncertainties to be unrealistically small. In this study, the BEAVRS benchmark is modeled with both 2D, full-core, multi-group transport calculations and 2-group nodal diffusion calculations. The calculated in-core detector U-235 fission rates are compared with measured fission rates supplied in the benchmark. The same analytical methods previously mentioned are again used to obtain fuel reactivity biases and uncertainties. Results demonstrate that fuel batch reactivities inferred from flux map data using full-core transport calculations are nearly identical to those inferred using nodal diffusion calculations. Consequently, nodal methods do not contribute significantly to reactivity decrement biases in the BEAVRS cores. It is recommended that fuel reactivity biases and uncertainties inferred from 3D nodal diffusion calculations remain valid. (author)
A numerical model for multigroup radiation hydrodynamics
We present in this paper a multigroup model for radiation hydrodynamics to account for variations of the gas opacity as a function of frequency. The entropy closure model (M1) is applied to multigroup radiation transfer in a radiation hydrodynamics code. In difference from the previous grey model, we are able to reproduce the crucial effects of frequency-variable gas opacities, a situation omnipresent in physics and astrophysics. We also account for the energy exchange between neighbouring groups which is important in flows with strong velocity divergence. These terms were computed using a finite volume method in the frequency domain. The radiative transfer aspect of the method was first tested separately for global consistency (reversion to grey model) and against a well-established kinetic model through Marshak wave tests with frequency-dependent opacities. Very good agreement between the multigroup M1 and kinetic models was observed in all tests. The successful coupling of the multigroup radiative transfer to the hydrodynamics was then confirmed through a second series of tests. Finally, the model was linked to a database of opacities for a Xe gas in order to simulate realistic multigroup radiative shocks in Xe. The differences with the previous grey models are discussed.
Ford, Jason E.; McCoy, Anne B.
2016-02-01
In this work the efficacy of a combined approach for capturing rovibrational coupling is investigated. Specifically, the multi-state rotational DMC method is used in combination with fixed-node DMC in a study of the rotation vibration energy levels of H2D+ and HD2+. Analysis of the results of these calculations shows very good agreement between the calculated energies and previously reported values. Where differences are found, they can be attributed to Coriolis couplings, which are large in these ions and which are not fully accounted for in this approach.
Highlights: • We present a computational scheme for the determination of reflector properties in a PWR. • The approach is based on the minimization of a functional. • We use a data assimilation method or a parametric complementarity principle. • The reference target is a solution obtained with the method of characteristics. • The simplified flux solution is based on diffusion theory or on the simplified Pn method. - Abstract: This paper presents a computational scheme for the determination of equivalent 2D multi-group spatially dependant reflector parameters in a Pressurized Water Reactor (PWR). The proposed strategy is to define a full-core calculation consistent with a reference lattice code calculation such as the Method Of Characteristics (MOC) as implemented in APOLLO2 lattice code. The computational scheme presented here relies on the data assimilation module known as “Assimilation de données et Aide à l’Optimisation (ADAO)” of the SALOME platform developed at Électricité De France (EDF), coupled with the full-core code COCAGNE and with the lattice code APOLLO2. A first code-to-code verification of the computational scheme is made using the OPTEX reflector model developed at École Polytechnique de Montréal (EPM). As a result, we obtain 2D multi-group, spatially dependant reflector parameters, using both diffusion or SPN operators. We observe important improvements of the power discrepancies distribution over the core when using reflector parameters computed with the proposed computational scheme, and the SPN operator enables additional improvements
Clerc, T., E-mail: thomas.clerc2@gmail.com [Institut de Génie Nucléaire, P.O. Box 6079, Station “Centre-Ville”, Montréal, Qc., Canada H3C 3A7 (Canada); Hébert, A., E-mail: alain.hebert@polymtl.ca [Institut de Génie Nucléaire, P.O. Box 6079, Station “Centre-Ville”, Montréal, Qc., Canada H3C 3A7 (Canada); Leroyer, H.; Argaud, J.P.; Bouriquet, B.; Ponçot, A. [Électricité de France, R and D, SINETICS, 1 Av. du Général de Gaulle, 92141 Clamart (France)
2014-07-01
Highlights: • We present a computational scheme for the determination of reflector properties in a PWR. • The approach is based on the minimization of a functional. • We use a data assimilation method or a parametric complementarity principle. • The reference target is a solution obtained with the method of characteristics. • The simplified flux solution is based on diffusion theory or on the simplified Pn method. - Abstract: This paper presents a computational scheme for the determination of equivalent 2D multi-group spatially dependant reflector parameters in a Pressurized Water Reactor (PWR). The proposed strategy is to define a full-core calculation consistent with a reference lattice code calculation such as the Method Of Characteristics (MOC) as implemented in APOLLO2 lattice code. The computational scheme presented here relies on the data assimilation module known as “Assimilation de données et Aide à l’Optimisation (ADAO)” of the SALOME platform developed at Électricité De France (EDF), coupled with the full-core code COCAGNE and with the lattice code APOLLO2. A first code-to-code verification of the computational scheme is made using the OPTEX reflector model developed at École Polytechnique de Montréal (EPM). As a result, we obtain 2D multi-group, spatially dependant reflector parameters, using both diffusion or SP{sub N} operators. We observe important improvements of the power discrepancies distribution over the core when using reflector parameters computed with the proposed computational scheme, and the SP{sub N} operator enables additional improvements.
1 - Description of problem or function: KENO is a multigroup, Monte Carlo criticality code containing a special geometry package which allows easy description of systems composed of cylinders, spheres, and cuboids (rectangular parallelepipeds) arranged in any order with only one restriction. They cannot be rotated or translated. Each geometrical region must be described as completely enclosing all regions interior to it. For systems not describable using this special geometry package, the program can use the generalized geometry package (GEOM) developed for the O5R Monte Carlo code. It allows any system that can be described by a collection of planes and/or quadratic surfaces, arbitrarily oriented and intersecting in arbitrary fashion. The entire problem can be mocked up in generalized geometry, or one generalized geometry unit or box type can be used alone or in combination with standard KENO units or box types. Rectangular arrays of fissile units are allowed with or without external reflector regions. Output from KENO consists of keff for the system plus an estimate of its standard deviation and the leakage, absorption, and fissions for each energy group plus the totals for all groups. Flux as a function of energy group and region and fission densities as a function of region are optional output. KENO-4: Added features include a neutron balance edit, PICTURE routines to check the input geometry, and a random number sequencing subroutine written in FORTRAN-4. 2 - Method of solution: The scattering treatment used in KENO assumes that the differential neutron scattering cross section can be represented by a P1 Legendre polynomial. Absorption of neutrons in KENO is not allowed. Instead, at each collision point of a neutron tracking history the weight of the neutron is reduced by the absorption probability. When the neutron weight has been reduced below a specified point for the region in which the collision occurs, Russian roulette is played to determine if the
Brinkman, Daniel
2013-05-01
We present and discuss a mathematical model for the operation of bilayer organic photovoltaic devices. Our model couples drift-diffusion-recombination equations for the charge carriers (specifically, electrons and holes) with a reaction-diffusion equation for the excitons/polaron pairs and Poisson\\'s equation for the self-consistent electrostatic potential. The material difference (i.e. the HOMO/LUMO gap) of the two organic substrates forming the bilayer device is included as a work-function potential. Firstly, we perform an asymptotic analysis of the scaled one-dimensional stationary state system: (i) with focus on the dynamics on the interface and (ii) with the goal of simplifying the bulk dynamics away from the interface. Secondly, we present a two-dimensional hybrid discontinuous Galerkin finite element numerical scheme which is very well suited to resolve: (i) the material changes, (ii) the resulting strong variation over the interface, and (iii) the necessary upwinding in the discretization of drift-diffusion equations. Finally, we compare the numerical results with the approximating asymptotics. © 2013 World Scientific Publishing Company.
Najafi, Amin
2014-05-01
Using the Monte Carlo simulations, we have calculated mean-square fluctuations in statistical mechanics, such as those for colloids energy configuration are set on square 2D periodic substrates interacting via a long range screened Coulomb potential on any specific and fixed substrate. Random fluctuations with small deviations from the state of thermodynamic equilibrium arise from the granular structure of them and appear as thermal diffusion with Gaussian distribution structure as well. The variations are showing linear form of the Fluctuation-Dissipation Theorem on the energy of particles constitutive a canonical ensemble with continuous diffusion process of colloidal particle systems. The noise-like variation of the energy per particle and the order parameter versus the Brownian displacement of sum of large number of random steps of particles at low temperatures phase are presenting a markovian process on colloidal particles configuration, too.
Using the Monte Carlo simulations, we have calculated mean-square fluctuations in statistical mechanics, such as those for colloids energy configuration are set on square 2D periodic substrates interacting via a long range screened Coulomb potential on any specific and fixed substrate. Random fluctuations with small deviations from the state of thermodynamic equilibrium arise from the granular structure of them and appear as thermal diffusion with Gaussian distribution structure as well. The variations are showing linear form of the Fluctuation-Dissipation Theorem on the energy of particles constitutive a canonical ensemble with continuous diffusion process of colloidal particle systems. The noise-like variation of the energy per particle and the order parameter versus the Brownian displacement of sum of large number of random steps of particles at low temperatures phase are presenting a markovian process on colloidal particles configuration, too.
Developments in MRI have made it possible to use diffusion-weighted MRI, perfusion MRI and proton MR spectroscopy (MRS) to study lesions in the brain. We evaluated whether these techniques provide useful, complementary information for grading gliomas, in comparison with conventional MRI. We studied 17 patients with histologically verified gliomas, adding multivoxel proton MRS, echoplanar diffusion and perfusion MRI the a routine MRI examination. The maximum relative cerebral blood volume (CBV), minimum apparent diffusion coefficient (ADC) and metabolic peak area ratios in proton MRS were calculated in solid parts of tumours on the same slice from each imaging data set. The mean minimum ADC of the 13 high-grade gliomas (0.92±0.27 x 10-3 mm2/s) was lower than that of the four low-grade gliomas (1.28±0.15 x 10-3 mm2/s) (P<0.05). Means of maximum choline (Cho)/N-acetylaspartate (NAA), Cho/creatine (Cr), Cho/Cr in normal brain (Cr-n) and minimum NAA/Cr ratios were 5.90±2.62, 4.73±2.22, 2.66±0.68 and 0.40±0.06, respectively, in the high-grade gliomas, and 1.65±1.37, 1.84±1.20, 1.61±1.29 and 1.65±1.61, respectively, in the low-grade gliomas. Significant differences were found on spectroscopy between the high- and low-grade gliomas (P<0.05). Mean maximum relative CBV in the high-grade gliomas (6.10±3.98) was higher than in the low-grade gliomas (1.74±0.57) (P<0.05). Echoplanar diffusion, perfusion MRI and multivoxel proton MRS can offer diagnostic information, not available with conventional MRI, in the assessment of glioma grade. (orig.)
Multigroup albedo method applied to gamma radiation shielding
The Albedo method, when applied to shielding calculations, is characterized by following the radiation through the materials, determining the reflected, absorbed and transmitted fractions of the incident current, independently of flux calculations. The excellent results obtained to neutron shielding cases in which the diffusion approximation could be applied motivated this work, where the method was applied in order to develop a multigroup and multilayered algorithm. A gamma radiation shielding simulation was carried out to a system constituted by three infinite slabs of varied materials and six energy groups. The results obtained by Albedo Method were the same generated by ANISN, a consecrated deterministic nuclear code. Concludingly, this work demonstrates the validity of Albedo Method to gamma radiation shielding analysis through its agreement with the full Transport Equation. (author)
Wells, Nathan P [Los Alamos National Laboratory; Lessard, Guillaume A [Los Alamos National Laboratory; Phipps, Marry E [Los Alamos National Laboratory; Goodwin, Peter M [Los Alamos National Laboratory; Werner, James H [Los Alamos National Laboratory; Lidke, Diane S [UNM; Wilson, Bridget S [UNM
2008-01-01
The ability to follow and observe single molecules as they function in live cells would represent a major milestone for molecular-cellular biology. Here we present a tracking microscope that is able to track quantum dots in 3 dimensions and simultaneously record time-resolved emission statistics from a single dot. This innovative microscopy approach is based on four spatial filters and closed loop feedback to constantly keep a single quantum dot in the focal spot. Using this microscope, we demonstrate the ability to follow quantum dot-labeled IgE antibodies bound to Fc{epsilon}Rl membrane receptors in live RBL-2H3 cells. The results are consistent with prior studies of 2 dimensional membrane diffusion (Andrews et al., Nat. Cell Biol., 10, 955, 2008). In addition, the microscope captures motion in the axial (Z) direction, which permits tracking of diffusing receptors relative the 'hills and valley' of the dynamically changing membrane landscape. Our novel approach is uniquely capable of following single-molecule dynamics on live cells with 3 dimensional spatial resolution.
Parallel computation of multigroup reactivity coefficient using iterative method
One of the research activities to support the commercial radioisotope production program is a safety research target irradiation FPM (Fission Product Molybdenum). FPM targets form a tube made of stainless steel in which the nuclear degrees of superimposed high-enriched uranium. FPM irradiation tube is intended to obtain fission. The fission material widely used in the form of kits in the world of nuclear medicine. Irradiation FPM tube reactor core would interfere with performance. One of the disorders comes from changes in flux or reactivity. It is necessary to study a method for calculating safety terrace ongoing configuration changes during the life of the reactor, making the code faster became an absolute necessity. Neutron safety margin for the research reactor can be reused without modification to the calculation of the reactivity of the reactor, so that is an advantage of using perturbation method. The criticality and flux in multigroup diffusion model was calculate at various irradiation positions in some uranium content. This model has a complex computation. Several parallel algorithms with iterative method have been developed for the sparse and big matrix solution. The Black-Red Gauss Seidel Iteration and the power iteration parallel method can be used to solve multigroup diffusion equation system and calculated the criticality and reactivity coeficient. This research was developed code for reactivity calculation which used one of safety analysis with parallel processing. It can be done more quickly and efficiently by utilizing the parallel processing in the multicore computer. This code was applied for the safety limits calculation of irradiated targets FPM with increment Uranium
Coremelt-2D Code for Analysis of Severe Accidents in a Sodium Fast Reactor
In the paper there is a description of COREMELT-2D code designed for carrying out coupled two-dimensional analysis of neutronic and thermohydraulic transients, which may occur in the core of sodium cooled fast reactor (SFR), including severe accidents resulting in damage of SFR core and relocation of its components with the change of their aggregative state, namely: boiling and condensation of coolant, damage and melting of fuel element claddings and fuel, relocation of molten core components, thermal interaction of fuel and coolant and freezing of steel and fuel. So, COREMELT-2D code is capable of analyzing all stages of ULOF accident up to expansion phase characterized by the intensive interaction of molten fuel and sodium. Modular structure of COREMELT-2D code consisting of thermohydraulic module COREMELT and neutronic module RADAR is presented. Preservation equations are solved in COREMELT module in two-dimensional cylindrical R-Z geometry in porous body approximation. RADAR module is used for solving multi-group neutron diffusion equation in R-Z and X-Y geometry. Application of the code for solving dynamics tasks with rather rapid changes of neutron constants requires efficient unit for constants preparation. For this purpose, steady state analysis TRIGEX code (HEX-Z geometry) is used, which includes the program of nuclear data preparation CONSYST connected to the ABBN-93 group constants library. In the paper presented are the results of comparative analytical studies on ULOF beyond design severe accident as applied to the BN-1200 reactor design made by COREMELT-2D code and by its previous version based on neutron kinetics point model. The results of analysis make it possible to evaluate the effect of space-time changes of reactor neutronics caused by sodium removal from the core as a result of sodium boiling. (author)
Raghib, Michael; Levin, Simon; Kevrekidis, Ioannis
2010-05-01
2. The long-time behavior of the msd of the centroid walk scales linearly with time for naïve groups (diffusion), but shows a sharp transition to quadratic scaling (advection) for informed ones. These observations suggest that the mesoscopic variables of interest are the magnitude of the drift, the diffusion coefficient and the time-scales at which the anomalous and the asymptotic behavior respectively dominate transport, the latter being linked to the time scale at which the group reaches a decision. In order to estimate these summary statistics from the msd, we assumed that the configuration centroid follows an uncoupled Continuous Time Random Walk (CTRW) with smooth jump and waiting time pdf's. The mesoscopic transport equation for this type of random walk corresponds to an Advection-Diffusion Equation with Memory (ADEM). The introduction of the memory, and thus non-Markovian effects, is necessary in order to correctly account for the two time scales present. Although we were not able to calculate the memory directly from the individual-level rules, we show that it can estimated from a single, relatively short, simulation run using a Mittag-Leffler function as template. With this function it is possible to predict accurately the behavior of the msd, as well as the full pdf for the position of the centroid. The resulting ADEM is self-consistent in the sense that transport parameters estimated from the memory via a Kubo relationship coincide with those estimated from the moments of the jump size pdf of the associated CTRW for a large number of group sizes, proportions of informed individuals, and degrees of bias along the preferred direction. We also discuss the phase diagrams for the transport coefficients estimated from this method, where we notice velocity-precision trade-offs, where precision is a measure of the deviation of realized group orientations with respect to the informed direction. We also note that the time scale to collective decision is invariant
Establishment of multi-groups atomic parametric database
A method is given to establish multi-groups atomic parametric database for multi-groups radiation transport equation. The equation can be used in calculating the X-ray radiation from plasma. Several methods to check the calculation of the multi-groups database is also given. A 20 groups atomic parametric database of Au element with grid of 20 (plasma density) x 20 (electron temperature) x 20 (photon temperature) is given too
胡法龙; 周灿灿; 李潮流; 徐红军; 周凤鸣; 司兆伟
2012-01-01
Based on current acquisition modes of MRIL-Prime NMR logging tool, 2D NMR signals could be obtained by the combination of logging data from different modes, then the fluid properties in complicated reservoirs could be distinguished by 2D diflusion-relaxation NMR logging data distribution of pore fluids, generated by multi-echotrain joint inversion. In comparison with ID NMR logging, this method could increase fluid information in diffusion regime, separate oil, gas and water signals in 2D space and enhance the identification capacity of fluid properties from NMR logging. The 2D NMR logging in the multi-echowave interval was applied in the oil pays in Well A and the water layers in Well B in the Nanpu Sag by MRIL-Prime tool, and the interpretation matches the well testing result. It indicates that 2D NMR logging has advantages on the identification of light oil, and fluids in macropore reservoirs than ID NMR logging.%基于MRIL-Prime核磁共振测井仪器现有采集模式,将不同采集模式测井信息进行组合后获得二维核磁共振信号,利用多回波串联合反演技术获得孔隙流体弛豫-扩散的二维核磁共振信息分布,用以识别复杂储集层流体性质.相对一维核磁共振测井,该流体性质识别方法增加了扩散域流体信息,可以在二维空间内将油、气、水信号分离,提高核磁共振测井流体性质识别能力.利用MRIL-Prime仪器对南堡凹陷A井油层和B井水层进行多回波间隔的二维核磁共振测井试验,解释结果与试油结果相吻合,说明二维核磁共振测井在轻质油识别和大孔隙储集层流体识别方面相对一维核磁共振测井技术有明显优势.
CASSANDRE, 2-D Reactor Dynamic FEM Program with Thermohydraulic Feedback
1 - Description of program or function: CASSANDRE is a two-dimensional (x-y or r-z) finite-elements neutronics code with thermohydraulic feedback for reactor dynamics prior to the disassembly phase. The code was conceived in order to be coupled with any thermohydraulics module, although thermohydraulics feedback is only considered in r-z geometry. In the steady state, criticality search is possible either by control-rod insertion or by homogeneous poisoning of the coolant. 2 - Method of solution: The program uses multigroup diffusion theory. Its main characteristics are the use of a generalized quasi-static model, the use of a flexible multigroup point-kinetics algorithm allowing for spectral matching, and the use of a finite elements description. 3 - Restrictions on the complexity of the problem: The user must prepare a cross section library
For satisfaction of future global customer needs, dedicated efforts are being coordinated internationally and pursued continuously at AREVA NP. The currently ongoing CONVERGENCE project is committed to the development of the ARCADIAR next generation core simulation software package. ARCADIAR will be put to global use by all AREVA NP business regions, for the entire spectrum of core design processes, licensing computations and safety studies. As part of the currently ongoing trend towards more sophisticated neutronics methodologies, an SP3 nodal transport concept has been developed for ARTEMIS which is the steady-state and transient core simulation part of ARCADIAR. For enabling a high computational performance, the SPN calculations are accelerated by applying multi-level coarse mesh re-balancing. In the current implementation, SP3 is about 1.4 times as expensive computationally as SP1 (diffusion). The developed SP3 solution concept is foreseen as the future computational workhorse for many-group 3D pin-by-pin full core computations by ARCADIAR. With the entire numerical workload being highly parallelizable through domain decomposition techniques, associated CPU-time requirements that adhere to the efficiency needs in the nuclear industry can be expected to become feasible in the near future. The accuracy enhancement obtainable by using SP3 instead of SP1 has been verified by a detailed comparison of ARTEMIS 16-group pin-by-pin SPN results with KAERI's DeCart reference results for the 2D pin-by-pin Purdue UO2/MOX benchmark. This article presents the accuracy enhancement verification and quantifies the achieved ARTEMIS-SP3 computational performance for a number of 2D and 3D multi-group and multi-box (up to pin-by-pin) core computations. (authors)
A Note on Multigroup Comparisons Using SAS PROC CALIS
Jones-Farmer, L. Allison; Pitts, Jennifer P.; Rainer, R. Kelly
2008-01-01
Although SAS PROC CALIS is not designed to perform multigroup comparisons, it is believed that SAS can be "tricked" into doing so for groups of equal size. At present, there are no comprehensive examples of the steps involved in performing a multigroup comparison in SAS. The purpose of this article is to illustrate these steps. We demonstrate…
Cross section probability tables in multi-group transport calculations
The use of cross section probability tables in multigroup transport calculations is presented. Emphasis is placed on how probability table parameters are generated in a multigroup cross section processor and how existing transport codes must be modifed to use them. In order to illustrate the accuracy obtained by using probability tables, results are presented for a variety of neutron and photon transport problems
In multigroup calculations of reactivity and sensitivity coefficients, methodical errors can appear if the interdependence of multigroup constants is not taken into account. For this effect to be taken into account, so-called implicit components of the aforementioned values are introduced. A simple technique for computing these values is proposed. It is based on the use of subgroup parameters.
Multigroup neutron dose calculations for proton therapy
We have developed tools for the preparation of coupled multigroup proton/neutron cross section libraries. Our method is to use NJOY to process evaluated nuclear data files for incident particles below 150 MeV and MCNPX to produce data for higher energies. We modified the XSEX3 program of the MCNPX code system to produce Legendre expansions of scattering matrices generated by sampling the physics models that are comparable to the output of the GROUPR routine of NJOY. Our code combines the low and high energy scattering data with user input stopping powers and energy deposition cross sections that we also calculated using MCNPX. Our code also calculates momentum transfer coefficients for the library and optionally applies an energy straggling model to the scattering cross sections and stopping powers. The motivation was initially for deterministic solution of space radiation shielding calculations using Attila, but noting that proton therapy treatment planning may neglect secondary neutron dose assessments because of difficulty and expense, we have also investigated the feasibility of multi group methods for this application. We have shown that multigroup MCNPX solutions for secondary neutron dose compare well with continuous energy solutions and are obtainable with less than half computational cost. This efficiency comparison neglects the cost of preparing the library data, but this becomes negligible when distributed over many multi group calculations. Our deterministic calculations illustrate recognized obstacles that may have to be overcome before discrete ordinates methods can be efficient alternatives for proton therapy neutron dose calculations
Multigroup neutron dose calculations for proton therapy
Kelsey Iv, Charles T [Los Alamos National Laboratory; Prinja, Anil K [Los Alamos National Laboratory
2009-01-01
We have developed tools for the preparation of coupled multigroup proton/neutron cross section libraries. Our method is to use NJOY to process evaluated nuclear data files for incident particles below 150 MeV and MCNPX to produce data for higher energies. We modified the XSEX3 program of the MCNPX code system to produce Legendre expansions of scattering matrices generated by sampling the physics models that are comparable to the output of the GROUPR routine of NJOY. Our code combines the low and high energy scattering data with user input stopping powers and energy deposition cross sections that we also calculated using MCNPX. Our code also calculates momentum transfer coefficients for the library and optionally applies an energy straggling model to the scattering cross sections and stopping powers. The motivation was initially for deterministic solution of space radiation shielding calculations using Attila, but noting that proton therapy treatment planning may neglect secondary neutron dose assessments because of difficulty and expense, we have also investigated the feasibility of multi group methods for this application. We have shown that multigroup MCNPX solutions for secondary neutron dose compare well with continuous energy solutions and are obtainable with less than half computational cost. This efficiency comparison neglects the cost of preparing the library data, but this becomes negligible when distributed over many multi group calculations. Our deterministic calculations illustrate recognized obstacles that may have to be overcome before discrete ordinates methods can be efficient alternatives for proton therapy neutron dose calculations.
Cascos, V; Martínez-Coronado, R; Alonso, J A; Fernández-Díaz, M T
2014-06-25
Sr0.7Ho0.3CoO3-δ oxide has been recently described as an excellent cathode material (1274 mW cm(-2) at 850 °C with pure H2 as fuel1) for solid oxide fuel cells (SOFCs) with LSGM as electrolyte. In this work, we describe a detailed study of its crystal structure conducted to find out the correlation between the excellent performance as a cathode and the structural features. The tetragonal crystal structure (e.g., I4/mmm) basically contains layers of octahedrally coordinated Co2O6 units alternated with layers of Co1O4 tetrahedra sharing corners. An "in situ" neutron power diffraction (NPD) experiment, between 25 and 800 °C, reveals the presence of a high oxygen deficiency affecting O4 oxygen atoms, with large displacement factors that suggest a large lability and mobility. Difference Fourier maps allow the visualization at high temperatures of the 2D diffusion pathways within the tetrahedral layers, where O3 and O4 oxygens participate. The measured thermal expansion coefficient is 16.61 × 10(-6) K(-1) between 300 and 850 °C, exhibiting an excellent chemical compatibility with the electrolyte. PMID:24873238
Multigroup Free-atom Doppler-broadening Approximation. Theory
Gray, Mark Girard [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-11-06
Multigroup cross sections at a one target temperature can be Doppler-broadened to multigroup cross sections at a higher target temperature by matrix multiplication if the group structure suf- ficiently resolves the original temperature continuous energy cross section. Matrix elements are the higher temperature group weighted averages of the integral over the lower temperature group boundaries of the free-atom Doppler-broadening kernel. The results match theory for constant and 1/v multigroup cross sections at 618 lanl group structure resolution.
Modelling and simulations of macroscopic multi-group pedestrian flow
Mahato, Naveen K; Tiwari, Sudarshan
2016-01-01
We consider a multi-group microscopic model for pedestrian flow describing the behaviour of large groups. It is based on an interacting particle system coupled to an eikonal equation. Hydrodynamic multi-group models are derived from the underlying particle system as well as scalar multi-group models. The eikonal equation is used to compute optimal paths for the pedestrians. Particle methods are used to solve the macroscopic equations. Numerical test cases are investigated and the models and, in particular, the resulting evacuation times are compared for a wide range of different parameters.
Multigroup fast fission factor treatment in a thermal reactor lattice
A multigroup procedure for the studies of the fast fission effects in the thermal reactor lattice and the calculation of the fast fission factor was developed. The Monte Carlo method and the multigroup procedure were combined to calculate the fast neutron interaction and backscattering effects in a reactor lattice. A set of probabilities calculated by the Monte Carlo method gives a multigroup spectrum of neutrons coming from the moderator and entering the fuel element. Thus, the assumptions adopted so far in defining and calculating the fast fission factor has been avoided, and a new definition including the backscattering and interaction effects in a reactor lattice have been given. (author)
Multigroup cross section library; WIMS library
The WIMS library has been extensively used in thermal reactor calculations. This multigroup constants library was originally developed from the UKNDL in the late 60's and has been updated in 1986. This library has been distributed with the WIMS-D code by NEA data bank. The references to WIMS library in literature are the 'old' which is the original as developed by the AEA Winfrith and the 'new' which is the current 1986 WIMS library. IAEA has organised a CRP where a new and fully updated WIMS library will soon be available. This paper gives an overview of the definitions of the group constants that go into any basic nuclear data library used for reactor calculations. This paper also outlines the contents of the WIMS library and some of its shortcomings
Multi-group neutron transport theory
Multi-group neutron transport theory. In the paper the general theory of the application of the K. M. Case method to N-group neutron transport theory in plane geometry is given. The eigenfunctions (distributions) for the system of Boltzmann equations have been derived and the completeness theorem has been proved. By means of general solution two examples important for reactor and shielding calculations are given: the solution of a critical and albedo problem for a slab. In both cases the system of singular integral equations for expansion coefficients into a full set of eigenfunction distributions has been reduced to the system of Fredholm-type integral equations. Some results can be applied also to some spherical problems. (author)
Application of equivalence methods on Monte Carlo method based homogenization multi-group constants
The multi-group constants generated via continuous energy Monte Carlo method do not satisfy the equivalence between reference calculation and diffusion calculation applied in reactor core analysis. To the satisfaction of the equivalence theory, general equivalence theory (GET) and super homogenization method (SPH) were applied to the Monte Carlo method based group constants, and a simplified reactor core and C5G7 benchmark were examined with the Monte Carlo constants. The results show that the calculating precision of group constants is improved, and GET and SPH are good candidates for the equivalence treatment of Monte Carlo homogenization. (authors)
Ventura, P; Li, L; Sofia, S; Basu, S; Demarque, P
2009-01-01
Understanding the reasons of the cyclic variation of the total solar irradiance is one of the most challenging targets of modern astrophysics. These studies prove to be essential also for a more climatologic issue, associated to the global warming. Any attempt to determine the solar components of this phenomenon must include the effects of the magnetic field, whose strength and shape in the solar interior are far from being completely known. Modelling the presence and the effects of a magnetic field requires a 2D approach, since the assumption of radial symmetry is too limiting for this topic. We present the structure of a 2D evolution code that was purposely designed for this scope; rotation, magnetic field and turbulence can be taken into account. Some preliminary results are presented and commented.
Benchmark Calculation for the VHTR 2-D Core by Using the DeCART Code
Cho, Jin-Young; Kim, Kang-Seog; Lee, Chung-Chan [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
2006-07-01
Recently, a hexagonal module has been equipped to the DeCART (Deterministic Core Analysis based on Ray Tracing) whole core code for a hexagonal core analysis. The equipment includes a ray tracing module to solve the 2-D whole-core transport problem and a multi-group CMFD module to perform an efficient transport calculation. In this paper, the capability of the DeCART hexagonal module is examined by solving VHTR core problems.
Benchmark Calculation for the VHTR 2-D Core by Using the DeCART Code
Recently, a hexagonal module has been equipped to the DeCART (Deterministic Core Analysis based on Ray Tracing) whole core code for a hexagonal core analysis. The equipment includes a ray tracing module to solve the 2-D whole-core transport problem and a multi-group CMFD module to perform an efficient transport calculation. In this paper, the capability of the DeCART hexagonal module is examined by solving VHTR core problems
Lotsch, Bettina V.
2015-07-01
Graphene's legacy has become an integral part of today's condensed matter science and has equipped a whole generation of scientists with an armory of concepts and techniques that open up new perspectives for the postgraphene area. In particular, the judicious combination of 2D building blocks into vertical heterostructures has recently been identified as a promising route to rationally engineer complex multilayer systems and artificial solids with intriguing properties. The present review highlights recent developments in the rapidly emerging field of 2D nanoarchitectonics from a materials chemistry perspective, with a focus on the types of heterostructures available, their assembly strategies, and their emerging properties. This overview is intended to bridge the gap between two major—yet largely disjunct—developments in 2D heterostructures, which are firmly rooted in solid-state chemistry or physics. Although the underlying types of heterostructures differ with respect to their dimensions, layer alignment, and interfacial quality, there is common ground, and future synergies between the various assembly strategies are to be expected.
A code to calculate multigroup constants for fast neutron reactor
KQCS-2 code is a new improved version of KQCS code, which was designed to calculate multigroup constants for fast neutron reactor. The changes and improvements on KQCS are described in this paper. (author)
Consistent Multigroup Theory Enabling Accurate Course-Group Simulation of Gen IV Reactors
Rahnema, Farzad; Haghighat, Alireza; Ougouag, Abderrafi
2013-11-29
The objective of this proposal is the development of a consistent multi-group theory that accurately accounts for the energy-angle coupling associated with collapsed-group cross sections. This will allow for coarse-group transport and diffusion theory calculations that exhibit continuous energy accuracy and implicitly treat cross- section resonances. This is of particular importance when considering the highly heterogeneous and optically thin reactor designs within the Next Generation Nuclear Plant (NGNP) framework. In such reactors, ignoring the influence of anisotropy in the angular flux on the collapsed cross section, especially at the interface between core and reflector near which control rods are located, results in inaccurate estimates of the rod worth, a serious safety concern. The scope of this project will include the development and verification of a new multi-group theory enabling high-fidelity transport and diffusion calculations in coarse groups, as well as a methodology for the implementation of this method in existing codes. This will allow for a higher accuracy solution of reactor problems while using fewer groups and will reduce the computational expense. The proposed research represents a fundamental advancement in the understanding and improvement of multi- group theory for reactor analysis.
Van Geemert, Rene [AREVA, AREVA NP, Erlangen (Germany)
2008-07-01
For satisfaction of future global customer needs, dedicated efforts are being coordinated internationally and pursued continuously at AREVA NP. The currently ongoing CONVERGENCE project is committed to the development of the ARCADIA{sup R} next generation core simulation software package. ARCADIA{sup R} will be put to global use by all AREVA NP business regions, for the entire spectrum of core design processes, licensing computations and safety studies. As part of the currently ongoing trend towards more sophisticated neutronics methodologies, an SP{sub 3} nodal transport concept has been developed for ARTEMIS which is the steady-state and transient core simulation part of ARCADIA{sup R}. For enabling a high computational performance, the SP{sub N} calculations are accelerated by applying multi-level coarse mesh re-balancing. In the current implementation, SP{sub 3} is about 1.4 times as expensive computationally as SP{sub 1} (diffusion). The developed SP{sub 3} solution concept is foreseen as the future computational workhorse for many-group 3D pin-by-pin full core computations by ARCADIA{sup R}. With the entire numerical workload being highly parallelizable through domain decomposition techniques, associated CPU-time requirements that adhere to the efficiency needs in the nuclear industry can be expected to become feasible in the near future. The accuracy enhancement obtainable by using SP{sub 3} instead of SP{sub 1} has been verified by a detailed comparison of ARTEMIS 16-group pin-by-pin SP{sub N} results with KAERI's DeCart reference results for the 2D pin-by-pin Purdue UO{sub 2}/MOX benchmark. This article presents the accuracy enhancement verification and quantifies the achieved ARTEMIS-SP{sub 3} computational performance for a number of 2D and 3D multi-group and multi-box (up to pin-by-pin) core computations. (authors)
Activated sludge model No. 2d, ASM2d
Henze, M.
1999-01-01
The Activated Sludge Model No. 2d (ASM2d) presents a model for biological phosphorus removal with simultaneous nitrification-denitrification in activated sludge systems. ASM2d is based on ASM2 and is expanded to include the denitrifying activity of the phosphorus accumulating organisms (PAOs...
Radiation Transport for Explosive Outflows: A Multigroup Hybrid Monte Carlo Method
Wollaeger, Ryan T; Graziani, Carlo; Couch, Sean M; Jordan, George C; Lamb, Donald Q; Moses, Gregory A
2013-01-01
We explore the application of Implicit Monte Carlo (IMC) and Discrete Diffusion Monte Carlo (DDMC) to radiation transport in strong fluid outflows with structured opacity. The IMC method of Fleck & Cummings is a stochastic computational technique for nonlinear radiation transport. IMC is partially implicit in time and may suffer in efficiency when tracking Monte Carlo particles through optically thick materials. The DDMC method of Densmore accelerates an IMC computation where the domain is diffusive. Recently, Abdikamalov extended IMC and DDMC to multigroup, velocity-dependent neutrino transport with the intent of modeling neutrino dynamics in core-collapse supernovae. Densmore has also formulated a multifrequency extension to the originally grey DDMC method. In this article we rigorously formulate IMC and DDMC over a high-velocity Lagrangian grid for possible application to photon transport in the post-explosion phase of Type Ia supernovae. The method described is suitable for a large variety of non-mono...
A general multigroup formulation of the analytic nodal method
In this paper the theoretical description of an alternative approach to the Analytic Nodal Method is given, in which a full multigroup formulations is developed. This approach differs from the well known QUANDRY approach in three aspects. Firstly, a notation which is more widely used in Quantum Mechanics has been adopted to enable a clear and concise presentation of this multigroup approach. A basis transformation is then used to reduce the directional equations to a scalar form and finally, Green's secondary identity is used to rewrite each of the resulting scalar equations in a form which eventually leads to a response matrix, as opposed to using classical methods to actually solve the coupled multigroup directional equations
AMPX-77, Modular System for Coupled Neutron-Gamma Multigroup Cross-Sections from ENDF/B-5
1 - Description of program or function: The AMPX system is a system of computer programs (modules) capable of producing coupled multigroup neutron-gamma-ray cross section sets. The system is one of the standards for producing multigroup neutron, gamma-ray production, gamma-ray interaction, and coupled neutron-gamma cross-section sets from ENDF data. AMPX-produced cross sections can be used directly with a variety of diffusion theory, discrete ordinates, and Monte Carlo radiation transport computer codes. A one-dimensional Sn calculation capability is provided for general use and for cross section collapsing. Treatments are included for resonance self-shielding effects. 2 - Method of solution: The system includes a full range of features needed to: (1) produce multigroup neutron, gamma-ray production, and/or gamma-ray interaction cross-section data, (2) resonance self-shield, (3) spectrally collapse, (4) convert cross-section libraries from one format to another format, (5) execute a one- dimensional (1-D) discrete-ordinates calculation, and (6) perform miscellaneous cross section-operations. 3 - Restrictions on the complexity of the problem: The principal restriction is the availability of adequate core storage. All large modules are variably dimensioned. Certain modules will automatically use external storage (disk,tape), if in-core storage is inadequate. While these procedures are of little consequence on today's large computers with 'virtual memory' capabilities, they can be important when small-core PC's or workstations are used
Smith, L.A.; Gallmeier, F.X. [Oak Ridge Institute for Science and Energy, TN (United States); Gehin, J.C. [Oak Ridge National Lab., TN (United States)] [and others
1995-05-01
The FOEHN critical experiment was analyzed to validate the use of multigroup cross sections and Oak Ridge National Laboratory neutronics computer codes in the design of the Advanced Neutron Source. The ANSL-V 99-group master cross section library was used for all the calculations. Three different critical configurations were evaluated using the multigroup KENO Monte Carlo transport code, the multigroup DORT discrete ordinates transport code, and the multigroup diffusion theory code VENTURE. The simple configuration consists of only the fuel and control elements with the heavy water reflector. The intermediate configuration includes boron endplates at the upper and lower edges of the fuel element. The complex configuration includes both the boron endplates and components in the reflector. Cross sections were processed using modules from the AMPX system. Both 99-group and 20-group cross sections were created and used in two-dimensional models of the FOEHN experiment. KENO calculations were performed using both 99-group and 20-group cross sections. The DORT and VENTURE calculations were performed using 20-group cross sections. Because the simple and intermediate configurations are azimuthally symmetric, these configurations can be explicitly modeled in R-Z geometry. Since the reflector components cannot be modeled explicitly using the current versions of these codes, three reflector component homogenization schemes were developed and evaluated for the complex configuration. Power density distributions were calculated with KENO using 99-group cross sections and with DORT and VENTURE using 20-group cross sections. The average differences between the measured values and the values calculated with the different computer codes range from 2.45 to 5.74%. The maximum differences between the measured and calculated thermal flux values for the simple and intermediate configurations are {approx} 13%, while the average differences are < 8%.
Demange, D.; Beauchene, P.; Casulleras, R.; Bejet, M. [ONERA, 92 - Chatillon (France); Maillet, D.; Sanson, O. [Lemta (France)
1996-12-31
A new experimental method of simultaneous measurement of thermal diffusivity along the two main directions of thin composite materials with a ceramic-based matrix has been developed by the ONERA, the French national office of aerospace studies and research. The principle of this method, derived from the `flash` method consists in the heterogeneous insolation of one face of a cylindrical sample (central spot or ring) in order to analyze the thermal transfers along the axial and radial directions of the sample. Experimental development are in progress and will be integrated to a flash diffusion-meter in operation at the ONERA. (J.S.) 11 refs.
Multigroup Confirmatory Factor Analysis: Locating the Invariant Referent Sets
French, Brian F.; Finch, W. Holmes
2008-01-01
Multigroup confirmatory factor analysis (MCFA) is a popular method for the examination of measurement invariance and specifically, factor invariance. Recent research has begun to focus on using MCFA to detect invariance for test items. MCFA requires certain parameters (e.g., factor loadings) to be constrained for model identification, which are…
Lectures on 2D gravity and 2D string theory
This report the following topics: loops and states in conformal field theory; brief review of the Liouville theory; 2D Euclidean quantum gravity I: path integral approach; 2D Euclidean quantum gravity II: canonical approach; states in 2D string theory; matrix model technology I: method of orthogonal polynomials; matrix model technology II: loops on the lattice; matrix model technology III: free fermions from the lattice; loops and states in matrix model quantum gravity; loops and states in the C=1 matrix model; 6V model fermi sea dynamics and collective field theory; and string scattering in two spacetime dimensions
Application de la methode des sous-groupes au calcul Monte-Carlo multigroupe
Martin, Nicolas
effects of the scattering reaction consistent with the subgroup method. In this study, we generalize the Discrete Angle Technique, already proposed for homogeneous, multigroup cross sections, to isotopic cross sections on the form of probability tables. In this technique, the angular density is discretized into probability tables. Similarly to the cross-section case, a moment approach is used to compute the probability tables for the scattering cosine. (4) The introduction of a leakage model based on the B1 fundamental mode approximation. Unlike deterministic lattice packages, most Monte Carlo-based lattice physics codes do not include leakage models. However the generation of homogenized and condensed group constants (cross sections, diffusion coefficients) require the critical flux. This project has involved the development of a program into the DRAGON framework, written in Fortran 2003 and wrapped with a driver in C, the GANLIB 5. Choosing Fortran 2003 has permitted the use of some modern features, such as the definition of objects and methods, data encapsulation and polymorphism. The validation of the proposed code has been performed by comparison with other numerical methods: (1) The continuous-energy Monte Carlo method of the SERPENT code. (2) The Collision Probability (CP) method and the discrete ordinates (SN) method of the DRAGON lattice code. (3) The multigroup Monte Carlo code MORET, coupled with the DRAGON code. Benchmarks used in this work are representative of some industrial configurations encountered in reactor and criticality-safety calculations: (1)Pressurized Water Reactors (PWR) cells and assemblies. (2) Canada-Deuterium Uranium Reactors (CANDU-6) clusters. (3) Critical experiments from the ICSBEP handbook (International Criticality Safety Benchmark Evaluation Program).
Multi-group calculations for fast reactors
The paper deals with various causes of error in calculations. The first part sets out the mathematical approximations (diffusion approximation, Sn method, etc.), the numerical resolution methods (effect of integration step), the models used, and the implications of these various factors in the determination of the principal characteristics of a fast neutron reactor. The second part studies the effect on reactivity of variations of element cross-sections, using various fuels, in a reactor of rather hard spectrum. (author)
2D-hahmoanimaation toteuttamistekniikat
Smolander, Aku
2009-01-01
Opinnäytetyössä tutkitaan erilaisia 2D-hahmoanimaation toteuttamistekniikoita. Aluksi luodaan yleiskatsaus animoinnin historiaan ja tekniikoihin piirtämisestä mallintamiseen. Alkukatsauksen jälkeen tutkitaan 2D-hahmon suunnittelua ja liikkeitä koskevia sääntöjä. Hahmoanimaation liikkeissä huomionarvoisia asioita ovat muun muassa ajastus, liioittelu, ennakointi ja painovoima. Seuraavaksi perehdytään itse 2D-hahmoanimaation toteuttamistekniikoihin. Tavoitteena on selvittää, tutkia ja vertailla ...
Multigroup cross sections of resonant nuclei considering moderator mass differences
The multigroup constants library MGCL in the nuclear criticality safety evaluation code system JACS has been produced by the Bondarenko method to treat self-shielding effects. For estimating errors of this treatment, the multigroup cross sections of MGCL are compared with those obtained by precise treatment, i.e. with the weighted cross sections by ultra-fine spectra of neutron. The precise calculations are made for homogeneous mixtures of a resonant nucleus (235U, 238U, 239Pu, 240Pu, 242Pu or 56Fe) and a fictitious moderator nucleus with mass number 1, 12 or 200. The ultra-fine spectrum is calculated by the RABBLE code. Distinct differences are found in the self-shielding factors by comparisons between both treatments. Moreover, as the mass number increases, depressions of the self-shielding factor at the resonance peaks and its enhancements at the window of resonances are observed. (author)
Cyclotron radiation by a multi-group method
A multi-energy group technique is developed to study conditions under which cyclotron radiation emission can shift a Maxwellian electron distribution into a non-Maxwellian; and if the electron distribution is non-Maxwellian, to study the rate of cyclotron radiation emission as compared to that emitted by a Maxwellian having the same mean electron density and energy. The assumptions in this study are: the electrons should be in an isotropic medium and the magnetic field should be uniform. The multi-group technique is coupled into a multi-group Fokker-Planck computer code to study electron behavior under the influence of cyclotron radiation emission in a self-consistent fashion. Several non-Maxwellian distributions were simulated to compare their cyclotron emissions with the corresponding energy and number density equivalent Maxwellian distribtions
Multigroup-multiwaves Lisrel modeling in tourist satisfaction analysis
Cristina Bernini; Silvia Cagnone
2013-01-01
The paper analyzes the influence of tourist heterogeneity on the Tourist Local System Overall Satisfaction and its changes over time. We investigate two aspects: if different tourists segmented according to their trip motivation (seaside, conference and sport) show the same pattern of evaluation toward some relevant features of the TLS and if the evaluation scheme is dynamic. At this aim, a Multigroup-Multiwaves Lisrel model is estimated on a data set from the Tourist Satisfaction Survey, con...
Optimal calculational schemes for solving multigroup photon transport problem
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
Nuclear data and multigroup methods in fast reactor calculations
The work deals with fast reactor multigroup calculations, and the efficient treatment of basic nuclear data, which serves as raw material for the calculations. Its purpose is twofold: to build a computer code system that handles a large, detailed library of basic neutron cross section data, (such as ENDF/B-III) and yields a compact set of multigroup cross sections for reactor calculations; to use the code system for comparative analysis of different libraries, in order to discover basic uncertainties that still exist in the measurement of neutron cross sections, and to determine their influence upon uncertainties in nuclear calculations. A program named NANICK which was written in two versions is presented. The first handles the American basic data library, ENDF/B-III, while the second handles the German basic data library, KEDAK. The mathematical algorithm is identical in both versions, and only the file management is different. This program calculates infinitely diluted multigroup cross sections and scattering matrices. It is complemented by the program NASIF that calculates shielding factors from resonance parameters. Different versions of NASIF were written to handle ENDF/B-III or KEDAK. New methods for evaluating in reactor calculations the long term behavior of the neutron flux as well as its fine structure are described and an efficient calculation of the shielding factors from resonance parameters is offered. (B.G.)
Starting from the radiation transport equation for homogeneous, refractive lossy media, we derive the corresponding time-dependent multifrequency diffusion equations. Zeroth and first moments of the transport equation couple the energy density, flux and pressure tensor. The system is closed by neglecting the temporal derivative of the flux and replacing the pressure tensor by its diagonal analogue. The radiation equations are coupled to a diffusion equation for the matter temperature. We are interested in modeling heating and cooling of silica (SiO2), at possibly rapid rates. Hence, in contrast to related work, we retain the temporal derivative of the radiation field. We derive boundary conditions at a planar air-silica interface taking account of reflectivities obtained from the Fresnel relations that include absorption. The spectral dimension is discretized into a finite number of intervals leading to a system of multigroup diffusion equations. Three simulations are presented. One models cooling of a silica slab, initially at 2500 K, for 10 s. The other two are 1D and 2D simulations of irradiating silica with a CO2 laser, λ = 10.59 μm. In 2D, a laser beam (Gaussian profile, r0 = 0.5 mm for 1/e decay) shines on a disk (radius = 0.4, thickness = 0.4 cm).
Optoelectronics with 2D semiconductors
Mueller, Thomas
2015-03-01
Two-dimensional (2D) atomic crystals, such as graphene and layered transition-metal dichalcogenides, are currently receiving a lot of attention for applications in electronics and optoelectronics. In this talk, I will review our research activities on electrically driven light emission, photovoltaic energy conversion and photodetection in 2D semiconductors. In particular, WSe2 monolayer p-n junctions formed by electrostatic doping using a pair of split gate electrodes, type-II heterojunctions based on MoS2/WSe2 and MoS2/phosphorene van der Waals stacks, 2D multi-junction solar cells, and 3D/2D semiconductor interfaces will be presented. Upon optical illumination, conversion of light into electrical energy occurs in these devices. If an electrical current is driven, efficient electroluminescence is obtained. I will present measurements of the electrical characteristics, the optical properties, and the gate voltage dependence of the device response. In the second part of my talk, I will discuss photoconductivity studies of MoS2 field-effect transistors. We identify photovoltaic and photoconductive effects, which both show strong photoconductive gain. A model will be presented that reproduces our experimental findings, such as the dependence on optical power and gate voltage. We envision that the efficient photon conversion and light emission, combined with the advantages of 2D semiconductors, such as flexibility, high mechanical stability and low costs of production, could lead to new optoelectronic technologies.
Accretion Disks Phase Transitions 2-D or not 2-D?
Abramowicz, M A; Igumenshchev, I V; Abramowicz, Marek Artur; Bjornsson, Gunnlaugur; Igumenshchev, Igor V.
2000-01-01
We argue that the proper way to treat thin-thick accretion-disk transitions should take into account the 2-D nature of the problem. We illustrate the physical inconsistency of the 1-D vertically integrated approach by discussing a particular example of the convective transport of energy.
Blanco, O R; Bambade, P
2015-01-01
The Oide effect considers the synchrotron radiation in the final focusing quadrupole and it sets a lower limit on the vertical beam size at the Interaction Point, particularly relevant for high energy linear colliders. The theory of the Oide effect was derived considering only the radiation in the focusing plane of the magnet. This article addresses the theoretical calculation of the radiation effect on the beam size consider- ing both focusing and defocusing planes of the quadrupole, refered to as 2D-Oide. The CLIC 3 TeV final quadrupole (QD0) and beam parameters are used to compare the theoretical results from the Oide effect and the 2D-Oide effect with particle tracking in PLACET. The 2D-oide demonstrates to be important as it increases by 17% the contribution to the beam size. Further insight into the aberrations induced by the synchrotron radiation opens the possibility to partially correct the 2D-Oide effect with octupole magn
SES2D is an interactive graphics code designed to generate plots of equation of state data from the Los Alamos National Laboratory Group T-4 computer libraries. This manual discusses the capabilities of the code. It describes the prompts and commands and illustrates their use with a sample run
A nodal expansion method for solving the multigroup SP3 equations in the reactor code DYN3D
The core model DYN3D which has been developed for three-dimensional analyses of steady states and transients in thermal reactors with quadratic or hexagonal fuel assemblies is based on nodal methods for the solution of the two-group neutron diffusion equation. Loading cores with higher content of MOX fuel, the increase of the fuel cycle length and new types of reactors are challenging for these standard methods. A nodal expansion method for solving the equations of the simplified P3 approximation (SP3) of the multigroup transport equation was developed to improve the accuracy of the DYN3D code. In this paper, the method used in DYN3D-SP3 is described. It is applied for the pin-wise calculation of a steady state of the OECD/NEA and U.S. NRC PWR MOX/UO2 Core Transient Benchmark. The eigenvalue keff, assembly powers and the pin powers are computed. The results calculated with different approaches including diffusion theory are compared with the reference solution obtained from a heterogeneous transport calculation with the code DeCART. Different approaches of the diffusion coefficient used in the SP3 equations are investigated. The SP3 results obtained with the transport cross section of multigroup diffusion theory show the smallest deviations from the reference solution. These deviations are in the same order as the results of the code DORT, whereas the DORT and DYN3D calculations were carried out with the same library of group constants for homogenized pin cells. (authors)
MUXS: a code to generate multigroup cross sections for sputtering calculations
This report documents MUXS, a computer code to generate multigroup cross sections for charged particle transport problems. Cross sections generated by MUXS can be used in many multigroup transport codes, with minor modifications to these codes, to calculate sputtering yields, reflection coefficients, penetration distances, etc
SERKON program for compiling a multigroup library to be used in BETTY calculation
A SERKON-type program was written to compile data sets generated by FEDGROUP-3 into a multigroup library for BETTY calculation. A multigroup library was generated from the ENDF/B-IV data file and tested against the TRX-1 and TRX-2 lattices with good results. (author)
Variational nodal solution algorithms for multigroup criticality problems
Variational nodal transport methods are generalized for the treatment of multigroup criticality problems. The generation of variational response matrices is streamlined and automated through the use of symbolic manipulation. A new red-black partitioned matrix algorithm for the solution of the within-group equations is formulated and shown to be at once both a regular matrix splitting and a synthetic acceleration method. The methods are implemented in X- Y geometry as a module of the Argonne National Laboratory code DIF3D. For few group problems highly accurate P3 eigenvalues are obtained with computing times comparable to those of an existing interface-current nodal transport method
Status of multigroup cross-section data for shielding applications
Multigroup cross-section libraries for shielding applications in formats for direct use in discrete ordinates or Monte Carlo codes have long been a part of the Data Library Collection (DLC) of the Radiation Shielding Information Center (RSIC). In recent years libraries in more flexible and comprehensive formats, which allow the user to derive his own problem-dependent sets, have been added to the collection. The current status of both types is described, as well as projections for adding data libraries based on ENDF/B-V
Multigroup Free-atom Doppler-broadening Approximation. Experiment
Gray, Mark Girard [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-11-06
The multigroup energy Doppler-broadening approximation agrees with continuous energy Dopplerbroadening generally to within ten percent for the total cross sections of ^{1}H,^{ 56}Fe, and ^{235}U at 250 lanl. Although this is probably not good enough for broadening from room temperature through the entire temperature range in production use, it is better than any interpolation scheme between temperatures proposed to date, and may be good enough for extrapolation from high temperatures. The method deserves further study since additional improvements are possible.
Nonparametric Multi-group Membership Model for Dynamic Networks
Kim, Myunghwan; Leskovec, Jure
2013-01-01
Relational data-like graphs, networks, and matrices-is often dynamic, where the relational structure evolves over time. A fundamental problem in the analysis of time-varying network data is to extract a summary of the common structure and the dynamics of the underlying relations between the entities. Here we build on the intuition that changes in the network structure are driven by the dynamics at the level of groups of nodes. We propose a nonparametric multi-group membership model for dynami...
SNAP - a three dimensional neutron diffusion code
This report describes a one- two- three-dimensional multi-group diffusion code, SNAP, which is primarily intended for neutron diffusion calculations but can also carry out gamma calculations if the diffusion approximation is accurate enough. It is suitable for fast and thermal reactor core calculations and for shield calculations. SNAP can solve the multi-group neutron diffusion equations using finite difference methods. The one-dimensional slab, cylindrical and spherical geometries and the two-dimensional case are all treated as simple special cases of three-dimensional geometries. Numerous reflective and periodic symmetry options are available and may be used to reduce the number of mesh points necessary to represent the system. Extrapolation lengths can be specified at internal and external boundaries. (Author)
H on He: sticking and 2d-superfluidity
The sticking coefficient, which governs the sticking time τs, is discussed for high surface-coverage conditions. We point out that τs must remain large compared to a characteristic vortex diffusion time, if the system is to display 2d-superfluidity
Highlights: • A new AFEN code, MGANSP3, is developed for simplified P3 (SP3) calculations. • Surface averaged partial currents are used for coupling the nodes. • Coarse group rebalancing method is applied to increase the speed of calculations. • Four benchmark problems are used to examine the accuracy of the MGANSP3 code. - Abstract: In this study, a new analytic function expansion nodal (AFEN) method was developed to solve multi-group and three dimensional neutron simplified P3 equations (SP3) in reactor cores with rectangular fuel assemblies. In this method, the intranodal fluxes are expanded into a set of analytic basis functions for each group and moment. The nodes are coupled through the surface averaged partial currents at each nodal interface. Thus, six boundary conditions at each group and Legendre moments have been considered. Coarse group rebalancing (CGR) method was applied to increase the speed of code calculations. The code takes few-groups cross sections produced by a lattice code such as WIMS and calculates the effective multiplication factor, zeroth and second moments of the flux in multi-group energy, reactivity, and the relative power density at each fuel assembly. The numerical results for different benchmark problems demonstrate that solution of SP3 equations by our AFEN method improves both effective multiplication factor (keff) and power distribution compared to our AFEN diffusion method, especially in heterogeneous geometry and mixed-oxide (MOX) fuel problems
Fallow), Stray
2009-01-01
Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and
2D-animaatiotuotannon optimointi
Saturo, Reetta
2015-01-01
Tämän opinnäytetyön tavoitteena on tutkia 2D-animaatiotuotannon optimoinnin mahdollisuuksia tiukan tuotantoaikataulun vaatimuksissa. Tutkielmassa tarkastellaan kahta asiakasprojektia, jotka on toteutettu pienellä tuotantotiimillä. Työkaluna animaatioissa on käytetty pääosin Adoben After Effects -ohjelmistoa. Tutkielman alussa esitellään animaatiotuotannot, joiden tuloksena syntyi kaksi lyhyttä mainoselokuvaa. Sen jälkeen käydään läpi animaatioelokuvan tuotantoprosessia vaiheittain ja tark...
BETA-S, Multi-Group Beta-Ray Spectra
1 - Description of program or function: BETA-S calculates beta-decay source terms and energy spectra in multigroup format for time-dependent radionuclide inventories of actinides, fission products, and activation products. Multigroup spectra may be calculated in any arbitrary energy-group structure. The code also calculates the total beta energy release rate from the sum of the average beta-ray energies as determined from the spectral distributions. BETA-S also provides users with an option to determine principal beta-decaying radionuclides contributing to each energy group. The CCC-545/SCALE 4.3 (or SCALE4.2) code system must be installed on the computer before installing BETA-S, which requires the SCALE subroutine library and nuclide-inventory generation from the ORIGEN-S code. 2 - Methods:Well-established models for beta-energy distributions are used to explicitly represent allowed, and 1., 2. - and 3. -forbidden transition types. Forbidden non-unique transitions are assumed to have a spectral shape of allowed transitions. The multigroup energy spectra are calculated by numerically integrating the energy distribution functions using an adaptive Simpson's Rule algorithm. Nuclide inventories are obtained from a binary interface produced by the ORIGEN-S code. BETA-S calculates the spectra for all isotopes on the binary interface that have associated beta-decay transition data in the ENSDF-95 library, developed for the BETA-S code. This library was generated from ENSDF data and contains 715 materials, representing approximately 8500 individual beta transition branches. 3 - Restrictions on the complexity of the problem: The algorithms do not treat positron decay transitions or internal conversion electrons. The neglect of positron transitions in inconsequential for most applications involving aggregate fission products, since most of the decay modes are via electrons. The neglect of internal conversion electrons may impact on the accuracy of the spectrum in the low
Generation of subgroup parameters from JENDL-2 based multigroup data set for FBR core materials
Subgroup method gives a more accurate treatment to the resonance absorption in nuclear reactors, especially when it is heterogeneous, than the usual multigroup method. An algorithm has been developed based on a modified form of Roth's procedure, to calculate subgroup parameters, from the multigroup table of self-shielding factors given against a set of temperatures and dilution cross sections. A program SPART has been written with this algorithm, and it has been used to generate subgroup parameters for some important fast reactor core materials from the JENDL-2 based multigroup set, recently created and validated at IGCAR. In this report, the algorithm is discussed, and the subgroup parameters generated are presented. (author)
无
2003-01-01
A novel pilot stage valve called simplified 2D valve, which utilizes both rotary and linear motions of a single spool, is presented.The rotary motion of the spool incorporating hydraulic resistance bridge, formed by a damper groove and a crescent overlap opening, is utilized as pilot to actuate linear motion of the spool.A criterion for stability is derived from the linear analysis of the valve.Special experiments are designed to acquire the mechanical stiffness, the pilot leakage and the step response.It is shown that the sectional size of the spiral groove affects the dynamic response and the stiffness contradictorily and is also very sensitive to the pilot leakage.Therefore, it is necessary to establish a balance between the static and dynamic characteristics in deciding the structural parameters.Nevertheless, it is possible to sustain the dynamic response at a fairly high level, while keeping the leakage of the pilot stage at an acceptable level.
Waldin, Nicholas
2016-06-24
2D color maps are often used to visually encode complex data characteristics such as heat or height. The comprehension of color maps in visualization is affected by the display (e.g., a monitor) and the perceptual abilities of the viewer. In this paper we present a novel method to measure a user\\'s ability to distinguish colors of a two-dimensional color map on a given monitor. We show how to adapt the color map to the user and display to optimally compensate for the measured deficiencies. Furthermore, we improve user acceptance of the calibration procedure by transforming the calibration into a game. The user has to sort colors along a line in a 3D color space in a competitive fashion. The errors the user makes in sorting these lines are used to adapt the color map to his perceptual capabilities.
Reflector modelling of small high leakage cores making use of multi-group nodal equivalence theory
This research focuses on modelling reflectors in typical material testing reactors (MTRs). Equivalence theory is used to homogenise and collapse detailed transport solutions to generate equivalent nodal parameters and albedo boundary conditions for reflectors, for subsequent use in full core nodal diffusion codes. This approach to reflector modelling has been shown to be accurate for two-group large commercial light water reactor (LWR) analysis, but has not been investigated for MTRs. MTRs are smaller, with much larger leakage, environment sensitivity and multi-group spectrum dependencies than LWRs. This study aims to determine if this approach to reflector modelling is an accurate and plausible homogenisation technique for the modelling of small MTR cores. The successful implementation will result in simplified core models, better accuracy and improved efficiency of computer simulations. Codes used in this study include SCALE 6.1, OSCAR-4 and EQUIVA (the last two codes are developed and used at Necsa). The results show a five times reduction in calculational time for the proposed reduced reactor model compared to the traditional explicit model. The calculated equivalent parameters however show some sensitivity to the environment used to generate them. Differences in the results compared to the current explicit model, require more careful investigation including comparisons with a reference result, before its implementation can be recommended. (authors)
Adaptive matrix formation (AMF) method has been developed for the numerical solution of the transient multigroup neutron diffusion and delayed precursor equations in two- and three-dimensional geometry. The method is applied to a general class of two- and three- dimensional problems. The results of numerical experiments, as well as comparison with space-time experimental results indicate that the method is accurate and that the two- and three-dimensional calculations can be performed at 'reasonable' computer costs. Moreover, the AMF method offers the flexibility of using smaller time steps between flux shape calculations to achieve a specified accuracy and capability, without encountering numerical problems that occur in the other conventional methods. There is a large considerable saving in computer time and costs due to the partitioning of the matrix adopted in the presented AMF method. The two- and three-dimensional problems were analyzed with the present calculations model to illustrate the accuracy and stability of the method. Furthermore, the stability of the investigated method has been tested for sinusoidal, ramp, and step-change reactivity insertions. The results are in a good agreement with those of the other less approximate methods, including the problems in which the reflector zone is perturbed
ATHENA2D, Simulation Hypothetical Recriticality Accident in a Thermal Neutron Spectrum
1 - Description of program or function: ATHENA2D was written to simulate a hypothetical water reflood of a highly-damaged light water reactor (such as the Three-Mile-Island Unit-2 after meltdown, with a packed debris bed near the center of the core), but with insufficiently-borated reflood water. A recriticality transient may result because of the potentially more reactive debris bed. ATHENA-2D solves the transient multigroup neutron diffusion equations in (r,z) geometry. Executing in parallel with the transient neutronics, is a single-phase computational fluid dynamics (CFD) model, driven by multichannel thermal hydraulics based on detailed pin models. Numerous PV-Wave procedure files are included on the distribution media, useful for those who already have PV-Wave from Visual Numerics. These procedures are documented in the 'README' files included on the distribution CD. Some reactor lattice computer code such as WIMS-E, CCC-576/WIMSD4, or CCC-656/WIMSD5B is required for the creation of macroscopic cross section libraries, given pin-cell geometries. WIMS-E is a commercial product available from AEA Technologies, England, WIMS is not included on the ATHENA2D distribution CD. Several auxiliary routines are included in the package. TFMAX: Utility that searches through ATHENA2D binary output to find the maximum fuel temperature over space and time. POSTVEL: Utility that searches through ATHENA2D binary output to find maximum scalar and flow field values (over space) and outputs normalization factors as a function of time. These results are used to correctly scale animations. CONVT: If executing ATHENA2D on a PC under Windows, this utility converts one form of binary output (directly from ATHENA2D) to another, which is readable by PV-Wave for Windows (PV-Wave is data animation and visualization software from Visual Numerics, Inc.) CALCMTX: Post-processing utility for calculating the model coefficients for the calculation matrix. 2 - Methods: Both the neutronics and
Development and verification of a nodal approach for solving the multigroup SP{sub 3} equations
Beckert, C. [Forschungszentrum Dresden-Rossendorf, Institute of Safety Research, P.O. Box 51 01 19, D-01314 Dresden (Germany); Grundmann, U. [Forschungszentrum Dresden-Rossendorf, Institute of Safety Research, P.O. Box 51 01 19, D-01314 Dresden (Germany)], E-mail: U.Grundmann@fzd.de
2008-01-15
The core model DYN3D which has been developed for three-dimensional analyses of steady states and transients in thermal reactors with quadratic or hexagonal fuel assemblies is based on nodal methods for the solution of the two-group neutron diffusion equation. Loading cores with higher content of MOX fuel, the increase of the fuel cycle length, and the consideration of new reactor types are challenging for these standard methods. A nodal expansion method for solving the equations of the simplified P{sub 3} (SP{sub 3}) approximation of the multigroup transport equation was developed to improve the accuracy of the DYN3D code. The method described in the paper is verified with pinwise calculations of a steady state of the OECD/NEA and US NRC PWR MOX/UO{sub 2} Core Transient Benchmark. The used 16-group cross section library was generated for DORT calculations with homogenized pin cells. Two different approximations of the diffusion coefficient which occurs in the within-group form of the SP{sub 3} equations are investigated. Using the transport cross section for the calculation of the diffusion coefficient gives much better results than those obtained with the removal cross section. The improvement of the results in comparison to a pinwise diffusion calculation is shown. The results are compared with the DORT and the heterogeneous reference solution of the code DeCART. Concerning the SP{sub 3} calculation using the diffusion coefficient based on the transport cross section (DYN3D-SP3-TR) the deviations of the eigenvalue k{sub eff} and the assembly powers from the transport solutions of DORT and DeCART are in the same order as those between the two transport solutions themselves. The improvement of the DYN3D-SP3-TR results in comparison to the diffusion calculation is presented. As the DYN3D-SP3-TR and DORT calculations are performed with homogenized pin cells, the pin powers of the two calculations are closer to each other than to the pin powers of the DeCART solution
Development and verification of a nodal approach for solving the multigroup SP3 equations
The core model DYN3D which has been developed for three-dimensional analyses of steady states and transients in thermal reactors with quadratic or hexagonal fuel assemblies is based on nodal methods for the solution of the two-group neutron diffusion equation. Loading cores with higher content of MOX fuel, the increase of the fuel cycle length, and the consideration of new reactor types are challenging for these standard methods. A nodal expansion method for solving the equations of the simplified P3 (SP3) approximation of the multigroup transport equation was developed to improve the accuracy of the DYN3D code. The method described in the paper is verified with pinwise calculations of a steady state of the OECD/NEA and US NRC PWR MOX/UO2 Core Transient Benchmark. The used 16-group cross section library was generated for DORT calculations with homogenized pin cells. Two different approximations of the diffusion coefficient which occurs in the within-group form of the SP3 equations are investigated. Using the transport cross section for the calculation of the diffusion coefficient gives much better results than those obtained with the removal cross section. The improvement of the results in comparison to a pinwise diffusion calculation is shown. The results are compared with the DORT and the heterogeneous reference solution of the code DeCART. Concerning the SP3 calculation using the diffusion coefficient based on the transport cross section (DYN3D-SP3-TR) the deviations of the eigenvalue keff and the assembly powers from the transport solutions of DORT and DeCART are in the same order as those between the two transport solutions themselves. The improvement of the DYN3D-SP3-TR results in comparison to the diffusion calculation is presented. As the DYN3D-SP3-TR and DORT calculations are performed with homogenized pin cells, the pin powers of the two calculations are closer to each other than to the pin powers of the DeCART solution. To estimate the contribution of
Multigroup covariance matrices for fast-reactor studies
This report presents the multigroup covariance matrices based on the ENDF/B-V nuclear data evaluations. The materials and reactions have been chosen according to the specifications of ORNL-5517. Several cross section covariances, other than those specified by that report, are included due to the derived nature of the uncertainty files in ENDF/B-V. The materials represented are Ni, Cr, 16O, 12C, Fe, Na, 235U, 238U, 239Pu, 240Pu, 241Pu, and 10B (present due to its correlation to 238U). The data have been originally processed into a 52-group energy structure by PUFF-II and subsequently collapsed to smaller subgroup strutures. The results are illustrated in 52-group correlation matrix plots and tabulated into thirteen groups for convenience
Multigroup-multiwaves Lisrel modeling in tourist satisfaction analysis
Cristina Bernini
2013-05-01
Full Text Available The paper analyzes the influence of tourist heterogeneity on the Tourist Local System Overall Satisfaction and its changes over time. We investigate two aspects: if different tourists segmented according to their trip motivation (seaside, conference and sport show the same pattern of evaluation toward some relevant features of the TLS and if the evaluation scheme is dynamic. At this aim, a Multigroup-Multiwaves Lisrel model is estimated on a data set from the Tourist Satisfaction Survey, conducted in Rimini from 2004 to 2006 by the Faculty of Statistics – University of Bologna. The analysis shows that tourist evaluation scheme toward Rimini is quite similar among groups and over time, suggesting that differences among tourists do not affect TLS satisfaction.
Intragroup Socialization for Adult Korean Adoptees: A Multigroup Analysis
Kimberly J. Langrehr
2014-06-01
Full Text Available The purpose of the current study was to test a model of socialization among a sample of adult Korean adoptees. Based on the tenants of homophily and social identity theory, it was hypothesized that participants’ early racial and ethnic socialization experiences would account for their current intragroup friendships as adults, and that this relationship would be mediated by early intragroup contact and moderated by early ethnic identity status. The two ethnic and racial socialization variables (i.e., ethnic heritage activities and racial in-exposure significantly accounted for participants’ relationships with other Korean adoptees and nonadopted Koreans, and the effects were partially explained by early intragroup contact. Results of multigroup testing indicated the proposed socialization model was non-invariant across groups, such that the effects of ethnic heritage activities on intragroup contact and the effect of racial in-exposure on friendships with Korean adoptees were significantly different based on early ethnic identity status.
MORET: Version 4.B. A multigroup Monte Carlo criticality code
MORET 4 is a three dimensional multigroup Monte Carlo code which calculates the effective multiplication factor (keff) of any configurations more or less complex as well as reaction rates in the different volumes of the geometry and the leakage out of the system. MORET 4 is the Monte Carlo code of the APOLLO2-MORET 4 standard route of CRISTAL, the French criticality package. It is the most commonly used Monte Carlo code for French criticality calculations. During the last four years, the MORET 4 team has developed or improved the following major points: modernization of the geometry, implementation of perturbation algorithms, source distribution convergence, statistical detection of stationarity, unbiased variance estimation and creation of pre-processing and post-processing tools. The purpose of this paper is not only to present the new features of MORET but also to detail clearly the physical models and the mathematical methods used in the code. (author)
Multigroup representation of fusion product orbits in a plasma column
A method is derived for describing the time-depending behavior of α particles produced in a radially nonuniform slender plasma column as a distribution function among the possible orbits. A multigroup numerical approximation is introduced to analyze the development of the distribution function and its moments. Results are presented of calculations of the time-dependent α-particle energy spectrum and radial density, energy, and electron heating profiles in plasma columns with radii comparable to the α Larmor radius. This technique allows calculation of the α particle history at much more rapid rates than allowed by Monte Carlo technuques: The characteristic time scale is the α-electron slowing-down time rather than the cyclotron period
In reactor physics, calculation schemes with deterministic codes are validated with respect to a reference Monte Carlo code. The remaining biases are attributed to the approximations and models induced by the multigroup theory (self-shielding models and expansion of the scattering law using Legendre polynomials) to represent physical phenomena (resonant absorption and scattering anisotropy respectively). This work focuses on the relevance of a polynomial expansion to model the scattering law. Since the outset of reactor physics, the latter has been expanded on a truncated Legendre polynomial basis. However, the transfer cross sections are highly anisotropic, with non-zero values for a very small range of the cosine of the scattering angle. Besides, the finer the energy mesh and the lighter the scattering nucleus, the more exacerbated is the peaked shape of this cross section. As such, the Legendre expansion is less suited to represent the scattering law. Furthermore, this model induces negative values which are non-physical. In this work, various scattering laws are briefly described and the limitations of the existing model are pointed out. Hence, piecewise-constant functions have been used to represent the multigroup scattering cross section. This representation requires a different model for the diffusion source. The discrete ordinates method which is widely employed to solve the transport equation has been adapted. Thus, the finite volume method for angular discretization has been developed and implemented in Paris environment which hosts the Sn solver, Snatch. The angular finite volume method has been compared to the collocation method with Legendre moments to ensure its proper performance. Moreover, unlike the latter, this method is adapted for both the Legendre moments and the piecewise-constant functions representations of the scattering cross section. This hybrid-source method has been validated for different cases: fuel cell in infinite lattice
Our purpose in this work is to demonstrate that the efficiency of dose-rate computations in 125I brachytherapy, using multigroup discrete ordinates radiation transport simulations, can be significantly enhanced using broad energy group cross sections without a loss of accuracy. To this end, the DANTSYS multigroup discrete ordinates neutral particle transport code was used to estimate the absorbed dose-rate distributions around an 125I-model 6702 seed in two-dimensional (2-D) cylindrical R-Z geometry for four different problems spanning the geometries found in clinical practice. First, simulations with a high resolution 210 energy groups library were used to analyze the photon flux spectral distribution throughout this set of problems. These distributions were used to design an energy group structure consisting of three broad groups along with suitable weighting functions from which the three-group cross sections were derived. The accuracy of 2-D DANTSYS dose-rate calculations was benchmarked against parallel Monte Carlo simulations. Ray effects were remedied by using the DANTSYS internal first collision source algorithm. It is demonstrated that the 125I primary photon spectrum leads to inappropriate weighting functions. An accuracy of ±5% is achieved in the four problem geometries considered using geometry-independent three-group libraries derived from either material-specific weighting functions or a single material-independent weighting function. Agreement between Monte Carlo and the three-group DANTSYS calculations, within three standard Monte Carlo deviations, is observed everywhere except for a limited region along the Z axis of rotational symmetry, where ray effects are difficult to mitigate. The three-group DANTSYS calculations are 10-13 times faster than ones with a 210-group cross section library for 125I dosimetry problems. Compared to 2-D EGS4 Monte Carlo calculations, the 3-group DANTSYS simulations are a 100-fold more efficient. Provided that these
Daskalov, George M; Baker, R S; Rogers, D W O; Williamson, J F
2002-02-01
Our purpose in this work is to demonstrate that the efficiency of dose-rate computations in 125I brachytherapy, using multigroup discrete ordinates radiation transport simulations, can be significantly enhanced using broad energy group cross sections without a loss of accuracy. To this end, the DANTSYS multigroup discrete ordinates neutral particle transport code was used to estimate the absorbed dose-rate distributions around an 125I-model 6702 seed in two-dimensional (2-D) cylindrical R-Z geometry for four different problems spanning the geometries found in clinical practice. First, simulations with a high resolution 210 energy groups library were used to analyze the photon flux spectral distribution throughout this set of problems. These distributions were used to design an energy group structure consisting of three broad groups along with suitable weighting functions from which the three-group cross sections were derived. The accuracy of 2-D DANTSYS dose-rate calculations was benchmarked against parallel Monte Carlo simulations. Ray effects were remedied by using the DANTSYS internal first collision source algorithm. It is demonstrated that the 125I primary photon spectrum leads to inappropriate weighting functions. An accuracy of +/-5% is achieved in the four problem geometries considered using geometry-independent three-group libraries derived from either material-specific weighting functions or a single material-independent weighting function. Agreement between Monte Carlo and the three-group DANTSYS calculations, within three standard Monte Carlo deviations, is observed everywhere except for a limited region along the Z axis of rotational symmetry, where ray effects are difficult to mitigate. The three-group DANTSYS calculations are 10-13 times faster than ones with a 210-group cross section library for 125I dosimetry problems. Compared to 2-D EGS4 Monte Carlo calculations, the 3-group DANTSYS simulations are a 100-fold more efficient. Provided that these
Kalpakkam multigroup cross section set for fast reactor applications - status and performance
This report documents the status of the presently created set of multigroup constants at Kalpakkam. The list of nuclides processed and the details of multigroup structure are given. Also included are the particulars of dilutions and temperatures for each nuclide in the multigroup cross section set for which self shielding factors have been calculated. Using this new multigroup cross section set, measured integral quantities such as K-eff, central reaction rate ratios, central reactivity worths etc. were calculated for a few fast critical benchmark assemblies and the calculated values of neutronic parameters obtained were compared with those obtained using the available Cadarache cross section library and those published in literature for ENDF/B-IV based set and Japanese evaluated nuclear data library (JENDL). The details of analyses are documented along with the conclusions. (author). 17 refs., 12 tabs
MCMG: a 3-D multigroup P3 Monte Carlo code and its benchmarks
In this paper a 3-D Monte Carlo multigroup neutron transport code MCMG has been developed from a coupled neutron and photon transport Monte Carlo code MCNP. The continuous-energy cross section library of the MCNP code is replaced by the multigroup cross section data generated by the transport lattice code, such as the WIMS code. It maintains the strong abilities of MCNP for geometry treatment, counting, variance reduction techniques and plotting. The multigroup neutron scattering cross sections adopt the Pn (n ≤ 3) approximation. The test results are in good agreement with the results of other methods and experiments. The number of energy groups can be varied from few groups to multigroup, and either macroscopic or microscopic cross section can be used. (author)
Coste-Delclaux, M
2006-03-15
This document describes the improvements carried out for modelling the self-shielding phenomenon in the multigroup transport code APOLLO2. They concern the space and energy treatment of the slowing-down equation, the setting up of quadrature formulas to calculate reaction rates, the setting-up of a method that treats directly a resonant mixture and the development of a sub-group method. We validate these improvements either in an elementary or in a global way. Now, we obtain, more accurate multigroup reaction rates and we are able to carry out a reference self-shielding calculation on a very fine multigroup mesh. To end, we draw a conclusion and give some prospects on the remaining work. (author)
A variational finite element-spherical harmonics method is presented for the solution of the even-parity multigroup equations with anisotropic scattering and sources. It is shown that by using a simple and natural formulation the numerical implementation of the method for any desired geometry is greatly eased and the anisotropy of scatter treated without any difficulty. Numerical examples demonstrate the ability of the resulting code to solve geometrically complex multigroup problems. (Author)
Radiation Transport for Explosive Outflows: A Multigroup Hybrid Monte Carlo Method
Wollaeger, Ryan T.; van Rossum, Daniel R.; Graziani, Carlo; Couch, Sean M.; Jordan, George C., IV; Lamb, Donald Q.; Moses, Gregory A.
2013-12-01
We explore Implicit Monte Carlo (IMC) and discrete diffusion Monte Carlo (DDMC) for radiation transport in high-velocity outflows with structured opacity. The IMC method is a stochastic computational technique for nonlinear radiation transport. IMC is partially implicit in time and may suffer in efficiency when tracking MC particles through optically thick materials. DDMC accelerates IMC in diffusive domains. Abdikamalov extended IMC and DDMC to multigroup, velocity-dependent transport with the intent of modeling neutrino dynamics in core-collapse supernovae. Densmore has also formulated a multifrequency extension to the originally gray DDMC method. We rigorously formulate IMC and DDMC over a high-velocity Lagrangian grid for possible application to photon transport in the post-explosion phase of Type Ia supernovae. This formulation includes an analysis that yields an additional factor in the standard IMC-to-DDMC spatial interface condition. To our knowledge the new boundary condition is distinct from others presented in prior DDMC literature. The method is suitable for a variety of opacity distributions and may be applied to semi-relativistic radiation transport in simple fluids and geometries. Additionally, we test the code, called SuperNu, using an analytic solution having static material, as well as with a manufactured solution for moving material with structured opacities. Finally, we demonstrate with a simple source and 10 group logarithmic wavelength grid that IMC-DDMC performs better than pure IMC in terms of accuracy and speed when there are large disparities between the magnitudes of opacities in adjacent groups. We also present and test our implementation of the new boundary condition.
Optimization of multi-group cross sections for fast reactor analysis
The selection of the number of broad energy groups, collapsed broad energy group boundaries, and their associated evaluation into collapsed macroscopic cross sections from a general 238-group ENDF/B-VII library dramatically impacted the k eigenvalue for fast reactor analysis. An analysis was undertaken to assess the minimum number of energy groups that would preserve problem physics; this involved studies using the 3D deterministic transport parallel code PENTRAN, the 2D deterministic transport code SCALE6.1, the Monte Carlo based MCNP5 code, and the YGROUP cross section collapsing tool on a spatially discretized MOX fuel pin comprised of 21% PUO2-UO2 with sodium coolant. The various cases resulted in a few hundred pcm difference between cross section libraries that included the 238 multi-group reference, and cross sections rendered using various reaction and adjoint weighted cross sections rendered by the YGROUP tool, and a reference continuous energy MCNP case. Particular emphasis was placed on the higher energies characteristic of fission neutrons in a fast spectrum; adjoint computations were performed to determine the average per-group adjoint fission importance for the MOX fuel pin. This study concluded that at least 10 energy groups for neutron transport calculations are required to accurately predict the eigenvalue for a fast reactor system to within 250 pcm of the 238 group case. In addition, the cross section collapsing/weighting schemes within YGROUP that provided a collapsed library rendering eigenvalues closest to the reference were the contribution collapsed, reaction rate weighted scheme. A brief analysis on homogenization of the MOX fuel pin is also provided, although more work is in progress in this area. (authors)
Learn Unity for 2D game development
Thorn, Alan
2013-01-01
The only Unity book specifically covering 2D game development Written by Alan Thorn, experience game developer and author of seven books on game programming Hands-on examples of all major aspects of 2D game development using Unity
2D growth processes: SLE and Loewner chains
Bauer, Michel [Service de Physique Theorique de Saclay, CE-Saclay, 91191 Gif-sur-Yvette (France) and Laboratoire de Physique Theorique, Ecole Normale Superieure, 24 rue Lhomond, 75005 Paris (France)]. E-mail: michel.bauer@cea.fr; Bernard, Denis [Service de Physique Theorique de Saclay, CE-Saclay, 91191 Gif-sur-Yvette (France) and Laboratoire de Physique Theorique, Ecole Normale Superieure, 24 rue Lhomond, 75005 Paris (France)]. E-mail: denis.bernard@cea.fr
2006-10-15
This review provides an introduction to two dimensional growth processes. Although it covers a variety of processes such as diffusion limited aggregation, it is mostly devoted to a detailed presentation of stochastic Schramm-Loewner evolutions (SLE) which are Markov processes describing interfaces in 2D critical systems. It starts with an informal discussion, using numerical simulations, of various examples of 2D growth processes and their connections with statistical mechanics. SLE is then introduced and Schramm's argument mapping conformally invariant interfaces to SLE is explained. A substantial part of the review is devoted to reveal the deep connections between statistical mechanics and processes, and more specifically to the present context, between 2D critical systems and SLE. Some of the remarkable properties of SLE are explained, together with the tools for computing with it. This review has been written with the aim of filling the gap between the mathematical and the physical literature on the subject.
2-D model for pollutant dispersion at the coastal outfall off Paradip
Suryanarayana, A.; Babu, M.T.; Vethamony, P.; Gouveia, A.D
Simulation of dispersion of the effluent discharge has been carried out using 2-D Model to verify the advection and diffusion of the pollutant patch of the proposed effluent disposal off Paradip, Orissa, India. The simulation of dispersion...
Variational methods in steady state diffusion problems
Classical variational techniques are used to obtain accurate solutions to the multigroup multiregion one dimensional steady state neutron diffusion equation. Analytic solutions are constructed for benchmark verification. Functionals with cubic trial functions and conservational lagrangian constraints are exhibited and compared with nonconservational functionals with respect to neutron balance and to relative flux and current at interfaces. Excellent agreement of the conservational functionals using cubic trial functions is obtained in comparison with analytic solutions
MCNP - transport calculations in ducts using multigroup albedo coefficients
In this work, the use of multigroup albedo coefficients in Monte Carlo calculations of particle reflection and transmission by ducts is investigated. The procedure consists in modifying the MCNP code so that an albedo matrix computed previously by deterministic methods or Monte Carlo is introduced into the program to describe particle reflection by a surface. This way it becomes possible to avoid the need of considering particle transport in the duct wall explicitly, changing the problem to a problem of transport in the duct interior only and reducing significantly the difficulty of the real problem. The probability of particle reflection at the duct wall is given, for each group, as the sum of the albedo coefficients over the final groups. The calculation is started by sampling a source particle and simulating its reflection on the duct wall by sampling a group for the emerging particle. The particle weight is then reduced by the reflection probability. Next, a new direction and trajectory for the particle is selected. Numerical results obtained for the model are compared with results from a discrete ordinates code and results from Monte Carlo simulations that take particle transport in the wall into account. (author)
Macroscopic multigroup constants for accelerator driven system core calculation
The high-level wastes stored in facilities above ground or shallow repositories, in close connection with its nuclear power plant, can take almost 106 years before the radiotoxicity became of the order of the background. While the disposal issue is not urgent from a technical viewpoint, it is recognized that extended storage in the facilities is not acceptable since these ones cannot provide sufficient isolation in the long term and neither is it ethical to leave the waste problem to future generations. A technique to diminish this time is to transmute these long-lived elements into short-lived elements. The approach is to use an Accelerator Driven System (ADS), a sub-critical arrangement which uses a Spallation Neutron Source (SNS), after separation the minor actinides and the long-lived fission products (LLFP), to convert them to short-lived isotopes. As an advanced reactor fuel, still today, there is a few data around these type of core systems. In this paper we generate macroscopic multigroup constants for use in calculations of a typical ADS fuel, take into consideration, the ENDF/BVI data file. Four energy groups are chosen to collapse the data from ENDF/B-VI data file by PREPRO code. A typical MOX fuel cell is used to validate the methodology. The results are used to calculate one typical subcritical ADS core. (author)
Surface modelling for 2D imagery
Lieng, Henrik
2014-01-01
Vector graphics provides powerful tools for drawing scalable 2D imagery. With the rise of mobile computers, of different types of displays and image resolutions, vector graphics is receiving an increasing amount of attention. However, vector graphics is not the leading framework for creating and manipulating 2D imagery. The reason for this reluctance of employing vector graphical frameworks is that it is difficult to handle complex behaviour of colour across the 2D domain. ...
Perspectives for spintronics in 2D materials
Wei Han
2016-03-01
Full Text Available The past decade has been especially creative for spintronics since the (rediscovery of various two dimensional (2D materials. Due to the unusual physical characteristics, 2D materials have provided new platforms to probe the spin interaction with other degrees of freedom for electrons, as well as to be used for novel spintronics applications. This review briefly presents the most important recent and ongoing research for spintronics in 2D materials.
Perspectives for spintronics in 2D materials
Han, Wei
2016-03-01
The past decade has been especially creative for spintronics since the (re)discovery of various two dimensional (2D) materials. Due to the unusual physical characteristics, 2D materials have provided new platforms to probe the spin interaction with other degrees of freedom for electrons, as well as to be used for novel spintronics applications. This review briefly presents the most important recent and ongoing research for spintronics in 2D materials.
Kaur, Kuldeep; Khan, Manju
2012-01-01
Let $p$ be an odd prime, $D_{2p}$ be the dihedral group of order 2p, and $F_{2}$ be the finite field with two elements. If * denotes the canonical involution of the group algebra $F_2D_{2p}$, then bicyclic units are unitary units. In this note, we investigate the structure of the group $\\mathcal{B}(F_2D_{2p})$, generated by the bicyclic units of the group algebra $F_2D_{2p}$. Further, we obtain the structure of the unit group $\\mathcal{U}(F_2D_{2p})$ and the unitary subgroup $\\mathcal{U}_*(F_...
Bedform characterization through 2D spectral analysis
Lefebvre, Alice; Ernstsen, Verner Brandbyge; Winter, Christian
energetic peak of the 2D spectrum was found and its energy, frequency and direction were calculated. A power-law was fitted to the average of slices taken through the 2D spectrum; its slope and y-intercept were calculated. Using these results the test area was morphologically classified into 4 distinct...... characteristics using twodimensional (2D) spectral analysis is presented and tested on seabed elevation data from the Knudedyb tidal inlet in the Danish Wadden Sea, where large compound bedforms are found. The bathymetric data were divided into 20x20 m areas on which a 2D spectral analysis was applied. The most...
Elena Purcaru
2011-09-01
Full Text Available The paper presents a solution for endcoding/decoding DNA information in 2D barcodes. First part focuses on the existing techniques and symbologies in 2D barcodes field. The 2D barcode PDF417 is presented as starting point. The adaptations and optimizations on PDF417 and on DataMatrix lead to the solution – DNA2DBC – DeoxyriboNucleic Acid Two Dimensional Barcode. The second part shows the DNA2DBC encoding/decoding process step by step. In conclusions are enumerated the most important features of 2D barcode implementation for DNA.
Purcaru, Elena
2012-01-01
The paper presents a solution for endcoding/decoding DNA information in 2D barcodes. First part focuses on the existing techniques and symbologies in 2D barcodes field. The 2D barcode PDF417 is presented as starting point. The adaptations and optimizations on PDF417 and on DataMatrix lead to the solution - DNA2DBC - DeoxyriboNucleic Acid Two Dimensional Barcode. The second part shows the DNA2DBC encoding/decoding process step by step. In conclusions are enumerated the most important features of 2D barcode implementation for DNA.
This paper presents a benchmark framework established as a basis for investigation of the validity of multi-group approximation with respect to the continuous energy approach, of the level of spatial homogenization with respect to heterogeneous solution, and of the level of angular approximation to the linear Boltzmann transport equation in respect to the Monte Carlo reference solution. Several steady-state solutions of this benchmark have been generated using three different computer codes focusing on the two-dimensional (2-D) geometry model. MCNP5 has been used to generate the reference solution using the continuous energy library. HELIOS is then used for both to solve the problem using a 45 group cross-section library and to generate new sets of few-group cross-sections for the core simulator NEM. The results from the diffusion option of the NEM code on pin-by-pin and Fuel Assembly (FA) basis are presented and discussed in the paper. The benchmark is being designed for evaluation of number of energy groups (number of energy groups and energy cut off points) and spatial (homogenized assembly level vs. homogenized pin cell level) representation needed for high-fidelity reactor core calculation schemes developed at the Pennsylvania State Univ. such as NEM SP3, hybrid NEM-BEM and some recent developments of embedded three-dimensional pin-by-pin diffusion / SP3 finite element calculation schemes. (authors)
Dorval, Eric
2016-01-01
Neutron transport calculations by Monte Carlo methods are finding increased application in nuclear reactor simulations. In particular, a versatile approach entails the use of a 2-step pro-cedure, with Monte Carlo as a few-group cross section data generator at lattice level, followed by deterministic multi-group diffusion calculations at core level. In this thesis, the Serpent 2 Monte Carlo reactor physics burnup calculation code is used in order to test a set of diffusion coefficient model...
Annotated Bibliography of EDGE2D Use
This annotated bibliography is intended to help EDGE2D users, and particularly new users, find existing published literature that has used EDGE2D. Our idea is that a person can find existing studies which may relate to his intended use, as well as gain ideas about other possible applications by scanning the attached tables
2D NMR studies of biomolecules
The work described in this thesis comprises two related subjects. The first part describes methods to derive high-resolution structures of proteins in solution using two-dimensional (2-D) NMR. The second part describes 2-D NMR studies on the interaction between proteins and DNA. (author). 261 refs.; 52 figs.; 23 tabs
Applications of 2D helical vortex dynamics
Okulov, Valery; Sørensen, Jens Nørkær
In the paper, we show how the assumption of helical symmetry in the context of 2D helical vortices can be exploited to analyse and to model various cases of rotating flows. From theory, examples of three basic applications of 2D dynamics of helical vortices embedded in flows with helical symmetry...
Annotated Bibliography of EDGE2D Use
J.D. Strachan and G. Corrigan
2005-06-24
This annotated bibliography is intended to help EDGE2D users, and particularly new users, find existing published literature that has used EDGE2D. Our idea is that a person can find existing studies which may relate to his intended use, as well as gain ideas about other possible applications by scanning the attached tables.
Development of a multi-group SN transport calculation code with unstructured tetrahedral meshes
This paper reviews the computational methods used in the MUST (Multi-group Unstructured geometry SN Transport) code for solving the multi-group Sn transport equation in general geometries and describes the status of development of MUST. MUST solves the multi-group transport equation with unstructured tetrahedral meshes for modeling complicated geometrical problems. For tetrahedral mesh generation, input generation, and output visualization, we developed a management program where the mesh generation is based on Gmsh and TetGen that are open softwares. The geometrical modeling is done with the commercial CAD softwares such as CATIA. MUST uses the discontinuous finite element method (DFEM) and two-sub cell balance methods with linear discontinuous expansion (LDEM-SCB) to spatially discretize the transport equation. We applied MUST to three neutron and gamma coupled test problems for testing MUST. (author)
Optimal control in multi-group coupled within-host and between-host models
Eric Numfor
2016-03-01
Full Text Available We formulate and then analyze a multi-group coupled within-host model of ODEs and between-host model of ODE and first-order PDEs, using the Human Immunodeficiency Virus (HIV for illustration. The basic reproduction number of the multi-group coupled epidemiological model is derived, steady states solutions are calculated and stability analysis of equilbria is investigated. An optimal control problem for our model with drug treatment on the multi-group within-host system is formulated and analyzed. Ekeland's principle is used in proving existence and uniqueness of an optimal control pair. Numerical simulations based on the semi-implicit finite difference schemes and the forward-backward sweep iterative method are obtained.
Development of a Multi-Group Neutron Cross Section Library Generation System for PWR
Kim, Kang Seog; Hong, Ser Gi; Song, Jae Seung; Lee, Kyung Hoon; Cho, Jin Young; Kim, Ha Yong; Koo, Bon Seung; Shim, Hyung Jin; Park, Sang Yoon
2008-10-15
This report describes a generation system of multi-group cross section library which is used in the KARMA lattice calculation code. In particular, the theoretical methodologies, program structures, and input preparations for the constituent programs of the system are described in detail. The library generation system consists of the following five programs : ANJOY, GREDIT, MERIT, SUBDATA, and LIBGEN. ANJOY generates automatically the NJOY input files and two batch files for automatic NJOY run for all the nuclides considered. The automatic NJOY run gives TAPE 23 (PENDF output file of BROADR module of NJOY) and TAPE24 (GENDF output file of GROUPR module of NJOY) files for each nuclide. GREDIT prepares a formatted multi-group cross section file in which the cross sections are tabulated versus temperature and background cross section after reading the TAPE24 file. MERIT generates the hydrogen equivalence factors and the resonance integral tables by solving the slowing down equation with ultra-fine group cross sections which are prepared with the TAPE 23 file. SUBDATA generates the subgroup data including subgroup levels and weights after reading the MERIT output file. Finally, LIBGEN generates the final multi-group library file by assembling the data prepared in the previous steps and by reading the other data such as fission product yield data and decay data.The multi-group cross section library includes general multi-group cross sections, resonance data, subgroup data, fission product yield data, kappa-values (energy release per fission), and all the data which are required in the depletion calculation. The addition or elimination of the cross sections for some nuclides can be easily done by changing the LIBGEN input file if the general multi-group cross section and the subgroup data files are prepared.
Development of a Multi-Group Neutron Cross Section Library Generation System for PWR
This report describes a generation system of multi-group cross section library which is used in the KARMA lattice calculation code. In particular, the theoretical methodologies, program structures, and input preparations for the constituent programs of the system are described in detail. The library generation system consists of the following five programs : ANJOY, GREDIT, MERIT, SUBDATA, and LIBGEN. ANJOY generates automatically the NJOY input files and two batch files for automatic NJOY run for all the nuclides considered. The automatic NJOY run gives TAPE 23 (PENDF output file of BROADR module of NJOY) and TAPE24 (GENDF output file of GROUPR module of NJOY) files for each nuclide. GREDIT prepares a formatted multi-group cross section file in which the cross sections are tabulated versus temperature and background cross section after reading the TAPE24 file. MERIT generates the hydrogen equivalence factors and the resonance integral tables by solving the slowing down equation with ultra-fine group cross sections which are prepared with the TAPE 23 file. SUBDATA generates the subgroup data including subgroup levels and weights after reading the MERIT output file. Finally, LIBGEN generates the final multi-group library file by assembling the data prepared in the previous steps and by reading the other data such as fission product yield data and decay data.The multi-group cross section library includes general multi-group cross sections, resonance data, subgroup data, fission product yield data, kappa-values (energy release per fission), and all the data which are required in the depletion calculation. The addition or elimination of the cross sections for some nuclides can be easily done by changing the LIBGEN input file if the general multi-group cross section and the subgroup data files are prepared
Driven microswimmers on a 2D substrate: A stochastic towed sled model
Marchegiani, Giampiero; Marchesoni, Fabio
2015-11-01
We investigate, both numerically and analytically, the diffusion properties of a stochastic sled sliding on a substrate, subject to a constant towing force. The problem is motivated by the growing interest in controlling transport of artificial microswimmers in 2D geometries at low Reynolds numbers. We simulated both symmetric and asymmetric towed sleds. Remarkable properties of their mobilities and diffusion constants include sidewise drifts and excess diffusion peaks. We interpret our numerical findings by making use of stochastic approximation techniques.
Driven microswimmers on a 2D substrate: A stochastic towed sled model
We investigate, both numerically and analytically, the diffusion properties of a stochastic sled sliding on a substrate, subject to a constant towing force. The problem is motivated by the growing interest in controlling transport of artificial microswimmers in 2D geometries at low Reynolds numbers. We simulated both symmetric and asymmetric towed sleds. Remarkable properties of their mobilities and diffusion constants include sidewise drifts and excess diffusion peaks. We interpret our numerical findings by making use of stochastic approximation techniques
DORT-PC, 2-D Discrete Ordinates Transport System
1 - Description of program or function: This version of DORT (ORNL Mod 5, 12 Oct 89, INEL Ver 2.1) was derived from the Cray UNICOS version distributed in CCC-543/TORT, which was developed at ORNL under Defense Nuclear Agency sponsorship. DORT is directly based on the earlier DOT codes. DORT-PC determines the fluence of particles throughout one- or two-dimensional geometric systems due to sources either generated as a result of particle interaction with the medium or incident upon the system from extraneous sources. The principal application is to the deep-penetration transport of neutrons and photons. Criticality (k-type and search) problems can also be solved. Numerous printed edits of the results are available, and results can be transferred to output files for subsequent analysis. 2 - Method of solution: The Boltzmann transport equation is solved, using either the method of discrete ordinates or diffusion theory approximation. In the discrete ordinates method, the primary mode of operation, balance equations are solved for the flow of particles moving in a set of discrete directions in each cell of a space mesh and in each group of a multigroup energy structure. Iterations are performed until all implicitness in the coupling of cells, directions, groups, and source regeneration has been resolved. Several methods are available to accelerate convergence. Anisotropic cross sections can be expressed in a Legendre expansion of arbitrary order. Output data sets can be used to provide an accurate restart of a previous problem or to deliver information to other codes. Several techniques are available to remove the effects of negative fluxes caused by the finite difference approximation and of negative scattering sources due to truncation of the cross-section expansion. The space mesh can be described such that the number of first-dimensional (i) intervals varies with the second dimension (j). The number of discrete directions can vary across the space mesh and with
Internal Photoemission Spectroscopy of 2-D Materials
Nguyen, Nhan; Li, Mingda; Vishwanath, Suresh; Yan, Rusen; Xiao, Shudong; Xing, Huili; Cheng, Guangjun; Hight Walker, Angela; Zhang, Qin
Recent research has shown the great benefits of using 2-D materials in the tunnel field-effect transistor (TFET), which is considered a promising candidate for the beyond-CMOS technology. The on-state current of TFET can be enhanced by engineering the band alignment of different 2D-2D or 2D-3D heterostructures. Here we present the internal photoemission spectroscopy (IPE) approach to determine the band alignments of various 2-D materials, in particular SnSe2 and WSe2, which have been proposed for new TFET designs. The metal-oxide-2-D semiconductor test structures are fabricated and characterized by IPE, where the band offsets from the 2-D semiconductor to the oxide conduction band minimum are determined by the threshold of the cube root of IPE yields as a function of photon energy. In particular, we find that SnSe2 has a larger electron affinity than most semiconductors and can be combined with other semiconductors to form near broken-gap heterojunctions with low barrier heights which can produce a higher on-state current. The details of data analysis of IPE and the results from Raman spectroscopy and spectroscopic ellipsometry measurements will also be presented and discussed.
Inertial solvation in femtosecond 2D spectra
Hybl, John; Albrecht Ferro, Allison; Farrow, Darcie; Jonas, David
2001-03-01
We have used 2D Fourier transform spectroscopy to investigate polar solvation. 2D spectroscopy can reveal molecular lineshapes beneath ensemble averaged spectra and freeze molecular motions to give an undistorted picture of the microscopic dynamics of polar solvation. The transition from "inhomogeneous" to "homogeneous" 2D spectra is governed by both vibrational relaxation and solvent motion. Therefore, the time dependence of the 2D spectrum directly reflects the total response of the solvent-solute system. IR144, a cyanine dye with a dipole moment change upon electronic excitation, was used to probe inertial solvation in methanol and propylene carbonate. Since the static Stokes' shift of IR144 in each of these solvents is similar, differences in the 2D spectra result from solvation dynamics. Initial results indicate that the larger propylene carbonate responds more slowly than methanol, but appear to be inconsistent with rotational estimates of the inertial response. To disentangle intra-molecular vibrations from solvent motion, the 2D spectra of IR144 will be compared to the time-dependent 2D spectra of the structurally related nonpolar cyanine dye HDITCP.
Application of diffusion theory to the transport of neutral particles in fusion plasmas
It is shown that the widely held view that diffusion theory can not provide good accuracy for the transport of neutral particles in fusion plasmas is misplaced. In fact, it is shown that multigroup diffusion theory gives quite good accuracy as compared to the transport theory. The reasons for this are elaborated and some of the physical and theoretical reasons which make the multigroup diffusion theory provide good accuracy are explained. Energy dependence must be taken into consideration to obtain a realistic neutral atom distribution in fusion plasmas. There are two reasons for this; presence of either is enough to necessitate an energy dependent treatment. First, the plasma temperature varies spatially, and second, the ratio of charge-exchange to total plasma-neutral interaction cross section (c) is not close to one. A computer code to solve the one-dimensional multigroup diffusion theory in general geometry (slab, cylindrical and spherical) has been written for use on Cray computers, and its results are compared with those from the one-dimensional transport code ANISN to support the above finding. A fast, compact and versatile two-dimensional finite element multigroup diffusion theory code, FINAT, in X-Y and R-Z cylindrical/toroidal geometries has been written for use on CRAY computers. This code has been compared with the two dimensional transport code DOT-4.3. The accuracy is very good, and FENAT runs much faster compared even to DOT-4.3 which is a finite difference code
2D supergravity in p+1 dimensions
Gustafsson, H.; Lindstrom, U.
1998-01-01
We describe new $N$-extended 2D supergravities on a $(p+1)$-dimensional (bosonic) space. The fundamental objects are moving frame densities that equip each $(p+1)$-dimensional point with a 2D ``tangent space''. The theory is presented in a $[p+1, 2]$ superspace. For the special case of $p=1$ we recover the 2D supergravities in an unusual form. The formalism has been developed with applications to the string-parton picture of $D$-branes at strong coupling in mind.
Elena Purcaru; Cristian Toma
2012-01-01
The paper presents a solution for endcoding/decoding DNA information in 2D barcodes. First part focuses on the existing techniques and symbologies in 2D barcodes field. The 2D barcode PDF417 is presented as starting point. The adaptations and optimizations on PDF417 and on DataMatrix lead to the solution – DNA2DBC – DeoxyriboNucleic Acid Two Dimensional Barcode. The second part shows the DNA2DBC encoding/decoding process step by step. In conclusions are enumerated the most important features ...
Two-dimensional multigroup finite element calculation of fast reactor in diffusion approximation
When a linear element of triangular shape is used the actual finite element calculation is relatively simple. Extensive programs for mesh generation were written for easy inputting the configuration of reactors. A number of other programs were written for plotting neutron flux fields in individual groups, the power distribution, spatial plotting of fields, etc. The operation of selected programs, data preparation and operating instructions are described and examples given of data and results. All programs are written in GIER ALGOL. The used method and the developed programs have demonstrated that they are a useful instrument for the calculation of criticality and the distribution of neutron flux and power of both fast and thermal reactors. (J.B.)
Ceolin, Celina; Vilhena, Marco T.; Bodmann, Bardo E.J., E-mail: vilhena@pq.cnpq.b, E-mail: bardo.bodmann@ufrgs.b [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Alvim, Antonio Carlos Marques, E-mail: alvim@nuclear.ufrj.b [Universidade Federal do Rio de Janeiro (PEN/COPPE/UFRJ), RJ (Brazil). Coordenacao dos Programas de Pos-Graduacao de Engenharia. Programa de Energia Nuclear
2011-07-01
The authors solved analytically the neutron kinetic equations in a homogeneous slab, assuming the multi group energy model and six delayed neutron precursor groups by the Generalized Integral Laplace Transform Technique (GILTT) for a multi-layered slab. To this end, averaged values for the nuclear parameters in the multi-layered slab are used and the solution is constructed following the idea of Adomian's decomposition method upon reducing the heterogeneous problem to a set of recursive problems with constant parameters in the multi-layered slab. More specifically, the corrections that render the initially homogeneous problem into a heterogeneous one are plugged into the equation as successive source terms. To the best of our knowledge this sort of solution is novel and not found in literature. We further present some numerical simulations. (author)
Adoption as a Social Marker: The Diffusion of Products in a Multigroup Environment
Smaldino, Paul E; Hillis, Vicken; Bednar, Jenna
2015-01-01
Social identities are among the key factors driving social behavior in complex societies. Recent attention to social identity in consumer behavior indicates that individuals avoid products that might signal membership in an outgroup. Yet the population-level consequences of adoption as identity signaling are largely unknown. Whereas previous work has focused on asymmetric attraction and repulsion among groups with different social identities, here we consider the spread of innovations in a structured population in which there are multiple groups who don't want to be mistaken for one another, using both analytical and agent-based modeling. This formal analysis, the first to take the spatial structure of a population into account, allows us to consider empirically important factors, including demographic skew and communication scale, that likely influence overall patterns of adoption. We find that as products become emergent social markers, aversion to outgroup-associated products can decrease overall patterns ...