A new diffusion nodal method based on analytic basis function expansion
International Nuclear Information System (INIS)
Noh, J.M.; Cho, N.Z.
1993-01-01
The transverse integration procedure commonly used in most advanced nodal methods results in some limitations. The first is that the transverse leakage term that appears in the transverse integration procedure must be appropriately approximated. In most advanced nodal methods, this term is expanded in a quadratic polynomial. The second arises when reconstructing the pinwise flux distribution within a node. The available one-dimensional flux shapes from nodal calculation in each spatial direction cannot be used directly in the flux reconstruction. Finally, the transverse leakage defined for a hexagonal node becomes so complicated as not to be easily handled and contains nonphysical singular terms. In this paper, a new nodal method called the analytic function expansion nodal (AFEN) method is described for both the rectangular geometry and the hexagonal geometry in order to overcome these limitations. This method does not solve the transverse-integrated one-dimensional diffusion equations but instead solves directly the original multidimensional diffusion equation within a node. This is a accomplished by expanding the solution (or the intranodal homogeneous flux distribution) in terms of nonseparable analytic basis functions satisfying the diffusion equation at any point in the node
SIRIUS - A one-dimensional multigroup analytic nodal diffusion theory code
Energy Technology Data Exchange (ETDEWEB)
Forslund, P. [Westinghouse Atom AB, Vaesteraas (Sweden)
2000-09-01
In order to evaluate relative merits of some proposed intranodal cross sections models, a computer code called Sirius has been developed. Sirius is a one-dimensional, multigroup analytic nodal diffusion theory code with microscopic depletion capability. Sirius provides the possibility of performing a spatial homogenization and energy collapsing of cross sections. In addition a so called pin power reconstruction method is available for the purpose of reconstructing 'heterogeneous' pin qualities. consequently, Sirius has the capability of performing all the calculations (incl. depletion calculations) which are an integral part of the nodal calculation procedure. In this way, an unambiguous numerical analysis of intranodal cross section models is made possible. In this report, the theory of the nodal models implemented in sirius as well as the verification of the most important features of these models are addressed.
On the extension of the analytic nodal diffusion solver ANDES to sodium fast reactors
International Nuclear Information System (INIS)
Ochoa, R.; Herrero, J.J.; Garcia-Herranz, N.
2011-01-01
Within the framework of the Collaborative Project for a European Sodium Fast Reactor, the reactor physics group at UPM is working on the extension of its in-house multi-scale advanced deterministic code COBAYA3 to Sodium Fast Reactors (SFR). COBAYA3 is a 3D multigroup neutron kinetics diffusion code that can be used either as a pin-by-pin code or as a stand-alone nodal code by using the analytic nodal diffusion solver ANDES. It is coupled with thermal-hydraulics codes such as COBRA-TF and FLICA, allowing transient analysis of LWR at both fine-mesh and coarse-mesh scales. In order to enable also 3D pin-by-pin and nodal coupled NK-TH simulations of SFR, different developments are in progress. This paper presents the first steps towards the application of COBAYA3 to this type of reactors. ANDES solver, already extended to triangular-Z geometry, has been applied to fast reactor steady-state calculations. The required cross section libraries were generated with ERANOS code for several configurations. Here some of the limitations encountered when attempting to apply the Analytical Coarse Mesh Finite Difference (ACMFD) method - implemented inside ANDES - to fast reactor calculations are discussed and the sensitivity of the method to the energy-group structure is studied. In order to reinforce some of the conclusions obtained two calculations are presented. The first one involves a 3D mini-core model in 33 groups, where the ANDES solver presents several issues. And secondly, a benchmark from the NEA for a small 3D FBR in hexagonal-Z geometry in 4 energy groups is used to verify the good convergence of the code in a few-energy-group structure. (author)
International Nuclear Information System (INIS)
Lozano, Juan-Andres; Garcia-Herranz, Nuria; Ahnert, Carol; Aragones, Jose-Maria
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 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
The analytic nodal method in cylindrical geometry
International Nuclear Information System (INIS)
Prinsloo, Rian H.; Tomasevic, Djordje I.
2008-01-01
Nodal diffusion methods have been used extensively in nuclear reactor calculations, specifically for their performance advantage, but also for their superior accuracy. More specifically, the Analytic Nodal Method (ANM), utilising the transverse integration principle, has been applied to numerous reactor problems with much success. In this work, a nodal diffusion method is developed for cylindrical geometry. Application of this method to three-dimensional (3D) cylindrical geometry has never been satisfactorily addressed and we propose a solution which entails the use of conformal mapping. A set of 1D-equations with an adjusted, geometrically dependent, inhomogeneous source, is obtained. This work describes the development of the method and associated test code, as well as its application to realistic reactor problems. Numerical results are given for the PBMR-400 MW benchmark problem, as well as for a 'cylindrisized' version of the well-known 3D LWR IAEA benchmark. Results highlight the improved accuracy and performance over finite-difference core solutions and investigate the applicability of nodal methods to 3D PBMR type problems. Results indicate that cylindrical nodal methods definitely have a place within PBMR applications, yielding performance advantage factors of 10 and 20 for 2D and 3D calculations, respectively, and advantage factors of the order of 1000 in the case of the LWR problem
Energy Technology Data Exchange (ETDEWEB)
Lozano, Juan Andres; Aragones, Jose Maria; Garcia-Herranz, Nuria [Universidad Politecnica de Madrid, 28006 Jose Gutierrez Abascal 2, Madrid (Spain)
2008-07-01
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)
Extension of the analytic nodal method to four energy groups
International Nuclear Information System (INIS)
Parsons, D.K.; Nigg, D.W.
1985-01-01
The Analytic Nodal Method is one of several recently-developed coarse mesh numerical methods for efficiently and accurately solving the multidimensional static and transient neutron diffusion equations. This summary describes a mathematically rigorous extension of the Analytic Nodal Method to the frequently more physically realistic four-group case. A few general theoretical considerations are discussed, followed by some calculated results for a typical steady-state two-dimensional PWR quarter core application. 8 refs
International Nuclear Information System (INIS)
Chung, S.K.; Hah, C.J.; Lee, H.C.; Kim, Y.H.; Cho, N.Z.
1996-01-01
Modern nodal methods usually employs the transverse integration technique in order to reduce a multi-dimensional diffusion equation to one-dimensional diffusion equations. The use of the transverse integration technique requires two major approximations such as a transverse leakage approximation and a one-dimensional flux approximation. Both the transverse leakage and the one-dimensional flux are approximated by polynomials. ANC (Advanced Nodal Code) developed by Westinghouse employs a modern nodal expansion method for the flux calculation, the equivalence theory for the homogenization error reduction and a group theory for pin power recovery. Unlike the conventional modern nodal methods, AFEN (Analytic Function Expansion Nodal) method expands homogeneous flux distributions within a node into non-separable analytic basis functions, which eliminate two major approximations of the modern nodal methods. A comparison study of AFEN with ANC has been performed to see the applicability of AFEN to commercial PWR and different types of reactors such as MOX fueled reactor. The qualification comparison results demonstrate that AFEN methodology is accurate enough to apply for commercial PWR analysis. The results show that AFEN provides very accurate results (core multiplication factor and assembly power distribution) for cores that exhibit strong flux gradients as in a MOX loaded core. (author)
International Nuclear Information System (INIS)
Lozano, Juan-Andres; Jimenez, Javier; Garcia-Herranz, Nuria; Aragones, Jose-Maria
2010-01-01
In this paper the extension of the multigroup nodal diffusion code ANDES, based on the Analytic Coarse Mesh Finite Difference (ACMFD) method, from Cartesian to hexagonal geometry is presented, as well as its coupling with the thermal-hydraulic (TH) code COBRA-IIIc for hexagonal core analysis. In extending the ACMFD method to hexagonal assemblies, triangular-Z nodes are used. In the radial plane, a direct transverse integration procedure is applied along the three directions that are orthogonal to the triangle interfaces. The triangular nodalization avoids the singularities, that appear when applying transverse integration to hexagonal nodes, and allows the advantage of the mesh subdivision capabilities implicit within that geometry. As for the thermal-hydraulics, the extension of the coupling scheme to hexagonal geometry has been performed with the capability to model the core using either assembly-wise channels (hexagonal mesh) or a higher refinement with six channels per fuel assembly (triangular mesh). Achieving this level of TH mesh refinement with COBRA-IIIc code provides a better estimation of the in-core 3D flow distribution, improving the TH core modelling. The neutronics and thermal-hydraulics coupled code, ANDES/COBRA-IIIc, previously verified in Cartesian geometry core analysis, can also be applied now to full three-dimensional VVER core problems, as well as to other thermal and fast hexagonal core designs. Verification results are provided, corresponding to the different cases of the OECD/NEA-NSC VVER-1000 Coolant Transient Benchmarks.
Analytic function expansion nodal method for nuclear reactor core design
International Nuclear Information System (INIS)
Noh, Hae Man
1995-02-01
In most advanced nodal methods the transverse integration is commonly used to reduce the multi-dimensional diffusion equation into equivalent one- dimensional diffusion equations when derving the nodal coupling equations. But the use of the transverse integration results in some limitations. The first limitation is that the transverse leakage term which appears in the transverse integration procedure must be appropriately approximated. The second limitation is that the one-dimensional flux shapes in each spatial direction resulted from the nodal calculation are not accurate enough to be directly used in reconstructing the pinwise flux distributions. Finally the transverse leakage defined for a non-rectangular node such as a hexagonal node or a triangular node is too complicated to be easily handled and may contain non-physical singular terms of step-function and delta-function types. In this thesis, the Analytic Function Expansion Nodal (AFEN) method and its two variations : the Polynomial Expansion Nodal (PEN) method and the hybrid of the AFEN and PEN methods, have been developed to overcome the limitations of the transverse integration procedure. All of the methods solve the multidimensional diffusion equation without the transverse integration. The AFEN method which we believe is the major contribution of this study to the reactor core analysis expands the homogeneous flux distributions within a node in non-separable analytic basis functions satisfying the neutron diffusion equations at any point of the node and expresses the coefficients of the flux expansion in terms of the nodal unknowns which comprise a node-average flux, node-interface fluxes, and corner-point fluxes. Then, the nodal coupling equations composed of the neutron balance equations, the interface current continuity equations, and the corner-point leakage balance equations are solved iteratively to determine all the nodal unknowns. Since the AFEN method does not use the transverse integration in
HEXAN - a hexagonal nodal code for solving the diffusion equation
International Nuclear Information System (INIS)
Makai, M.
1982-07-01
This report describes the theory of and provides a user's manual for the HEXAN program, which is a nodal program for the solution of the few-group diffusion equation in hexagonal geometry. Based upon symmetry considerations, the theory provides an analytical solution in a homogeneous node. WWER and HTGR test problem solutions are presented. The equivalence of the finite-difference scheme and the response matrix method is proven. The properties of a symmetric node's response matrix are investigated. (author)
Applications of a systematic homogenization theory for nodal diffusion methods
International Nuclear Information System (INIS)
Zhang, Hong-bin; Dorning, J.J.
1992-01-01
The authors recently have developed a self-consistent and systematic lattice cell and fuel bundle homogenization theory based on a multiple spatial scales asymptotic expansion of the transport equation in the ratio of the mean free path to the reactor characteristics dimension for use with nodal diffusion methods. The mathematical development leads naturally to self-consistent analytical expressions for homogenized diffusion coefficients and cross sections and flux discontinuity factors to be used in nodal diffusion calculations. The expressions for the homogenized nuclear parameters that follow from the systematic homogenization theory (SHT) are different from those for the traditional flux and volume-weighted (FVW) parameters. The calculations summarized here show that the systematic homogenization theory developed recently for nodal diffusion methods yields accurate values for k eff and assembly powers even when compared with the results of a fine mesh transport calculation. Thus, it provides a practical alternative to equivalence theory and GET (Ref. 3) and to simplified equivalence theory, which requires auxiliary fine-mesh calculations for assemblies embedded in a typical environment to determine the discontinuity factors and the equivalent diffusion coefficient for a homogenized assembly
A comparison of Nodal methods in neutron diffusion calculations
Energy Technology Data Exchange (ETDEWEB)
Tavron, Barak [Israel Electric Company, Haifa (Israel) Nuclear Engineering Dept. Research and Development Div.
1996-12-01
The nuclear engineering department at IEC uses in the reactor analysis three neutron diffusion codes based on nodal methods. The codes, GNOMERl, ADMARC2 and NOXER3 solve the neutron diffusion equation to obtain flux and power distributions in the core. The resulting flux distributions are used for the furl cycle analysis and for fuel reload optimization. This work presents a comparison of the various nodal methods employed in the above codes. Nodal methods (also called Coarse-mesh methods) have been designed to solve problems that contain relatively coarse areas of homogeneous composition. In the nodal method parts of the equation that present the state in the homogeneous area are solved analytically while, according to various assumptions and continuity requirements, a general solution is sought out. Thus efficiency of the method for this kind of problems, is very high compared with the finite element and finite difference methods. On the other hand, using this method one can get only approximate information about the node vicinity (or coarse-mesh area, usually a feel assembly of a 20 cm size). These characteristics of the nodal method make it suitable for feel cycle analysis and reload optimization. This analysis requires many subsequent calculations of the flux and power distributions for the feel assemblies while there is no need for detailed distribution within the assembly. For obtaining detailed distribution within the assembly methods of power reconstruction may be applied. However homogenization of feel assembly properties, required for the nodal method, may cause difficulties when applied to fuel assemblies with many absorber rods, due to exciting strong neutron properties heterogeneity within the assembly. (author).
A nonlinear analytic function expansion nodal method for transient calculations
Energy Technology Data Exchange (ETDEWEB)
Joo, Han Gyn; Park, Sang Yoon; Cho, Byung Oh; Zee, Sung Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1998-12-31
The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation of the solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized, In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of application to the NEACRP PWR rod ejection benchmark problems. 6 refs., 2 figs., 1 tab. (Author)
A nonlinear analytic function expansion nodal method for transient calculations
Energy Technology Data Exchange (ETDEWEB)
Joo, Han Gyn; Park, Sang Yoon; Cho, Byung Oh; Zee, Sung Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1999-12-31
The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation of the solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized, In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of application to the NEACRP PWR rod ejection benchmark problems. 6 refs., 2 figs., 1 tab. (Author)
Energy Technology Data Exchange (ETDEWEB)
Tomasevic, Dj; Altiparmarkov, D [Institut za Nuklearne Nauke Boris Kidric, Belgrade (Yugoslavia)
1988-07-01
A variational nodal diffusion method with accurate treatment of transverse leakage shape is developed and presented in this paper. Using Legendre expansion in transverse coordinates higher order quasi-one-dimensional nodal equations are formulated. Numerical solution has been carried out using analytical solutions in alternating directions assuming Legendre expansion of the RHS term. The method has been tested against 2D and 3D IAEA benchmark problem, as well as 2D CANDU benchmark problem. The results are highly accurate. The first order approximation yields to the same order of accuracy as the standard nodal methods with quadratic leakage approximation, while the second order reaches reference solution. (author)
The implementation of a simplified spherical harmonics semi-analytic nodal method in PANTHER
International Nuclear Information System (INIS)
Hall, S.K.; Eaton, M.D.; Knight, M.P.
2013-01-01
Highlights: ► An SP N nodal method is proposed. ► Consistent CMFD derived and tested. ► Mark vacuum boundary conditions applied. ► Benchmarked against other diffusions and transport codes. - Abstract: In this paper an SP N nodal method is proposed which can utilise existing multi-group neutron diffusion solvers to obtain the solution. The semi-analytic nodal method is used in conjunction with a coarse mesh finite difference (CMFD) scheme to solve the resulting set of equations. This is compared against various nuclear benchmarks to show that the method is capable of computing an accurate solution for practical cases. A few different CMFD formulations are implemented and their performance compared. It is found that the effective diffusion coefficent (EDC) can provide additional stability and require less power iterations on a coarse mesh. A re-arrangement of the EDC is proposed that allows the iteration matrix to be computed at the beginning of a calculation. Successive nodal updates only modify the source term unlike existing CMFD methods which update the iteration matrix. A set of Mark vacuum boundary conditions are also derived which can be applied to the SP N nodal method extending its validity. This is possible due to a similarity transformation of the angular coupling matrix, which is used when applying the nodal method. It is found that the Marshak vacuum condition can also be derived, but would require the significant modification of existing neutron diffusion codes to implement it
Benchmarking with high-order nodal diffusion methods
International Nuclear Information System (INIS)
Tomasevic, D.; Larsen, E.W.
1993-01-01
Significant progress in the solution of multidimensional neutron diffusion problems was made in the late 1970s with the introduction of nodal methods. Modern nodal reactor analysis codes provide significant improvements in both accuracy and computing speed over earlier codes based on fine-mesh finite difference methods. In the past, the performance of advanced nodal methods was determined by comparisons with fine-mesh finite difference codes. More recently, the excellent spatial convergence of nodal methods has permitted their use in establishing reference solutions for some important bench-mark problems. The recent development of the self-consistent high-order nodal diffusion method and its subsequent variational formulation has permitted the calculation of reference solutions with one node per assembly mesh size. In this paper, we compare results for four selected benchmark problems to those obtained by high-order response matrix methods and by two well-known state-of-the-art nodal methods (the open-quotes analyticalclose quotes and open-quotes nodal expansionclose quotes methods)
A Hennart nodal method for the diffusion equation
International Nuclear Information System (INIS)
Lesaint, P.; Noceir, S.; Verwaerde, D.
1995-01-01
A modification of the Hennart nodal method for neutron diffusion problems is presented. The final system of equations obtained by this method is not positive definite. However, a flux elimination technique leads to a simple positive definite system, which can be solved by the traditional iterative methods. Calculations of a two-dimensional International Atomic Energy Agency benchmark problem are performed and compared with results of the original Hennart nodal method and some finite element methods. The high computational efficiency of this modified nodal method is clearly demonstrated
Nodal integral method for the neutron diffusion equation in cylindrical geometry
International Nuclear Information System (INIS)
Azmy, Y.Y.
1987-01-01
The nodal methodology is based on retaining a higher a higher degree of analyticity in the process of deriving the discrete-variable equations compared to conventional numerical methods. As a result, extensive numerical testing of nodal methods developed for a wide variety of partial differential equations and comparison of the results to conventional methods have established the superior accuracy of nodal methods on coarse meshes. Moreover, these tests have shown that nodal methods are more computationally efficient than finite difference and finite-element methods in the sense that they require shorter CPU times to achieve comparable accuracy in the solutions. However, nodal formalisms and the final discrete-variable equations they produce are, in general, more complicated than their conventional counterparts. This, together with anticipated difficulties in applying the transverse-averaging procedure in curvilinear coordinates, has limited the applications of nodal methods, so far, to Cartesian geometry, and with additional approximations to hexagonal geometry. In this paper the authors report recent progress in deriving and numerically implementing a nodal integral method (NIM) for solving the neutron diffusion equation in cylindrical r-z geometry. Also, presented are comparisons of numerical solutions to two test problems with those obtained by the Exterminator-2 code, which indicate the superior accuracy of the nodal integral method solutions on much coarser meshes
Nodal spectrum method for solving neutron diffusion equation
International Nuclear Information System (INIS)
Sanchez, D.; Garcia, C. R.; Barros, R. C. de; Milian, D.E.
1999-01-01
Presented here is a new numerical nodal method for solving static multidimensional neutron diffusion equation in rectangular geometry. Our method is based on a spectral analysis of the nodal diffusion equations. These equations are obtained by integrating the diffusion equation in X, Y directions and then considering flat approximations for the current. These flat approximations are the only approximations that are considered in this method, as a result the numerical solutions are completely free from truncation errors. We show numerical results to illustrate the methods accuracy for coarse mesh calculations
A simplified presentation of the multigroup analytic nodal method in 2-D Cartesian geometry
International Nuclear Information System (INIS)
Hebert, Alain
2008-01-01
The nodal diffusion algorithms used in many production reactor simulation codes are originating from a common ancestry developed in the 1970s, the analytic nodal method (ANM) of the QUANDRY code. However, this original presentation of the ANM is complex and makes difficult the calculation of the nodal coupling matrices. Moreover, QUANDRY is limited to two-energy groups and its generalization to more groups appears laborious. We are presenting a simplified implementation of the ANM requiring only limited programming work. This formulation is consistent with the initial QUANDRY implementation and is easily generalizable to arbitrary G-group problems. A Matlab script is provided to highlight the simplicity of our presentation. For the sake of clarity, our implementation is limited to G-group, 2-D Cartesian geometry
Real depletion in nodal diffusion codes
International Nuclear Information System (INIS)
Petkov, P.T.
2002-01-01
The fuel depletion is described by more than one hundred fuel isotopes in the advanced lattice codes like HELIOS, but only a few fuel isotopes are accounted for even in the advanced steady-state diffusion codes. The general assumption that the number densities of the majority of the fuel isotopes depend only on the fuel burnup is seriously in error if high burnup is considered. The real depletion conditions in the reactor core differ from the asymptotic ones at the stage of lattice depletion calculations. This study reveals which fuel isotopes should be explicitly accounted for in the diffusion codes in order to predict adequately the real depletion effects in the core. A somewhat strange conclusion is that if the real number densities of the main fissionable isotopes are not explicitly accounted for in the diffusion code, then Sm-149 should not be accounted for either, because the net error in k-inf is smaller (Authors)
SPANDOM - source projection analytic nodal discrete ordinates method
International Nuclear Information System (INIS)
Kim, Tae Hyeong; Cho, Nam Zin
1994-01-01
We describe a new discrete ordinates nodal method for the two-dimensional transport equation. We solve the discrete ordinates equation analytically after the source term is projected and represented in polynomials. The method is applied to two fast reactor benchmark problems and compared with the TWOHEX code. The results indicate that the present method accurately predicts not only multiplication factor but also flux distribution
An Adaptive Approach to Variational Nodal Diffusion Problems
International Nuclear Information System (INIS)
Zhang Hui; Lewis, E.E.
2001-01-01
An adaptive grid method is presented for the solution of neutron diffusion problems in two dimensions. The primal hybrid finite elements employed in the variational nodal method are used to reduce the diffusion equation to a coupled set of elemental response matrices. An a posteriori error estimator is developed to indicate the magnitude of local errors stemming from the low-order elemental interface approximations. An iterative procedure is implemented in which p refinement is applied locally by increasing the polynomial order of the interface approximations. The automated algorithm utilizes the a posteriori estimator to achieve local error reductions until an acceptable level of accuracy is reached throughout the problem domain. Application to a series of X-Y benchmark problems indicates the reduction of computational effort achievable by replacing uniform with adaptive refinement of the spatial approximations
Two-dimensional analytical solution for nodal calculation of nuclear reactors
International Nuclear Information System (INIS)
Silva, Adilson C.; Pessoa, Paulo O.; Silva, Fernando C.; Martinez, Aquilino S.
2017-01-01
Highlights: • A proposal for a coarse mesh nodal method is presented. • The proposal uses the analytical solution of the two-dimensional neutrons diffusion equation. • The solution is performed homogeneous nodes with dimensions of the fuel assembly. • The solution uses four average fluxes on the node surfaces as boundary conditions. • The results show good accuracy and efficiency. - Abstract: In this paper, the two-dimensional (2D) neutron diffusion equation is analytically solved for two energy groups (2G). The spatial domain of reactor core is divided into a set of nodes with uniform nuclear parameters. To determine iteratively the multiplication factor and the neutron flux in the reactor we combine the analytical solution of the neutron diffusion equation with an iterative method known as power method. The analytical solution for different types of regions that compose the reactor is obtained, such as fuel and reflector regions. Four average fluxes in the node surfaces are used as boundary conditions for analytical solution. Discontinuity factors on the node surfaces derived from the homogenization process are applied to maintain averages reaction rates and the net current in the fuel assembly (FA). To validate the results obtained by the analytical solution a relative power density distribution in the FAs is determined from the neutron flux distribution and compared with the reference values. The results show good accuracy and efficiency.
Nodal Diffusion Burnable Poison Treatment for Prismatic Reactor Cores
International Nuclear Information System (INIS)
Ougouag, A.M.; Ferrer, R.M.
2010-01-01
The prismatic block version of the High Temperature Reactor (HTR) considered as a candidate Very High Temperature Reactor (VHTR)design may use burnable poison pins in locations at some corners of the fuel blocks (i.e., assembly equivalent structures). The presence of any highly absorbing materials, such as these burnable poisons, within fuel blocks for hexagonal geometry, graphite-moderated High Temperature Reactors (HTRs) causes a local inter-block flux depression that most nodal diffusion-based method have failed to properly model or otherwise represent. The location of these burnable poisons near vertices results in an asymmetry in the morphology of the assemblies (or blocks). Hence the resulting inadequacy of traditional homogenization methods, as these 'spread' the actually local effect of the burnable poisons throughout the assembly. Furthermore, the actual effect of the burnable poison is primarily local with influence in its immediate vicinity, which happens to include a small region within the same assembly as well as similar regions in the adjacent assemblies. Traditional homogenization methods miss this artifact entirely. This paper presents a novel method for treating the local effect of the burnable poison explicitly in the context of a modern nodal method.
Five-point form of the nodal diffusion method and comparison with finite-difference
International Nuclear Information System (INIS)
Azmy, Y.Y.
1988-01-01
Nodal Methods have been derived, implemented and numerically tested for several problems in physics and engineering. In the field of nuclear engineering, many nodal formalisms have been used for the neutron diffusion equation, all yielding results which were far more computationally efficient than conventional Finite Difference (FD) and Finite Element (FE) methods. However, not much effort has been devoted to theoretically comparing nodal and FD methods in order to explain the very high accuracy of the former. In this summary we outline the derivation of a simple five-point form for the lowest order nodal method and compare it to the traditional five-point, edge-centered FD scheme. The effect of the observed differences on the accuracy of the respective methods is established by considering a simple test problem. It must be emphasized that the nodal five-point scheme derived here is mathematically equivalent to previously derived lowest order nodal methods. 7 refs., 1 tab
A practical implementation of the higher-order transverse-integrated nodal diffusion method
International Nuclear Information System (INIS)
Prinsloo, Rian H.; Tomašević, Djordje I.; Moraal, Harm
2014-01-01
Highlights: • A practical higher-order nodal method is developed for diffusion calculations. • The method resolves the issue of the transverse leakage approximation. • The method achieves much superior accuracy as compared to standard nodal methods. • The calculational cost is only about 50% greater than standard nodal methods. • The method is packaged in a module for connection to existing nodal codes. - Abstract: Transverse-integrated nodal diffusion methods currently represent the standard in full core neutronic simulation. The primary shortcoming of this approach is the utilization of the quadratic transverse leakage approximation. This approach, although proven to work well for typical LWR problems, is not consistent with the formulation of nodal methods and can cause accuracy and convergence problems. In this work, an improved, consistent quadratic leakage approximation is formulated, which derives from the class of higher-order nodal methods developed some years ago. Further, a number of iteration schemes are developed around this consistent quadratic leakage approximation which yields accurate node average results in much improved calculational times. The most promising of these iteration schemes results from utilizing the consistent leakage approximation as a correction method to the standard quadratic leakage approximation. Numerical results are demonstrated on a set of benchmark problems and further applied to a realistic reactor problem, particularly the SAFARI-1 reactor, operating at Necsa, South Africa. The final optimal solution strategy is packaged into a standalone module which may simply be coupled to existing nodal diffusion codes
Application of the SPH method in nodal diffusion analyses of SFR cores
Energy Technology Data Exchange (ETDEWEB)
Nikitin, Evgeny; Fridman, Emil [Helmholtz-Zentrum Dresden-Rossendorf e.V., Dresden (Germany). Div. Reactor Safety; Mikityuk, K. [Paul Scherrer Institut, Villigen (Switzerland)
2016-07-01
The current study investigated the potential of the SPH method, applied to correct the few-group XS produced by Serpent, to further improve the accuracy of the nodal diffusion solutions. The procedure for the generation of SPH-corrected few-group XS is presented in the paper. The performance of the SPH method was tested on a large oxide SFR core from the OECD/NEA SFR benchmark. The reference SFR core was modeled with the DYN3D and PARCS nodal diffusion codes using the SPH-corrected few-group XS generated by Serpent. The nodal diffusion results obtained with and without SPH correction were compared to the reference full-core Serpent MC solution. It was demonstrated that the application of the SPH method improves the accuracy of the nodal diffusion solutions, particularly for the rodded core state.
A two-dimensional, semi-analytic expansion method for nodal calculations
International Nuclear Information System (INIS)
Palmtag, S.P.
1995-08-01
Most modern nodal methods used today are based upon the transverse integration procedure in which the multi-dimensional flux shape is integrated over the transverse directions in order to produce a set of coupled one-dimensional flux shapes. The one-dimensional flux shapes are then solved either analytically or by representing the flux shape by a finite polynomial expansion. While these methods have been verified for most light-water reactor applications, they have been found to have difficulty predicting the large thermal flux gradients near the interfaces of highly-enriched MOX fuel assemblies. A new method is presented here in which the neutron flux is represented by a non-seperable, two-dimensional, semi-analytic flux expansion. The main features of this method are (1) the leakage terms from the node are modeled explicitly and therefore, the transverse integration procedure is not used, (2) the corner point flux values for each node are directly edited from the solution method, and a corner-point interpolation is not needed in the flux reconstruction, (3) the thermal flux expansion contains hyperbolic terms representing analytic solutions to the thermal flux diffusion equation, and (4) the thermal flux expansion contains a thermal to fast flux ratio term which reduces the number of polynomial expansion functions needed to represent the thermal flux. This new nodal method has been incorporated into the computer code COLOR2G and has been used to solve a two-dimensional, two-group colorset problem containing uranium and highly-enriched MOX fuel assemblies. The results from this calculation are compared to the results found using a code based on the traditional transverse integration procedure
International Nuclear Information System (INIS)
Ferri, A.A.
1986-01-01
Nodal methods applied in order to calculate the power distribution in a nuclear reactor core are presented. These methods have received special attention, because they yield accurate results in short computing times. Present nodal schemes contain several unknowns per node and per group. In the methods presented here, non linear feedback of the coupling coefficients has been applied to reduce this number to only one unknown per node and per group. The resulting algorithm is a 7- points formula, and the iterative process has proved stable in the response matrix scheme. The intranodal flux shape is determined by partial integration of the diffusion equations over two of the coordinates, leading to a set of three coupled one-dimensional equations. These can be solved by using a polynomial approximation or by integration (analytic solution). The tranverse net leakage is responsible for the coupling between the spatial directions, and two alternative methods are presented to evaluate its shape: direct parabolic approximation and local model expansion. Numerical results, which include the IAEA two-dimensional benchmark problem illustrate the efficiency of the developed methods. (M.E.L.) [es
A fast nodal neutron diffusion method for cartesian geometry
International Nuclear Information System (INIS)
Makai, M.; Maeder, C.
1983-01-01
A numerical method based on an analytical solution to the three-dimensional two-group diffusion equation has been derived assuming that the flux is a sum of the functions of one variable. In each mesh the incoming currents are used as boundary conditions. The final equations for the average flux and the outgoing currents are of the response matrix type. The method is presented in a form that can be extended to the general multigroup case. In the SEXI computer program developed on the basis of this method, the response matrix elements are recalculated in each outer iteration to minimize the data transfer between disk storage and central memory. The efficiency of the method is demonstrated for a light water reactor (LWR) benchmark problem. The SEXI program has been incorporated into the LWR simulator SILWER code as a possible option
ANOVA-HDMR structure of the higher order nodal diffusion solution
International Nuclear Information System (INIS)
Bokov, P. M.; Prinsloo, R. H.; Tomasevic, D. I.
2013-01-01
Nodal diffusion methods still represent a standard in global reactor calculations, but employ some ad-hoc approximations (such as the quadratic leakage approximation) which limit their accuracy in cases where reference quality solutions are sought. In this work we solve the nodal diffusion equations utilizing the so-called higher-order nodal methods to generate reference quality solutions and to decompose the obtained solutions via a technique known as High Dimensional Model Representation (HDMR). This representation and associated decomposition of the solution provides a new formulation of the transverse leakage term. The HDMR structure is investigated via the technique of Analysis of Variance (ANOVA), which indicates why the existing class of transversely-integrated nodal methods prove to be so successful. Furthermore, the analysis leads to a potential solution method for generating reference quality solutions at a much reduced calculational cost, by applying the ANOVA technique to the full higher order solution. (authors)
MicroRNA expression in nodal and extranodal Diffuse Large B-cell Lymphoma
DEFF Research Database (Denmark)
Mandrup, Charlotte; Petersen, Anders; Højfeldt, Anne Dirks
MicroRNA expression in nodal and extranodal Diffuse Large B-cell Lymphoma C. Mandrup1, A. Petersen1, A. D. Hoejfeldt1, H. F. Thomsen1, J. Madsen1, J. Dahlgaard1, P. Johansen2, A. Bukh1, K. Dybkaer1 and H. E Johnsen1. 1Department of Hematology, 2Pathological Institute, Aalborg Hospital, Aarhus...... University Hospital, Aalborg, Denmark Introduction: The aim of this project was to analyse microRNA (miRNA) expression in nodal and extranodal diffuse large B-cell lymphoma (DLBCL). Manifestation at diagnosis may be nodal and/or extranodal. At present, there are no known determinants for none...... of the manifestations, and no way to predict the potential progression from nodal to extranodal disease. miRNA are small regulatory RNA molecules with core function to repress/cleave sequence complementary mRNA targets. Abnormalities in miRNA genetics and expression are known to affect initiation and development...
Spectral nodal method for one-speed X,Y-geometry Eigenvalue diffusion problems
International Nuclear Information System (INIS)
Dominguez, Dany S.; Lorenzo, Daniel M.; Hernandez, Carlos G.; Barros, Ricardo C.; Silva, Fernando C. da
2001-01-01
Presented here is a new numerical nodal method for steady-state multidimensional neutron diffusion equation in rectangular geometry. Our method is based on a spectral analysis of the transverse-integrated nodal diffusion equations. These equations are obtained by integrating the diffusion equation in X and Y directions, and then considering flat approximations for the transverse leakage terms. These flat approximations are the only approximations that we consider in this method; as a result the numerical solutions are completely free from truncation errors in slab geometry. We show numerical results to illustrate the method's accuracy for coarse mesh calculations in a heterogeneous medium. (author)
STEP- A three-dimensional nodal diffusion code for LMR's
Energy Technology Data Exchange (ETDEWEB)
Kim, Yeong Il; Kim, Taek Kyum [Korea Atomic Energy Research Institute, Taejon (Korea)
1999-12-01
STEP is a three-dimensional multigroup nodal diffusion code for the neutronics analysis of the LMR core. STEP employs DIF3D and HEXNOD nodal methods. In DIF3D, one-dimensional fluxes are approximated by polynomials while HEXNOD analytically solves transverse-integrated one-dimensional diffusion equations. The nodal equations are solved using a conventional fission source iteration procedure accelerated by coarse-mesh rebalancing and asymptotic extrapolation. At each fission source iteration, the interface currents for each group are computed by solving the response matrix equations with a known group source term. These partial currents are used to updata flux moments. This solution is accomplished by inner iteration, a series of sweeps through the spatial mesh. Inner iterations are performed by sweeping the axial mesh plane in a standard red-black checkerboard ordering, i.e. the odd-numbered planes are processed during the first pass, followed by the even-numbered planes on the second pass. On each plane, the nodes are swept in the four-color checkerboard ordering. STEP accepts microscopic cross section data from the CCCC standard interface file ISOTXS currently used for the neutronics analysis of LMR's at KAERI as well as macroscopic 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. Energy is released from both fission ad capture. The thermal-hydraulics model calculates average fuel and coolant temperatures. STEP takes account of feedback effects from both fuel temperature and coolant temperature changes. The thermal-hydraulics model is a conservative, single channel model where there is no heat transfer between assemblies. Thus, STEP gives conservative results which, however, are of useful information for core design and can be useful tool for neutronics analysis of LMR core design and will be used for the base program of a future
Error quantification of the axial nodal diffusion kernel of the DeCART code
International Nuclear Information System (INIS)
Cho, J. Y.; Kim, K. S.; Lee, C. C.
2006-01-01
This paper is to quantify the transport effects involved in the axial nodal diffusion kernel of the DeCART code. The transport effects are itemized into three effects, the homogenization, the diffusion, and the nodal effects. A five pin model consisting of four fuel pins and one non-fuel pin is demonstrated to quantify the transport effects. The transport effects are analyzed for three problems, the single pin (SP), guide tube (GT) and control rod (CR) problems by replacing the non-fuel pin with the fuel pin, a guide-tube and a control rod pins, respectively. The homogenization and diffusion effects are estimated to be about -4 and -50 pcm for the eigenvalue, and less than 2 % for the node power. The nodal effect on the eigenvalue is evaluated to be about -50 pcm in the SP and GT problems, and +350 pcm in the CR problem. Regarding the node power, this effect induces about a 3 % error in the SP and GT problems, and about a 20 % error in the CR problem. The large power error in the CR problem is due to the plane thickness, and it can be decreased by using the adaptive plane size. From the error quantification, it is concluded that the homogenization and the diffusion effects are not controllable if DeCART maintains the diffusion kernel for the axial solution, but the nodal effect is controllable by introducing the adaptive plane size scheme. (authors)
ANDREA: Advanced nodal diffusion code for reactor analysis
International Nuclear Information System (INIS)
Belac, J.; Josek, R.; Klecka, L.; Stary, V.; Vocka, R.
2005-01-01
A new macro code is being developed at NRI which will allow coupling of the advanced thermal-hydraulics model with neutronics calculations as well as efficient use in core loading pattern optimization process. This paper describes the current stage of the macro code development. The core simulator is based on the nodal expansion method, Helios lattice code is used for few group libraries preparation. Standard features such as pin wise power reconstruction and feedback iterations on critical control rod position, boron concentration and reactor power are implemented. A special attention is paid to the system and code modularity in order to enable flexible and easy implementation of new features in future. Precision of the methods used in the macro code has been verified on available benchmarks. Testing against Temelin PWR operational data is under way (Authors)
International Nuclear Information System (INIS)
Kirk, B.L.; Azmy, Y.
1994-01-01
A modified scheme is developed for solving the two-dimensional nodal diffusion equations on distributed memory computers. The scheme is aimed at minimizing the volume of communication among processors while maximizing the tasks in parallel. Results show a significant improvement in parallel efficiency on the Intel iPSC/860 hypercube compared to previous algorithms
A nodal method applied to a diffusion problem with generalized coefficients
International Nuclear Information System (INIS)
Laazizi, A.; Guessous, N.
1999-01-01
In this paper, we consider second order neutrons diffusion problem with coefficients in L ∞ (Ω). Nodal method of the lowest order is applied to approximate the problem's solution. The approximation uses special basis functions in which the coefficients appear. The rate of convergence obtained is O(h 2 ) in L 2 (Ω), with a free rectangular triangulation. (authors)
Inclusion of nodal option in diffusion conventional codes
International Nuclear Information System (INIS)
Prati, A.; Anaf, J.
1985-01-01
The GCMDT (Generalized Coarse Mesh Diffusion Theory) is studied to use in the 2DB diffusion conventional code. An adequate formalism for its implementation in codes of 'Mesh-Centered' is developed for retangular, triangular and hexagonal geometries. (M.C.K.) [pt
International Nuclear Information System (INIS)
Zhou, Xiafeng; Guo, Jiong; Li, Fu
2015-01-01
Highlights: • NEMs are innovatively applied to solve convection diffusion equation. • Stability, accuracy and numerical diffusion for NEM are analyzed for the first time. • Stability and numerical diffusion depend on the NEM expansion order and its parity. • NEMs have higher accuracy than both second order upwind and QUICK scheme. • NEMs with different expansion orders are integrated into a unified discrete form. - Abstract: The traditional finite difference method or finite volume method (FDM or FVM) is used for HTGR thermal-hydraulic calculation at present. However, both FDM and FVM require the fine mesh sizes to achieve the desired precision and thus result in a limited efficiency. Therefore, a more efficient and accurate numerical method needs to be developed. Nodal expansion method (NEM) can achieve high accuracy even on the coarse meshes in the reactor physics analysis so that the number of spatial meshes and computational cost can be largely decreased. Because of higher efficiency and accuracy, NEM can be innovatively applied to thermal-hydraulic calculation. In the paper, NEMs with different orders of basis functions are successfully developed and applied to multi-dimensional steady convection diffusion equation. Numerical results show that NEMs with three or higher order basis functions can track the reference solutions very well and are superior to second order upwind scheme and QUICK scheme. However, the false diffusion and unphysical oscillation behavior are discovered for NEMs. To explain the reasons for the above-mentioned behaviors, the stability, accuracy and numerical diffusion properties of NEM are analyzed by the Fourier analysis, and by comparing with exact solutions of difference and differential equation. The theoretical analysis results show that the accuracy of NEM increases with the expansion order. However, the stability and numerical diffusion properties depend not only on the order of basis functions but also on the parity of
Energy Technology Data Exchange (ETDEWEB)
Zhou, Xiafeng, E-mail: zhou-xf11@mails.tsinghua.edu.cn; Guo, Jiong, E-mail: guojiong12@tsinghua.edu.cn; Li, Fu, E-mail: lifu@tsinghua.edu.cn
2015-12-15
Highlights: • NEMs are innovatively applied to solve convection diffusion equation. • Stability, accuracy and numerical diffusion for NEM are analyzed for the first time. • Stability and numerical diffusion depend on the NEM expansion order and its parity. • NEMs have higher accuracy than both second order upwind and QUICK scheme. • NEMs with different expansion orders are integrated into a unified discrete form. - Abstract: The traditional finite difference method or finite volume method (FDM or FVM) is used for HTGR thermal-hydraulic calculation at present. However, both FDM and FVM require the fine mesh sizes to achieve the desired precision and thus result in a limited efficiency. Therefore, a more efficient and accurate numerical method needs to be developed. Nodal expansion method (NEM) can achieve high accuracy even on the coarse meshes in the reactor physics analysis so that the number of spatial meshes and computational cost can be largely decreased. Because of higher efficiency and accuracy, NEM can be innovatively applied to thermal-hydraulic calculation. In the paper, NEMs with different orders of basis functions are successfully developed and applied to multi-dimensional steady convection diffusion equation. Numerical results show that NEMs with three or higher order basis functions can track the reference solutions very well and are superior to second order upwind scheme and QUICK scheme. However, the false diffusion and unphysical oscillation behavior are discovered for NEMs. To explain the reasons for the above-mentioned behaviors, the stability, accuracy and numerical diffusion properties of NEM are analyzed by the Fourier analysis, and by comparing with exact solutions of difference and differential equation. The theoretical analysis results show that the accuracy of NEM increases with the expansion order. However, the stability and numerical diffusion properties depend not only on the order of basis functions but also on the parity of
A self-consistent nodal method in response matrix formalism for the multigroup diffusion equations
International Nuclear Information System (INIS)
Malambu, E.M.; Mund, E.H.
1996-01-01
We develop a nodal method for the multigroup diffusion equations, based on the transverse integration procedure (TIP). The efficiency of the method rests upon the convergence properties of a high-order multidimensional nodal expansion and upon numerical implementation aspects. The discrete 1D equations are cast in response matrix formalism. The derivation of the transverse leakage moments is self-consistent i.e. does not require additional assumptions. An outstanding feature of the method lies in the linear spatial shape of the local transverse leakage for the first-order scheme. The method is described in the two-dimensional case. The method is validated on some classical benchmark problems. (author)
Hybrid nodal methods in the solution of the diffusion equations in X Y geometry
International Nuclear Information System (INIS)
Hernandez M, N.; Alonso V, G.; Valle G, E. del
2003-01-01
In 1979, Hennart and collaborators applied several schemes of classic finite element in the numerical solution of the diffusion equations in X Y geometry and stationary state. Almost two decades then, in 1996, himself and other collaborators carried out a similar work but using nodal schemes type finite element. Continuing in this last direction, in this work a group it is described a set of several Hybrid Nodal schemes denominated (NH) as well as their application to solve the diffusion equations in multigroup in stationary state and X Y geometry. The term hybrid nodal it means that such schemes interpolate not only Legendre moments of face and of cell but also the values of the scalar flow of neutrons in the four corners of each cell or element of the spatial discretization of the domain of interest. All the schemes here considered are polynomials like they were it their predecessors. Particularly, its have developed and applied eight different hybrid nodal schemes that its are very nearby related with those developed by Hennart and collaborators in the past. It is treated of schemes in those that nevertheless that decreases the number of interpolation parameters it is conserved the accurate in relation to the bi-quadratic and bi-cubic schemes. Of these eight, three were described and applied in a previous work. It is the bi-lineal classic scheme as well as the hybrid nodal schemes, bi-quadratic and bi-cubic for that here only are described the other 5 hybrid nodal schemes although they are provided numerical results for several test problems with all them. (Author)
An analytical nodal method for time-dependent one-dimensional discrete ordinates problems
International Nuclear Information System (INIS)
Barros, R.C. de
1992-01-01
In recent years, relatively little work has been done in developing time-dependent discrete ordinates (S N ) computer codes. Therefore, the topic of time integration methods certainly deserves further attention. In this paper, we describe a new coarse-mesh method for time-dependent monoenergetic S N transport problesm in slab geometry. This numerical method preserves the analytic solution of the transverse-integrated S N nodal equations by constants, so we call our method the analytical constant nodal (ACN) method. For time-independent S N problems in finite slab geometry and for time-dependent infinite-medium S N problems, the ACN method generates numerical solutions that are completely free of truncation errors. Bsed on this positive feature, we expect the ACN method to be more accurate than conventional numerical methods for S N transport calculations on coarse space-time grids
International Nuclear Information System (INIS)
Yamamoto, Akio; Tatsumi, Masahiro
2006-01-01
In this paper, the scattered source subtraction (SSS) method is newly proposed to improve the spatial discretization error of the semi-analytic nodal method with the flat-source approximation. In the SSS method, the scattered source is subtracted from both side of the diffusion or the transport equation to make spatial variation of the source term to be small. The same neutron balance equation is still used in the SSS method. Since the SSS method just modifies coefficients of node coupling equations (those used in evaluation for the response of partial currents), its implementation is easy. Validity of the present method is verified through test calculations that are carried out in PWR multi-assemblies configurations. The calculation results show that the SSS method can significantly improve the spatial discretization error. Since the SSS method does not have any negative impact on execution time, convergence behavior and memory requirement, it will be useful to reduce the spatial discretization error of the semi-analytic nodal method with the flat-source approximation. (author)
Depletion Calculations for MTR Core Using MCNPX and Multi-Group Nodal Diffusion Methods
International Nuclear Information System (INIS)
Jaradata, Mustafa K.; Park, Chang Je; Lee, Byungchul
2013-01-01
In order to maintain a self-sustaining steady-state chain reaction, more fuel than is necessary in order to maintain a steady state chain reaction must be loaded. The introduction of this excess fuel increases the net multiplication capability of the system. In this paper MCNPX and multi-group nodal diffusion theory will be used for depletion calculations for MTR core. The eigenvalue and power distribution in the core will be compared for different burnup. Multi-group nodal diffusion theory with combination of NEWT-TRITON system was used to perform depletion calculations for 3Χ3 MTR core. 2G and 6G approximations were used and compared with MCNPX results for 2G approximation the maximum difference from MCNPX was 40 mk and for 6G approximation was 6 mk which is comparable to the MCNPX results. The calculated power using nodal code was almost the same MCNPX results. Finally the results of the multi-group nodal theory were acceptable and comparable to the calculated using MCNPX
An analytical approach for a nodal scheme of two-dimensional neutron transport problems
International Nuclear Information System (INIS)
Barichello, L.B.; Cabrera, L.C.; Prolo Filho, J.F.
2011-01-01
Research highlights: → Nodal equations for a two-dimensional neutron transport problem. → Analytical Discrete Ordinates Method. → Numerical results compared with the literature. - Abstract: In this work, a solution for a two-dimensional neutron transport problem, in cartesian geometry, is proposed, on the basis of nodal schemes. In this context, one-dimensional equations are generated by an integration process of the multidimensional problem. Here, the integration is performed for the whole domain such that no iterative procedure between nodes is needed. The ADO method is used to develop analytical discrete ordinates solution for the one-dimensional integrated equations, such that final solutions are analytical in terms of the spatial variables. The ADO approach along with a level symmetric quadrature scheme, lead to a significant order reduction of the associated eigenvalues problems. Relations between the averaged fluxes and the unknown fluxes at the boundary are introduced as the usually needed, in nodal schemes, auxiliary equations. Numerical results are presented and compared with test problems.
International Nuclear Information System (INIS)
Fujimura, Toichiro; Okumura, Keisuke
2002-11-01
A prototype version of a diffusion code has been developed to analyze the hexagonal core as reduced moderation reactor and the applicability of some acceleration methods have been investigated to accelerate the convergence of the iterative solution method. The hexagonal core is divided into regular triangular prisms in the three-dimensional code MOSRA-Prism and a polynomial expansion nodal method is applied to approximate the neutron flux distribution by a cubic polynomial. The multi-group diffusion equation is solved iteratively with ordinal inner and outer iterations and the effectiveness of acceleration methods is ascertained by applying an adaptive acceleration method and a neutron source extrapolation method, respectively. The formulation of the polynomial expansion nodal method is outlined in the report and the local and global effectiveness of the acceleration methods is discussed with various sample calculations. A new general expression of vacuum boundary condition, derived in the formulation is also described. (author)
Application of nonlinear nodal diffusion method for a small research reactor
International Nuclear Information System (INIS)
Jaradat, Mustafa K.; Alawneh, Luay M.; Park, Chang Je; Lee, Byungchul
2014-01-01
Highlights: • We applied nonlinear unified nodal method for 10 MW IAEA MTR benchmark problem. • TRITION–NEWT system was used to obtain two-group burnup dependent cross sections. • The criticality and power distribution compared with reference (IAEA-TECDOC-233). • Comparison between different fuel materials was conducted. • Satisfactory results were provided using UNM for MTR core calculations. - Abstract: Nodal diffusion methods are usually used for LWR calculations and rarely used for research reactor calculations. A unified nodal method with an implementation of the coarse mesh finite difference acceleration was developed for use in plate type research reactor calculations. It was validated for two PWR benchmark problems and then applied for IAEA MTR benchmark problem for static calculations to check the validity and accuracy of the method. This work was conducted to investigate the unified nodal method capability to treat material testing reactor cores. A 10 MW research reactor core is considered with three calculation cases for low enriched uranium fuel depending on the core burnup status of fresh, beginning-of-life, and end-of-life cores. The validation work included criticality calculations, flux distribution, and power distribution; in addition, a comparison between different fuel materials with the same uranium content was conducted. The homogenized two-group cross sections were generated using the TRITON–NEWT system. The results were compared with a reference, which was taken from IAEA-TECDOC-233. The unified nodal method provides satisfactory results for an all-rod out case, and the three-dimensional, two-group diffusion model can be considered accurate enough for MTR core calculations
International Nuclear Information System (INIS)
Ackroyd, R.T.
1987-01-01
A least squares principle is described which uses a penalty function treatment of boundary and interface conditions. Appropriate choices of the trial functions and vectors employed in a dual representation of an approximate solution established complementary principles for the diffusion equation. A geometrical interpretation of the principles provides weighted residual methods for diffusion theory, thus establishing a unification of least squares, variational and weighted residual methods. The complementary principles are used with either a trial function for the flux or a trial vector for the current to establish for regular meshes a connection between finite element, finite difference and nodal methods, which can be exact if the mesh pitches are chosen appropriately. Whereas the coefficients in the usual nodal equations have to be determined iteratively, those derived via the complementary principles are given explicitly in terms of the data. For the further development of the connection between finite element, finite difference and nodal methods, some hybrid variational methods are described which employ both a trial function and a trial vector. (author)
Energy Technology Data Exchange (ETDEWEB)
Hernandez M, N. [CFE, Carretera Cardel-Nautla Km. 43.5, 91680 Veracruz (Mexico); Alonso V, G.; Valle G, E. del [IPN-ESFM, 07738 Mexico D.F. (Mexico)]. e-mail: nhmiranda@mexico.com
2003-07-01
In 1979, Hennart and collaborators applied several schemes of classic finite element in the numerical solution of the diffusion equations in X Y geometry and stationary state. Almost two decades then, in 1996, himself and other collaborators carried out a similar work but using nodal schemes type finite element. Continuing in this last direction, in this work a group it is described a set of several Hybrid Nodal schemes denominated (NH) as well as their application to solve the diffusion equations in multigroup in stationary state and X Y geometry. The term hybrid nodal it means that such schemes interpolate not only Legendre moments of face and of cell but also the values of the scalar flow of neutrons in the four corners of each cell or element of the spatial discretization of the domain of interest. All the schemes here considered are polynomials like they were it their predecessors. Particularly, its have developed and applied eight different hybrid nodal schemes that its are very nearby related with those developed by Hennart and collaborators in the past. It is treated of schemes in those that nevertheless that decreases the number of interpolation parameters it is conserved the accurate in relation to the bi-quadratic and bi-cubic schemes. Of these eight, three were described and applied in a previous work. It is the bi-lineal classic scheme as well as the hybrid nodal schemes, bi-quadratic and bi-cubic for that here only are described the other 5 hybrid nodal schemes although they are provided numerical results for several test problems with all them. (Author)
A coarse-mesh nodal method-diffusive-mesh finite difference method
International Nuclear Information System (INIS)
Joo, H.; Nichols, W.R.
1994-01-01
Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross sections (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly-coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extreme values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes, and can lead to a difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the Diffusive-Mesh Finite Difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper
Wielandt method applied to the diffusion equations discretized by finite element nodal methods
International Nuclear Information System (INIS)
Mugica R, A.; Valle G, E. del
2003-01-01
Nowadays the numerical methods of solution to the diffusion equation by means of algorithms and computer programs result so extensive due to the great number of routines and calculations that should carry out, this rebounds directly in the execution times of this programs, being obtained results in relatively long times. This work shows the application of an acceleration method of the convergence of the classic method of those powers that it reduces notably the number of necessary iterations for to obtain reliable results, what means that the compute times they see reduced in great measure. This method is known in the literature like Wielandt method and it has incorporated to a computer program that is based on the discretization of the neutron diffusion equations in plate geometry and stationary state by polynomial nodal methods. In this work the neutron diffusion equations are described for several energy groups and their discretization by means of those called physical nodal methods, being illustrated in particular the quadratic case. It is described a model problem widely described in the literature which is solved for the physical nodal grade schemes 1, 2, 3 and 4 in three different ways: to) with the classic method of the powers, b) method of the powers with the Wielandt acceleration and c) method of the powers with the Wielandt modified acceleration. The results for the model problem as well as for two additional problems known as benchmark problems are reported. Such acceleration method can also be implemented to problems of different geometry to the proposal in this work, besides being possible to extend their application to problems in 2 or 3 dimensions. (Author)
Two-dimensional semi-analytic nodal method for multigroup pin power reconstruction
International Nuclear Information System (INIS)
Seung Gyou, Baek; Han Gyu, Joo; Un Chul, Lee
2007-01-01
A pin power reconstruction method applicable to multigroup problems involving square fuel assemblies is presented. The method is based on a two-dimensional semi-analytic nodal solution which consists of eight exponential terms and 13 polynomial terms. The 13 polynomial terms represent the particular solution obtained under the condition of a 2-dimensional 13 term source expansion. In order to achieve better approximation of the source distribution, the least square fitting method is employed. The 8 exponential terms represent a part of the analytically obtained homogeneous solution and the 8 coefficients are determined by imposing constraints on the 4 surface average currents and 4 corner point fluxes. The surface average currents determined from a transverse-integrated nodal solution are used directly whereas the corner point fluxes are determined during the course of the reconstruction by employing an iterative scheme that would realize the corner point balance condition. The outgoing current based corner point flux determination scheme is newly introduced. The accuracy of the proposed method is demonstrated with the L336C5 benchmark problem. (authors)
International Nuclear Information System (INIS)
Kirk, B.L.; Azmy, Y.Y.
1992-01-01
In this paper the one-group, steady-state neutron diffusion equation in two-dimensional Cartesian geometry is solved using the nodal integral method. The discrete variable equations comprise loosely coupled sets of equations representing the nodal balance of neutrons, as well as neutron current continuity along rows or columns of computational cells. An iterative algorithm that is more suitable for solving large problems concurrently is derived based on the decomposition of the spatial domain and is accelerated using successive overrelaxation. This algorithm is very well suited for parallel computers, especially since the spatial domain decomposition occurs naturally, so that the number of iterations required for convergence does not depend on the number of processors participating in the calculation. Implementation of the authors' algorithm on the Intel iPSC/2 hypercube and Sequent Balance 8000 parallel computer is presented, and measured speedup and efficiency for test problems are reported. The results suggest that the efficiency of the hypercube quickly deteriorates when many processors are used, while the Sequent Balance retains very high efficiency for a comparable number of participating processors. This leads to the conjecture that message-passing parallel computers are not as well suited for this algorithm as shared-memory machines
International Nuclear Information System (INIS)
Maldonado, G.I.; Turinsky, P.J.
1995-01-01
The determination of the family of optimum core loading patterns for pressurized water reactors (PWRs) involves the assessment of the core attributes for thousands of candidate loading patterns. For this reason, the computational capability to efficiently and accurately evaluate a reactor core's eigenvalue and power distribution versus burnup using a nodal diffusion generalized perturbation theory (GPT) model is developed. The GPT model is derived from the forward nonlinear iterative nodal expansion method (NEM) to explicitly enable the preservation of the finite difference matrix structure. This key feature considerably simplifies the mathematical formulation of NEM GPT and results in reduced memory storage and CPU time requirements versus the traditional response-matrix approach to NEM. In addition, a treatment within NEM GPT can account for localized nonlinear feedbacks, such as that due to fission product buildup and thermal-hydraulic effects. When compared with a standard nonlinear iterative NEM forward flux solve with feedbacks, the NEM GPT model can execute between 8 and 12 times faster. These developments are implemented within the PWR in-core nuclear fuel management optimization code FORMOSA-P, combining the robustness of its adaptive simulated annealing stochastic optimization algorithm with an NEM GPT neutronics model that efficiently and accurately evaluates core attributes associated with objective functions and constraints of candidate loading patterns
The Nodal Polynomial Expansion method to solve the multigroup diffusion equations
International Nuclear Information System (INIS)
Ribeiro, R.D.M.
1983-03-01
The methodology of the solutions of the multigroup diffusion equations and uses the Nodal Polynomial Expansion Method is covered. The EPON code was developed based upon the above mentioned method for stationary state, rectangular geometry, one-dimensional or two-dimensional and for one or two energy groups. Then, one can study some effects such as the influence of the baffle on the thermal flux by calculating the flux and power distribution in nuclear reactors. Furthermore, a comparative study with other programs which use Finite Difference (CITATION and PDQ5) and Finite Element (CHD and FEMB) Methods was undertaken. As a result, the coherence, feasibility, speed and accuracy of the methodology used were demonstrated. (Author) [pt
International Nuclear Information System (INIS)
Filho, J. F. P.; Barichello, L. B.
2013-01-01
In this work, an analytical discrete ordinates method is used to solve a nodal formulation of a neutron transport problem in x, y-geometry. The proposed approach leads to an important reduction in the order of the associated eigenvalue systems, when combined with the classical level symmetric quadrature scheme. Auxiliary equations are proposed, as usually required for nodal methods, to express the unknown fluxes at the boundary introduced as additional unknowns in the integrated equations. Numerical results, for the problem defined by a two-dimensional region with a spatially constant and isotropically emitting source, are presented and compared with those available in the literature. (authors)
Energy Technology Data Exchange (ETDEWEB)
Zmijarevic, I; Tomashevic, Dj [Institut za Nuklearne Nauke Boris Kidric, Belgrade (Yugoslavia)
1988-07-01
This paper presents Chebychev acceleration of outer iterations of a nodal diffusion code of high accuracy. Extrapolation parameters, unique for all moments are calculated using the node integrated distribution of fission source. Sample calculations are presented indicating the efficiency of method. (author)
Energy Technology Data Exchange (ETDEWEB)
Lawrence, R.D.
1983-03-01
A nodal method is developed for the solution of the neutron-diffusion equation in two- and three-dimensional hexagonal geometries. The nodal scheme has been incorporated as an option in the finite-difference diffusion-theory code DIF3D, and is intended for use in the analysis of current LMFBR designs. The nodal equations are derived using higher-order polynomial approximations to the spatial dependence of the flux within the hexagonal-z node. The final equations, which are cast in the form of inhomogeneous response-matrix equations for each energy group, involved spatial moments of the node-interior flux distribution plus surface-averaged partial currents across the faces of the node. These equations are solved using a conventional fission-source iteration accelerated by coarse-mesh rebalance and asymptotic source extrapolation. This report describes the mathematical development and numerical solution of the nodal equations, as well as the use of the nodal option and details concerning its programming structure. This latter information is intended to supplement the information provided in the separate documentation of the DIF3D code.
International Nuclear Information System (INIS)
Lawrence, R.D.
1983-03-01
A nodal method is developed for the solution of the neutron-diffusion equation in two- and three-dimensional hexagonal geometries. The nodal scheme has been incorporated as an option in the finite-difference diffusion-theory code DIF3D, and is intended for use in the analysis of current LMFBR designs. The nodal equations are derived using higher-order polynomial approximations to the spatial dependence of the flux within the hexagonal-z node. The final equations, which are cast in the form of inhomogeneous response-matrix equations for each energy group, involved spatial moments of the node-interior flux distribution plus surface-averaged partial currents across the faces of the node. These equations are solved using a conventional fission-source iteration accelerated by coarse-mesh rebalance and asymptotic source extrapolation. This report describes the mathematical development and numerical solution of the nodal equations, as well as the use of the nodal option and details concerning its programming structure. This latter information is intended to supplement the information provided in the separate documentation of the DIF3D code
International Nuclear Information System (INIS)
Lee, Joo Hee
2006-02-01
There is growing interest in developing pebble bed reactors (PBRs) as a candidate of very high temperature gas-cooled reactors (VHTRs). Until now, most existing methods of nuclear design analysis for this type of reactors are base on old finite-difference solvers or on statistical methods. But for realistic analysis of PBRs, there is strong desire of making available high fidelity nodal codes in three-dimensional (r,θ,z) cylindrical geometry. Recently, the Analytic Function Expansion Nodal (AFEN) method developed quite extensively in Cartesian (x,y,z) geometry and in hexagonal-z geometry was extended to two-group (r,z) cylindrical geometry, and gave very accurate results. In this thesis, we develop a method for the full three-dimensional cylindrical (r,θ,z) geometry and implement the method into a code named TOPS. The AFEN methodology in this geometry as in hexagonal geometry is 'robus' (e.g., no occurrence of singularity), due to the unique feature of the AFEN method that it does not use the transverse integration. The transverse integration in the usual nodal methods, however, leads to an impasse, that is, failure of the azimuthal term to be transverse-integrated over r-z surface. We use 13 nodal unknowns in an outer node and 7 nodal unknowns in an innermost node. The general solution of the node can be expressed in terms of that nodal unknowns, and can be updated using the nodal balance equation and the current continuity condition. For more realistic analysis of PBRs, we implemented em Marshak boundary condition to treat the incoming current zero boundary condition and the partial current translation (PCT) method to treat voids in the core. The TOPS code was verified in the various numerical tests derived from Dodds problem and PBMR-400 benchmark problem. The results of the TOPS code show high accuracy and fast computing time than the VENTURE code that is based on finite difference method (FDM)
International Nuclear Information System (INIS)
Halilou, A.; Lounici, A.
1981-01-01
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
Energy Technology Data Exchange (ETDEWEB)
Duerigen, Susan
2013-05-15
The superior advantage of a nodal method for reactor cores with hexagonal fuel assemblies discretized as cells consisting of equilateral triangles is its mesh refinement capability. In this thesis, a diffusion and a simplified P{sub 3} (or SP{sub 3}) neutron transport nodal method are developed based on trigonal geometry. Both models are implemented in the reactor dynamics code DYN3D. As yet, no other well-established nodal core analysis code comprises an SP{sub 3} transport theory model based on trigonal meshes. The development of two methods based on different neutron transport approximations but using identical underlying spatial trigonal discretization allows a profound comparative analysis of both methods with regard to their mathematical derivations, nodal expansion approaches, solution procedures, and their physical performance. The developed nodal approaches can be regarded as a hybrid NEM/AFEN form. They are based on the transverse-integration procedure, which renders them computationally efficient, and they use a combination of polynomial and exponential functions to represent the neutron flux moments of the SP{sub 3} and diffusion equations, which guarantees high accuracy. The SP{sub 3} equations are derived in within-group form thus being of diffusion type. On this basis, the conventional diffusion solver structure can be retained also for the solution of the SP{sub 3} transport problem. The verification analysis provides proof of the methodological reliability of both trigonal DYN3D models. By means of diverse hexagonal academic benchmark and realistic detailed-geometry full-transport-theory problems, the superiority of the SP{sub 3} transport over the diffusion model is demonstrated in cases with pronounced anisotropy effects, which is, e.g., highly relevant to the modeling of fuel assemblies comprising absorber material.
Analytical solutions to matrix diffusion problems
Energy Technology Data Exchange (ETDEWEB)
Kekäläinen, Pekka, E-mail: pekka.kekalainen@helsinki.fi [Laboratory of Radiochemistry, Department of Chemistry, P.O. Box 55, FIN-00014 University of Helsinki (Finland)
2014-10-06
We report an analytical method to solve in a few cases of practical interest the equations which have traditionally been proposed for the matrix diffusion problem. In matrix diffusion, elements dissolved in ground water can penetrate the porous rock surronuding the advective flow paths. In the context of radioactive waste repositories this phenomenon provides a mechanism by which the area of rock surface in contact with advecting elements is greatly enhanced, and can thus be an important delay mechanism. The cases solved are relevant for laboratory as well for in situ experiments. Solutions are given as integral representations well suited for easy numerical solution.
International Nuclear Information System (INIS)
Barros, R.C. de.
1992-05-01
Presented here is a new numerical nodal method for the simulation of the axial power distribution within nuclear reactors using the one-dimensional one speed kinetics diffusion model with one group of delayed neutron precursors. Our method is based on a spectral analysis of the nodal kinetics equations. These equations are obtained by integrating the original kinetics equations separately over a time step and over a spatial node, and then considering flat approximations for the forward difference terms. These flat approximations are the only approximations that are considered in the method. As a result, the spectral nodal method for space - time reactor kinetics generates numerical solutions for space independent problems or for time independent problems that are completely free from truncation errors. We show numerical results to illustrate the method's accuracy for coarse mesh calculations. (author)
MOSRA-Light; high speed three-dimensional nodal diffusion code for vector computers
Energy Technology Data Exchange (ETDEWEB)
Okumura, Keisuke [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1998-10-01
MOSRA-Light is a three-dimensional neutron diffusion calculation code for X-Y-Z geometry. It is based on the 4th order polynomial nodal expansion method (NEM). As the 4th order NEM is not sensitive to mesh sizes, accurate calculation is possible by the use of coarse meshes of about 20 cm. The drastic decrease of number of unknowns in a 3-dimensional problem results in very fast computation. Furthermore, it employs newly developed computation algorithm `boundary separated checkerboard sweep method` appropriate to vector computers. This method is very efficient because the speedup factor by vectorization increases, as a scale of problem becomes larger. Speed-up factor compared to the scalar calculation is from 20 to 40 in the case of PWR core calculation. Considering the both effects by the vectorization and the coarse mesh method, total speedup factor is more than 1000 as compared with conventional scalar code with the finite difference method. MOSRA-Light can be available on most of vector or scalar computers with the UNIX or it`s similar operating systems (e.g. freeware like Linux). Users can easily install it by the help of the conversation style installer. This report contains the general theory of NEM, the fast computation algorithm, benchmark calculation results and detailed information for usage of this code including input data instructions and sample input data. (author)
MOSRA-Light; high speed three-dimensional nodal diffusion code for vector computers
International Nuclear Information System (INIS)
Okumura, Keisuke
1998-10-01
MOSRA-Light is a three-dimensional neutron diffusion calculation code for X-Y-Z geometry. It is based on the 4th order polynomial nodal expansion method (NEM). As the 4th order NEM is not sensitive to mesh sizes, accurate calculation is possible by the use of coarse meshes of about 20 cm. The drastic decrease of number of unknowns in a 3-dimensional problem results in very fast computation. Furthermore, it employs newly developed computation algorithm 'boundary separated checkerboard sweep method' appropriate to vector computers. This method is very efficient because the speedup factor by vectorization increases, as a scale of problem becomes larger. Speed-up factor compared to the scalar calculation is from 20 to 40 in the case of PWR core calculation. Considering the both effects by the vectorization and the coarse mesh method, total speedup factor is more than 1000 as compared with conventional scalar code with the finite difference method. MOSRA-Light can be available on most of vector or scalar computers with the UNIX or it's similar operating systems (e.g. freeware like Linux). Users can easily install it by the help of the conversation style installer. This report contains the general theory of NEM, the fast computation algorithm, benchmark calculation results and detailed information for usage of this code including input data instructions and sample input data. (author)
Convergence properties of iterative algorithms for solving the nodal diffusion equations
International Nuclear Information System (INIS)
Azmy, Y.Y.; Kirk, B.L.
1990-01-01
We drive the five point form of the nodal diffusion equations in two-dimensional Cartesian geometry and develop three iterative schemes to solve the discrete-variable equations: the unaccelerated, partial Successive Over Relaxation (SOR), and the full SOR methods. By decomposing the iteration error into its Fourier modes, we determine the spectral radius of each method for infinite medium, uniform model problems, and for the unaccelerated and partial SOR methods for finite medium, uniform model problems. Also for the two variants of the SOR method we determine the optimal relaxation factor that results in the smallest number of iterations required for convergence. Our results indicate that the number of iterations for the unaccelerated and partial SOR methods is second order in the number of nodes per dimension, while, for the full SOR this behavior is first order, resulting in much faster convergence for very large problems. We successfully verify the results of the spectral analysis against those of numerical experiments, and we show that for the full SOR method the linear dependence of the number of iterations on the number of nodes per dimension is relatively insensitive to the value of the relaxation parameter, and that it remains linear even for heterogenous problems. 14 refs., 1 fig
De Novo Nodal Diffuse Large B-Cell Lymphoma: Identification of Biologic Prognostic Factors
International Nuclear Information System (INIS)
Abd El-Hameed, A.
2005-01-01
Diffuse large B-cell Lymphoma (DLBCL) represents the most frequent type of non-Hodgkin lymphoma (NHL). Although combination chemotherapy has improved the outcome, long-term cure is now possible for approximately 50% of all patients. making the search for parameters identifying patients at high risk particularly needed. The presence of bcl-2 gene rearrangement in de novo DLBCL suggests a possible follicle center cell origin and perhaps a distinct clinical behavior. This study investigated the frequency and prognostic significance of t( 14; 18) translocation and bcl-2 protein overexpression in a cohort of patients with de novo nodal DLBCL who where uniformly evaluated and treated. Material and Methods: A total of 40 patients with de novo nodal DLBCL treated at National Cancer Institute (NCI), Cairo University were investigated. Formal infixed, paraffin-embedded sections were analyzed for: I) bcl-2 gene rearrangement including major break point region (mbr) and minor cluster region (mcr) by polymerase chain reaction (PCR). and 2) bcl-2 protein expression by immunohistochemistry using Dako 124 clone. Results were correlated with the clinical features and subsequent clinical course. Bcl-2 gene rearrangement was detected in 8 cases (20%). 2 cases at mbr, and 6 cases at mcr. Bcl-2 protein (> I 0%) was expressed in 24 cases (60%), irrespective of the presence of t( 14; 18) translocation. The t( 14; 18), and bcl-2 protein overexpression were more frequently associated with failure to achieve a complete response to therapy (ρ=0.008. and 0.04. respectively). DLBCL patients with t(14;18), and bcl-2 protein expression had a significantly reduced 5-year disease free survival (ρ=0.04, and 0.01, respectively). The t( 14; 18) translocation, and bcl-2 protein expression define a group of DLBCL patients with a poor prognosis, and could be used to tailor treatment, and to identify candidates for therapeutic approaches. Geographic differences in t(14;18) may be related to the
International Nuclear Information System (INIS)
Zhang, H.; Rizwan-uddin; Dorning, J.J.
1995-01-01
A diffusion equation-based systematic homogenization theory and a self-consistent dehomogenization theory for fuel assemblies have been developed for use with coarse-mesh nodal diffusion calculations of light water reactors. The theoretical development is based on a multiple-scales asymptotic expansion carried out through second order in a small parameter, the ratio of the average diffusion length to the reactor characteristic dimension. By starting from the neutron diffusion equation for a three-dimensional heterogeneous medium and introducing two spatial scales, the development systematically yields an assembly-homogenized global diffusion equation with self-consistent expressions for the assembly-homogenized diffusion tensor elements and cross sections and assembly-surface-flux discontinuity factors. The rector eigenvalue 1/k eff is shown to be obtained to the second order in the small parameter, and the heterogeneous diffusion theory flux is shown to be obtained to leading order in that parameter. The latter of these two results provides a natural procedure for the reconstruction of the local fluxes and the determination of pin powers, even though homogenized assemblies are used in the global nodal diffusion calculation
Diffusion-accelerated solution of the 2-D x-y Sn equations with linear-bilinear nodal differencing
International Nuclear Information System (INIS)
Wareing, T.A.; Walters, W.F.; Morel, J.E.
1994-01-01
Recently a new diffusion-synthetic acceleration scheme was developed for solving the 2-D S n Equations in x-y geometry with bilinear-discontinuous finite element spatial discretization using a bilinear-discontinuous diffusion differencing scheme for the diffusion acceleration equations. This method differs from previous methods in that it is conditional efficient for problems with isotropic or nearly isotropic scattering. We have used the same bilinear-discontinuous diffusion scheme, and associated solution technique, to accelerate the x-y geometry S n equations with linear-bilinear nodal spatial differencing. We find that this leads to an unconditionally efficient solution method for problems with isotropic or nearly isotropic scattering. computational results are given which demonstrate this property
International Nuclear Information System (INIS)
Fedon-Magnaud, C.; Hennart, J.P.; Lautard, J.J.
1983-03-01
An unified formulation of non conforming finite elements with quadrature formula and simple nodal scheme is presented. The theoretical convergence is obtained for the previous scheme when the mesh is refined. Numerical tests are provided in order to bear out the theorical results
International Nuclear Information System (INIS)
Ribeiro, R.D.M.; Vellozo, S.O.; Botelho, D.A.
1983-01-01
The EPON computer code based in a Nodal Polynomial Expansion Method, wrote in Fortran IV, for steady-state, square geometry, one-dimensional or two-dimensional geometry and for one or two-energy group is presented. The neutron and power flux distributions for nuclear power plants were calculated, comparing with codes that use similar or different methodologies. The availability, economy and speed of the methodology is demonstrated. (E.G.) [pt
Nodal method for fast reactor analysis
International Nuclear Information System (INIS)
Shober, R.A.
1979-01-01
In this paper, a nodal method applicable to fast reactor diffusion theory analysis has been developed. This method has been shown to be accurate and efficient in comparison to highly optimized finite difference techniques. The use of an analytic solution to the diffusion equation as a means of determining accurate coupling relationships between nodes has been shown to be highly accurate and efficient in specific two-group applications, as well as in the current multigroup method
International Nuclear Information System (INIS)
Menezes, Welton Alves; Alves Filho, Hermes; Barros, Ricardo C.
2009-01-01
In this paper the X,Y-geometry SD-SGF-CN spectral nodal method, cf. spectral diamond-spectral Green's function-constant nodal, is used to determine the one-speed node-edge average angular fluxes in heterogeneous domains. This hybrid spectral nodal method uses the spectral diamond (SD) auxiliary equation for the multiplying regions and the spectral Green's function (SGF) auxiliary equation for the non-multiplying regions of the domain. Moreover, we consider constant approximations for the transverse-leakage terms in the transverse integrated S N nodal equations. We solve the SD-SGF-CN equations using the one-node block inversion (NBI) iterative scheme, which uses the most recent estimates available for the node-entering fluxes to evaluate the node-exiting fluxes in the directions that constitute the incoming fluxes for the adjacent node. Using these results, we offer an algorithm for analytical reconstruction of the coarse-mesh nodal solution within each spatial node, as localized numerical solutions are not generated by usual accurate nodal methods. Numerical results are presented to illustrate the accuracy of the present algorithm. (author)
Energy Technology Data Exchange (ETDEWEB)
Cho, Nam Zin; Lee, Joo Hee; Lee, Jae Jun; Yu, Hui; Lee, Gil Soo [Korea Advanced Institute of Science and Tehcnology, Daejeon (Korea, Republic of)
2006-03-15
There is growing interest in developing Pebble Bed Reactors(PBRs) as a candidate of Very High Temperature gas-cooled Reactors(VHTRs). Until now, most existing methods of nuclear design analysis for this type of reactors are base on old finite-difference solvers or on statistical methods. And other existing nodal cannot be adapted for this kind of reactors because of transverse integration problem. In this project, we developed the TOPS code in three dimensional cylindrical geometry based on Analytic Function Expansion Nodal (AFEN) method developed at KAIST. The TOPS code showed better results in computing time than FDM and MCNP. Also TOPS showed very accurate results in reactor analysis.
International Nuclear Information System (INIS)
Cho, Nam Zin; Lee, Joo Hee; Lee, Jae Jun; Yu, Hui; Lee, Gil Soo
2006-03-01
There is growing interest in developing Pebble Bed Reactors(PBRs) as a candidate of Very High Temperature gas-cooled Reactors(VHTRs). Until now, most existing methods of nuclear design analysis for this type of reactors are base on old finite-difference solvers or on statistical methods. And other existing nodal cannot be adapted for this kind of reactors because of transverse integration problem. In this project, we developed the TOPS code in three dimensional cylindrical geometry based on Analytic Function Expansion Nodal (AFEN) method developed at KAIST. The TOPS code showed better results in computing time than FDM and MCNP. Also TOPS showed very accurate results in reactor analysis
International Nuclear Information System (INIS)
Barros, R. C.; Filho, H. A.; Platt, G. M.; Oliveira, F. B. S.; Militao, D. S.
2009-01-01
Coarse-mesh numerical methods are very efficient in the sense that they generate accurate results in short computational time, as the number of floating point operations generally decrease, as a result of the reduced number of mesh points. On the other hand, they generate numerical solutions that do not give detailed information on the problem solution profile, as the grid points can be located considerably away from each other. In this paper we describe two analytical reconstruction schemes for the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates (S N ) transport model in slab geometry. The first scheme we describe is based on the analytical reconstruction of the coarse-mesh solution within each discretization cell of the spatial grid set up on the slab. The second scheme is based on the angular reconstruction of the discrete ordinates solution between two contiguous ordinates of the angular quadrature set used in the S N model. Numerical results are given so we can illustrate the accuracy of the two reconstruction schemes, as described in this paper. (authors)
Exact analytical solutions for nonlinear reaction-diffusion equations
International Nuclear Information System (INIS)
Liu Chunping
2003-01-01
By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way
Analytically solvable models of reaction-diffusion systems
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E P; Kassner, K [Institut fuer Theoretische Physik, Otto-von-Guericke-Universitaet, Universitaetsplatz 2, 39106 Magdeburg (Germany)
2004-05-01
We consider a class of analytically solvable models of reaction-diffusion systems. An analytical treatment is possible because the nonlinear reaction term is approximated by a piecewise linear function. As particular examples we choose front and pulse solutions to illustrate the matching procedure in the one-dimensional case.
International Nuclear Information System (INIS)
Shuto, Kiyohiko; Saito, Hiroshige; Ohira, Gaku
2009-01-01
We evaluated the power of diffusion-weighted MR imaging with background body signal suppression (DWIBS) in patients with postoperative lymph node recurrence of esophageal cancer and compared with fluorodeoxyglucose-positron emission tomography (FDG-PET) findings. Forty-seven suspected lesions by multi detector row CT (MDCT) were enrolled. No significant difference between DWIBS and PET was observed in sensitivity (95% vs 97%), positive predictive value (PPV) (83% vs 90%) and overall accuracy rate (81% vs 87%). The apparent diffusion coefficients (ADCs) (x 10 -3 mm 2 /s) of recurrent nodes, primary cancer and normal esophagus were 1.124, 1.058 and 2.079, respectively. ADCs of recurrent nodes were significantly lower than those of normal esophagus (p<0.0001). The cut-off ADC line of 1.5 revealed 100% overall accuracy for separating the recurrent lesion from normal esophagus. Noninvasive DWIBS may become a valid modality to discriminate nodal recurrence of esophageal cancer by no means inferior to PET. (author)
International Nuclear Information System (INIS)
Azmy, Y.Y.; Kirk, B.L.
1990-01-01
Modern parallel computer architectures offer an enormous potential for reducing CPU and wall-clock execution times of large-scale computations commonly performed in various applications in science and engineering. Recently, several authors have reported their efforts in developing and implementing parallel algorithms for solving the neutron diffusion equation on a variety of shared- and distributed-memory parallel computers. Testing of these algorithms for a variety of two- and three-dimensional meshes showed significant speedup of the computation. Even for very large problems (i.e., three-dimensional fine meshes) executed concurrently on a few nodes in serial (nonvector) mode, however, the measured computational efficiency is very low (40 to 86%). In this paper, the authors present a highly efficient (∼85 to 99.9%) algorithm for solving the two-dimensional nodal diffusion equations on the Sequent Balance 8000 parallel computer. Also presented is a model for the performance, represented by the efficiency, as a function of problem size and the number of participating processors. The model is validated through several tests and then extrapolated to larger problems and more processors to predict the performance of the algorithm in more computationally demanding situations
International Nuclear Information System (INIS)
Garcia-Herranz, Nuria; Cabellos, Oscar; Aragones, Jose M.; Ahnert, Carol
2003-01-01
In order to take into account in a more effective and accurate way the intranodal heterogeneities in coarse-mesh finite-difference (CMFD) methods, a new equivalent parameter generation methodology has been developed and tested. This methodology accounts for the dependence of the nodal homogeneized two-group cross sections and nodal coupling factors, with interface flux discontinuity (IFD) factors that account for heterogeneities on the flux-spectrum and burnup intranodal distributions as well as on neighbor effects.The methodology has been implemented in an analytic CMFD method, rigorously obtained for homogeneous nodes with transverse leakage and generalized now for heterogeneous nodes by including IFD heterogeneity factors. When intranodal mesh node heterogeneity vanishes, the heterogeneous solution tends to the analytic homogeneous nodal solution. On the other hand, when intranodal heterogeneity increases, a high accuracy is maintained since the linear and nonlinear feedbacks on equivalent parameters have been shown to be as a very effective way of accounting for heterogeneity effects in two-group multidimensional coarse-mesh diffusion calculations
Energy Technology Data Exchange (ETDEWEB)
Mugica R, A.; Valle G, E. del [IPN, ESFM, 07738 Mexico D.F. (Mexico)]. e-mail: mugica@esfm.ipn.mx
2003-07-01
Nowadays the numerical methods of solution to the diffusion equation by means of algorithms and computer programs result so extensive due to the great number of routines and calculations that should carry out, this rebounds directly in the execution times of this programs, being obtained results in relatively long times. This work shows the application of an acceleration method of the convergence of the classic method of those powers that it reduces notably the number of necessary iterations for to obtain reliable results, what means that the compute times they see reduced in great measure. This method is known in the literature like Wielandt method and it has incorporated to a computer program that is based on the discretization of the neutron diffusion equations in plate geometry and stationary state by polynomial nodal methods. In this work the neutron diffusion equations are described for several energy groups and their discretization by means of those called physical nodal methods, being illustrated in particular the quadratic case. It is described a model problem widely described in the literature which is solved for the physical nodal grade schemes 1, 2, 3 and 4 in three different ways: to) with the classic method of the powers, b) method of the powers with the Wielandt acceleration and c) method of the powers with the Wielandt modified acceleration. The results for the model problem as well as for two additional problems known as benchmark problems are reported. Such acceleration method can also be implemented to problems of different geometry to the proposal in this work, besides being possible to extend their application to problems in 2 or 3 dimensions. (Author)
Energy Technology Data Exchange (ETDEWEB)
Basso Barichello, Liliane; Dias da Cunha, Rudnei [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Inst. de Matematica; Becker Picoloto, Camila [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Tres, Anderson [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada
2015-05-15
A nodal formulation of a fixed-source two-dimensional neutron transport problem, in Cartesian geometry, defined in a heterogeneous medium, is solved by an analytical approach. Explicit expressions, in terms of the spatial variables, are derived for averaged fluxes in each region in which the domain is subdivided. The procedure is an extension of an analytical discrete ordinates method, the ADO method, for the solution of the two-dimensional homogeneous medium case. The scheme is developed from the discrete ordinates version of the two-dimensional transport equation along with the level symmetric quadrature scheme. As usual for nodal schemes, relations between the averaged fluxes and the unknown angular fluxes at the contours are introduced as auxiliary equations. Numerical results are in agreement with results available in the literature.
International Nuclear Information System (INIS)
Petkov, Petko T.
2000-01-01
Most of the few-group three-dimensional nodal diffusion codes used for neutronics calculations of the WWER reactors use albedo type boundary conditions on the core-reflector boundary. The conventional albedo are group-to-group reflection probabilities, defined on each outer node face. The method of characteristics is used to calculate accurate albedo by the following procedure. A many-group two-dimensional heterogeneous core-reflector problem, including a sufficient part of the core and detailed description of the adjacent reflector, is solved first. From this solution the angular flux on the core-reflector boundary is calculated in all groups for all traced neutron directions. Accurate boundary conditions can be calculated for the radial, top and bottom reflectors as well as for the absorber part of the WWER-440 reactor control assemblies. The algorithm can be used to estimate also albedo, coupling outer node faces on the radial reflector in the axial direction. Numerical results for the WWER-440 reactor are presented. (Authors)
International Nuclear Information System (INIS)
Coulomb, F.
1989-06-01
The aim of this work is to study methods for solving the diffusion equation, based on a primal or mixed-dual finite elements discretization and well suited for use on multiprocessors computers; domain decomposition methods are the subject of the main part of this study, the linear systems being solved by the block-Jacobi method. The origin of the diffusion equation is explained in short, and various variational formulations are reminded. A survey of iterative methods is given. The elemination of the flux or current is treated in the case of a mixed method. Numerical tests are performed on two examples of reactors, in order to compare mixed elements and Lagrange elements. A theoretical study of domain decomposition is led in the case of Lagrange finite elements, and convergence conditions for the block-Jacobi method are derived; the dissection decomposition is previously the purpose of a particular numerical analysis. In the case of mixed-dual finite elements, a study is led on examples and is confirmed by numerical tests performed for the dissection decomposition; furthermore, after being justified, decompositions along axes of symmetry are numerically tested. In the case of a decomposition into two subdomains, the dissection decomposition and the decomposition with an integrated interface are compared. Alternative directions methods are defined; the convergence of those relative to Lagrange elements is shown; in the case of mixed elements, convergence conditions are found [fr
Liu, Song; Zhang, Yujuan; Xia, Jie; Chen, Ling; Guan, Wenxian; Guan, Yue; Ge, Yun; He, Jian; Zhou, Zhengyang
2017-10-01
To explore the application of histogram analysis in preoperative T and N staging of gastric cancers, with a focus on characteristic parameters of apparent diffusion coefficient (ADC) maps. Eighty-seven patients with gastric cancers underwent diffusion weighted magnetic resonance imaging (b=0, 1000s/mm 2 ), which generated ADC maps. Whole-volume histogram analysis was performed on ADC maps and 7 characteristic parameters were obtained. All those patients underwent surgery and postoperative pathologic T and N stages were determined. Four parameters, including skew, kurtosis, s-sD av and sample number, showed significant differences among gastric cancers at different T and N stages. Most parameters correlated with T and N stages significantly and worked in differentiating gastric cancers at different T or N stages. Especially skew yielded a sensitivity of 0.758, a specificity of 0.810, and an area under the curve (AUC) of 0.802 for differentiating gastric cancers with and without lymph node metastasis (Phistogram analysis could help assessing preoperative T and N stages of gastric cancers. Copyright © 2017. Published by Elsevier Inc.
Analytical solution to the hybrid diffusion-transport equation
International Nuclear Information System (INIS)
Nanneh, M.M.; Williams, M.M.R.
1986-01-01
A special integral equation was derived in previous work using a hybrid diffusion-transport theory method for calculating the flux distribution in slab lattices. In this paper an analytical solution of this equation has been carried out on a finite reactor lattice. The analytical results of disadvantage factors are shown to be accurate in comparison with the numerical results and accurate transport theory calculations. (author)
Nodal approximations of varying order by energy group for solving the diffusion equation
International Nuclear Information System (INIS)
Broda, J.T.
1992-02-01
The neutron flux across the nuclear reactor core is of interest to reactor designers and others. The diffusion equation, an integro-differential equation in space and energy, is commonly used to determine the flux level. However, the solution of a simplified version of this equation when automated is very time consuming. Since the flux level changes with time, in general, this calculation must be made repeatedly. Therefore solution techniques that speed the calculation while maintaining accuracy are desirable. One factor that contributes to the solution time is the spatial flux shape approximation used. It is common practice to use the same order flux shape approximation in each energy group even though this method may not be the most efficient. The one-dimensional, two-energy group diffusion equation was solved, for the node average flux and core k-effective, using two sets of spatial shape approximations for each of three reactor types. A fourth-order approximation in both energy groups forms the first set of approximations used. The second set used combines a second-order approximation with a fourth-order approximation in energy group two. Comparison of the results from the two approximation sets show that the use of a different order spatial flux shape approximation results in considerable loss in accuracy for the pressurized water reactor modeled. However, the loss in accuracy is small for the heavy water and graphite reactors modeled. The use of different order approximations in each energy group produces mixed results. Further investigation into the accuracy and computing time is required before any quantitative advantage of the use of the second-order approximation in energy group one and the fourth-order approximation in energy group two can be determined
Analytical solutions of one-dimensional advection–diffusion
Indian Academy of Sciences (India)
Analytical solutions are obtained for one-dimensional advection –diffusion equation with variable coefficients in a longitudinal ﬁnite initially solute free domain,for two dispersion problems.In the ﬁrst one,temporally dependent solute dispersion along uniform ﬂow in homogeneous domain is studied.In the second problem the ...
International Nuclear Information System (INIS)
Lee, Deokjung; Downar, Thomas J.; Kim, Yonghee
2004-01-01
An innovative hybrid spatial discretization method is proposed to improve the computational efficiency of pin-wise heterogeneous three-dimensional light water reactor (LWR) core neutronics analysis. The newly developed method employs the standard finite difference method in the x and y directions and the well-known nodal methods [nodal expansion method (NEM) and analytic nodal method (ANM) as needed] in the z direction. Four variants of the hybrid method are investigated depending on the axial nodal methodologies: HYBRID A, NEM with the conventional quadratic transverse leakage; HYBRID B, the conventional NEM method except that the transverse-leakage shapes are obtained from a fine-mesh local problem (FMLP) around the control rod tip; HYBRID C, the same as HYBRID B except that ANM with a high-order transverse leakage obtained from the FMLP is used in the vicinity of the control rod tip; and HYBRID D, the same as HYBRID C except that the transverse leakage is determined using the buckling approximation instead of the FMLP around the control rod tip. Benchmark calculations demonstrate that all the hybrid algorithms are consistent and stable and that the HYBRID C method provides the best numerical performance in the case of rodded LWR problems with pin-wise homogenized cross sections
International Nuclear Information System (INIS)
Turinsky, P.J.; Al-Chalabi, R.M.K.; Engrand, P.; Sarsour, H.N.; Faure, F.X.; Guo, W.
1994-06-01
NESTLE is a FORTRAN77 code that solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). NESTLE can solve the eigenvalue (criticality); eigenvalue adjoint; external fixed-source steady-state; or external fixed-source. or eigenvalue initiated transient problems. The code name NESTLE originates from the multi-problem solution capability, abbreviating Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two or four energy groups can be utilized, with all energy groups being thermal groups (i.e. upscatter exits) if desired. Core geometries modelled include Cartesian and Hexagonal. Three, two and one dimensional models can be utilized with various symmetries. The non-linear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NSTLE can be utilized to solve either the nodal or Finite Difference Method representation of the few-group neutron diffusion equation
International Nuclear Information System (INIS)
Putney, J.M.
1983-05-01
The characteristics of a simple parallel micro-processor (PMP) are reviewed and its software requirements discussed. One of the more immediate applications is the multi-spatial simulation of a nuclear reactor station. This is of particular interest because 3D reactor simulation might then be possible as part of operating procedure for PFR and CDFR. A major part of a multi-spatial reactor simulator is the solution of the neutron diffusion equation. A procedure is described for solving the equation on a PMP, which is applied to the nodal expansion method with modifications to the nodal expansion codes RECNEC and HEXNEC. Estimations of the micro-processor requirements for the simulation of both PFR and CDFR are given. (U.K.)
International Nuclear Information System (INIS)
Caron, D.; Dulla, S.; Ravetto, P.
2016-01-01
Highlights: • The implementation of the quasi-static method in 3D nodal diffusion theory model in hexagonal-z geometry is described. • Different formulations of the quasi-static technique are discussed. • The results presented illustrate the features of the various formulations, highlighting advantages and drawbacks. • A novel adaptive procedure for the selection of the time interval between shape recalculations is presented. - Abstract: The ability to accurately model the dynamic behaviour of the neutron distribution in a nuclear system is a fundamental aspect of reactor design and safety assessment. Due to the heavy computational burden associated to the direct time inversion of the full model, the quasi-static method has become a standard approach to the numerical solution of the nuclear reactor dynamic equations on the full phase space. The present paper is opened by an introductory critical review of the basics of the quasi-static scheme for the general neutron kinetic problem. Afterwards, the implementation of the quasi-static method in the context of a three-dimensional nodal diffusion theory model in hexagonal-z geometry is described, including some peculiar aspects of the adjoint nodal equations and the explicit formulation of the quasi-static nodal equations. The presentation includes the discussion of different formulations of the quasi-static technique. The results presented illustrate the features of the various formulations, highlighting the corresponding advantages and drawbacks. An adaptive procedure for the selection of the time interval between shape recalculations is also presented, showing its usefulness in practical applications.
International Nuclear Information System (INIS)
Esquivel E, J.; Alonso V, G.; Del Valle G, E.
2015-09-01
The solution of the neutron diffusion equation either for reactors in steady state or time dependent, is obtained through approximations generated by implementing of nodal methods such as RTN-0 (Raviart-Thomas-Nedelec of zero index), which is used in this study. Since the nodal methods are applied in quadrangular geometries, in this paper a technique in which the hexagonal geometry through the transfinite interpolation of Gordon-Hall becomes the appropriate geometry to make use of the nodal method RTN-0 is presented. As a result, a computer program was developed, whereby is possible to obtain among other results the neutron multiplication effective factor (k eff ), and the distribution of radial and/or axial power. To verify the operation of the code, was applied to three benchmark problems: in the first two reactors VVER and FBR, results k eff and power distribution are obtained, considering the steady state case of reactor; while the third problem a type VVER is analyzed, in its case dependent of time, which qualitative results are presented on the behavior of the reactor power. (Author)
Analytical model of diffuse reflectance spectrum of skin tissue
Energy Technology Data Exchange (ETDEWEB)
Lisenko, S A; Kugeiko, M M; Firago, V A [Belarusian State University, Minsk (Belarus); Sobchuk, A N [B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk (Belarus)
2014-01-31
We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions. (biophotonics)
Choi, Young Jun; Lee, Jeong Hyun; Kim, Hye Ok; Kim, Dae Yoon; Yoon, Ra Gyoung; Cho, So Hyun; Koh, Myeong Ju; Kim, Namkug; Kim, Sang Yoon; Baek, Jung Hwan
2016-01-01
To explore the added value of histogram analysis of apparent diffusion coefficient (ADC) values over magnetic resonance (MR) imaging and fluorine 18 ((18)F) fluorodeoxyglucose (FDG) positron emission tomography (PET)/computed tomography (CT) for the detection of occult palatine tonsil squamous cell carcinoma (SCC) in patients with cervical nodal metastasis from a cancer of an unknown primary site. The institutional review board approved this retrospective study, and the requirement for informed consent was waived. Differences in the bimodal histogram parameters of the ADC values were assessed among occult palatine tonsil SCC (n = 19), overt palatine tonsil SCC (n = 20), and normal palatine tonsils (n = 20). One-way analysis of variance was used to analyze differences among the three groups. Receiver operating characteristic curve analysis was used to determine the best differentiating parameters. The increased sensitivity of histogram analysis over MR imaging and (18)F-FDG PET/CT for the detection of occult palatine tonsil SCC was evaluated as added value. Histogram analysis showed statistically significant differences in the mean, standard deviation, and 50th and 90th percentile ADC values among the three groups (P histogram analysis was 52.6% over MR imaging alone and 15.8% over combined conventional MR imaging and (18)F-FDG PET/CT. Adding ADC histogram analysis to conventional MR imaging can improve the detection sensitivity for occult palatine tonsil SCC in patients with a cervical nodal metastasis originating from a cancer of an unknown primary site. © RSNA, 2015.
International Nuclear Information System (INIS)
Geemert, René van
2014-01-01
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 SP N 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
Analytic study of 1D diffusive relativistic shock acceleration
Energy Technology Data Exchange (ETDEWEB)
Keshet, Uri, E-mail: ukeshet@bgu.ac.il [Physics Department, Ben-Gurion University of the Negev, POB 653, Be' er-Sheva 84105 (Israel)
2017-10-01
Diffusive shock acceleration (DSA) by relativistic shocks is thought to generate the dN / dE ∝ E{sup −p} spectra of charged particles in various astronomical relativistic flows. We show that for test particles in one dimension (1D), p {sup −1}=1−ln[γ{sub d}(1+β{sub d})]/ln[γ{sub u}(1+β{sub u})], where β{sub u}(β{sub d}) is the upstream (downstream) normalized velocity, and γ is the respective Lorentz factor. This analytically captures the main properties of relativistic DSA in higher dimensions, with no assumptions on the diffusion mechanism. Unlike 2D and 3D, here the spectrum is sensitive to the equation of state even in the ultra-relativistic limit, and (for a J(üttner-Synge equation of state) noticeably hardens with increasing 1<γ{sub u}<57, before logarithmically converging back to p (γ{sub u→∞})=2. The 1D spectrum is sensitive to drifts, but only in the downstream, and not in the ultra-relativistic limit.
Development of nodal interface conditions for a PN approximation nodal model
International Nuclear Information System (INIS)
Feiz, M.
1993-01-01
A relation was developed for approximating higher order odd-moments from lower order odd-moments at the nodal interfaces of a Legendre polynomial nodal model. Two sample problems were tested using different order P N expansions in adjacent nodes. The developed relation proved to be adequate and matched the nodal interface flux accurately. The development allows the use of different order expansions in adjacent nodes, and will be used in a hybrid diffusion-transport nodal model. (author)
Super-nodal methods for space-time kinetics
Mertyurek, Ugur
The purpose of this research has been to develop an advanced Super-Nodal method to reduce the run time of 3-D core neutronics models, such as in the NESTLE reactor core simulator and FORMOSA nuclear fuel management optimization codes. Computational performance of the neutronics model is increased by reducing the number of spatial nodes used in the core modeling. However, as the number of spatial nodes decreases, the error in the solution increases. The Super-Nodal method reduces the error associated with the use of coarse nodes in the analyses by providing a new set of cross sections and ADFs (Assembly Discontinuity Factors) for the new nodalization. These so called homogenization parameters are obtained by employing consistent collapsing technique. During this research a new type of singularity, namely "fundamental mode singularity", is addressed in the ANM (Analytical Nodal Method) solution. The "Coordinate Shifting" approach is developed as a method to address this singularity. Also, the "Buckling Shifting" approach is developed as an alternative and more accurate method to address the zero buckling singularity, which is a more common and well known singularity problem in the ANM solution. In the course of addressing the treatment of these singularities, an effort was made to provide better and more robust results from the Super-Nodal method by developing several new methods for determining the transverse leakage and collapsed diffusion coefficient, which generally are the two main approximations in the ANM methodology. Unfortunately, the proposed new transverse leakage and diffusion coefficient approximations failed to provide a consistent improvement to the current methodology. However, improvement in the Super-Nodal solution is achieved by updating the homogenization parameters at several time points during a transient. The update is achieved by employing a refinement technique similar to pin-power reconstruction. A simple error analysis based on the relative
The adjoint variational nodal method
International Nuclear Information System (INIS)
Laurin-Kovitz, K.; Lewis, E.E.
1993-01-01
The widespread use of nodal methods for reactor core calculations in both diffusion and transport approximations has created a demand for the corresponding adjoint solutions as a prerequisite for performing perturbation calculations. With some computational methods, however, the solution of the adjoint problem presents a difficulty; the physical adjoint obtained by discretizing the adjoint equation is not the same as the mathematical adjoint obtained by taking the transpose of the coefficient matrix, which results from the discretization of the forward equation. This difficulty arises, in particular, when interface current nodal methods based on quasi-one-dimensional solution of the diffusion or transport equation are employed. The mathematical adjoint is needed to perform perturbation calculations. The utilization of existing nodal computational algorithms, however, requires the physical adjoint. As a result, similarity transforms or related techniques must be utilized to relate physical and mathematical adjoints. Thus far, such techniques have been developed only for diffusion theory
International Nuclear Information System (INIS)
Torej, Allen J.; Rizwan-Uddin
2001-01-01
The nodal integral method (NIM) has been developed for several problems, including the Navier-Stokes equations, the convection-diffusion equation, and the multigroup neutron diffusion equations. The coarse-mesh efficiency of the NIM is not fully realized in problems characterized by a wide range of spatial scales. However, the combination of adaptive mesh refinement (AMR) capability with the NIM can recover the coarse mesh efficiency by allowing high degrees of resolution in specific localized areas where it is needed and by using a lower resolution everywhere else. Furthermore, certain features of the NIM can be fruitfully exploited in the application of the AMR process. In this paper, we outline a general approach to couple nodal schemes with AMR and then apply it to the convection-diffusion (energy) equation. The development of the NIM with AMR capability (NIMAMR) is based on the well-known Berger-Oliger method for structured AMR. In general, the main components of all AMR schemes are 1. the solver; 2. the level-grid hierarchy; 3. the selection algorithm; 4. the communication procedures; 5. the governing algorithm. The first component, the solver, consists of the numerical scheme for the governing partial differential equations and the algorithm used to solve the resulting system of discrete algebraic equations. In the case of the NIM-AMR, the solver is the iterative approach to the solution of the set of discrete equations obtained by applying the NIM. Furthermore, in the NIM-AMR, the level-grid hierarchy (the second component) is based on the Hierarchical Adaptive Mesh Refinement (HAMR) system,6 and hence, the details of the hierarchy are omitted here. In the selection algorithm, regions of the domain that require mesh refinement are identified. The criterion to select regions for mesh refinement can be based on the magnitude of the gradient or on the Richardson truncation error estimate. Although an excellent choice for the selection criterion, the Richardson
A new analytical solution to the diffusion problem: Fourier series ...
African Journals Online (AJOL)
This paper reviews briefly the origin of Fourier Series Method. The paper then gives a vivid description of how the method can be applied to solve a diffusion problem, subject to some boundary conditions. The result obtained is quite appealing as it can be used to solve similar examples of diffusion equations. JONAMP Vol.
Analytic Method for Pressure Recovery in Truncated Diffusers ...
African Journals Online (AJOL)
A prediction method is presented for the static pressure recovery in subsonic axisymmetric truncated conical diffusers. In the analysis, a turbulent boundary layer is assumed at the diffuser inlet and a potential core exists throughout the flow. When flow separation occurs, this approach cannot be used to predict the maximum ...
A model of modulated diffusion. I. Analytical results
International Nuclear Information System (INIS)
Bazzani, A.; Turcchetti, G.; Vaienti, S.
1994-01-01
We introduce an integrable isochronous system and perturb its frequency by an external-deterministic or purely random-noise. Under the perturbation the action variable evolves in time: the corresponding diffusion coefficient is exactly computed and its dependence on the magnitude of the perturbation is carefully investigated. Different behaviors are found and justified: the quasilinear approximation, the superlinear regime, and the ballistic motion
Analytical approach for collective diffusion: one-dimensional heterogeneous lattice
Czech Academy of Sciences Publication Activity Database
Tarasenko, Alexander
2016-01-01
Roč. 144, č. 14 (2016), 1-11, č. článku 144105. ISSN 0021-9606 Institutional support: RVO:68378271 Keywords : diffusion * Monte Carlo simulations * one-dimensional heterogeneous lattice Subject RIV: BE - Theoretical Physics Impact factor: 2.965, year: 2016
An improved analytical model of diffusion through the RIST target
Bennett, J R J
2003-01-01
The diffusion and effusion through the RIST target is calculated using a more realistic model than previously. Extremely good fits to the data are obtained and new values of the time constants of effusion through the target and the ioniser are found.
Energy Technology Data Exchange (ETDEWEB)
Lumb, Matthew P. [The George Washington University, 2121 I Street NW, Washington, DC 20037 (United States); Naval Research Laboratory, Washington, DC 20375 (United States); Steiner, Myles A.; Geisz, John F. [National Renewable Energy Laboratory, Golden, Colorado 80401 (United States); Walters, Robert J. [Naval Research Laboratory, Washington, DC 20375 (United States)
2014-11-21
The analytical drift-diffusion formalism is able to accurately simulate a wide range of solar cell architectures and was recently extended to include those with back surface reflectors. However, as solar cells approach the limits of material quality, photon recycling effects become increasingly important in predicting the behavior of these cells. In particular, the minority carrier diffusion length is significantly affected by the photon recycling, with consequences for the solar cell performance. In this paper, we outline an approach to account for photon recycling in the analytical Hovel model and compare analytical model predictions to GaAs-based experimental devices operating close to the fundamental efficiency limit.
International Nuclear Information System (INIS)
Sato, Haruo
2001-01-01
A program (TDROCK1. FOR) for simulation and analysis of through-diffusion experiments for a single layer of diffusion media was developed. This program was made by Pro-Fortran language, which was suitable for scientific and technical calculations, and relatively easy explicit difference method was adopted for an analysis. In the analysis, solute concentration in the tracer cell as a function of time that we could not treat to date can be input and the decrease in the solute concentration as a function of time by diffusion from the tracer cell to the measurement cell, the solute concentration distribution in the porewater of diffusion media and the solute concentration in the measurement cell as a function of time can be calculated. In addition, solution volume in both cells and diameter and thickness of the diffusion media are also variable as an input condition. This simulation program could well explain measured result by simulating solute concentration in the measurement cell as a function of time for case which apparent and effective diffusion coefficients were already known. Based on this, the availability and applicability of this program to actual analysis and simulation were confirmed. This report describes the theoretical treatment for the through-diffusion experiments for a single layer of diffusion media, analytical model, an example of source program and the manual. (author)
Energy Technology Data Exchange (ETDEWEB)
Esquivel E, J.; Alonso V, G. [ININ, Carretera Mexico-Toluca s/n, 52750 Ocoyoacac, Estado de Mexico (Mexico); Del Valle G, E., E-mail: jaime.esquivel@inin.gob.mx [IPN, Escuela Superior de Fisica y Matematicas, Av. IPN s/n, Col. Lindavista, 07738 Ciudad de Mexico (Mexico)
2015-09-15
The solution of the neutron diffusion equation either for reactors in steady state or time dependent, is obtained through approximations generated by implementing of nodal methods such as RTN-0 (Raviart-Thomas-Nedelec of zero index), which is used in this study. Since the nodal methods are applied in quadrangular geometries, in this paper a technique in which the hexagonal geometry through the transfinite interpolation of Gordon-Hall becomes the appropriate geometry to make use of the nodal method RTN-0 is presented. As a result, a computer program was developed, whereby is possible to obtain among other results the neutron multiplication effective factor (k{sub eff}), and the distribution of radial and/or axial power. To verify the operation of the code, was applied to three benchmark problems: in the first two reactors VVER and FBR, results k{sub eff} and power distribution are obtained, considering the steady state case of reactor; while the third problem a type VVER is analyzed, in its case dependent of time, which qualitative results are presented on the behavior of the reactor power. (Author)
Analytical performance bounds for multi-tensor diffusion-MRI.
Ahmed Sid, Farid; Abed-Meraim, Karim; Harba, Rachid; Oulebsir-Boumghar, Fatima
2017-02-01
To examine the effects of MR acquisition parameters on brain white matter fiber orientation estimation and parameter of clinical interest in crossing fiber areas based on the Multi-Tensor Model (MTM). We compute the Cramér-Rao Bound (CRB) for the MTM and the parameter of clinical interest such as the Fractional Anisotropy (FA) and the dominant fiber orientations, assuming that the diffusion MRI data are recorded by a multi-coil, multi-shell acquisition system. Considering the sum-of-squares method for the reconstructed magnitude image, we introduce an approximate closed-form formula for Fisher Information Matrix that has the simplicity and easy interpretation advantages. In addition, we propose to generalize the FA and the mean diffusivity to the multi-tensor model. We show the application of the CRB to reduce the scan time while preserving a good estimation precision. We provide results showing how the increase of the number of acquisition coils compensates the decrease of the number of diffusion gradient directions. We analyze the impact of the b-value and the Signal-to-Noise Ratio (SNR). The analysis shows that the estimation error variance decreases with a quadratic rate with the SNR, and that the optimum b-values are not unique but depend on the target parameter, the context, and eventually the target cost function. In this study we highlight the importance of choosing the appropriate acquisition parameters especially when dealing with crossing fiber areas. We also provide a methodology for the optimal tuning of these parameters using the CRB. Copyright © 2016 Elsevier Inc. All rights reserved.
Analytical modal diffusion theory based on flux separability
International Nuclear Information System (INIS)
Segev, M.
1987-01-01
The theory provides for an iterative solution of the mathematical problem of generating the assembly-wise power distribution in a LWR through the solution of the 2-group, multidimensional, diffusion equation. The companion problems of assembly pre-homogenization and of pin power reconstruction are of no direct concern presently. The theoretical development stems from the assumption of flux separability in X, Y and Z. The assumption derives from the notion that separability holds in a great part of the interior of a LWR assembly. More important, well accurate power maps are generated with a code based on the theoretical develpment yielded by the basic assumption
A family of analytical solutions of a nonlinear diffusion-convection equation
Hayek, Mohamed
2018-01-01
Despite its popularity in many engineering fields, the nonlinear diffusion-convection equation has no general analytical solutions. This work presents a family of closed-form analytical traveling wave solutions for the nonlinear diffusion-convection equation with power law nonlinearities. This kind of equations typically appears in nonlinear problems of flow and transport in porous media. The solutions that are addressed are simple and fully analytical. Three classes of analytical solutions are presented depending on the type of the nonlinear diffusion coefficient (increasing, decreasing or constant). It has shown that the structure of the traveling wave solution is strongly related to the diffusion term. The main advantage of the proposed solutions is that they are presented in a unified form contrary to existing solutions in the literature where the derivation of each solution depends on the specific values of the diffusion and convection parameters. The proposed closed-form solutions are simple to use, do not require any numerical implementation, and may be implemented in a simple spreadsheet. The analytical expressions are also useful to mathematically analyze the structure and properties of the solutions.
Heterogeneous treatment in the variational nodal method
International Nuclear Information System (INIS)
Fanning, T.H.
1995-01-01
The variational nodal transport method is reduced to its diffusion form and generalized for the treatment of heterogeneous nodes while maintaining nodal balances. Adapting variational methods to heterogeneous nodes requires the ability to integrate over a node with discontinuous cross sections. In this work, integrals are evaluated using composite gaussian quadrature rules, which permit accurate integration while minimizing computing time. Allowing structure within a nodal solution scheme avoids some of the necessity of cross section homogenization, and more accurately defines the intra-nodal flux shape. Ideally, any desired heterogeneity can be constructed within the node; but in reality, the finite set of basis functions limits the practical resolution to which fine detail can be defined within the node. Preliminary comparison tests show that the heterogeneous variational nodal method provides satisfactory results even if some improvements are needed for very difficult, configurations
Higher order polynomial expansion nodal method for hexagonal core neutronics analysis
International Nuclear Information System (INIS)
Jin, Young Cho; Chang, Hyo Kim
1998-01-01
A higher-order polynomial expansion nodal(PEN) method is newly formulated as a means to improve the accuracy of the conventional PEN method solutions to multi-group diffusion equations in hexagonal core geometry. The new method is applied to solving various hexagonal core neutronics benchmark problems. The computational accuracy of the higher order PEN method is then compared with that of the conventional PEN method, the analytic function expansion nodal (AFEN) method, and the ANC-H method. It is demonstrated that the higher order PEN method improves the accuracy of the conventional PEN method and that it compares very well with the other nodal methods like the AFEN and ANC-H methods in accuracy
Energy Technology Data Exchange (ETDEWEB)
Bennacer, R. [Neuville sur Oise, LEEVAM 5 mail Gay Lussac, Cergy-Pontoise Cedex (France); Mohamad, A.A. [CEERE University of Calgary, Department of Mechanical and Manufacturing Engineering, Calgary, Alberta (Canada); Ganaoui, M.El [Faculte des Sciences et Techniques de Limoges, Limoges (France)
2005-02-01
Double-diffusive natural convection within a multilayer anisotropic porous medium is studied numerically and analytically. The domain composed of two horizontal porous layers is subjected to a uniform horizontal heat flux and a vertical mass flux, where only the lower one is thermally anisotropic. Darcy model with classical Boussinesq approximation is used in formulating the mathematical model. The effect of thermal anisotropy and the relative width of the two layers on the flow and transfers is illustrated with characterising the transitions from the diffusive to the convective solution. Results were well compared with respect to a developed analytical approach, based on a parallel flow approximation for thermally anisotropic multilayer media. (orig.)
International Nuclear Information System (INIS)
Akiyama, Atsuyoshi; Katoh, Tadahiko; Kikutani, Eiji; Koiso, Haruyo; Kurokawa, Shin-ichi; Oide, Katsunobu.
1984-06-01
NODAL is an interpreter language for accelerator control developed at CERN SPS and has been used successfully since 1974. At present NODAL or NODAL-like languages are used at DESY PETRA and CERN CPS. At KEK, we have also adopted NODAL for the control of TRISTAN, a 30 GeV x 30 GeV electron-positron colliding beam facility. The KEK version of NODAL has the following improvements on the SPS NODAL: (1) the fast execution speed due to the compiler-interpreter scheme, and (2) the full-screen editing facility. This manual explains how to use the KEK NODAL. It is based on the manual of the SPS NODAL, THE NODAL SYSTEM FOR THE SPS, by M.C. Crowley-Milling and G.C. Shering, CERN 78-07. We have made some additions and modifications to make the manual more appropriate for the KEK NODAL system, paying attention to retaining the good features of the original SPS NODAL manual. We acknowledge Professor M.C. Crowley-Milling, Dr G.C. Shering and CERN for their kind permission for this modification. (author)
International Nuclear Information System (INIS)
Kurokawa, S.; Abe, K.; Akiyama, A.; Katoh, T.; Kikutani, E.; Koiso, H.; Kurihara, N.; Oide, K.; Shinomoto, M.
1985-01-01
The KEK NODAL system, which is based on the NODAL devised at the CERN SPS, works on an optical-fiber token ring network of twenty-four minicomputers (Hitachi HIDIC 80's) to control the TRISTAN accelerator complex, now being constructed at KEK. KEK NODAL retains main features of the original NODAL: the interpreting scheme, the multi-computer programming facility, and the data-module concept. In addition, it has the following characteristics: fast execution due to the compiler-interpreter method, a multicomputer file system, a full-screen editing facility, and a dynamic linkage scheme of data modules and NODAL functions. The structure of the KEK NODAL system under PMS, a real-time multitasking operating system of HIDIC 80, is described; the NODAL file system is also explained
The analytical solution to the 1D diffusion equation in heterogeneous media
International Nuclear Information System (INIS)
Ganapol, B.D.; Nigg, D.W.
2011-01-01
The analytical solution to the time-independent multigroup diffusion equation in heterogeneous plane cylindrical and spherical media is presented. The solution features the simplicity of the one-group formulation while addressing the complication of multigroup diffusion in a fully heterogeneous medium. Beginning with the vector form of the diffusion equation, the approach, based on straightforward mathematics, resolves a set of coupled second order ODEs. The analytical form is facilitated through matrix diagonalization of the neutron interaction matrix rendering the multigroup solution as a series of one-group solutions which, when re-assembled, gives the analytical solution. Customized Eigenmode solutions of the one-group diffusion operator then represent the homogeneous solution in a uniform spatial domain. Once the homogeneous solution is known, the particular solution naturally emerges through variation of parameters. The analytical expression is then numerically implemented through recurrence. Finally, we apply the theory to assess the accuracy of a second order finite difference scheme and to a 1D slab BWR reactor in the four-group approximation. (author)
Analytical approximate solutions of the time-domain diffusion equation in layered slabs.
Martelli, Fabrizio; Sassaroli, Angelo; Yamada, Yukio; Zaccanti, Giovanni
2002-01-01
Time-domain analytical solutions of the diffusion equation for photon migration through highly scattering two- and three-layered slabs have been obtained. The effect of the refractive-index mismatch with the external medium is taken into account, and approximate boundary conditions at the interface between the diffusive layers have been considered. A Monte Carlo code for photon migration through a layered slab has also been developed. Comparisons with the results of Monte Carlo simulations showed that the analytical solutions correctly describe the mean path length followed by photons inside each diffusive layer and the shape of the temporal profile of received photons, while discrepancies are observed for the continuous-wave reflectance or transmittance.
International Nuclear Information System (INIS)
Ceolin, Celina; Vilhena, Marco T.; Petersen, Claudio Z.
2009-01-01
In this work we report an analytical solution for the monoenergetic neutron diffusion kinetic equation in cartesian geometry. Bearing in mind that the equation for the delayed neutron precursor concentration is a first order linear differential equation in the time variable, to make possible the application of the GITT approach to the kinetic equation, we introduce a fictitious diffusion term multiplied by a positive small value ε. By this procedure, we are able to solve this set of equations. Indeed, applying the GITT technique to the modified diffusion kinetic equation, we come out with a matrix differential equation which has a well known analytical solution when ε goes to zero. We report numerical simulations as well study of numerical convergence of the results attained. (author)
Hosseinbor, Ameer Pasha; Chung, Moo K; Wu, Yu-Chien; Alexander, Andrew L
2011-01-01
The estimation of the ensemble average propagator (EAP) directly from q-space DWI signals is an open problem in diffusion MRI. Diffusion spectrum imaging (DSI) is one common technique to compute the EAP directly from the diffusion signal, but it is burdened by the large sampling required. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed. One, in particular, is Diffusion Propagator Imaging (DPI) which is based on the Laplace's equation estimation of diffusion signal for each shell acquisition. Viewed intuitively in terms of the heat equation, the DPI solution is obtained when the heat distribution between temperatuere measurements at each shell is at steady state. We propose a generalized extension of DPI, Bessel Fourier Orientation Reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition. That is, the heat distribution between shell measurements is no longer at steady state. In addition to being analytical, the BFOR solution also includes an intrinsic exponential smootheing term. We illustrate the effectiveness of the proposed method by showing results on both synthetic and real MR datasets.
Diffusion of rural innovations: some analytical issues and the case of wood-burning stoves
Energy Technology Data Exchange (ETDEWEB)
Agarwal, B
1983-04-01
The literature on the diffusion of rural innovations in Third World countries reveals a spectrum of approaches to the diffusion process. It is argued here that the effectiveness of a particular approach in the diffusion of particular innovations would depend on the technical, the economic, and the social characteristics of the innovations. A typology of innovations in terms of these characteristics has been drawn up. This provides the analytical framework within which the instance of wood-burning stoves is concerned. A priori, the characteristics of this innovation are seen to be such as to necessitate the close involvement of the users approach to diffusion. Available evidence relating to actual experience with promoting woodburning stoves is seen to bear this out. 62 references.
Semi-analytical solutions of the Schnakenberg model of a reaction-diffusion cell with feedback
Al Noufaey, K. S.
2018-06-01
This paper considers the application of a semi-analytical method to the Schnakenberg model of a reaction-diffusion cell. The semi-analytical method is based on the Galerkin method which approximates the original governing partial differential equations as a system of ordinary differential equations. Steady-state curves, bifurcation diagrams and the region of parameter space in which Hopf bifurcations occur are presented for semi-analytical solutions and the numerical solution. The effect of feedback control, via altering various concentrations in the boundary reservoirs in response to concentrations in the cell centre, is examined. It is shown that increasing the magnitude of feedback leads to destabilization of the system, whereas decreasing this parameter to negative values of large magnitude stabilizes the system. The semi-analytical solutions agree well with numerical solutions of the governing equations.
Model-free and analytical EAP reconstruction via spherical polar Fourier diffusion MRI.
Cheng, Jian; Ghosh, Aurobrata; Jiang, Tianzi; Deriche, Rachid
2010-01-01
How to estimate the diffusion Ensemble Average Propagator (EAP) from the DWI signals in q-space is an open problem in diffusion MRI field. Many methods were proposed to estimate the Orientation Distribution Function (ODF) that is used to describe the fiber direction. However, ODF is just one of the features of the EAP. Compared with ODF, EAP has the full information about the diffusion process which reflects the complex tissue micro-structure. Diffusion Orientation Transform (DOT) and Diffusion Spectrum Imaging (DSI) are two important methods to estimate the EAP from the signal. However, DOT is based on mono-exponential assumption and DSI needs a lot of samplings and very large b values. In this paper, we propose Spherical Polar Fourier Imaging (SPFI), a novel model-free fast robust analytical EAP reconstruction method, which almost does not need any assumption of data and does not need too many samplings. SPFI naturally combines the DWI signals with different b-values. It is an analytical linear transformation from the q-space signal to the EAP profile represented by Spherical Harmonics (SH). We validated the proposed methods in synthetic data, phantom data and real data. It works well in all experiments, especially for the data with low SNR, low anisotropy, and non-exponential decay.
An analytical solution for the two-group kinetic neutron diffusion equation in cylindrical geometry
International Nuclear Information System (INIS)
Fernandes, Julio Cesar L.; Vilhena, Marco Tullio; Bodmann, Bardo Ernst
2011-01-01
Recently the two-group Kinetic Neutron Diffusion Equation with six groups of delay neutron precursor in a rectangle was solved by the Laplace Transform Technique. In this work, we report on an analytical solution for this sort of problem but in cylindrical geometry, assuming a homogeneous and infinite height cylinder. The solution is obtained applying the Hankel Transform to the Kinetic Diffusion equation and solving the transformed problem by the same procedure used in the rectangle. We also present numerical simulations and comparisons against results available in literature. (author)
Generalized Analytical Treatment Of The Source Strength In The Solution Of The Diffusion Equation
International Nuclear Information System (INIS)
Essa, Kh.S.M.; EI-Otaify, M.S.
2007-01-01
The source release strength (which is an integral part of the mathematical formulation of the diffusion equation) together with the boundary conditions leads to three different forms of the diffusion equation. The obtained forms have been solved analytically under different boundary conditions, by using transformation of axis, cosine, and Fourier transformation. Three equivalent alternative mathematical formulations of the problem have been obtained. The estimated solution of the concentrations at the ground source has been used for comparison with observed concentrations data for SF 6 tracer experiments in low wind and unstable conditions at lIT Delhi sports ground. A good agreement between estimated and observed concentrations is found
Analytical solutions of a fractional diffusion-advection equation for solar cosmic-ray transport
International Nuclear Information System (INIS)
Litvinenko, Yuri E.; Effenberger, Frederic
2014-01-01
Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.
International Nuclear Information System (INIS)
Esmail, S.F.H.
2011-01-01
The mathematical formulation of numerous physical problems a results in differential equations actually partial or ordinary differential equations.In our study we are interested in solutions of partial differential equations.The aim of this work is to calculate the concentrations of the pollution, by solving the atmospheric diffusion equation(ADE) using different mathematical methods of solution. It is difficult to solve the general form of ADE analytically, so we use some assumptions to get its solution.The solutions of it depend on the eddy diffusivity profiles(k) and the wind speed u. We use some physical assumptions to simplify its formula and solve it. In the present work, we solve the ADE analytically in three dimensions using Green's function method, Laplace transform method, normal mode method and these separation of variables method. Also, we use ADM as a numerical method. Finally, comparisons are made with the results predicted by the previous methods and the observed data.
Energy Technology Data Exchange (ETDEWEB)
Can, Ahmet [Department of Mechanical Engineering, University of Trakya, 22030 Edirne (Turkey)
2007-02-15
This paper presents an analytical method, which determines the moisture diffusion coefficients for the natural and forced convection hot air drying of pumpkin seeds and their temperature dependence. In order to obtain scientific data, the pumpkin seed drying process was investigated under both natural and forced hot air convection regimes. This paper presents the experimental results in which the drying air was heated by solar energy. (author)
Analytical Solutions of Ionic Diffusion and Heat Conduction in Multilayered Porous Media
Directory of Open Access Journals (Sweden)
Yu Bai
2015-01-01
Full Text Available Ionic diffusion and heat conduction in a multiple layered porous medium have many important engineering applications. One of the examples is the chloride ions from deicers penetrating into concrete structures such as bridge decks. Different overlays can be placed on top of concrete surface to slowdown the chloride penetration. In this paper, the chloride ion diffusion equations were established for concrete structures with multiple layers of protective system. By using Laplace transformation, an analytical solution was developed first for chloride concentration profiles in two-layered system and then extended to multiple layered systems with nonconstant boundary conditions, including the constant boundary and linear boundary conditions. Because ionic diffusion in saturated media and heat conduction are governed by the same form of partial differential equations with different materials parameters, the analytical solution was further extended to handle heat conduction in a multiple layered system under nonconstant boundary conditions. The numerical results were compared with available test data. The basic trends of the analytical solution and the test data agreed quite well.
International Nuclear Information System (INIS)
Ganapol, B.D.
2011-01-01
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.
Analytic solution for one-dimensional diffusion of radionuclides from a waste package
International Nuclear Information System (INIS)
Oliver, D.L.
1985-01-01
This work implements an analytical solution for diffusion of radionuclides from a cylindrical waste form through the packing material into the surrounding host rock. Recent interest in predicting the performance of a proposed geological repository for nuclear waste has led to the development of several computer programs to predict the performance of such a repository for the next several millenia. These numerical codes are generally designed to accommodate a broad spectrum of geometrical configurations and repository conditions in order to accurately predict the behavior of the radionuclides in the repository environment. Confidence in such general purpose codes is gained by verifying the numerical modeling and the software through comparison of the numerical predictions generated by these computer codes with analytical solutions to reasonably complex problems. The analysis discussed herein implements the analytic solution, proposed by J.C. Jaeger in 1941 for radial diffusion through two concentric circular cylinders. Jaeger's solution was applied to the problem of diffusional mass transfer from a long cylindrical waste form and subsequently into the surrounding geological formation. Analytic predictions of fractional release rates, including the effects of sorption, were generated
An analytic solution for one-dimensional diffusion of radionuclides from a waste package
International Nuclear Information System (INIS)
1985-01-01
This work implements an analytical solution for diffusion of radionuclides from a cylindrical waste form through the packing material into the surrounding host rock. Recent interest in predicting the performance of a proposed geological repository for nuclear waste has led to the development of several computer programs to predict the performance of such a repository for the next several millenia. These numerical codes are generally designed to accommodate a broad spectrum of geometrical configurations and repository conditions in order to accurately predict the behavior of the radionuclides in the repository environment. Confidence in such general purpose codes is gained by verifying the numerical modeling and the software through comparison of the numerical predictions generated by these computer codes with analytical solutions to reasonably complex problems. The analysis discussed herein implements the analytic solution, proposed by J.C. Jaeger in 1941 for radial diffusion through two concentric circular cylinders. Jaeger's solution was applied to the problem of diffusional mass transfer from a long cylindrical waste form and subsequently into the surrounding geological formation. Analytic predictions of fractional release rates, including the effects of sorption, were generated. 6 refs., 2 figs., 2 tabs
On the non-uniqueness of the nodal mathematical adjoint
International Nuclear Information System (INIS)
Müller, Erwin
2014-01-01
Highlights: • We evaluate three CMFD schemes for computing the nodal mathematical adjoint. • The nodal mathematical adjoint is not unique and can be non-positive (nonphysical). • Adjoint and forward eigenmodes are compatible if produced by the same CMFD method. • In nodal applications the excited eigenmodes are purely mathematical entities. - Abstract: Computation of the neutron adjoint flux within the framework of modern nodal diffusion methods is often facilitated by reducing the nodal equation system for the forward flux into a simpler coarse-mesh finite-difference form and then transposing the resultant matrix equations. The solution to the transposed problem is known as the nodal mathematical adjoint. Since the coarse-mesh finite-difference reduction of a given nodal formulation can be obtained in a number of ways, different nodal mathematical adjoint solutions can be computed. This non-uniqueness of the nodal mathematical adjoint challenges the credibility of the reduction strategy and demands a verdict as to its suitability in practical applications. This is the matter under consideration in this paper. A selected number of coarse-mesh finite-difference reduction schemes are described and compared. Numerical calculations are utilised to illustrate the differences in the adjoint solutions as well as to appraise the impact on such common applications as the computation of core point kinetics parameters. Recommendations are made for the proper application of the coarse-mesh finite-difference reduction approach to the nodal mathematical adjoint problem
Diffusion weighted MRI by spatiotemporal encoding: Analytical description and in vivo validations
Solomon, Eddy; Shemesh, Noam; Frydman, Lucio
2013-07-01
Diffusion-weighted (DW) MRI is a powerful modality for studying microstructure in normal and pathological tissues. The accuracy derived from DW MRI depends on the acquisition of quality images, and on a precise assessment of the b-values involved. Conventional DW MRI tends to be of limited use in regions suffering from large magnetic field or chemical shift heterogeneities, which severely distort the MR images. In this study we propose novel sequences based on SPatio-temporal ENcoding (SPEN), which overcome such shortcomings owing to SPEN's inherent robustness to offsets. SPEN, however, relies on the simultaneous application of gradients and radiofrequency-swept pulses, which may impart different diffusion weightings along the spatial axes. These will be further complicated in DW measurements by the diffusion-sensitizing gradients, and will in general lead to complex, spatially-dependent b-values. This study presents a formalism for analyzing these diffusion-weighted SPEN (dSPEN) data, which takes into account the concomitant effects of adiabatic pulses, of the imaging as well as diffusion gradients, and of the cross-terms between them. These analytical b-values derivations are subject to experimental validations in phantom systems and ex vivo spinal cords. Excellent agreement is found between the theoretical predictions and these dSPEN experiments. The ensuing methodology is then demonstrated by in vivo mapping of diffusion in human breast - organs where conventional k-space DW acquisition methods are challenged by both field and chemical shift heterogeneities. These studies demonstrate the increased robustness of dSPEN vis-à-vis comparable DW echo planar imaging, and demonstrate the value of this new methodology for medium- or high-field diffusion measurements in heterogeneous systems.
Improvement of neutron kinetics module in TRAC-BF1code: one-dimensional nodal collocation method
Energy Technology Data Exchange (ETDEWEB)
Jambrina, Ana; Barrachina, Teresa; Miro, Rafael; Verdu, Gumersindo, E-mail: ajambrina@iqn.upv.es, E-mail: tbarrachina@iqn.upv.es, E-mail: rmiro@iqn.upv.es, E-mail: gverdu@iqn.upv.es [Universidade Politecnica de Valencia (UPV), Valencia (Spain); Soler, Amparo, E-mail: asoler@iberdrola.es [SEA Propulsion S.L., Madrid (Spain); Concejal, Alberto, E-mail: acbe@iberdrola.es [Iberdrola Ingenieria y Construcion S.A.U., Madrid (Spain)
2013-07-01
The TRAC-BF1 one-dimensional kinetic model is a formulation of the neutron diffusion equation in the two energy groups' approximation, based on the analytical nodal method (ANM). The advantage compared with a zero-dimensional kinetic model is that the axial power profile may vary with time due to thermal-hydraulic parameter changes and/or actions of the control systems but at has the disadvantages that in unusual situations it fails to converge. The nodal collocation method developed for the neutron diffusion equation and applied to the kinetics resolution of TRAC-BF1 thermal-hydraulics, is an adaptation of the traditional collocation methods for the discretization of partial differential equations, based on the development of the solution as a linear combination of analytical functions. It has chosen to use a nodal collocation method based on a development of Legendre polynomials of neutron fluxes in each cell. The qualification is carried out by the analysis of the turbine trip transient from the NEA benchmark in Peach Bottom NPP using both the original 1D kinetics implemented in TRAC-BF1 and the 1D nodal collocation method. (author)
Nguyen, Tuan A H; Biggs, Simon R; Nguyen, Anh V
2018-05-30
Current analytical models for sessile droplet evaporation do not consider the nonuniform temperature field within the droplet and can overpredict the evaporation by 20%. This deviation can be attributed to a significant temperature drop due to the release of the latent heat of evaporation along the air-liquid interface. We report, for the first time, an analytical solution of the sessile droplet evaporation coupled with this interfacial cooling effect. The two-way coupling model of the quasi-steady thermal diffusion within the droplet and the quasi-steady diffusion-controlled droplet evaporation is conveniently solved in the toroidal coordinate system by applying the method of separation of variables. Our new analytical model for the coupled vapor concentration and temperature fields is in the closed form and is applicable for a full range of spherical-cap shape droplets of different contact angles and types of fluids. Our analytical results are uniquely quantified by a dimensionless evaporative cooling number E o whose magnitude is determined only by the thermophysical properties of the liquid and the atmosphere. Accordingly, the larger the magnitude of E o , the more significant the effect of the evaporative cooling, which results in stronger suppression on the evaporation rate. The classical isothermal model is recovered if the temperature gradient along the air-liquid interface is negligible ( E o = 0). For substrates with very high thermal conductivities (isothermal substrates), our analytical model predicts a reversal of temperature gradient along the droplet-free surface at a contact angle of 119°. Our findings pose interesting challenges but also guidance for experimental investigations.
Recent advances in computational-analytical integral transforms for convection-diffusion problems
Cotta, R. M.; Naveira-Cotta, C. P.; Knupp, D. C.; Zotin, J. L. Z.; Pontes, P. C.; Almeida, A. P.
2017-10-01
An unifying overview of the Generalized Integral Transform Technique (GITT) as a computational-analytical approach for solving convection-diffusion problems is presented. This work is aimed at bringing together some of the most recent developments on both accuracy and convergence improvements on this well-established hybrid numerical-analytical methodology for partial differential equations. Special emphasis is given to novel algorithm implementations, all directly connected to enhancing the eigenfunction expansion basis, such as a single domain reformulation strategy for handling complex geometries, an integral balance scheme in dealing with multiscale problems, the adoption of convective eigenvalue problems in formulations with significant convection effects, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Then, selected examples are presented that illustrate the improvement achieved in each class of extension, in terms of convergence acceleration and accuracy gain, which are related to conjugated heat transfer in complex or multiscale microchannel-substrate geometries, multidimensional Burgers equation model, and diffusive metal extraction through polymeric hollow fiber membranes. Numerical results are reported for each application and, where appropriate, critically compared against the traditional GITT scheme without convergence enhancement schemes and commercial or dedicated purely numerical approaches.
Directory of Open Access Journals (Sweden)
A. V. Artemyev
2013-04-01
Full Text Available The lifetimes of electrons trapped in Earth's radiation belts can be calculated from quasi-linear pitch-angle diffusion by whistler-mode waves, provided that their frequency spectrum is broad enough and/or their average amplitude is not too large. Extensive comparisons between improved analytical lifetime estimates and full numerical calculations have been performed in a broad parameter range representative of a large part of the magnetosphere from L ~ 2 to 6. The effects of observed very oblique whistler waves are taken into account in both numerical and analytical calculations. Analytical lifetimes (and pitch-angle diffusion coefficients are found to be in good agreement with full numerical calculations based on CRRES and Cluster hiss and lightning-generated wave measurements inside the plasmasphere and Cluster lower-band chorus waves measurements in the outer belt for electron energies ranging from 100 keV to 5 MeV. Comparisons with lifetimes recently obtained from electron flux measurements on SAMPEX, SCATHA, SAC-C and DEMETER also show reasonable agreement.
Analytical-numerical method for treatment of turbulent diffusion of particles in the air
International Nuclear Information System (INIS)
Arsov, L.J.
1976-01-01
This work deals with the problem of air pollution around a stationary punctual source. For description of air pollution from a punctual source a mathematical model is suggested, and for calculation of effluents concentration an analytical-numerical algorithm is given. In addition to the analitical treatment the mathematical model is far more flexible and complete. Eddy diffusivity is represented by an arbitrary function, and an arbitrary wind velocity profile ahs been proposed. The apsorption of the ground is introduced through a variable apsorption coefficient, and the sedimentation through the mean velocity of deposition. To determine the movement of particles a parabolic equation of diffusion is used. The method has been tested through calculation of effluents concentration for different values of physical parameters
Analytical modeling for fractional multi-dimensional diffusion equations by using Laplace transform
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Devendra Kumar
2015-01-01
Full Text Available In this paper, we propose a simple numerical algorithm for solving multi-dimensional diffusion equations of fractional order which describes density dynamics in a material undergoing diffusion by using homotopy analysis transform method. The fractional derivative is described in the Caputo sense. This homotopy analysis transform method is an innovative adjustment in Laplace transform method and makes the calculation much simpler. The technique is not limited to the small parameter, such as in the classical perturbation method. The scheme gives an analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive.
Directory of Open Access Journals (Sweden)
S. Das
2013-12-01
Full Text Available In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error with the proper choices of parameters are calculated numerically and presented through graphs and tables for different particular cases.
International Nuclear Information System (INIS)
Moraes, Pedro Gabriel B.; Leite, Michel C.A.; Barros, Ricardo C.
2013-01-01
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
An Analytical Model for Adsorption and Diffusion of Atoms/Ions on Graphene Surface
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Yan-Zi Yu
2015-01-01
Full Text Available Theoretical investigations are made on adsorption and diffusion of atoms/ions on graphene surface based on an analytical continuous model. An atom/ion interacts with every carbon atom of graphene through a pairwise potential which can be approximated by the Lennard-Jones (L-J potential. Using the Fourier expansion of the interaction potential, the total interaction energy between the adsorption atom/ion and a monolayer graphene is derived. The energy-distance relationships in the normal and lateral directions for varied atoms/ions, including gold atom (Au, platinum atom (Pt, manganese ion (Mn2+, sodium ion (Na1+, and lithium-ion (Li1+, on monolayer graphene surface are analyzed. The equilibrium position and binding energy of the atoms/ions at three particular adsorption sites (hollow, bridge, and top are calculated, and the adsorption stability is discussed. The results show that H-site is the most stable adsorption site, which is in agreement with the results of other literatures. What is more, the periodic interaction energy and interaction forces of lithium-ion diffusing along specific paths on graphene surface are also obtained and analyzed. The minimum energy barrier for diffusion is calculated. The possible applications of present study include drug delivery system (DDS, atomic scale friction, rechargeable lithium-ion graphene battery, and energy storage in carbon materials.
A nodal expansion method using conformal mapping for hexagonal geometry
International Nuclear Information System (INIS)
Chao, Y.A.; Shatilla, Y.A.
1993-01-01
Hexagonal nodal methods adopting the same transverse integration process used for square nodal methods face the subtle theoretical problem that this process leads to highly singular nonphysical terms in the diffusion equation. Lawrence, in developing the DIF3D-N code, tried to approximate the singular terms with relatively simple polynomials. In the HEX-NOD code, Wagner ignored the singularities to simplify the diffusion equation and introduced compensating terms in the nodal equations to restore the nodal balance relation. More recently developed hexagonal nodal codes, such as HEXPE-DITE and the hexagonal version of PANTHER, used methods similar to Wagner's. It will be shown that for light water reactor applications, these two different approximations significantly degraded the accuracy of the respective method as compared to the established square nodal methods. Alternatively, the method of conformal mapping was suggested to map a hexagon to a rectangle, with the unique feature of leaving the diffusion operator invariant, thereby fundamentally resolving the problems associated with transverse integration. This method is now implemented in the Westinghouse hexagonal nodal code ANC-H. In this paper we report on the results of comparing the three methods for a variety of problems via benchmarking against the fine-mesh finite difference code
Energy Technology Data Exchange (ETDEWEB)
Gammon, M.; Shalchi, A., E-mail: andreasm4@yahoo.com [Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2 (Canada)
2017-10-01
In several astrophysical applications one needs analytical forms of cosmic-ray diffusion parameters. Some examples are studies of diffusive shock acceleration and solar modulation. In the current article we explore perpendicular diffusion based on the unified nonlinear transport theory. While we focused on magnetostatic turbulence in Paper I, we included the effect of dynamical turbulence in Paper II of the series. In the latter paper we assumed that the temporal correlation time does not depend on the wavenumber. More realistic models have been proposed in the past, such as the so-called damping model of dynamical turbulence. In the present paper we derive analytical forms for the perpendicular diffusion coefficient of energetic particles in two-component turbulence for this type of time-dependent turbulence. We present new formulas for the perpendicular diffusion coefficient and we derive a condition for which the magnetostatic result is recovered.
Nodal methods in numerical reactor calculations
International Nuclear Information System (INIS)
Hennart, J.P.; Valle, E. del
2004-01-01
The present work describes the antecedents, developments and applications started in 1972 with Prof. Hennart who was invited to be part of the staff of the Nuclear Engineering Department at the School of Physics and Mathematics of the National Polytechnic Institute. Since that time and up to 1981, several master theses based on classical finite element methods were developed with applications in point kinetics and in the steady state as well as the time dependent multigroup diffusion equations. After this period the emphasis moved to nodal finite elements in 1, 2 and 3D cartesian geometries. All the thesis were devoted to the numerical solution of the neutron multigroup diffusion and transport equations, few of them including the time dependence, most of them related with steady state diffusion equations. The main contributions were as follows: high order nodal schemes for the primal and mixed forms of the diffusion equations, block-centered finite-differences methods, post-processing, composite nodal finite elements for hexagons, and weakly and strongly discontinuous schemes for the transport equation. Some of these are now being used by several researchers involved in nuclear fuel management. (Author)
Nodal methods in numerical reactor calculations
Energy Technology Data Exchange (ETDEWEB)
Hennart, J P [UNAM, IIMAS, A.P. 20-726, 01000 Mexico D.F. (Mexico); Valle, E del [National Polytechnic Institute, School of Physics and Mathematics, Department of Nuclear Engineering, Mexico, D.F. (Mexico)
2004-07-01
The present work describes the antecedents, developments and applications started in 1972 with Prof. Hennart who was invited to be part of the staff of the Nuclear Engineering Department at the School of Physics and Mathematics of the National Polytechnic Institute. Since that time and up to 1981, several master theses based on classical finite element methods were developed with applications in point kinetics and in the steady state as well as the time dependent multigroup diffusion equations. After this period the emphasis moved to nodal finite elements in 1, 2 and 3D cartesian geometries. All the thesis were devoted to the numerical solution of the neutron multigroup diffusion and transport equations, few of them including the time dependence, most of them related with steady state diffusion equations. The main contributions were as follows: high order nodal schemes for the primal and mixed forms of the diffusion equations, block-centered finite-differences methods, post-processing, composite nodal finite elements for hexagons, and weakly and strongly discontinuous schemes for the transport equation. Some of these are now being used by several researchers involved in nuclear fuel management. (Author)
A nodal collocation method for the calculation of the lambda modes of the P L equations
International Nuclear Information System (INIS)
Capilla, M.; Talavera, C.F.; Ginestar, D.; Verdu, G.
2005-01-01
P L equations are classical approximations to the neutron transport equation admitting a diffusive form. Using this property, a nodal collocation method is developed for the P L approximations, which is based on the expansion of the flux in terms of orthonormal Legendre polynomials. This method approximates the differential lambda modes problem by an algebraic eigenvalue problem from which the fundamental and the subcritical modes of the system can be calculated. To test the performance of this method, two problems have been considered, a homogeneous slab, which admits an analytical solution, and a seven-region slab corresponding to a more realistic problem
Development of a polynomial nodal model to the multigroup transport equation in one dimension
International Nuclear Information System (INIS)
Feiz, M.
1986-01-01
A polynomial nodal model that uses Legendre polynomial expansions was developed for the multigroup transport equation in one dimension. The development depends upon the least-squares minimization of the residuals using the approximate functions over the node. Analytical expressions were developed for the polynomial coefficients. The odd moments of the angular neutron flux over the half ranges were used at the internal interfaces, and the Marshak boundary condition was used at the external boundaries. Sample problems with fine-mesh finite-difference solutions of the diffusion and transport equations were used for comparison with the model
International Nuclear Information System (INIS)
Kriventsev, Vladimir
2000-09-01
Most of thermal hydraulic processes in nuclear engineering can be described by general convection-diffusion equations that are often can be simulated numerically with finite-difference method (FDM). An effective scheme for finite-difference discretization of such equations is presented in this report. The derivation of this scheme is based on analytical solutions of a simplified one-dimensional equation written for every control volume of the finite-difference mesh. These analytical solutions are constructed using linearized representations of both diffusion coefficient and source term. As a result, the Efficient Finite-Differencing (EFD) scheme makes it possible to significantly improve the accuracy of numerical method even using mesh systems with fewer grid nodes that, in turn, allows to speed-up numerical simulation. EFD has been carefully verified on the series of sample problems for which either analytical or very precise numerical solutions can be found. EFD has been compared with other popular FDM schemes including novel, accurate (as well as sophisticated) methods. Among the methods compared were well-known central difference scheme, upwind scheme, exponential differencing and hybrid schemes of Spalding. Also, newly developed finite-difference schemes, such as the the quadratic upstream (QUICK) scheme of Leonard, the locally analytic differencing (LOAD) scheme of Wong and Raithby, the flux-spline scheme proposed by Varejago and Patankar as well as the latest LENS discretization of Sakai have been compared. Detailed results of this comparison are given in this report. These tests have shown a high efficiency of the EFD scheme. For most of sample problems considered EFD has demonstrated the numerical error that appeared to be in orders of magnitude lower than that of other discretization methods. Or, in other words, EFD has predicted numerical solution with the same given numerical error but using much fewer grid nodes. In this report, the detailed
Response matrix properties and convergence implications for an interface-current nodal formulation
International Nuclear Information System (INIS)
Yang, W.S.
1995-01-01
An analytic study was performed of the properties and the associated convergence implications of the response matrix equations derived via the widely used nodal expansion method. By using the DIF3D nodal formulation in hexagonal-z geometry as a concrete example, an analytic expression for the response matrix is first derived by using the hexagonal prism symmetry transformations. The spectral radius of the local response matrix is shown to be always 2 -norm of the response matrix is shown to be ∞ -norm is not always 2 - and l ∞ -norms of the response matrix are found to increase as the removal cross section decreases. On the other hand, for a given removal cross section, each of these matrix norms takes its minimum at a certain diffusion coefficient and increases as the diffusion coefficient deviates from this value. Based on these matrix norms, sufficient conditions for the convergence of the iteration schemes for solving the response matrix equations are discussed. The range of node-height-to-hexagon-pitch ratios that guarantees a positive solution is derived as a function of the diffusion coefficient and the removal cross section
Analytic treatment of nuclear spin-lattice relaxation for diffusion in a cone model
Sitnitsky, A. E.
2011-12-01
We consider nuclear spin-lattice relaxation rate resulted from a diffusion equation for rotational wobbling in a cone. We show that the widespread point of view that there are no analytical expressions for correlation functions for wobbling in a cone model is invalid and prove that nuclear spin-lattice relaxation in this model is exactly tractable and amenable to full analytical description. The mechanism of relaxation is assumed to be due to dipole-dipole interaction of nuclear spins and is treated within the framework of the standard Bloemberger, Purcell, Pound-Solomon scheme. We consider the general case of arbitrary orientation of the cone axis relative the magnetic field. The BPP-Solomon scheme is shown to remain valid for systems with the distribution of the cone axes depending only on the tilt relative the magnetic field but otherwise being isotropic. We consider the case of random isotropic orientation of cone axes relative the magnetic field taking place in powders. Also we consider the cases of their predominant orientation along or opposite the magnetic field and that of their predominant orientation transverse to the magnetic field which may be relevant for, e.g., liquid crystals. Besides we treat in details the model case of the cone axis directed along the magnetic field. The latter provides direct comparison of the limiting case of our formulas with the textbook formulas for free isotropic rotational diffusion. The dependence of the spin-lattice relaxation rate on the cone half-width yields results similar to those predicted by the model-free approach.
Bzdušek, Tomáš; Wu, QuanSheng; Rüegg, Andreas; Sigrist, Manfred; Soluyanov, Alexey A
2016-10-06
The band theory of solids is arguably the most successful theory of condensed-matter physics, providing a description of the electronic energy levels in various materials. Electronic wavefunctions obtained from the band theory enable a topological characterization of metals for which the electronic spectrum may host robust, topologically protected, fermionic quasiparticles. Many of these quasiparticles are analogues of the elementary particles of the Standard Model, but others do not have a counterpart in relativistic high-energy theories. A complete list of possible quasiparticles in solids is lacking, even in the non-interacting case. Here we describe the possible existence of a hitherto unrecognized type of fermionic excitation in metals. This excitation forms a nodal chain-a chain of connected loops in momentum space-along which conduction and valence bands touch. We prove that the nodal chain is topologically distinct from previously reported excitations. We discuss the symmetry requirements for the appearance of this excitation and predict that it is realized in an existing material, iridium tetrafluoride (IrF 4 ), as well as in other compounds of this class of materials. Using IrF 4 as an example, we provide a discussion of the topological surface states associated with the nodal chain. We argue that the presence of the nodal-chain fermions will result in anomalous magnetotransport properties, distinct from those of materials exhibiting previously known excitations.
Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence
Energy Technology Data Exchange (ETDEWEB)
Heusen, M.; Shalchi, A., E-mail: husseinm@myumanitoba.ca, E-mail: andreasm4@yahoo.com [Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T 2N2 (Canada)
2017-04-20
In the literature, one can find various analytical theories for perpendicular diffusion of energetic particles interacting with magnetic turbulence. Besides quasi-linear theory, there are different versions of the nonlinear guiding center (NLGC) theory and the unified nonlinear transport (UNLT) theory. For turbulence with high Kubo numbers, such as two-dimensional turbulence or noisy reduced magnetohydrodynamic turbulence, the aforementioned nonlinear theories provide similar results. For slab and small Kubo number turbulence, however, this is not the case. In the current paper, we compare different linear and nonlinear theories with each other and test-particle simulations for a noisy slab model corresponding to small Kubo number turbulence. We show that UNLT theory agrees very well with all performed test-particle simulations. In the limit of long parallel mean free paths, the perpendicular mean free path approaches asymptotically the quasi-linear limit as predicted by the UNLT theory. For short parallel mean free paths we find a Rechester and Rosenbluth type of scaling as predicted by UNLT theory as well. The original NLGC theory disagrees with all performed simulations regardless what the parallel mean free path is. The random ballistic interpretation of the NLGC theory agrees much better with the simulations, but compared to UNLT theory the agreement is inferior. We conclude that for this type of small Kubo number turbulence, only the latter theory allows for an accurate description of perpendicular diffusion.
Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence
International Nuclear Information System (INIS)
Heusen, M.; Shalchi, A.
2017-01-01
In the literature, one can find various analytical theories for perpendicular diffusion of energetic particles interacting with magnetic turbulence. Besides quasi-linear theory, there are different versions of the nonlinear guiding center (NLGC) theory and the unified nonlinear transport (UNLT) theory. For turbulence with high Kubo numbers, such as two-dimensional turbulence or noisy reduced magnetohydrodynamic turbulence, the aforementioned nonlinear theories provide similar results. For slab and small Kubo number turbulence, however, this is not the case. In the current paper, we compare different linear and nonlinear theories with each other and test-particle simulations for a noisy slab model corresponding to small Kubo number turbulence. We show that UNLT theory agrees very well with all performed test-particle simulations. In the limit of long parallel mean free paths, the perpendicular mean free path approaches asymptotically the quasi-linear limit as predicted by the UNLT theory. For short parallel mean free paths we find a Rechester and Rosenbluth type of scaling as predicted by UNLT theory as well. The original NLGC theory disagrees with all performed simulations regardless what the parallel mean free path is. The random ballistic interpretation of the NLGC theory agrees much better with the simulations, but compared to UNLT theory the agreement is inferior. We conclude that for this type of small Kubo number turbulence, only the latter theory allows for an accurate description of perpendicular diffusion.
A theoretical study on a convergence problem of nodal methods
Energy Technology Data Exchange (ETDEWEB)
Shaohong, Z.; Ziyong, L. [Shanghai Jiao Tong Univ., 1954 Hua Shan Road, Shanghai, 200030 (China); Chao, Y. A. [Westinghouse Electric Company, P. O. Box 355, Pittsburgh, PA 15230-0355 (United States)
2006-07-01
The effectiveness of modern nodal methods is largely due to its use of the information from the analytical flux solution inside a homogeneous node. As a result, the nodal coupling coefficients depend explicitly or implicitly on the evolving Eigen-value of a problem during its solution iteration process. This poses an inherently non-linear matrix Eigen-value iteration problem. This paper points out analytically that, whenever the half wave length of an evolving node interior analytic solution becomes smaller than the size of that node, this non-linear iteration problem can become inherently unstable and theoretically can always be non-convergent or converge to higher order harmonics. This phenomenon is confirmed, demonstrated and analyzed via the simplest 1-D problem solved by the simplest analytic nodal method, the Analytic Coarse Mesh Finite Difference (ACMFD, [1]) method. (authors)
The Analytical Diffusion-Expansion Model for Forbush Decreases Caused by Flux Ropes
Dumbovic, M.; Temmer, M.
2017-12-01
Identification and tracking of interplanetary coronal mass ejections (ICMEs) throughout the heliosphere is a growingly important aspect of space weather research. One of the "signatures" of ICME passage is the corresponding Forbush decrease (FD), a short term decrease in the galactic cosmic ray flux. These depressions are observed at the surface of the Earth for over 50 years, by several spacecraft in interplanetary space in the past couple of decades, and recently also on Mars' surface with Curiosity rover. In order to use FDs as ICME signatures efficiently, it is important to model ICME interaction with energetic particles by taking into account ICME evolution and constraining the model with observational data. We present an analytical diffusion-expansion FD model ForbMod which is based on the widely used approach of the initially empty, closed magnetic structure (i.e. flux rope) which fills up slowly with particles by perpendicular diffusion. The model is restricted to explain only the depression caused by the magnetic structure of the ICME and not of the associated shock. We use remote CME observations and a 3D reconstruction method (the Graduated Cylindrical Shell method) to constrain initial and boundary conditions of the FD model and take into account CME evolutionary properties by incorporating flux rope expansion. Several options of flux rope expansion are regarded as the competing mechanism to diffusion which can lead to different FD characteristics. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 745782.
International Nuclear Information System (INIS)
Oliveira, F.L. de; Maiorino, J.R.; Santos, R.S.
2007-01-01
This paper describes a closed form solution obtained by the expansion method for the general time dependent diffusion model with delayed emission for source transients in homogeneous media. In particular, starting from simple models, and increasing the complexity, numerical results were obtained for different types of source transients. Thus, first an analytical solution of the one group without precursors was solved, followed by considering one precursors family. The general case of G-groups with R families of precursor although having a closed form solution, cannot be solved analytically, since there are no explicit formulae for the eigenvalues, and numerical methods must be used to solve such problem. To illustrate the general solution, the multi-group (three groups) time-dependent without precursors was also solved and the results inter compared with results obtained by the previous one group models for a given fast homogeneous media, and different types of source transients. The results are being compared with the obtained by numerical methods. (author)
International Nuclear Information System (INIS)
Guzman, Juan; Maximov, Serguei; Escarela-Perez, Rafael; López-García, Irvin; Moranchel, Mario
2015-01-01
The diffusion and distribution coefficients are important parameters in the design of barrier systems used in radioactive repositories. These coefficients can be determined using a two-reservoir configuration, where a saturated porous medium is allocated between two reservoirs filled by stagnant water. One of the reservoirs contains a high concentration of radioisotopes. The goal of this work is to obtain an analytical solution for the concentration of all radioisotopes in the decay chain of a two-reservoir configuration. The analytical solution must be obtained by taking into account the diffusion and sorption processes. Concepts such as overvalued concentration, diffusion and decay factors are employed to this end. It is analytically proven that a factor of the solution is identical for all chains (considering a time scaling factor), if certain parameters do not change. In addition, it is proven that the concentration sensitivity, due to the distribution coefficient variation, depends of the porous medium thickness, which is practically insensitive for small porous medium thicknesses. The analytical solution for the radioisotope concentration is compared with experimental and numerical results available in literature. - Highlights: • Saturated porous media allocated between two reservoirs. • Analytical solution of the isotope transport equation. • Transport considers diffusion, sorption and decay chain
Experimental discovery of nodal chains
Yan, Qinghui; Liu, Rongjuan; Yan, Zhongbo; Liu, Boyuan; Chen, Hongsheng; Wang, Zhong; Lu, Ling
2018-05-01
Three-dimensional Weyl and Dirac nodal points1 have attracted widespread interest across multiple disciplines and in many platforms but allow for few structural variations. In contrast, nodal lines2-4 can have numerous topological configurations in momentum space, forming nodal rings5-9, nodal chains10-15, nodal links16-20 and nodal knots21,22. However, nodal lines are much less explored because of the lack of an ideal experimental realization23-25. For example, in condensed-matter systems, nodal lines are often fragile to spin-orbit coupling, located away from the Fermi level, coexist with energy-degenerate trivial bands or have a degeneracy line that disperses strongly in energy. Here, overcoming all these difficulties, we theoretically predict and experimentally observe nodal chains in a metallic-mesh photonic crystal having frequency-isolated linear band-touching rings chained across the entire Brillouin zone. These nodal chains are protected by mirror symmetry and have a frequency variation of less than 1%. We use angle-resolved transmission measurements to probe the projected bulk dispersion and perform Fourier-transformed field scans to map out the dispersion of the drumhead surface state. Our results establish an ideal nodal-line material for further study of topological line degeneracies with non-trivial connectivity and consequent wave dynamics that are richer than those in Weyl and Dirac materials.
A new analytical formulation of retention effects on particle diffusion processes
Directory of Open Access Journals (Sweden)
Luiz Bevilacqua
2011-12-01
Full Text Available The ultimate purpose of this paper is to present a new analytical formulation to simulate diffusion with retention in a reactive medium under stable thermodynamic conditions. The analysis of diffusion with retention in a continuum medium is developed after the solution of an equivalent problem using a discrete approach. The new law may be interpreted as the reduction of all diffusion processes with retention to a unifying phenomenon that can adequately simulate the retention effect namely a circulatory motion. It is remarkable that the governing equation requires a fourth order differential term as suggested by the discrete approach. The relative fraction of diffusion particles β is introduced as a control parameter in the diffusion-retention law as suggested by the discrete approach. This control parameter is essential to avoid retention isolated from the diffusion process. Two matrices referring to material properties are introduced and related to the real phenomenon through the circulation hypothesis. The governing equation may be highly non-linear even if the material properties are constant, but the retention effect is a function of the concentration level, that is, β is a function of the concentration.O objetivo último desse trabalho é apresentar uma nova formulação analítica para simular difusão com retenção em um meio reativo sob condições termodinamicamente estáveis. A análise da difusão com retenção em um meio contínuo é desenvolvida a partir da solução de um problema equivalente usando uma abordagem discreta. A nova lei pode ser interpretada como a redução de todos os processos de difusão com retenção a um fenômeno unificador que pode simular adequadamente a retenção. O propósito principal desse trabalho é apresentar uma nova formulação analítica para simular difusão com retenção em meio reativo termodinamicamente estável. A análise da difusão com retenção em um meio contínuo é desenvolvido
Bilinear nodal transport method in weighted diamond difference form
International Nuclear Information System (INIS)
Azmy, Y.Y.
1987-01-01
Nodal methods have been developed and implemented for the numerical solution of the discrete ordinates neutron transport equation. Numerical testing of these methods and comparison of their results to those obtained by conventional methods have established the high accuracy of nodal methods. Furthermore, it has been suggested that the linear-linear approximation is the most computationally efficient, practical nodal approximation. Indeed, this claim has been substantiated by comparing the accuracy in the solution, and the CPU time required to achieve convergence to that solution by several nodal approximations, as well as the diamond difference scheme. Two types of linear-linear nodal methods have been developed in the literature: analytic linear-linear (NLL) methods, in which the transverse-leakage terms are derived analytically, and approximate linear-linear (PLL) methods, in which these terms are approximated. In spite of their higher accuracy, NLL methods result in very complicated discrete-variable equations that exhibit a high degree of coupling, thus requiring special solution algorithms. On the other hand, the sacrificed accuracy in PLL methods is compensated for by the simple discrete-variable equations and diamond-difference-like solution algorithm. In this paper the authors outline the development of an NLL nodal method, the bilinear method, which can be written in a weighted diamond difference form with one spatial weight per dimension that is analytically derived rather than preassigned in an ad hoc fashion
Hosseinbor, A. Pasha; Chung, Moo K.; Wu, Yu-Chien; Alexander, Andrew L.
2012-01-01
The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents. The EAP can thus provide richer information about complex tissue microstructure properties than the orientation distribution function (ODF), an angular feature of the EAP. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed, such as diffusion propagator imaging (DPI) and spherical polar Fourier imaging (SPFI). In this study, a new analytical EAP reconstruction method is proposed, called Bessel Fourier orientation reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition, and is validated on both synthetic and real datasets. A significant portion of the paper is dedicated to comparing BFOR, SPFI, and DPI using hybrid, non-Cartesian sampling for multiple b-value acquisitions. Ways to mitigate the effects of Gibbs ringing on EAP reconstruction are also explored. In addition to analytical EAP reconstruction, the aforementioned modeling bases can be used to obtain rotationally invariant q-space indices of potential clinical value, an avenue which has not yet been thoroughly explored. Three such measures are computed: zero-displacement probability (Po), mean squared displacement (MSD), and generalized fractional anisotropy (GFA). PMID:22963853
Avoided intersections of nodal lines
International Nuclear Information System (INIS)
Monastra, Alejandro G; Smilansky, Uzy; Gnutzmann, Sven
2003-01-01
We consider real eigenfunctions of the Schroedinger operator in 2D. The nodal lines of separable systems form a regular grid, and the number of nodal crossings equals the number of nodal domains. In contrast, for wavefunctions of non-integrable systems nodal intersections are rare, and for random waves, the expected number of intersections in any finite area vanishes. However, nodal lines display characteristic avoided crossings which we study in this work. We define a measure for the avoidance range and compute its distribution for the random wave ensemble. We show that the avoidance range distribution of wavefunctions of chaotic systems follows the expected random wave distributions, whereas for wavefunctions of classically integrable but quantum non-separable systems, the distribution is quite different. Thus, the study of the avoidance distribution provides more support to the conjecture that nodal structures of chaotic systems are reproduced by the predictions of the random wave ensemble
International Nuclear Information System (INIS)
Alonso-Vargas, G.
1991-01-01
A computer program has been developed which uses a technique of synthetic acceleration by diffusion by analytical schemes. Both in the diffusion equation as in that of transport, analytical schemes were used which allowed a substantial time saving in the number of iterations required by source iteration method to obtain the K e ff. The program developed ASD (Synthetic Diffusion Acceleration) by diffusion was written in FORTRAN and can be executed on a personal computer with a hard disc and mathematical O-processor. The program is unlimited as to the number of regions and energy groups. The results obtained by the ASD program for K e ff is nearly completely concordant with those of obtained utilizing the ANISN-PC code for different analytical type problems in this work. The ASD program allowed obtention of an approximate solution of the neutron transport equation with a relatively low number of internal reiterations with good precision. One of its applications would be in the direct determinations of axial distribution neutronic flow in a fuel assembly as well as in the obtention of the effective multiplication factor. (Author)
Development and validation of a nodal code for core calculation
International Nuclear Information System (INIS)
Nowakowski, Pedro Mariano
2004-01-01
The code RHENO solves the multigroup three-dimensional diffusion equation using a nodal method of polynomial expansion.A comparative study has been made between this code and present internationals nodal diffusion codes, resulting that the RHENO is up to date.The RHENO has been integrated to a calculation line and has been extend to make burnup calculations.Two methods for pin power reconstruction were developed: modulation and imbedded. The modulation method has been implemented in a program, while the implementation of the imbedded method will be concluded shortly.The validation carried out (that includes experimental data of a MPR) show very good results and calculation efficiency
Nodal algorithm derived from a new variational principle
International Nuclear Information System (INIS)
Watson, Fernando V.
1995-01-01
As a by-product of the research being carried on by the author on methods of recovering pin power distribution of PWR cores, a nodal algorithm based on a modified variational principle for the two group diffusion equations has been obtained. The main feature of the new algorithm is the low dimensionality achieved by the reduction of the original diffusion equations to a system of algebraic Eigen equations involving the average sources only, instead of sources and interface group currents used in conventional nodal methods. The advantage of this procedure is discussed and results generated by the new algorithm and by a finite difference code are compared. (author). 2 refs, 7 tabs
International Nuclear Information System (INIS)
Kubaschewski, O.
1983-01-01
The diffusion rate values of titanium, its compounds and alloys are summarized and tabulated. The individual chemical diffusion coefficients and self-diffusion coefficients of certain isotopes are given. Experimental methods are listed which were used for the determination of diffusion coefficients. Some values have been taken over from other studies. Also given are graphs showing the temperature dependences of diffusion and changes in the diffusion coefficient with concentration changes
International Nuclear Information System (INIS)
Montan, D.N.
1987-02-01
This report is intended to describe, document and provide instructions for the use of new versions of a set of computer programs commonly referred to as the PLUS family. These programs were originally designed to numerically evaluate simple analytical solutions of the diffusion equation. The new versions include linear thermo-elastic effects from thermal fields calculated by the diffusion equation. After the older versions of the PLUS family were documented a year ago, it was realized that the techniques employed in the programs were well suited to the addition of linear thermo-elastic phenomena. This has been implemented and this report describes the additions. 3 refs., 14 figs
Nodal approximations in space and time for neutron kinetics
International Nuclear Information System (INIS)
Grossman, L.M.; Hennart, J.P.
2005-01-01
A general formalism is described of the nodal type in time and space for the neutron kinetics equations. In space, several nodal methods are given of the Raviart-Thomas type (RT0 and RT1), of the Brezzi-Douglas-Marini type (BDM0 and BDM1) and of the Brezzi-Douglas-Fortin-Marini type (BDFM 1). In time, polynomial and analytical approximations are derived. In the analytical case, they are based on the inclusion of an exponential term in the basis function. They can be continuous or discontinuous in time, leading in particular to the well-known Crank-Nicolson, Backward Euler and θ schemes
LOLA SYSTEM: A code block for nodal PWR simulation. Part. I - Simula-3 Code
Energy Technology Data Exchange (ETDEWEB)
Aragones, J M; Ahnert, C; Gomez Santamaria, J; Rodriguez Olabarria, I
1985-07-01
Description of the theory and users manual of the SIMULA-3 code, which is part of the core calculation system by nodal theory in one group, called LOLA SYSTEM. SIMULA-3 is the main module of the system, it uses a modified nodal theory, with interface leakages equivalent to the diffusion theory. (Author) 4 refs.
LOLA SYSTEM: A code block for nodal PWR simulation. Part. I - Simula-3 Code
International Nuclear Information System (INIS)
Aragones, J. M.; Ahnert, C.; Gomez Santamaria, J.; Rodriguez Olabarria, I.
1985-01-01
Description of the theory and users manual of the SIMULA-3 code, which is part of the core calculation system by nodal theory in one group, called LOLA SYSTEM. SIMULA-3 is the main module of the system, it uses a modified nodal theory, with interface leakages equivalent to the diffusion theory. (Author) 4 refs
International Nuclear Information System (INIS)
Skaali, T.B.
1980-10-01
NODAL is a high level programming language based on FOCAL and SNOBOL4, with some influence from BASIC. The language was developed to operate on the computer network controlling the SPS accelerator at CERN. NODAL is an interpretive language designed for interactive use. This is the most important aspect of the language, and is reflected in its structure. The interactive facilities make it possible to write, debug and modify programs much faster than with compiler based languages like FORTRAN and ALGOL. Apart from a few minor modifications, the basic part of the Oslo University NODAL system does not differ from the CERN version. However, the Oslo University implementation has been expanded with new functions which enable the user to execute many of the SINTRAN III monitor calls from the NODAL level. In particular the most important RT monitor calls have been implemented in this way, a property which renders possible the use of NODAL as a RT program administrator. (JIW)
Energy Technology Data Exchange (ETDEWEB)
Fernandes, Julio Cesar L.; Vilhena, Marco Tullio, E-mail: julio.lombaldo@ufrgs.b, E-mail: vilhena@pq.cnpq.b [Universidade Federal do Rio Grande do Sul (DMPA/UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada. Programa de Pos Graduacao em Matematica Aplicada; Borges, Volnei; Bodmann, Bardo Ernest, E-mail: bardo.bodmann@ufrgs.b, E-mail: borges@ufrgs.b [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica
2011-07-01
The principal idea of this work, consist on formulate an analytical method to solved problems for diffusion of neutrons with isotropic scattering in one-dimensional cylindrical geometry. In this area were develop many works that study the same problem in different system of coordinates as well as cartesian system, nevertheless using numerical methods to solve the shielding problem. In view of good results in this works, we starting with the idea that we can represent a source in the origin of the cylindrical system by a Delta Dirac distribution, we describe the physical modeling and solved the neutron diffusion equation inside of cylinder of radius R. For the case of transport equation, the formulation of discrete ordinates S{sub N} consists in discretize the angular variables in N directions and in using a quadrature angular set for approximate the sources of scattering, where the Diffusion equation consist on S{sub 2} approximated transport equation in discrete ordinates. We solved the neutron diffusion equation with an analytical form by the finite Hankel transform. Was presented also the build-up factor for the case that we have neutron flux inside the cylinder. (author)
International Nuclear Information System (INIS)
Fernandes, Julio Cesar L.; Vilhena, Marco Tullio; Borges, Volnei; Bodmann, Bardo Ernest
2011-01-01
The principal idea of this work, consist on formulate an analytical method to solved problems for diffusion of neutrons with isotropic scattering in one-dimensional cylindrical geometry. In this area were develop many works that study the same problem in different system of coordinates as well as cartesian system, nevertheless using numerical methods to solve the shielding problem. In view of good results in this works, we starting with the idea that we can represent a source in the origin of the cylindrical system by a Delta Dirac distribution, we describe the physical modeling and solved the neutron diffusion equation inside of cylinder of radius R. For the case of transport equation, the formulation of discrete ordinates S N consists in discretize the angular variables in N directions and in using a quadrature angular set for approximate the sources of scattering, where the Diffusion equation consist on S 2 approximated transport equation in discrete ordinates. We solved the neutron diffusion equation with an analytical form by the finite Hankel transform. Was presented also the build-up factor for the case that we have neutron flux inside the cylinder. (author)
International Nuclear Information System (INIS)
Oliveira, Fernando Luiz de
2008-01-01
This work describes an analytical solution obtained by the expansion method for the spatial kinetics using the diffusion model with delayed emission for source transients in homogeneous media. In particular, starting from simple models, and increasing the complexity, numerical results were obtained for different types of source transients. An analytical solution of the one group without precursors was solved, followed by considering one precursors family. The general case of G-groups with R families of precursor although having a closed form solution, cannot be solved analytically, since there are no explicit formulae for the eigenvalues, and numerical methods must be used to solve such problem. To illustrate the general solution, the multi-group (three groups) time-dependent problem without precursors was solved and the numerical results of a finite difference code were compared with the exact results for different transients. (author)
International Nuclear Information System (INIS)
Li, Jia; Fang, Qihong; Wu, Hong; Liu, Youwen; Wen, Pihua
2015-01-01
Highlights: • Diffusion induced stress is established. • Yield stress is dependent upon concentration. • Plastic deformation induced stress lowers tensile stress. • Plastic deformation suppresses crack nucleation. • Plastic deformation occurs not only at lithiated phase but also at electrode interior. - Abstract: This paper is theoretically suggested to describe diffusion induced stress in the elastoplastic hollow spherical silicon electrode for plastic deformation using both analytical model and molecular simulation. Based on the plastic deformation and the yield criterion, we develop this model accounting for the lithium-ion diffusion effect in hollow electrode, focusing on the concentration and stress distributions undergoing lithium-ion insertion. The results show that the two ways, applied compressive stress to inner surface or limited inner surface with higher concentration using biological membranes maintaining concentration difference, lead to the compressive stress induced by the lithium-ion diffusion effect. Hollow spherical electrode reduces effectively diffusion induced stress through controlling and tuning electrode parameters to obtain the reasonably low yield strength. According to MD simulations, plastic deformation phenomenon not only occurs at interface layer of lithiated phase, but also penetrates at electrode interior owning to confinement imposed by lithiated phase. These criteria that radial and hoop stresses reduce dramatically when plastic deformation occurs near the end faces of hollow electrode, may help guide development of new materials for lithium-ion batteries with enhanced mechanical durability, by means of reasonable designing yield strength to maintain mechanical stress below fracture strength, thereby increasing battery life.
Analytical developments in the Wong-Fung-Tam-Gao radiation model of thermal diffusivity
International Nuclear Information System (INIS)
Lucia, U.; Maino, G.
2004-01-01
When the thermal diffusivity, χ, of a thin film on a substrate is measured by means of the mirage method, the photothermal deflection of the probe beam is determined by the heat radiation field contributed by the film and the substrate, heated by the pump beam. A two-dimensional algorithm is here presented in order to deduce the measure of the diffusivities of the film and the substrate in one set of mirage detection from the experimental data
Rybalkin, Andrey
Numerical assessments of radon diffusion together with analytical estimates for short-time and long-time exposure were the first objective of this thesis with the goal to demonstrate how radon propagates in various media. Theoretical predictions were compared to numerical simulations, and obtained values of total radon activities inside each material match quite well with the analytical estimates. These estimates, for activated and nonactivated charcoal, were then used to evaluate the possibility of designing a charcoal system to be used as a radon detector. Another objective was to use nonactivated charcoal samples and measure the level of radon accumulation, and use these data to estimate radon diffusion and adsorption coefficients. The analytical approach was developed to estimate these values. Radon adsorption coefficient in nonactivated charcoal was found to be from 0.2 to 0.4 m3/kg. Radon diffusion coefficient for nonactivated charcoal is in the range of 1.2×10-11 to 5.1×10-10 m2/s in comparison to activated charcoal with adsorption coefficient of 4 m3/kg and diffusion coefficient of 1.43×10-9 m2/s. The third objective was to use GEANT4 numerical code to simulate decay of 238U series and 222Rn in an arbitrary soil sample. Based on that model, the goal was to provide a guideline for merging GEANT4 radioactive decay modeling with the diffusion of radon in a soil sample. It is known that radon can be used as an earthquake predictor by measuring its concentration in groundwater, or if possible, along the faults. Numerical simulations of radon migration by diffusion only were made to estimate how fast and how far radon can move along the fault strands. Among the known cases of successful correlations between radon concentration anomalies and earthquake are the 1966 Tashkent and 1976 Songpan-Pingwu earthquakes. Thus, an idea of radon monitoring along the Wasatch Fault, using system of activated/nonactivated charcoals together with solid state radon detectors is
International Nuclear Information System (INIS)
Oide, Katsunobu.
1982-11-01
A NODAL interpreter which works under CP/M operating system is made for microcomputers. This interpreter language named NODAL-80 has a similar structure to the NODAL of SPS, but its commands, variables, and expressions are modified to increase the flexibility of programming. NODAL-80 also uses a simple intermediate code to make the execution speed fast without imposing any restriction on the dynamic feature of NODAL language. (author)
International Nuclear Information System (INIS)
Ho, Koon-Sing; Lui, Kwok-On; Lee, Kin-Ho; Chan, Wing-Tat
2013-01-01
The intensity of individual gold nanoparticles with nominal diameters of 80, 100, 150, and 200 nm was measured using single-particle inductively coupled plasma-mass spectrometry (ICP-MS). Since the particles are not perfectly monodisperse, a distribution of ICP-MS intensity was obtained for each nominal diameter. The distribution of particle mass was determined from the transmission electron microscopy (TEM) image of the particles. The distribution of ICP-MS intensity and the distribution of particle mass for each nominal diameter were correlated to give a calibration curve. The calibration curves are linear, but the slope decreases as the nominal diameter increases. The reduced slope is probably due to a smaller degree of vaporization of the large particles. In addition to the degree of particle vaporization, the rate of analyte diffusion in the ICP is an important factor that determines the measured ICP-MS intensity. Simulated ICP-MS intensity versus particle size was calculated using a simple computer program that accounts for the vaporization rate of the gold nanoparticles and the diffusion rate and degree of ionization of the gold atoms. The curvature of the simulated calibration curves changes with sampling depth because the effects of particle vaporization and analyte diffusion on the ICP-MS intensity are dependent on the residence time of the particle in the ICP. Calibration curves of four hypothetical particles representing the four combinations of high and low boiling points (2000 and 4000 K) and high and low analyte diffusion rates (atomic masses of 10 and 200 Da) were calculated to further illustrate the relative effects of particle vaporization and analyte diffusion. The simulated calibration curves show that the sensitivity of single-particle ICP-MS is smaller than that of the ICP-MS measurement of continuous flow of standard solutions by a factor of 2 or more. Calibration using continuous flow of standard solution is semi-quantitative at best. An
Czech Academy of Sciences Publication Activity Database
Tarasenko, Alexander; Boháč, Petr; Jastrabík, Lubomír
2015-01-01
Roč. 74, Nov (2015), s. 556-560 ISSN 1386-9477 R&D Projects: GA MŠk LO1409; GA TA ČR TA03010743 Institutional support: RVO:68378271 Keywords : surface diffusion * heterogeneous lattices * lattice-gas models * kinetic Monte Carlo simulation Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.904, year: 2015
International Nuclear Information System (INIS)
Hall, S.K.; Eaton, M.D.; Williams, M.M.R.
2012-01-01
Highlights: ► Isogeometric analysis used to obtain solutions to the neutron diffusion equation. ► Exact geometry captured for a circular fuel pin within a square moderator. ► Comparisons are made between the finite element method and isogeometric analysis. ► Error and observed order of convergence found using an analytic solution. -- Abstract: In this paper the neutron diffusion equation is solved using Isogeometric Analysis (IGA), which is an attempt to generalise Finite Element Analysis (FEA) to include exact geometries. In contrast to FEA, the basis functions are rational functions instead of polynomials. These rational functions, called non-uniform rational B-splines, are used to capture both the geometry and approximate the solution. The method of manufactured solutions is used to verify a MatLab implementation of IGA, which is then applied to a pincell problem. This is a circular uranium fuel pin within a square block of graphite moderator. A new method is used to compute an analytic solution to a simplified version of this problem, and is then used to observe the order of convergence of the numerical scheme. Comparisons are made against quadratic finite elements for the pincell problem, and it is found that the disadvantage factor computed using IGA is less accurate. This is due to a cancellation of errors in the FEA solution. A modified pincell problem with vacuum boundary conditions is then considered. IGA is shown to outperform FEA in this situation.
International Nuclear Information System (INIS)
Ceolin, Celina
2010-01-01
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)
Nodal methods for problems in fluid mechanics and neutron transport
International Nuclear Information System (INIS)
Azmy, Y.Y.
1985-01-01
A new high-accuracy, coarse-mesh, nodal integral approach is developed for the efficient numerical solution of linear partial differential equations. It is shown that various special cases of this general nodal integral approach correspond to several high efficiency nodal methods developed recently for the numerical solution of neutron diffusion and neutron transport problems. The new approach is extended to the nonlinear Navier-Stokes equations of fluid mechanics; its extension to these equations leads to a new computational method, the nodal integral method which is implemented for the numerical solution of these equations. Application to several test problems demonstrates the superior computational efficiency of this new method over previously developed methods. The solutions obtained for several driven cavity problems are compared with the available experimental data and are shown to be in very good agreement with experiment. Additional comparisons also show that the coarse-mesh, nodal integral method results agree very well with the results of definitive ultra-fine-mesh, finite-difference calculations for the driven cavity problem up to fairly high Reynolds numbers
Czech Academy of Sciences Publication Activity Database
Šesnic, S.; Dorić, V.; Poljak, D.; Šušnjara, A.; Artaud, J.F.
2018-01-01
Roč. 46, č. 4 (2018), s. 1027-1034 ISSN 0093-3813 R&D Projects: GA MŠk(CZ) 8D15001 Institutional support: RVO:61389021 Keywords : Finite element analysis * Tokamaks * current diffusion equation (CDE) * finite-element method (FEM) Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.052, year: 2016
An analytic algorithm for the space-time fractional reaction-diffusion equation
Directory of Open Access Journals (Sweden)
M. G. Brikaa
2015-11-01
Full Text Available In this paper, we solve the space-time fractional reaction-diffusion equation by the fractional homotopy analysis method. Solutions of different examples of the reaction term will be computed and investigated. The approximation solutions of the studied models will be put in the form of convergent series to be easily computed and simulated. Comparison with the approximation solution of the classical case of the studied modeled with their approximation errors will also be studied.
Directory of Open Access Journals (Sweden)
Lihuan Guo
2018-04-01
Full Text Available As the information communication and investment of crowdfunding campaigns are usually accomplished online, online crowdfunding theoretically breaks the limitation of space. However, investors’ behaviors still show significant home bias; furthermore, from a dynamic view, the changes in home bias during the funding duration reflect the investment preference. This paper studies the dynamics of home bias in crowdfunding investment as well as the distance diffusion of home bias in the crowdfunding market through data mining and econometric models. The distance between investors and founders gradually increases from 3605 km to 4229 km as the funding progresses, and home bias shows different diffusion patterns between categories. For most of the campaigns, the distance between backers and founders of the successful campaigns is always greater than that of the failed ones; thus, the distance diffusion impacts the pledge results. However, the study also finds that for some categories, home bias does not play a positive role in investment or that it even shows negative impacts, among which food and technology are two extreme categories. The study provides a theoretical basis from the perspective of user behavior to analyze online investment and to improve the promotion of crowdfunding campaigns.
Song, Yun S; Steinrücken, Matthias
2012-03-01
The transition density function of the Wright-Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright-Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation-selection balance.
International Nuclear Information System (INIS)
Mochi, Ignacio
2005-01-01
The principal parameters of nuclear reactors are determined in the conceptual design stage.For that purpose, it is necessary to have flexible calculation tools that represent the principal dependencies of such parameters.This capability is of critical importance in the design of innovative nuclear reactors.In order to have a proper tool that could assist the conceptual design of innovative nuclear reactors, we developed and implemented a neutronic core calculus code: DIANA (Diffusion Integral Analytic Neutron Analysis).To calculate the required parameters, this code generates its own cross sections using an analytic two group, two zones diffusion scheme based only on a minimal set of data (i.e. 2200 m/s and fission averaged microscopic cross sections, Wescott factors and Effective Resonance Integrals).Both to calculate cross sections and core parameters, DIANA takes into account heterogeneity effects that are included when it evaluates each zone.Among them lays the disadvantage factor of each energy group.DIANA was totally implemented through Object Oriented Programming using C++ language. This eases source code understanding and would allow a quick expansion of its capabilities if needed.The final product is a versatile and easy-to-use code that allows core calculations with a minimal amount of data.It also contains the required tools needed to perform many variational calculations such as the parameterisation of effective multiplication factors for different radii of the core.The diffusion scheme s simplicity allows an easy following of the involved phenomena, making DIANA the most suitable tool to design reactors whose physics lays beyond the parameters of present reactors.All this reasons make DIANA a good candidate for future innovative reactor analysis
Nodal metastasis in thyroid cancer
International Nuclear Information System (INIS)
Samuel, A.M.
1999-01-01
The biological behavior and hence the prognosis of thyroid cancer (TC) depends among other factors on the extent of spread of the disease outside the thyroid bed. This effect is controversial, especially for nodal metastasis of well differentiated thyroid carcinoma (WDC). Nodal metastasis at the time of initial diagnosis behaves differently depending on the histology, age of the patient, presence of extrathyroidal extension, and the sex of the individual. The type of the surgery, administration of 131 I and thyroxin suppression also to some extent influence the rate of recurrence and mortality. Experience has shown that it is not as innocuous as a small intrathyroidal tumor without any invasion outside the thyroid bed and due consideration should be accorded to the management strategies for handling patients with nodal metastasis
Error estimation for variational nodal calculations
International Nuclear Information System (INIS)
Zhang, H.; Lewis, E.E.
1998-01-01
Adaptive grid methods are widely employed in finite element solutions to both solid and fluid mechanics problems. Either the size of the element is reduced (h refinement) or the order of the trial function is increased (p refinement) locally to improve the accuracy of the solution without a commensurate increase in computational effort. Success of these methods requires effective local error estimates to determine those parts of the problem domain where the solution should be refined. Adaptive methods have recently been applied to the spatial variables of the discrete ordinates equations. As a first step in the development of adaptive methods that are compatible with the variational nodal method, the authors examine error estimates for use in conjunction with spatial variables. The variational nodal method lends itself well to p refinement because the space-angle trial functions are hierarchical. Here they examine an error estimator for use with spatial p refinement for the diffusion approximation. Eventually, angular refinement will also be considered using spherical harmonics approximations
Nodal kinetics model upgrade in the Penn State coupled TRAC/NEM codes
International Nuclear Information System (INIS)
Beam, Tara M.; Ivanov, Kostadin N.; Baratta, Anthony J.; Finnemann, Herbert
1999-01-01
The Pennsylvania State University currently maintains and does development and verification work for its own versions of the coupled three-dimensional kinetics/thermal-hydraulics codes TRAC-PF1/NEM and TRAC-BF1/NEM. The subject of this paper is nodal model enhancements in the above mentioned codes. Because of the numerous validation studies that have been performed on almost every aspect of these codes, this upgrade is done without a major code rewrite. The upgrade consists of four steps. The first two steps are designed to improve the accuracy of the kinetics model, based on the nodal expansion method. The polynomial expansion solution of 1D transverse integrated diffusion equation is replaced with a solution, which uses a semi-analytic expansion. Further the standard parabolic polynomial representation of the transverse leakage in the above 1D equations is replaced with an improved approximation. The last two steps of the upgrade address the code efficiency by improving the solution of the time-dependent NEM equations and implementing a multi-grid solver. These four improvements are implemented into the standalone NEM kinetics code. Verification of this code was accomplished based on the original verification studies. The results show that the new methods improve the accuracy and efficiency of the code. The verification of the upgraded NEM model in the TRAC-PF1/NEM and TRAC-BF1/NEM coupled codes is underway
A spectral nodal method for discrete ordinates problems in x,y geometry
International Nuclear Information System (INIS)
Barros, R.C. de; Larsen, E.W.
1991-06-01
A new nodal method is proposed for the solution of S N problems in x- y-geometry. This method uses the Spectral Green's Function (SGF) scheme for solving the one-dimensional transverse-integrated nodal transport equations with no spatial truncation error. Thus, the only approximations in the x, y-geometry nodal method occur in the transverse leakage terms, as in diffusion theory. We approximate these leakage terms using a flat or constant approximation, and we refer to the resulting method as the SGF-Constant Nodal (SGF-CN) method. We show in numerical calculations that the SGF-CN method is much more accurate than other well-known transport nodal methods for coarse-mesh deep-penetration S N problems, even though the transverse leakage terms are approximated rather simply. (author)
Investigation on generalized Variational Nodal Methods for heterogeneous nodes
International Nuclear Information System (INIS)
Wang, Yongping; Wu, Hongchun; Li, Yunzhao; Cao, Liangzhi; Shen, Wei
2017-01-01
Highlights: • We developed two heterogeneous nodal methods based on the Variational Nodal Method. • Four problems were solved to evaluate the two heterogeneous nodal methods. • The function expansion method is good at treating continuous-changing heterogeneity. • The finite sub-element method is good at treating discontinuous-changing heterogeneity. - Abstract: The Variational Nodal Method (VNM) is generalized for heterogeneous nodes and applied to four kinds of problems including Molten Salt Reactor (MSR) core problem with continuous cross section profile, Pressurized Water Reactor (PWR) control rod cusping effect problem, PWR whole-core pin-by-pin problem, and heterogeneous PWR core problem without fuel-coolant homogenization in each pin cell. Two approaches have been investigated for the treatment of the nodal heterogeneity in this paper. To concentrate on spatial heterogeneity, diffusion approximation was adopted for the angular variable in neutron transport equation. To provide demonstrative numerical results, the codes in this paper were developed in slab geometry. The first method, named as function expansion (FE) method, expands nodal flux by orthogonal polynomials and the nodal cross sections are also expressed as spatial depended functions. The second path, named as finite sub-element (FS) method, takes advantage of the finite-element method by dividing each node into numbers of homogeneous sub-elements and expanding nodal flux into the combination of linear sub-element trial functions. Numerical tests have been carried out to evaluate the ability of the two nodal (coarse-mesh) heterogeneous VNMs by comparing with the fine-mesh homogeneous VNM. It has been demonstrated that both heterogeneous approaches can handle heterogeneous nodes. The FE method is good at continuous-changing heterogeneity as in the MSR core problem, while the FS method is good at discontinuous-changing heterogeneity such as the PWR pin-by-pin problem and heterogeneous PWR core
Nodal in computerized control systems of accelerators
International Nuclear Information System (INIS)
Kagarmanov, A.A.; Koval'tsov, V.I.; Korobov, S.A.
1994-01-01
Brief description of the Nodal language programming structure is presented. Its possibilities as high-level programming language for accelerator control systems are considered. The status of the Nodal language in the HEPI is discussed. 3 refs
The diffusion of renewable energy technology: an analytical framework and key issues for research
International Nuclear Information System (INIS)
Jacobsson, S.; Johnson, A.
2000-01-01
During the last two decades there has been a great deal of research on renewable energy technologies. It is commonly thought that very little has come out of this research in terms of commercially interesting technologies. The first objective of this paper is to demonstrate that this perception is no longer correct; in the 1990s there has been a double-digit growth rate in the market for some renewable energy technologies. The consequent alteration in the energy system, is, however, a slow, painful and highly uncertain process. This process, we argue, needs to be studied using an innovation system perspective where the focus is on networks, institutions and firms' perceptions, competencies and strategies. The second objective of the paper is therefore to present the bare bones of such an analytical framework. A third objective is to identify a set of key issues related to the speed and direction of that transformation process which needs to be studied further. (author)
An alternative solver for the nodal expansion method equations - 106
International Nuclear Information System (INIS)
Carvalho da Silva, F.; Carlos Marques Alvim, A.; Senra Martinez, A.
2010-01-01
An automated procedure for nuclear reactor core design is accomplished by using a quick and accurate 3D nodal code, aiming at solving the diffusion equation, which describes the spatial neutron distribution in the reactor. This paper deals with an alternative solver for nodal expansion method (NEM), with only two inner iterations (mesh sweeps) per outer iteration, thus having the potential to reduce the time required to calculate the power distribution in nuclear reactors, but with accuracy similar to the ones found in conventional NEM. The proposed solver was implemented into a computational system which, besides solving the diffusion equation, also solves the burnup equations governing the gradual changes in material compositions of the core due to fuel depletion. Results confirm the effectiveness of the method for practical purposes. (authors)
A variational synthesis nodal discrete ordinates method
International Nuclear Information System (INIS)
Favorite, J.A.; Stacey, W.M.
1999-01-01
A self-consistent nodal approximation method for computing discrete ordinates neutron flux distributions has been developed from a variational functional for neutron transport theory. The advantage of the new nodal method formulation is that it is self-consistent in its definition of the homogenized nodal parameters, the construction of the global nodal equations, and the reconstruction of the detailed flux distribution. The efficacy of the method is demonstrated by two-dimensional test problems
Fuller, Nathaniel J.; Licata, Nicholas A.
2018-05-01
Obtaining a detailed understanding of the physical interactions between a cell and its environment often requires information about the flow of fluid surrounding the cell. Cells must be able to effectively absorb and discard material in order to survive. Strategies for nutrient acquisition and toxin disposal, which have been evolutionarily selected for their efficacy, should reflect knowledge of the physics underlying this mass transport problem. Motivated by these considerations, in this paper we discuss the results from an undergraduate research project on the advection-diffusion equation at small Reynolds number and large Péclet number. In particular, we consider the problem of mass transport for a Stokesian spherical swimmer. We approach the problem numerically and analytically through a rescaling of the concentration boundary layer. A biophysically motivated first-passage problem for the absorption of material by the swimming cell demonstrates quantitative agreement between the numerical and analytical approaches. We conclude by discussing the connections between our results and the design of smart toxin disposal systems.
International Nuclear Information System (INIS)
Xiao, Boqi; Fan, Jintu; Ding, Feng
2014-01-01
The study of water and gas transport through fibrous gas diffusion layer (GDL) is important to the optimization of proton exchange membrane fuel cells (PEMFCs). In this work, analytical models of dimensionless permeability, and water and gas relative permeabilities of fibrous GDL in PEMFCs are derived using fractal theory. In our models, the structure of fibrous GDL is characterized in terms of porosity, tortuosity fractal dimension (D T ), pore area fractal dimensions (d f ), water phase (d f,w ) and gas phase (d f,g ) fractal dimensions. The predicted dimensionless permeability, water and gas relative permeabilities based on the proposed models are in good agreement with experimental data and predictions of numerical simulations reported in the literature. The model reveals that, although water phase and gas phase fractal dimensions strongly depend on porosity, the water and gas relative permeabilities are independent of porosity and are a function of water saturation only. It is also shown that the dimensionless permeability decreases significantly with the increase of tortuosity fractal dimension. On the other hand, there is only a small decrease in the water and gas relative permeabilities when tortuosity fractal dimension increases. One advantage of the proposed analytical model is that it contains no empirical constant, which is normally required in past models
Using nodal expansion method in calculation of reactor core with square fuel assemblies
International Nuclear Information System (INIS)
Abdollahzadeh, M. Y.; Boroushaki, M.
2009-01-01
A polynomial nodal method is developed to solve few-group neutron diffusion equations in cartesian geometry. In this article, the effective multiplication factor, group flux and power distribution based on the nodal polynomial expansion procedure is presented. In addition, by comparison of the results the superiority of nodal expansion method on finite-difference and finite-element are fully demonstrated. The comparison of the results obtained by these method with those of the well known benchmark problems have shown that they are in very good agreement.
Rules for Phase Shifts of Quantum Oscillations in Topological Nodal-Line Semimetals
Li, Cequn; Wang, C. M.; Wan, Bo; Wan, Xiangang; Lu, Hai-Zhou; Xie, X. C.
2018-04-01
Nodal-line semimetals are topological semimetals in which band touchings form nodal lines or rings. Around a loop that encloses a nodal line, an electron can accumulate a nontrivial π Berry phase, so the phase shift in the Shubnikov-de Haas (SdH) oscillation may give a transport signature for the nodal-line semimetals. However, different experiments have reported contradictory phase shifts, in particular, in the WHM nodal-line semimetals (W =Zr /Hf , H =Si /Ge , M =S /Se /Te ). For a generic model of nodal-line semimetals, we present a systematic calculation for the SdH oscillation of resistivity under a magnetic field normal to the nodal-line plane. From the analytical result of the resistivity, we extract general rules to determine the phase shifts for arbitrary cases and apply them to ZrSiS and Cu3 PdN systems. Depending on the magnetic field directions, carrier types, and cross sections of the Fermi surface, the phase shift shows rich results, quite different from those for normal electrons and Weyl fermions. Our results may help explore transport signatures of topological nodal-line semimetals and can be generalized to other topological phases of matter.
The application of modern nodal methods to PWR reactor physics analysis
International Nuclear Information System (INIS)
Knight, M.P.
1988-06-01
The objective of this research is to develop efficient computational procedures for PWR reactor calculations, based on modern nodal methods. The analytic nodal method, which is characterised by the use of exact exponential expansions in transverse-integrated equations, is implemented within an existing finite-difference code. This shows considerable accuracy and efficiency on standard benchmark problems, very much in line with existing experience with nodal methods., Assembly powers can be calculated to within 2.0% with just one mesh per assembly. (author)
International Nuclear Information System (INIS)
Al-Chalabi, R.M.; Turinsky, P.J.; Faure, F.-X.; Sarsour, H.N.; Engrand, P.R.
1993-01-01
The NESTLE nodal kinetics code has been developed for utilization as a stand-alone code for steady-state and transient reactor neutronic analysis and for incorporation into system transient codes, such as TRAC and RELAP. The latter is desirable to increase the simulation fidelity over that obtained from currently employed zero- and one-dimensional neutronic models and now feasible due to advances in computer performance and efficiency of nodal methods. As a stand-alone code, requirements are that it operate on a range of computing platforms from memory-limited personal computers (PCs) to supercomputers with vector processors. This paper summarizes the features of NESTLE that reflect the utilization and requirements just noted
Nodal lymphomas of the abdomen
International Nuclear Information System (INIS)
Bruneton, J.N.; Caramella, E.; Manzino, J.J.
1986-01-01
Modern imaging modalities have greatly contributed to current knowledge about intra-abdominal nodal lymphomas. Since both intra and retroperitoneal node involvement can be demonstrated by computed tomography (CT) and ultrasonography, it seems legitimate to treat these two sites together in the same chapter, particularly since the older separation between intraperitoneal and retroperitoneal nodal disease was based to a large degree on the limitations of lymphography. Hodgkin's disease (HD) has benefited less from recent technological advances. The diversity in the incidence of nodal involvement between HD and NHL, the diagnostic capabilities of modern imaging techniques, and the histopathological features of lymphomatous non-Hodgkin and Hodgkin nodes, justify adoption of an investigatory approach which takes all of these factors into account. Details of this investigative strategy are discussed in this paper following a review of available imaging modalities. In current practice, the four main methods for the exploration of abdominal lymph nodes are lymphography, ultrasonography, CT, and radionuclide studies. The first three techniques are also utilized to guide biopsies for staging purposes and for the evaluation of response to treatment
A polygonal nodal SP3 method for whole core Pin-by-Pin neutronics calculation
Energy Technology Data Exchange (ETDEWEB)
Li, Yunzhao; Wu, Hongchun; Cao, Liangzhi, E-mail: xjtulyz@gmail.com, E-mail: hongchun@mail.xjtu.edu.cn, E-mail: caolz@mail.xjtu.edu.cn [School of Nuclear Science and Technology, Xi' an Jiaotong University, Shaanxi (China)
2011-07-01
In this polygonal nodal-SP3 method, neutron transport equation is transformed by employing an isotropic SP3 method into two coupled equations that are both in the same mathematic form with the diffusion equation, and then a polygonal nodal method is proposed to solve the two coupled equations. In the polygonal nodal method, adjacent nodes are coupled through partial currents, and a nodal response matrix between incoming and outgoing currents is obtained by expanding detailed nodal flux distribution into a sum of exponential functions. This method avoids the transverse integral technique, which is widely used in regular nodal method and can not be used in triangular geometry because of the mathematical singularity. It is demonstrated by the numerical results of the test problems that the k{sub eff} and power distribution agree well with other codes, the triangular nodal-SP3 method appears faster, and that whole core pin-by-pin transport calculation with fine meshes is feasible after parallelization and acceleration. (author)
Hybrid microscopic depletion model in nodal code DYN3D
International Nuclear Information System (INIS)
Bilodid, Y.; Kotlyar, D.; Shwageraus, E.; Fridman, E.; Kliem, S.
2016-01-01
Highlights: • A new hybrid method of accounting for spectral history effects is proposed. • Local concentrations of over 1000 nuclides are calculated using micro depletion. • The new method is implemented in nodal code DYN3D and verified. - Abstract: The paper presents a general hybrid method that combines the micro-depletion technique with correction of micro- and macro-diffusion parameters to account for the spectral history effects. The fuel in a core is subjected to time- and space-dependent operational conditions (e.g. coolant density), which cannot be predicted in advance. However, lattice codes assume some average conditions to generate cross sections (XS) for nodal diffusion codes such as DYN3D. Deviation of local operational history from average conditions leads to accumulation of errors in XS, which is referred as spectral history effects. Various methods to account for the spectral history effects, such as spectral index, burnup-averaged operational parameters and micro-depletion, were implemented in some nodal codes. Recently, an alternative method, which characterizes fuel depletion state by burnup and 239 Pu concentration (denoted as Pu-correction) was proposed, implemented in nodal code DYN3D and verified for a wide range of history effects. The method is computationally efficient, however, it has applicability limitations. The current study seeks to improve the accuracy and applicability range of Pu-correction method. The proposed hybrid method combines the micro-depletion method with a XS characterization technique similar to the Pu-correction method. The method was implemented in DYN3D and verified on multiple test cases. The results obtained with DYN3D were compared to those obtained with Monte Carlo code Serpent, which was also used to generate the XS. The observed differences are within the statistical uncertainties.
International Nuclear Information System (INIS)
Anistratov, Dmitriy Y.; Adams, Marvin L.; Palmer, Todd S.; Smith, Kord S.; Clarno, Kevin; Hikaru Hiruta; Razvan Nes
2003-01-01
OAK (B204) Final Report, NERI Project: ''An Innovative Reactor Analysis Methodology Based on a Quasidiffusion Nodal Core Model'' The present generation of reactor analysis methods uses few-group nodal diffusion approximations to calculate full-core eigenvalues and power distributions. The cross sections, diffusion coefficients, and discontinuity factors (collectively called ''group constants'') in the nodal diffusion equations are parameterized as functions of many variables, ranging from the obvious (temperature, boron concentration, etc.) to the more obscure (spectral index, moderator temperature history, etc.). These group constants, and their variations as functions of the many variables, are calculated by assembly-level transport codes. The current methodology has two main weaknesses that this project addressed. The first weakness is the diffusion approximation in the full-core calculation; this can be significantly inaccurate at interfaces between different assemblies. This project used the nodal diffusion framework to implement nodal quasidiffusion equations, which can capture transport effects to an arbitrary degree of accuracy. The second weakness is in the parameterization of the group constants; current models do not always perform well, especially at interfaces between unlike assemblies. The project developed a theoretical foundation for parameterization and homogenization models and used that theory to devise improved models. The new models were extended to tabulate information that the nodal quasidiffusion equations can use to capture transport effects in full-core calculations
Parra-Robles, J; Ajraoui, S; Deppe, M H; Parnell, S R; Wild, J M
2010-06-01
Models of lung acinar geometry have been proposed to analytically describe the diffusion of (3)He in the lung (as measured with pulsed gradient spin echo (PGSE) methods) as a possible means of characterizing lung microstructure from measurement of the (3)He ADC. In this work, major limitations in these analytical models are highlighted in simple diffusion weighted experiments with (3)He in cylindrical models of known geometry. The findings are substantiated with numerical simulations based on the same geometry using finite difference representation of the Bloch-Torrey equation. The validity of the existing "cylinder model" is discussed in terms of the physical diffusion regimes experienced and the basic reliance of the cylinder model and other ADC-based approaches on a Gaussian diffusion behaviour is highlighted. The results presented here demonstrate that physical assumptions of the cylinder model are not valid for large diffusion gradient strengths (above approximately 15 mT/m), which are commonly used for (3)He ADC measurements in human lungs. (c) 2010 Elsevier Inc. All rights reserved.
One-dimensional nodal neutronics routines for the TRAC-BD1 thermal-hydraulics program
International Nuclear Information System (INIS)
Nigg, D.W.
1983-09-01
Nuclear reactor core transient neutronic behavior is currently modeled in the TRAC-BD1 code using a point-reactor kinetics formulation. This report describes a set of subroutines based on the Analytic Nodal Method that were written to provide TRAC-BD1 with a one-dimensional space-dependent neutronics capability. Use of the routines is illustrated with several test problems. The results of these problems show that the Analytic Nodal neutronics routines have desirable accuracy and computing time characteristics and should be a useful addition to TRAC-BD1
Development of 3D multi-group neutron diffusion code for hexagonal geometry
International Nuclear Information System (INIS)
Sun Wei; Wang Kan; Ni Dongyang; Li Qing
2013-01-01
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)
The Nudo, Rollo, Melon codes and nodal correlations
International Nuclear Information System (INIS)
Perlado, J.M.; Aragones, J.M.; Minguez, E.; Pena, J.
1975-01-01
Analysis of nodal calculation and checking results by the reference reactor experimental data. Nudo code description, adapting experimental data to nodal calculations. Rollo, Melon codes as improvement in the cycle life calculations of albedos, mixing parameters and nodal correlations. (author)
Group-decoupled multi-group pin power reconstruction utilizing nodal solution 1D flux profiles
International Nuclear Information System (INIS)
Yu, Lulin; Lu, Dong; Zhang, Shaohong; Wang, Dezhong
2014-01-01
Highlights: • A direct fitting multi-group pin power reconstruction method is developed. • The 1D nodal solution flux profiles are used as the condition. • The least square fit problem is analytically solved. • A slowing down source improvement method is applied. • The method shows good accuracy for even challenging problems. - Abstract: A group-decoupled direct fitting method is developed for multi-group pin power reconstruction, which avoids both the complication of obtaining 2D analytic multi-group flux solution and any group-coupled iteration. A unique feature of the method is that in addition to nodal volume and surface average fluxes and corner fluxes, transversely-integrated 1D nodal solution flux profiles are also used as the condition to determine the 2D intra-nodal flux distribution. For each energy group, a two-dimensional expansion with a nine-term polynomial and eight hyperbolic functions is used to perform a constrained least square fit to the 1D intra-nodal flux solution profiles. The constraints are on the conservation of nodal volume and surface average fluxes and corner fluxes. Instead of solving the constrained least square fit problem numerically, we solve it analytically by fully utilizing the symmetry property of the expansion functions. Each of the 17 unknown expansion coefficients is expressed in terms of nodal volume and surface average fluxes, corner fluxes and transversely-integrated flux values. To determine the unknown corner fluxes, a set of linear algebraic equations involving corner fluxes is established via using the current conservation condition on all corners. Moreover, an optional slowing down source improvement method is also developed to further enhance the accuracy of the reconstructed flux distribution if needed. Two test examples are shown with very good results. One is a four-group BWR mini-core problem with all control blades inserted and the other is the seven-group OECD NEA MOX benchmark, C5G7
NOMAD: a nodal microscopic analysis method for nuclear fuel depletion
International Nuclear Information System (INIS)
Rajic, H.L.; Ougouag, A.M.
1987-01-01
Recently developed assembly homogenization techniques made possible very efficient global burnup calculations based on modern nodal methods. There are two possible ways of modeling the global depletion process: macroscopic and microscopic depletion models. Using a microscopic global depletion approach NOMAD (NOdal Microscopic Analysis Method for Nuclear Fuel Depletion), a multigroup, two- and three-dimensional, multicycle depletion code was devised. The code uses the ILLICO nodal diffusion model. The formalism of the ILLICO methodology is extended to treat changes in the macroscopic cross sections during a depletion cycle without recomputing the coupling coefficients. This results in a computationally very efficient method. The code was tested against a well-known depletion benchmark problem. In this problem a two-dimensional pressurized water reactor is depleted through two cycles. Both cycles were run with 1 x 1 and 2 x 2 nodes per assembly. It is obvious that the one node per assembly solution gives unacceptable results while the 2 x 2 solution gives relative power errors consistently below 2%
A quasi-static polynomial nodal method for nuclear reactor analysis
International Nuclear Information System (INIS)
Gehin, J.C.
1992-09-01
Modern nodal methods are currently available which can accurately and efficiently solve the static and transient neutron diffusion equations. Most of the methods, however, are limited to two energy groups for practical application. The objective of this research is the development of a static and transient, multidimensional nodal method which allows more than two energy groups and uses a non-linear iterative method for efficient solution of the nodal equations. For both the static and transient methods, finite-difference equations which are corrected by the use of discontinuity factors are derived. The discontinuity factors are computed from a polynomial nodal method using a non-linear iteration technique. The polynomial nodal method is based upon a quartic approximation and utilizes a quadratic transverse-leakage approximation. The solution of the time-dependent equations is performed by the use of a quasi-static method in which the node-averaged fluxes are factored into shape and amplitude functions. The application of the quasi-static polynomial method to several benchmark problems demonstrates that the accuracy is consistent with that of other nodal methods. The use of the quasi-static method is shown to substantially reduce the computation time over the traditional fully-implicit time-integration method. Problems involving thermal-hydraulic feedback are accurately, and efficiently, solved by performing several reactivity/thermal-hydraulic updates per shape calculation
A quasi-static polynomial nodal method for nuclear reactor analysis
Energy Technology Data Exchange (ETDEWEB)
Gehin, Jess C. [Massachusetts Inst. of Tech., Cambridge, MA (United States)
1992-09-01
Modern nodal methods are currently available which can accurately and efficiently solve the static and transient neutron diffusion equations. Most of the methods, however, are limited to two energy groups for practical application. The objective of this research is the development of a static and transient, multidimensional nodal method which allows more than two energy groups and uses a non-linear iterative method for efficient solution of the nodal equations. For both the static and transient methods, finite-difference equations which are corrected by the use of discontinuity factors are derived. The discontinuity factors are computed from a polynomial nodal method using a non-linear iteration technique. The polynomial nodal method is based upon a quartic approximation and utilizes a quadratic transverse-leakage approximation. The solution of the time-dependent equations is performed by the use of a quasi-static method in which the node-averaged fluxes are factored into shape and amplitude functions. The application of the quasi-static polynomial method to several benchmark problems demonstrates that the accuracy is consistent with that of other nodal methods. The use of the quasi-static method is shown to substantially reduce the computation time over the traditional fully-implicit time-integration method. Problems involving thermal-hydraulic feedback are accurately, and efficiently, solved by performing several reactivity/thermal-hydraulic updates per shape calculation.
International Nuclear Information System (INIS)
Shih, Helen A.; Harisinghani, Mukesh; Zietman, Anthony L.; Wolfgang, John A.; Saksena, Mansi; Weissleder, Ralph
2005-01-01
Purpose: Toxicity from pelvic irradiation could be reduced if fields were limited to likely areas of nodal involvement rather than using the standard 'four-field box.' We employed a novel magnetic resonance lymphangiographic technique to highlight the likely sites of occult nodal metastasis from prostate cancer. Methods and Materials: Eighteen prostate cancer patients with pathologically confirmed node-positive disease had a total of 69 pathologic nodes identifiable by lymphotropic nanoparticle-enhanced MRI and semiquantitative nodal analysis. Fourteen of these nodes were in the para-aortic region, and 55 were in the pelvis. The position of each of these malignant nodes was mapped to a common template based on its relation to skeletal or vascular anatomy. Results: Relative to skeletal anatomy, nodes covered a diffuse volume from the mid lumbar spine to the superior pubic ramus and along the sacrum and pelvic side walls. In contrast, the nodal metastases mapped much more tightly relative to the large pelvic vessels. A proposed pelvic clinical target volume to encompass the region at greatest risk of containing occult nodal metastases would include a 2.0-cm radial expansion volume around the distal common iliac and proximal external and internal iliac vessels that would encompass 94.5% of the pelvic nodes at risk as defined by our node-positive prostate cancer patient cohort. Conclusions: Nodal metastases from prostate cancer are largely localized along the major pelvic vasculature. Defining nodal radiation treatment portals based on vascular rather than bony anatomy may allow for a significant decrease in normal pelvic tissue irradiation and its associated toxicities
Solution and Study of the Two-Dimensional Nodal Neutron Transport Equation
International Nuclear Information System (INIS)
Panta Pazos, Ruben; Biasotto Hauser, Eliete; Tullio de Vilhena, Marco
2002-01-01
In the last decade Vilhena and coworkers reported an analytical solution to the two-dimensional nodal discrete-ordinates approximations of the neutron transport equation in a convex domain. The key feature of these works was the application of the combined collocation method of the angular variable and nodal approach in the spatial variables. By nodal approach we mean the transverse integration of the SN equations. This procedure leads to a set of one-dimensional S N equations for the average angular fluxes in the variables x and y. These equations were solved by the old version of the LTS N method, which consists in the application of the Laplace transform to the set of nodal S N equations and solution of the resulting linear system by symbolic computation. It is important to recall that this procedure allow us to increase N the order of S N up to 16. To overcome this drawback we step forward performing a spectral painstaking analysis of the nodal S N equations for N up to 16 and we begin the convergence of the S N nodal equations defining an error for the angular flux and estimating the error in terms of the truncation error of the quadrature approximations of the integral term. Furthermore, we compare numerical results of this approach with those of other techniques used to solve the two-dimensional discrete approximations of the neutron transport equation. (authors)
Optical conductivity of three and two dimensional topological nodal-line semimetals
Barati, Shahin; Abedinpour, Saeed H.
2017-10-01
The peculiar shape of the Fermi surface of topological nodal-line semimetals at low carrier concentrations results in their unusual optical and transport properties. We analytically investigate the linear optical responses of three- and two-dimensional nodal-line semimetals using the Kubo formula. The optical conductivity of a three-dimensional nodal-line semimetal is anisotropic. Along the axial direction (i.e., the direction perpendicular to the nodal-ring plane), the Drude weight has a linear dependence on the chemical potential at both low and high carrier dopings. For the radial direction (i.e., the direction parallel to the nodal-ring plane), this dependence changes from linear into quadratic in the transition from low into high carrier concentration. The interband contribution into optical conductivity is also anisotropic. In particular, at large frequencies, it saturates to a constant value for the axial direction and linearly increases with frequency along the radial direction. In two-dimensional nodal-line semimetals, no interband optical transition could be induced and the only contribution to the optical conductivity arises from the intraband excitations. The corresponding Drude weight is independent of the carrier density at low carrier concentrations and linearly increases with chemical potential at high carrier doping.
International Nuclear Information System (INIS)
Iyiola, O.S.; Tasbozan, O.; Kurt, A.; Çenesiz, Y.
2017-01-01
In this paper, we consider the system of conformable time-fractional Robertson equations with one-dimensional diffusion having widely varying diffusion coefficients. Due to the mismatched nature of the initial and boundary conditions associated with Robertson equation, there are spurious oscillations appearing in many computational algorithms. Our goal is to obtain an approximate solutions of this system of equations using the q-homotopy analysis method (q-HAM) and examine the widely varying diffusion coefficients and the fractional order of the derivative.
Nodal pricing in a coupled electricity market
Bjørndal, Endre; Bjørndal, Mette; Cai, Hong
2014-01-01
This paper investigates a pricing model for an electricity market with a hybrid congestion management method, i.e. part of the system applies a nodal pricing scheme and the rest applies a zonal pricing scheme. The model clears the zonal and nodal pricing areas simultaneously. The nodal pricing area is affected by the changes in the zonal pricing area since it is directly connected to the zonal pricing area by commercial trading. The model is tested on a 13-node power system. Within the area t...
Maternal Nodal inversely affects NODAL and STOX1 expression in the fetal placenta
Directory of Open Access Journals (Sweden)
Hari Krishna Thulluru
2013-08-01
Full Text Available Nodal, a secreted signaling protein from the TGFβ-super family plays a vital role during early embryonic development. Recently, it was found that maternal decidua-specific Nodal knockout mice show intrauterine growth restriction (IUGR and preterm birth. As the chromosomal location of NODAL is in the same linkage area as the susceptibility gene STOX1, associated with the familial form of early-onset, IUGR-complicated pre-eclampsia, their potential maternal-fetal interaction was investigated. Pre-eclamptic mothers with children who carried the STOX1 susceptibility allele themselves all carried the NODAL H165R SNP, which causes a 50% reduced activity. Surprisingly, in decidua Nodal knockout mice the fetal placenta showed up-regulation of STOX1 and NODAL expression. Conditioned media of human first trimester decidua and a human endometrial stromal cell line (T-HESC treated with siRNAs against NODAL or carrying the H165R SNP were also able to induce NODAL and STOX1 expression when added to SGHPL-5 first trimester extravillous trophoblast cells. Finally, a human TGFß-BMP-Signaling-Pathway PCR-Array on decidua and the T-HESC cell line with Nodal knockdown revealed upregulation of Activin-A, which was confirmed in conditioned media by ELISA. We show that maternal decidua Nodal knockdown gives upregulation of NODAL and STOX1 mRNA expression in fetal extravillous trophoblast cells, potentially via upregulation of Activin-A in the maternal decidua. As both Activin-A and Nodal have been implicated in pre-eclampsia, being increased in serum of pre-eclamptic women and upregulated in pre-eclamptic placentas respectively, this interaction at the maternal-fetal interface might play a substantial role in the development of pre-eclampsia.
Quantum oscillations in nodal line systems
Yang, Hui; Moessner, Roderich; Lim, Lih-King
2018-04-01
We study signatures of magnetic quantum oscillations in three-dimensional nodal line semimetals at zero temperature. The extended nature of the degenerate bands can result in a Fermi surface geometry with topological genus one, as well as a Fermi surface of electron and hole pockets encapsulating the nodal line. Moreover, the underlying two-band model to describe a nodal line is not unique, in that there are two classes of Hamiltonian with distinct band topology giving rise to the same Fermi-surface geometry. After identifying the extremal cyclotron orbits in various magnetic field directions, we study their concomitant Landau levels and resulting quantum oscillation signatures. By Landau-fan-diagram analyses, we extract the nontrivial π Berry phase signature for extremal orbits linking the nodal line.
Sensitivity of SBLOCA analysis to model nodalization
International Nuclear Information System (INIS)
Lee, C.; Ito, T.; Abramson, P.B.
1983-01-01
The recent Semiscale test S-UT-8 indicates the possibility for primary liquid to hang up in the steam generators during a SBLOCA, permitting core uncovery prior to loop-seal clearance. In analysis of Small Break Loss of Coolant Accidents with RELAP5, it is found that resultant transient behavior is quite sensitive to the selection of nodalization for the steam generators. Although global parameters such as integrated mass loss, primary inventory and primary pressure are relatively insensitive to the nodalization, it is found that the predicted distribution of inventory around the primary is significantly affected by nodalization. More detailed nodalization predicts that more of the inventory tends to remain in the steam generators, resulting in less inventory in the reactor vessel and therefore causing earlier and more severe core uncovery
Twisted Vector Bundles on Pointed Nodal Curves
Indian Academy of Sciences (India)
Abstract. Motivated by the quest for a good compactification of the moduli space of -bundles on a nodal curve we establish a striking relationship between Abramovich's and Vistoli's twisted bundles and Gieseker vector bundles.
International Nuclear Information System (INIS)
Crowley-Milling, M.C.; Shering, G.C.
1978-01-01
A comprehensive description is given of the NODAL system used for computer control of the CERN Super-Proton Synchrotron. Details are given of NODAL, a high-level programming language based on FOCAL and SNOBOL4, designed for interactive use. It is shown how this interpretive language is used with a network of computers and how it can be extended by adding machine-code modules. The report updates and replaces an earlier one published in 1974. (Auth.)
Nodal coupling by response matrix principles
International Nuclear Information System (INIS)
Ancona, A.; Becker, M.; Beg, M.D.; Harris, D.R.; Menezes, A.D.; VerPlanck, D.M.; Pilat, E.
1977-01-01
The response matrix approach has been used in viewing a reactor node in isolation and in characterizing the node by reflection and trans-emission factors. These are then used to generate invariant imbedding parameters, which in turn are used in a nodal reactor simulator code to compute core power distributions in two and three dimensions. Various nodal techniques are analyzed and converted into a single invariant imbedding formalism
Magnonic triply-degenerate nodal points
Owerre, S. A.
2017-12-01
We generalize the concept of triply-degenerate nodal points to non-collinear antiferromagnets. Here, we introduce this concept to insulating quantum antiferromagnets on the decorated honeycomb lattice, with spin-1 bosonic quasiparticle excitations known as magnons. We demonstrate the existence of magnonic surface states with constant energy contours that form pairs of magnonic arcs connecting the surface projection of the magnonic triple nodal points. The quasiparticle excitations near the triple nodal points represent three-component bosons beyond that of magnonic Dirac, Weyl, and nodal-line cases. They can be regarded as a direct reflection of the intrinsic spin carried by magnons. Furthermore, we show that the magnonic triple nodal points can split into magnonic Weyl points, as the system transits from a non-collinear spin structure to a non-coplanar one with a non-zero scalar spin chirality. Our results not only apply to insulating antiferromagnets, but also provide a platform to seek for triple nodal points in metallic antiferromagnets.
International Nuclear Information System (INIS)
Yin Chen; Xu Mingyu
2009-01-01
We set up a one-dimensional mathematical model with a Caputo fractional operator of a drug released from a polymeric matrix that can be dissolved into a solvent. A two moving boundaries problem in fractional anomalous diffusion (in time) with order α element of (0, 1] under the assumption that the dissolving boundary can be dissolved slowly is presented in this paper. The two-parameter regular perturbation technique and Fourier and Laplace transform methods are used. A dimensionless asymptotic analytical solution is given in terms of the Wright function
Energy Technology Data Exchange (ETDEWEB)
Samin, Adib; Lahti, Erik; Zhang, Jinsuo, E-mail: zhang.3558@osu.edu [Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19" t" h Avenue, Columbus, Ohio 43210 (United States)
2015-08-15
Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes.
International Nuclear Information System (INIS)
th Avenue, Columbus, Ohio 43210 (United States))" data-affiliation=" (Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, Ohio 43210 (United States))" >Samin, Adib; th Avenue, Columbus, Ohio 43210 (United States))" data-affiliation=" (Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, Ohio 43210 (United States))" >Lahti, Erik; th Avenue, Columbus, Ohio 43210 (United States))" data-affiliation=" (Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, Ohio 43210 (United States))" >Zhang, Jinsuo
2015-01-01
Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extended to cases that are more general and may be useful for benchmarking purposes
International Nuclear Information System (INIS)
Mueller, E.M.
1989-05-01
This research is concerned with the development and analysis of methods for generating equivalent nodal diffusion parameters for the radial reflector of a PWR. The requirement that the equivalent reflector data be insensitive to changing core conditions is set as a principle objective. Hence, the environment dependence of the currently most reputable nodal reflector models, almost all of which are based on the nodal equivalence theory homgenization methods of Koebke and Smith, is investigated in detail. For this purpose, a special 1-D nodal equivalence theory reflector model, called the NGET model, is developed and used in 1-D and 2-D numerical experiments. The results demonstrate that these modern radial reflector models exhibit sufficient sensitivity to core conditions to warrant the development of alternative models. A new 1-D nodal reflector model, which is based on a novel combination of the nodal equivalence theory and the response matrix homogenization methods, is developed. Numerical results varify that this homogenized baffle/reflector model, which is called the NGET-RM model, is highly insensitive to changing core conditions. It is also shown that the NGET-RM model is not inferior to any of the existing 1-D nodal reflector models and that it has features which makes it an attractive alternative model for multi-dimensional reactor analysis. 61 refs., 40 figs., 36 tabs
cmpXLatt: Westinghouse automated testing tool for nodal cross section models
International Nuclear Information System (INIS)
Guimaraes, Petri Forslund; Rönnberg, Kristian
2011-01-01
The procedure for evaluating the merits of different nodal cross section representation models is normally both cumbersome and time consuming, and includes many manual steps when preparing appropriate benchmark problems. Therefore, a computer tool called cmpXLatt has been developed at Westinghouse in order to facilitate the process of performing comparisons between nodal diffusion theory results and corresponding transport theory results on a single node basis. Due to the large number of state points that can be evaluated by cmpXLatt, a systematic and comprehensive way of performing verification and validation of nodal cross section models is provided. This paper presents the main features of cmpXLatt and demonstrates the benefits of using cmpXLatt in a real life application. (author)
Ginzburg, Irina; Vikhansky, Alexander
2018-05-01
The extended method of moments (EMM) is elaborated in recursive algorithmic form for the prediction of the effective diffusivity, the Taylor dispersion dyadic and the associated longitudinal high-order coefficients in mean-concentration profiles and residence-time distributions. The method applies in any streamwise-periodic stationary d-dimensional velocity field resolved in the piecewise continuous heterogeneous porosity field. It is demonstrated that EMM reduces to the method of moments and the volume-averaging formulation in microscopic velocity field and homogeneous soil, respectively. The EMM simultaneously constructs two systems of moments, the spatial and the temporal, without resorting to solving of the high-order upscaled PDE. At the same time, the EMM is supported with the reconstruction of distribution from its moments, allowing to visualize the deviation from the classical ADE solution. The EMM can be handled by any linear advection-diffusion solver with explicit mass-source and diffusive-flux jump condition on the solid boundary and permeable interface. The prediction of the first four moments is decisive in the optimization of the dispersion, asymmetry, peakedness and heavy-tails of the solute distributions, through an adequate design of the composite materials, wetlands, chemical devices or oil recovery. The symbolic solutions for dispersion, skewness and kurtosis are constructed in basic configurations: diffusion process and Darcy flow through two porous blocks in "series", straight and radial Poiseuille flow, porous flow governed by the Stokes-Brinkman-Darcy channel equation and a fracture surrounded by penetrable diffusive matrix or embedded in porous flow. We examine the moments dependency upon porosity contrast, aspect ratio, Péclet and Darcy numbers, but also for their response on the effective Brinkman viscosity applied in flow modeling. Two numerical Lattice Boltzmann algorithms, a direct solver of the microscopic ADE in heterogeneous
International Nuclear Information System (INIS)
Najera H, M.C.
2003-01-01
As they have gone being managed complex systems that fulfill tasks inside industrial or nuclear processes, it becomes necessary the development of technical novel of control, in which can incorporate heuristic knowledge of operation without to necessarily use the theories of classic control based mainly in mathematical models. One of the control techniques that allows to carry out this is the control based on diffuse logic. For the case of a model of the nuclear research reactor Triga Mark III of the National Institute of Nuclear Research have been developed diverse algorithms of diffuse control that have as objective the regulation of the neutron power in the nucleus. The aggregation stages and desdifussification in these algorithms discretize the universe of values of the control variable, being required a high number of operations for their execution. With the purpose of reducing this number of operations and to obtain results more exact in the generation of the aggregated group in each cycle of control and in the determination of the center of gravity of this added group, it is presented the development of an analytical method for these calculations. The main objectives outlined in this entitled thesis D esign of an analytical aggregate of a diffuse controller rules and their application in the pattern of a nuclear research reactor , they are: to improve the behavior of control systems in closed knot based on diffuse logic by means of the development of an analytical method that determines an aggregated group resultant of the activation of rules in the diffuse controller and the obtaining of the exit variable using an exact solution of the technique of the center of gravity; and to compare the operation of these methods with those traditionally used ones that consider the discretization of the universe of the exit variable so much for the aggregation like for the desdiffusification. The chapters 1 and 2 present an introduction at two fundamental themes of the
Calvo-López, Antonio; Ymbern, Oriol; Puyol, Mar; Casalta, Joan Manel; Alonso-Chamarro, Julián
2015-05-18
The design, construction and evaluation of a versatile cyclic olefin copolymer (COC)-based continuous flow potentiometric microanalyzer to monitor the presence of ammonium ion in recycling water processes for future manned space missions is presented. The microsystem integrates microfluidics, a gas-diffusion module and a detection system in a single substrate. The gas-diffusion module was integrated by a hydrophobic polyvinylidene fluoride (PVDF) membrane. The potentiometric detection system is based on an all-solid state ammonium selective electrode and a screen-printed Ag/AgCl reference electrode. The analytical features provided by the analytical microsystem after the optimization process were a linear range from 0.15 to 500 mg L(-1) and a detection limit of 0.07 ± 0.01 mg L(-1). Nevertheless, the operational features can be easily adapted to other applications through the modification of the hydrodynamic variables of the microfluidic platform. Copyright © 2014 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Peng Hong Liem; Surian Pinem; Tagor Malem Sembiring; Tran Hoai Nam
2015-01-01
A coupled neutronics thermal-hydraulics code NODAL3 has been developed based on the nodal few-group neutron diffusion theory in 3-dimensional Cartesian geometry for a typical pressurized water reactor (PWR) static and transient analyses, especially for reactivity initiated accidents (RIA). The spatial variables are treated by using a polynomial nodal method (PNM) while for the neutron dynamic solver the adiabatic and improved quasi-static methods are adopted. A simple single channel thermal-hydraulics module and its steam table is implemented into the code. Verification works on static and transient benchmarks are being conducting to assess the accuracy of the code. For the static benchmark verification, the IAEA-2D, IAEA-3D, BIBLIS and KOEBERG light water reactor (LWR) benchmark problems were selected, while for the transient benchmark verification, the OECD NEACRP 3-D LWR Core Transient Benchmark and NEA-NSC 3-D/1-D PWR Core Transient Benchmark (Uncontrolled Withdrawal of Control Rods at Zero Power). Excellent agreement of the NODAL3 results with the reference solutions and other validated nodal codes was confirmed. (author)
Directory of Open Access Journals (Sweden)
Md. Nur Alam
2016-06-01
Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.
Analytical modelling of hydrogen transport in reactor containments
International Nuclear Information System (INIS)
Manno, V.P.
1983-09-01
A versatile computational model of hydrogen transport in nuclear plant containment buildings is developed. The background and significance of hydrogen-related nuclear safety issues are discussed. A computer program is constructed that embodies the analytical models. The thermofluid dynamic formulation spans a wide applicability range from rapid two-phase blowdown transients to slow incompressible hydrogen injection. Detailed ancillary models of molecular and turbulent diffusion, mixture transport properties, multi-phase multicomponent thermodynamics and heat sink modelling are addressed. The numerical solution of the continuum equations emphasizes both accuracy and efficiency in the employment of relatively coarse discretization and long time steps. Reducing undesirable numerical diffusion is addressed. Problem geometry options include lumped parameter zones, one dimensional meshs, two dimensional Cartesian or axisymmetric coordinate systems and three dimensional Cartesian or cylindrical regions. An efficient lumped nodal model is included for simulation of events in which spatial resolution is not significant. Several validation calculations are reported
Czech Academy of Sciences Publication Activity Database
Tarasenko, Alexander
2018-01-01
Roč. 95, Jan (2018), s. 37-40 ISSN 1386-9477 R&D Projects: GA MŠk LO1409; GA MŠk LM2015088 Institutional support: RVO:68378271 Keywords : lattice gas systems * kinetic Monte Carlo simulations * diffusion and migration Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 2.221, year: 2016
Directory of Open Access Journals (Sweden)
Gao Lin
2017-01-01
Full Text Available Recently, a new integral transform similar to Sumudu transform has been proposed by Yang [1]. Some of the properties of the integral transform are expanded in the present article. Meanwhile, new applications to the linear wave and diffusion equations in semi-infinite domains are discussed in detail. The proposed method provides an alternative approach to solve the partial differential equations in mathematical physics.
Encapsulation of nodal segments of lobelia chinensis
Directory of Open Access Journals (Sweden)
Weng Hing Thong
2015-04-01
Full Text Available Lobelia chinensis served as an important herb in traditional chinese medicine. It is rare in the field and infected by some pathogens. Therefore, encapsulation of axillary buds has been developed for in vitro propagation of L. chinensis. Nodal explants of L. chinensis were used as inclusion materials for encapsulation. Various combinations of calcium chloride and sodium alginate were tested. Encapsulation beads produced by mixing 50 mM calcium chloride and 3.5% sodium alginate supported the optimal in vitro conversion potential. The number of multiple shoots formed by encapsulated nodal segments was not significantly different from the average of shoots produced by non-encapsulated nodal segments. The encapsulated nodal segments regenerated in vitro on different medium. The optimal germination and regeneration medium was Murashige-Skoog medium. Plantlets regenerated from the encapsulated nodal segments were hardened, acclimatized and established well in the field, showing similar morphology with parent plants. This encapsulation technology would serve as an alternative in vitro regeneration system for L. chinensis.
Hiel, C. C.; Adamson, M. J.
1986-01-01
The epoxy resins currently in use can slowly absorb moisture from the atmosphere over a long period. This reduces those mechanical properties of composites which depend strongly on the matrix, such as compressive strength and buckling instabilities. The effect becomes greater at elevated temperatures. The paper will discuss new phenomena which occur under simultaneous temperature and moisture variations. An analytical model will also be discussed and documented.
Complex models of nodal nuclear data
International Nuclear Information System (INIS)
Dufek, Jan
2011-01-01
During the core simulations, nuclear data are required at various nodal thermal-hydraulic and fuel burnup conditions. The nodal data are also partially affected by thermal-hydraulic and fuel burnup conditions in surrounding nodes as these change the neutron energy spectrum in the node. Therefore, the nodal data are functions of many parameters (state variables), and the more state variables are considered by the nodal data models the more accurate and flexible the models get. The existing table and polynomial regression models, however, cannot reflect the data dependences on many state variables. As for the table models, the number of mesh points (and necessary lattice calculations) grows exponentially with the number of variables. As for the polynomial regression models, the number of possible multivariate polynomials exceeds the limits of existing selection algorithms that should identify a few dozens of the most important polynomials. Also, the standard scheme of lattice calculations is not convenient for modelling the data dependences on various burnup conditions since it performs only a single or few burnup calculations at fixed nominal conditions. We suggest a new efficient algorithm for selecting the most important multivariate polynomials for the polynomial regression models so that dependences on many state variables can be considered. We also present a new scheme for lattice calculations where a large number of burnup histories are accomplished at varied nodal conditions. The number of lattice calculations being performed and the number of polynomials being analysed are controlled and minimised while building the nodal data models of a required accuracy. (author)
Nodal Structure of the Electronic Wigner Function
DEFF Research Database (Denmark)
Schmider, Hartmut; Dahl, Jens Peder
1996-01-01
On the example of several atomic and small molecular systems, the regular behavior of nodal patterns in the electronic one-particle reduced Wigner function is demonstrated. An expression found earlier relates the nodal pattern solely to the dot-product of the position and the momentum vector......, if both arguments are large. An argument analogous to the ``bond-oscillatory principle'' for momentum densities links the nuclear framework in a molecule to an additional oscillatory term in momenta parallel to bonds. It is shown that these are visible in the Wigner function in terms of characteristic...
International Nuclear Information System (INIS)
Narain, Rajendra
1995-01-01
Using the concept of Very Intense Continuous High Flux Pulsed Reactor to obtain a rotating high flux pulse in an annular core an analytical treatment for the quasi-static solution with a moving reflector is presented. Under quasi-static situation, time averaged values for important parameters like multiplication factor, flux, leakage do not change with time. As a result the instantaneous solution can be considered to be separable in time and space after correcting for the coordinates for the motion of the pulser. The space behaviour of the pulser is considered as exp(-αx 2 ). Movement of delayed neutron precursors is also taken into account. (author). 4 refs
Energy Technology Data Exchange (ETDEWEB)
Rundle-Thiele, Dayle [Centre for Clinical Research, University of Queensland, Brisbane, Queensland (Australia); Day, Bryan; Stringer, Brett [Brain Cancer Research Unit, Queensland Institute of Medical Research, Brisbane, Queensland (Australia); Fay, Michael [Department of Radiation Oncology, Royal Brisbane and Women' s Hospital, Brisbane, Queensland (Australia); Martin, Jennifer [Discipline of Clinical Pharmacology, School of Medicine and Public Health, University of Newcastle, Newcastle, New South Wales (Australia); Jeffree, Rosalind L [Department of Neurosurgery, Royal Brisbane and Women' s Hospital, Brisbane, Queensland (Australia); Thomas, Paul [Queensland PET Service, Royal Brisbane and Women' s Hospital, Brisbane, Queensland (Australia); Bell, Christopher [Centre for Clinical Research, University of Queensland, Brisbane, Queensland (Australia); Salvado, Olivier [CSIRO Digital Productivity Flagship, CSIRO, Herston, Queensland (Australia); Gal, Yaniv [Centre for Medical Diagnostic Technologies in Queensland, University of Queensland, Brisbane, Queensland (Australia); Coulthard, Alan [Discipline of Medical Imaging, University of Queensland, St Lucia, Queensland (Australia); Department of Medical Imaging, Royal Brisbane and Women' s Hospital, Brisbane, Queensland (Australia); Crozier, Stuart [Centre for Medical Diagnostic Technologies in Queensland, University of Queensland, Brisbane, Queensland (Australia); Rose, Stephen, E-mail: stephen.rose@csiro.au [CSIRO Digital Productivity Flagship, CSIRO, Herston, Queensland (Australia); Centre for Clinical Research, University of Queensland, Brisbane, Queensland (Australia)
2015-06-15
Accurate knowledge of O{sup 6}-methylguanine methyltransferase (MGMT) gene promoter subtype in patients with glioblastoma (GBM) is important for treatment. However, this test is not always available. Pre-operative diffusion MRI (dMRI) can be used to probe tumour biology using the apparent diffusion coefficient (ADC); however, its ability to act as a surrogate to predict MGMT status has shown mixed results. We investigated whether this was due to variations in the method used to analyse ADC. We undertook a retrospective study of 32 patients with GBM who had MGMT status measured. Matching pre-operative MRI data were used to calculate the ADC within contrast enhancing regions of tumour. The relationship between ADC and MGMT was examined using two published ADC methods. A strong trend between a measure of ‘minimum ADC’ and methylation status was seen. An elevated minimum ADC was more likely in the methylated compared to the unmethylated MGMT group (U = 56, P = 0.0561). In contrast, utilising a two-mixture model histogram approach, a significant reduction in mean measure of the ‘low ADC’ component within the histogram was associated with an MGMT promoter methylation subtype (P < 0.0246). This study shows that within the same patient cohort, the method selected to analyse ADC measures has a significant bearing on the use of that metric as a surrogate marker of MGMT status. Thus for dMRI data to be clinically useful, consistent methods of data analysis need to be established prior to establishing any relationship with genetic or epigenetic profiling.
International Nuclear Information System (INIS)
Rundle-Thiele, Dayle; Day, Bryan; Stringer, Brett; Fay, Michael; Martin, Jennifer; Jeffree, Rosalind L; Thomas, Paul; Bell, Christopher; Salvado, Olivier; Gal, Yaniv; Coulthard, Alan; Crozier, Stuart; Rose, Stephen
2015-01-01
Accurate knowledge of O 6 -methylguanine methyltransferase (MGMT) gene promoter subtype in patients with glioblastoma (GBM) is important for treatment. However, this test is not always available. Pre-operative diffusion MRI (dMRI) can be used to probe tumour biology using the apparent diffusion coefficient (ADC); however, its ability to act as a surrogate to predict MGMT status has shown mixed results. We investigated whether this was due to variations in the method used to analyse ADC. We undertook a retrospective study of 32 patients with GBM who had MGMT status measured. Matching pre-operative MRI data were used to calculate the ADC within contrast enhancing regions of tumour. The relationship between ADC and MGMT was examined using two published ADC methods. A strong trend between a measure of ‘minimum ADC’ and methylation status was seen. An elevated minimum ADC was more likely in the methylated compared to the unmethylated MGMT group (U = 56, P = 0.0561). In contrast, utilising a two-mixture model histogram approach, a significant reduction in mean measure of the ‘low ADC’ component within the histogram was associated with an MGMT promoter methylation subtype (P < 0.0246). This study shows that within the same patient cohort, the method selected to analyse ADC measures has a significant bearing on the use of that metric as a surrogate marker of MGMT status. Thus for dMRI data to be clinically useful, consistent methods of data analysis need to be established prior to establishing any relationship with genetic or epigenetic profiling
Static benchmarking of the NESTLE advanced nodal code
International Nuclear Information System (INIS)
Mosteller, R.D.
1997-01-01
Results from the NESTLE advanced nodal code are presented for multidimensional numerical benchmarks representing four different types of reactors, and predictions from NESTLE are compared with measured data from pressurized water reactors (PWRs). The numerical benchmarks include cases representative of PWRs, boiling water reactors (BWRs), CANDU heavy water reactors (HWRs), and high-temperature gas-cooled reactors (HTGRs). The measured PWR data include critical soluble boron concentrations and isothermal temperature coefficients of reactivity. The results demonstrate that NESTLE correctly solves the multigroup diffusion equations for both Cartesian and hexagonal geometries, that it reliably calculates k eff and reactivity coefficients for PWRs, and that--subsequent to the incorporation of additional thermal-hydraulic models--it will be able to perform accurate calculations for the corresponding parameters in BWRs, HWRs, and HTGRs as well
Energy Technology Data Exchange (ETDEWEB)
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.
Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny; Birkholzer, Jens T.
2017-11-01
There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1-D, 2-D, and 3-D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, td. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, td0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the first two terms for high-accuracy approximations (with less than 10-7 relative error) for 1-D isotropic (spheres, cylinders, slabs) and 2-D/3-D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1-D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2-D/3-D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.
Isospectral graphs with identical nodal counts
International Nuclear Information System (INIS)
Oren, Idan; Band, Ram
2012-01-01
According to a recent conjecture, isospectral objects have different nodal count sequences (Gnutzmann et al 2005 J. Phys. A: Math. Gen. 38 8921–33). We study generalized Laplacians on discrete graphs, and use them to construct the first non-trivial counterexamples to this conjecture. In addition, these examples demonstrate a surprising connection between isospectral discrete and quantum graphs. (paper)
Comparison of neutronic transport equation resolution nodal methods
International Nuclear Information System (INIS)
Zamonsky, O.M.; Gho, C.J.
1990-01-01
In this work, some transport equation resolution nodal methods are comparatively studied: the constant-constant (CC), linear-nodal (LN) and the constant-quadratic (CQ). A nodal scheme equivalent to finite differences has been used for its programming, permitting its inclusion in existing codes. Some bidimensional problems have been solved, showing that linear-nodal (LN) are, in general, obtained with accuracy in CPU shorter times. (Author) [es
International Nuclear Information System (INIS)
Kim, Yoo Na; Yi, Chin A.; Lee, Kyung Soo; Lee, Ho Yun; Kim, Tae Sung; Chung, Myung Jin; Kwon, O.Jung; Chung, Man Pyo; Kim, Byung-Tae; Choi, Joon Young; Kim, Seon Woo; Han, Joungho; Shim, Young Mog
2012-01-01
To determine the positive reading criteria for malignant nodes when interpreting combined MRI and PET/CT images for preoperative nodal staging in non-small-cell lung cancer (NSCLC). Forty-nine patients with biopsy-proven NSCLC underwent both PET/CT and thoracic MRI [diffusion weighted imaging (DWI)]. Each nodal station was evaluated for the presence of metastasis by applying either inclusive (positive if either one read positive) or exclusive (positive if both read positive) criteria in the combined interpretation of PET/CT and MRI. Nodal stage was confirmed pathologically. The combined diagnostic accuracy of PET/CT and MRI was determined on per-nodal station and per-patient bases and compared with that of PET/CT alone. In 49 patients, 39 (19%) of 206 nodal stations harboured malignant cells. Out of 206 nodal stations, 186 (90%) had concordant readings, while the rest (10%) had discordant readings. Inclusive criteria of combined PET/CT and MRI helped increase sensitivity for detecting nodal metastasis (69%) compared with PET/CT alone (46%; P = 0.003), while specificity was not significantly decreased. Inclusive criteria in combined MRI and PET/CT readings help improve significantly the sensitivity for detecting nodal metastasis compared with PET/CT alone and may decrease unnecessary open thoracotomy. (orig.)
Directory of Open Access Journals (Sweden)
Tagor Malem Sembiring
2017-01-01
Full Text Available The in-house coupled neutronic and thermal-hydraulic (N/T-H code of BATAN (National Nuclear Energy Agency of Indonesia, NODAL3, based on the few-group neutron diffusion equation in 3-dimensional geometry using the polynomial nodal method, has been verified with static and transient PWR benchmark cases. This paper reports the verification of NODAL3 code in the NEA-NSC PWR uncontrolled control rods withdrawal at zero power benchmark. The objective of this paper is to determine the accuracy of NODAL3 code in solving the continuously slow and fast reactivity insertions due to single and group of control rod bank withdrawn while the power and temperature increment are limited by the Doppler coefficient. The benchmark is chosen since many organizations participated using various methods and approximations, so the calculation results of NODAL3 can be compared to other codes’ results. The calculated parameters are performed for the steady-state, transient core averaged, and transient hot pellet results. The influence of radial and axial nodes number was investigated for all cases. The results of NODAL3 code are in very good agreement with the reference solutions if the radial and axial nodes number is 2 × 2 and 2 × 18 (total axial layers, respectively.
A geometrically exact beam element based on the absolute nodal coordinate formulation
International Nuclear Information System (INIS)
Gerstmayr, Johannes; Matikainen, Marko K.; Mikkola, Aki M.
2008-01-01
In this study, Reissner's classical nonlinear rod formulation, as implemented by Simo and Vu-Quoc by means of the large rotation vector approach, is implemented into the framework of the absolute nodal coordinate formulation. The implementation is accomplished in the planar case accounting for coupled axial, bending, and shear deformation. By employing the virtual work of elastic forces similarly to Simo and Vu-Quoc in the absolute nodal coordinate formulation, the numerical results of the formulation are identical to those of the large rotation vector formulation. It is noteworthy, however, that the material definition in the absolute nodal coordinate formulation can differ from the material definition used in Reissner's beam formulation. Based on an analytical eigenvalue analysis, it turns out that the high frequencies of cross section deformation modes in the absolute nodal coordinate formulation are only slightly higher than frequencies of common shear modes, which are present in the classical large rotation vector formulation of Simo and Vu-Quoc, as well. Thus, previous claims that the absolute nodal coordinate formulation is inefficient or would lead to ill-conditioned finite element matrices, as compared to classical approaches, could be refuted. In the introduced beam element, locking is prevented by means of reduced integration of certain parts of the elastic forces. Several classical large deformation static and dynamic examples as well as an eigenvalue analysis document the equivalence of classical nonlinear rod theories and the absolute nodal coordinate formulation for the case of appropriate material definitions. The results also agree highly with those computed in commercial finite element codes
Energy Technology Data Exchange (ETDEWEB)
Tumelero, Fernanda; Bodmann, Bardo E. J.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos Graduacao em Engenharia Mecanica; Lapa, Celso M.F., E-mail: fernanda.tumelero@yahoo.com.br, E-mail: bardo.bodmann@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: lapa@ien.gov.br [Instituto de Engenharia Nuclear (IEN/CNEN-RJ), Rio de Janeiro, RJ (Brazil)
2017-07-01
In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron flux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modified decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satisfied by the recursion initialization, while from the rst recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution. (author)
Directory of Open Access Journals (Sweden)
Yoon Jung Choi
2017-01-01
Full Text Available Purpose. This study investigated the impact of the different region of interest (ROI approaches on measurement of apparent diffusion coefficient (ADC values in the breast firbroglandular tissue (FT. Methods. Breast MR images of 38 women diagnosed with unilateral breast cancer were studied. Percent density (PD and ADC were measured from the contralateral normal breast. Four different ROIs were used for ADC measurement. The measured PD and ADC were correlated. Results. Among the four ROIs, the manually placed small ROI on FT gave the highest mean ADC (ADC = 1839 ± 343 [×10−6 mm2/s], while measurement from the whole breast gave the lowest mean ADC (ADC = 933 ± 383 [×10−6 mm2/s]. The ADC measured from the whole breast was highly correlated with PD with r=0.95. In slice-to-slice comparison, the central slices with more FT had higher ADC values than the peripheral slices did, presumably due to less partial volume effect from fat. Conclusions. Our results indicated that the measured ADC heavily depends on the composition of breast tissue contained in the ROI used for the ADC measurements. Women with low breast density showing lower ADC values were most likely due to the partial volume effect of fatty tissues.
Analytical method for reconstruction pin to pin of the nuclear power density distribution
Energy Technology Data Exchange (ETDEWEB)
Pessoa, Paulo O.; Silva, Fernando C.; Martinez, Aquilino S., E-mail: ppessoa@con.ufrj.br, E-mail: fernando@con.ufrj.br, E-mail: aquilino@imp.ufrj.br [Coordenacao dos Programas de Pos-Graduacao em Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil)
2013-07-01
An accurate and efficient method for reconstructing pin to pin of the nuclear power density distribution, involving the analytical solution of the diffusion equation for two-dimensional neutron energy groups in homogeneous nodes, is presented. The boundary conditions used for analytic as solution are the four currents or fluxes on the surface of the node, which are obtained by Nodal Expansion Method (known as NEM) and four fluxes at the vertices of a node calculated using the finite difference method. The analytical solution found is the homogeneous distribution of neutron flux. Detailed distributions pin to pin inside a fuel assembly are estimated by the product of homogeneous flux distribution by local heterogeneous form function. Furthermore, the form functions of flux and power are used. The results obtained with this method have a good accuracy when compared with reference values. (author)
Analytical method for reconstruction pin to pin of the nuclear power density distribution
International Nuclear Information System (INIS)
Pessoa, Paulo O.; Silva, Fernando C.; Martinez, Aquilino S.
2013-01-01
An accurate and efficient method for reconstructing pin to pin of the nuclear power density distribution, involving the analytical solution of the diffusion equation for two-dimensional neutron energy groups in homogeneous nodes, is presented. The boundary conditions used for analytic as solution are the four currents or fluxes on the surface of the node, which are obtained by Nodal Expansion Method (known as NEM) and four fluxes at the vertices of a node calculated using the finite difference method. The analytical solution found is the homogeneous distribution of neutron flux. Detailed distributions pin to pin inside a fuel assembly are estimated by the product of homogeneous flux distribution by local heterogeneous form function. Furthermore, the form functions of flux and power are used. The results obtained with this method have a good accuracy when compared with reference values. (author)
International Nuclear Information System (INIS)
Verdu, G.; Capilla, M.; Talavera, C. F.; Ginestar, D.
2012-01-01
PL equations are classical high order approximations to the transport equations which are based on the expansion of the angular dependence of the angular neutron flux and the nuclear cross sections in terms of spherical harmonics. A nodal collocation method is used to discretize the PL equations associated with a neutron source transport problem. The performance of the method is tested solving two 1D problems with analytical solution for the transport equation and a classical 2D problem. (authors)
Energy Technology Data Exchange (ETDEWEB)
Verdu, G. [Departamento de Ingenieria Quimica Y Nuclear, Universitat Politecnica de Valencia, Cami de Vera, 14, 46022. Valencia (Spain); Capilla, M.; Talavera, C. F.; Ginestar, D. [Dept. of Nuclear Engineering, Departamento de Matematica Aplicada, Universitat Politecnica de Valencia, Cami de Vera, 14, 46022. Valencia (Spain)
2012-07-01
PL equations are classical high order approximations to the transport equations which are based on the expansion of the angular dependence of the angular neutron flux and the nuclear cross sections in terms of spherical harmonics. A nodal collocation method is used to discretize the PL equations associated with a neutron source transport problem. The performance of the method is tested solving two 1D problems with analytical solution for the transport equation and a classical 2D problem. (authors)
International Nuclear Information System (INIS)
Palmiotti, G.; Carrico, C.B.; Lewis, E.E.
1995-10-01
The theoretical basis, implementation information and numerical results are presented for VARIANT (VARIational Anisotropic Neutron Transport), a FORTRAN module of the DIF3D code system at Argonne National Laboratory. VARIANT employs the variational nodal method to solve multigroup steady-state neutron diffusion and transport problems. The variational nodal method is a hybrid finite element method that guarantees nodal balance and permits spatial refinement through the use of hierarchical complete polynomial trial functions. Angular variables are expanded with complete or simplified P 1 , P 3 or P 5 5 spherical harmonics approximations with full anisotropic scattering capability. Nodal response matrices are obtained, and the within-group equations are solved by red-black or four-color iteration, accelerated by a partitioned matrix algorithm. Fission source and upscatter iterations strategies follow those of DIF3D. Two- and three-dimensional Cartesian and hexagonal geometries are implemented. Forward and adjoint eigenvalue, fixed source, gamma heating, and criticality (concentration) search problems may be performed
Pathology of nodal marginal zone lymphomas.
Pileri, Stefano; Ponzoni, Maurilio
Nodal marginal zone B cell lymphomas (NMZLs) are a rare group of lymphoid disorders part of the spectrum of marginal zone B-cell lymphomas, which encompass splenic marginal one B-cell lymphoma (SMZL) and extra nodal marginal zone of B-cell lymphoma (EMZL), often of MALT-type. Two clinicopathological forms of NMZL are recognized: adult-type and pediatric-type, respectively. NMZLs show overlapping features with other types of MZ, but distinctive features as well. In this review, we will focus on the salient distinguishing features of NMZL mostly under morphological/immunophenotypical/molecular perspectives in views of the recent acquisitions and forthcoming updated 2016 WHO classification of lymphoid malignancies. Copyright © 2016 Elsevier Ltd. All rights reserved.
Quantum anomalies in nodal line semimetals
Burkov, A. A.
2018-04-01
Topological semimetals are a new class of condensed matter systems with nontrivial electronic structure topology. Their unusual observable properties may often be understood in terms of quantum anomalies. In particular, Weyl and Dirac semimetals, which have point band-touching nodes, are characterized by the chiral anomaly, which leads to the Fermi arc surface states, anomalous Hall effect, negative longitudinal magnetoresistance, and planar Hall effect. In this paper, we explore analogous phenomena in nodal line semimetals. We demonstrate that such semimetals realize a three-dimensional analog of the parity anomaly, which is a known property of two-dimensional Dirac semimetals arising, for example, on the surface of a three-dimensional topological insulator. We relate one of the characteristic properties of nodal line semimetals, namely, the drumhead surface states, to this anomaly, and derive the field theory, which encodes the corresponding anomalous response.
Temporal quadratic expansion nodal Green's function method
International Nuclear Information System (INIS)
Liu Cong; Jing Xingqing; Xu Xiaolin
2000-01-01
A new approach is presented to efficiently solve the three-dimensional space-time reactor dynamics equation which overcomes the disadvantages of current methods. In the Temporal Quadratic Expansion Nodal Green's Function Method (TQE/NGFM), the Quadratic Expansion Method (QEM) is used for the temporal solution with the Nodal Green's Function Method (NGFM) employed for the spatial solution. Test calculational results using TQE/NGFM show that its time step size can be 5-20 times larger than that of the Fully Implicit Method (FIM) for similar precision. Additionally, the spatial mesh size with NGFM can be nearly 20 times larger than that using the finite difference method. So, TQE/NGFM is proved to be an efficient reactor dynamics analysis method
Barrier tunneling of the loop-nodal semimetal in the hyperhoneycomb lattice
Guan, Ji-Huan; Zhang, Yan-Yang; Lu, Wei-Er; Xia, Yang; Li, Shu-Shen
2018-05-01
We theoretically investigate the barrier tunneling in the 3D model of the hyperhoneycomb lattice, which is a nodal-line semimetal with a Dirac loop at zero energy. In the presence of a rectangular potential, the scattering amplitudes for different injecting states around the nodal loop are calculated, by using analytical treatments of the effective model, as well as numerical simulations of the tight binding model. In the low energy regime, states with remarkable transmissions are only concentrated in a small range around the loop plane. When the momentum of the injecting electron is coplanar with the nodal loop, nearly perfect transmissions can occur for a large range of injecting azimuthal angles if the potential is not high. For higher potential energies, the transmission shows a resonant oscillation with the potential, but still with peaks being perfect transmissions that do not decay with the potential width. These strikingly robust transports of the loop-nodal semimetal can be approximately explained by a momentum dependent Dirac Hamiltonian.
Acceleration of the FERM nodal program
International Nuclear Information System (INIS)
Nakata, H.
1985-01-01
It was tested three acceleration methods trying to reduce the number of outer iterations in the FERM nodal program. The results obtained indicated that the Chebychev polynomial acceleration method with variable degree results in a economy of 50% in the computer time. Otherwise, the acceleration method by source asymptotic extrapolation or by zonal rebalance did not result in economy of the global computer time, however some acceleration had been verified in outer iterations. (M.C.K.) [pt
Acceleration of the nodal program FERM
International Nuclear Information System (INIS)
Nakata, H.
1985-01-01
Acceleration of the nodal FERM was tried by three acceleration schemes. Results of the calculations showed the best acceleration with the Tchebyshev method where the savings in the computing time were of the order of 50%. Acceleration with the Assymptotic Source Extrapoltation Method and with the Coarse-Mesh Rebalancing Method did not result in any improvement on the global computational time, although a reduction in the number of outer iterations was observed. (Author) [pt
Current trends in methods for neutron diffusion calculations
International Nuclear Information System (INIS)
Adams, C.H.
1977-01-01
Current work and trends in the application of neutron diffusion theory to reactor design and analysis are reviewed. Specific topics covered include finite-difference methods, synthesis methods, nodal calculations, finite-elements and perturbation theory
International Nuclear Information System (INIS)
Poursalehi, N.; Zolfaghari, A.; Minuchehr, A.
2013-01-01
Highlights: ► A new adaptive h-refinement approach has been developed for a class of nodal method. ► The resulting system of nodal equations is more amenable to efficient numerical solution. ► The benefit of the approach is reducing computational efforts relative to the uniform fine mesh modeling. ► Spatially adaptive approach greatly enhances the accuracy of the solution. - Abstract: The aim of this work is to develop a spatially adaptive coarse mesh strategy that progressively refines the nodes in appropriate regions of domain to solve the neutron balance equation by zeroth order nodal expansion method. A flux gradient based a posteriori estimation scheme has been utilized for checking the approximate solutions for various nodes. The relative surface net leakage of nodes has been considered as an assessment criterion. In this approach, the core module is called in by adaptive mesh generator to determine gradients of node surfaces flux to explore the possibility of node refinements in appropriate regions and directions of the problem. The benefit of the approach is reducing computational efforts relative to the uniform fine mesh modeling. For this purpose, a computer program ANRNE-2D, Adaptive Node Refinement Nodal Expansion, has been developed to solve neutron diffusion equation using average current nodal expansion method for 2D rectangular geometries. Implementing the adaptive algorithm confirms its superiority in enhancing the accuracy of the solution without using fine nodes throughout the domain and increasing the number of unknown solution. Some well-known benchmarks have been investigated and improvements are reported
DEFF Research Database (Denmark)
Zhao, Qian; Wang, Peng; Goel, Lalit
2013-01-01
The deregulation of power systems allows customers to participate in power market operation. In deregulated power systems, nodal price and nodal reliability are adopted to represent locational operation cost and reliability performance. Since contingency reserve (CR) plays an important role...... in reliable operation, the CR commitment should be considered in operational reliability analysis. In this paper, a CR model based on customer reliability requirements has been formulated and integrated into power market settlement. A two-step market clearing process has been proposed to determine generation...
Reconstruction of pin burnup characteristics from nodal calculations in hexagonal geometry
International Nuclear Information System (INIS)
Yang, W.S.; Finck, P.J.; Khalil, H.S.
1990-01-01
A reconstruction method has been developed for recovering pin burnup characteristics from fuel cycle calculations performed in hexagonal-z geometry using the nodal diffusion option of the DIF3D/REBUS-3 code system. Intra-modal distributions of group fluxes, nuclide densities, power density, burnup, and fluence are efficiently computed using polynomial shapes constrained to satisfy nodal information. The accuracy of the method has been tested by performing several numerical benchmark calculations and by comparing predicted local burnups to values measured for experimental assemblies in EBR-11. The results indicate that the reconstruction methods are quite accurate, yielding maximum errors in power and nuclide densities that are less than 2% for driver assemblies and typically less than 5% for blanket assemblies. 14 refs., 2 figs., 5 tabs
International Nuclear Information System (INIS)
Lawrence, R.D.; Dorning, J.J.
1980-01-01
A coarse-mesh discrete nodal integral transport theory method has been developed for the efficient numerical solution of multidimensional transport problems of interest in reactor physics and shielding applications. The method, which is the discrete transport theory analogue and logical extension of the nodal Green's function method previously developed for multidimensional neutron diffusion problems, utilizes the same transverse integration procedure to reduce the multidimensional equations to coupled one-dimensional equations. This is followed by the conversion of the differential equations to local, one-dimensional, in-node integral equations by integrating back along neutron flight paths. One-dimensional and two-dimensional transport theory test problems have been systematically studied to verify the superior computational efficiency of the new method
Directory of Open Access Journals (Sweden)
Surian Pinem
2014-01-01
Full Text Available A coupled neutronics thermal-hydraulics code NODAL3 has been developed based on the few-group neutron diffusion equation in 3-dimensional geometry for typical PWR static and transient analyses. The spatial variables are treated by using a polynomial nodal method while for the neutron dynamic solver the adiabatic and improved quasistatic methods are adopted. In this paper we report the benchmark calculation results of the code against the OECD/NEA CRP PWR rod ejection cases. The objective of this work is to determine the accuracy of NODAL3 code in analysing the reactivity initiated accident due to the control rod ejection. The NEACRP PWR rod ejection cases are chosen since many organizations participated in the NEA project using various methods as well as approximations, so that, in addition to the reference solutions, the calculation results of NODAL3 code can also be compared to other codes’ results. The transient parameters to be verified are time of power peak, power peak, final power, final average Doppler temperature, maximum fuel temperature, and final coolant temperature. The results of NODAL3 code agree well with the PHANTHER reference solutions in 1993 and 1997 (revised. Comparison with other validated codes, DYN3D/R and ANCK, shows also a satisfactory agreement.
International Nuclear Information System (INIS)
Cho, J. Y.; Noh, J. M.; Cheong, H. K.; Choo, H. K.
1998-01-01
In order to simplify the previous spectral history effect correction based on the polynomial expansion nodal method, a new spectral history effect correction is proposed. The new spectral history correction eliminates four microscopic depletion points out of total 13 depletion points in the previous correction by approximating the group cross sections with exponential function. The neutron flux to homogenize the group cross sections for the correction of the spectral history effect is calculated by the analytic function expansion nodal method in stead of the conventional polynomial expansion nodal method. This spectral history correction model is verified against the three MOX benchmark cores: a checkerboard type, a small core with 25 fuel assemblies, and a large core with 177 fuel assemblies. The benchmark results prove that this new spectral history correction model is superior to the previous one even with the reduced number of the local microscopic depletion points
Topological surface states in nodal superconductors.
Schnyder, Andreas P; Brydon, Philip M R
2015-06-24
Topological superconductors have become a subject of intense research due to their potential use for technical applications in device fabrication and quantum information. Besides fully gapped superconductors, unconventional superconductors with point or line nodes in their order parameter can also exhibit nontrivial topological characteristics. This article reviews recent progress in the theoretical understanding of nodal topological superconductors, with a focus on Weyl and noncentrosymmetric superconductors and their protected surface states. Using selected examples, we review the bulk topological properties of these systems, study different types of topological surface states, and examine their unusual properties. Furthermore, we survey some candidate materials for topological superconductivity and discuss different experimental signatures of topological surface states.
Twisted vector bundles on pointed nodal curves
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
by identifying the points p1 and p2. If m ≥ 2, let R1,...,Rm−1 be m − 1 copies of the projective line P1 and let xi,yi be two distinct points in Ri. Let R be the nodal curve which arises from the union. R0 ⊔ R1 ⊔···⊔ Rm−1 ⊔ Rm by identifying p1 ∈ R0 and p2 ∈ Rm with x1 ∈ R1 and ym−1 ∈ Rm−1 respectively and by identifying ...
Solution of the isotopic depletion equation using decomposition method and analytical solution
Energy Technology Data Exchange (ETDEWEB)
Prata, Fabiano S.; Silva, Fernando C.; Martinez, Aquilino S., E-mail: fprata@con.ufrj.br, E-mail: fernando@con.ufrj.br, E-mail: aquilino@lmp.ufrj.br [Coordenacao dos Programas de Pos-Graduacao de Engenharia (PEN/COPPE/UFRJ), RJ (Brazil). Programa de Engenharia Nuclear
2011-07-01
In this paper an analytical calculation of the isotopic depletion equations is proposed, featuring a chain of major isotopes found in a typical PWR reactor. Part of this chain allows feedback reactions of (n,2n) type. The method is based on decoupling the equations describing feedback from the rest of the chain by using the decomposition method, with analytical solutions for the other isotopes present in the chain. The method was implemented in a PWR reactor simulation code, that makes use of the nodal expansion method (NEM) to solve the neutron diffusion equation, describing the spatial distribution of neutron flux inside the reactor core. Because isotopic depletion calculation module is the most computationally intensive process within simulation systems of nuclear reactor core, it is justified to look for a method that is both efficient and fast, with the objective of evaluating a larger number of core configurations in a short amount of time. (author)
Solution of the isotopic depletion equation using decomposition method and analytical solution
International Nuclear Information System (INIS)
Prata, Fabiano S.; Silva, Fernando C.; Martinez, Aquilino S.
2011-01-01
In this paper an analytical calculation of the isotopic depletion equations is proposed, featuring a chain of major isotopes found in a typical PWR reactor. Part of this chain allows feedback reactions of (n,2n) type. The method is based on decoupling the equations describing feedback from the rest of the chain by using the decomposition method, with analytical solutions for the other isotopes present in the chain. The method was implemented in a PWR reactor simulation code, that makes use of the nodal expansion method (NEM) to solve the neutron diffusion equation, describing the spatial distribution of neutron flux inside the reactor core. Because isotopic depletion calculation module is the most computationally intensive process within simulation systems of nuclear reactor core, it is justified to look for a method that is both efficient and fast, with the objective of evaluating a larger number of core configurations in a short amount of time. (author)
Robust doubly charged nodal lines and nodal surfaces in centrosymmetric systems
Bzdušek, Tomáš; Sigrist, Manfred
2017-10-01
Weyl points in three spatial dimensions are characterized by a Z -valued charge—the Chern number—which makes them stable against a wide range of perturbations. A set of Weyl points can mutually annihilate only if their net charge vanishes, a property we refer to as robustness. While nodal loops are usually not robust in this sense, it has recently been shown using homotopy arguments that in the centrosymmetric extension of the AI symmetry class they nevertheless develop a Z2 charge analogous to the Chern number. Nodal loops carrying a nontrivial value of this Z2 charge are robust, i.e., they can be gapped out only by a pairwise annihilation and not on their own. As this is an additional charge independent of the Berry π -phase flowing along the band degeneracy, such nodal loops are, in fact, doubly charged. In this manuscript, we generalize the homotopy discussion to the centrosymmetric extensions of all Atland-Zirnbauer classes. We develop a tailored mathematical framework dubbed the AZ +I classification and show that in three spatial dimensions such robust and multiply charged nodes appear in four of such centrosymmetric extensions, namely, AZ +I classes CI and AI lead to doubly charged nodal lines, while D and BDI support doubly charged nodal surfaces. We remark that no further crystalline symmetries apart from the spatial inversion are necessary for their stability. We provide a description of the corresponding topological charges, and develop simple tight-binding models of various semimetallic and superconducting phases that exhibit these nodes. We also indicate how the concept of robust and multiply charged nodes generalizes to other spatial dimensions.
Radiotherapy of adult nodal non Hodgkin's lymphoma
International Nuclear Information System (INIS)
Gamen, G.; Thirion, P.
1999-01-01
The role of radiotherapy in the treatment of nodal non-Hodgkin's lymphoma has been modified by the introduction of efficient chemotherapy and the development of different pathological classifications. The recommended treatment of early-stage aggressive lymphomas is primarily a combination chemotherapy. The interest of adjuvant radiotherapy remains unclear and has to be established through large prospective trials. If radiation therapy has to be delivered, the historical results of exclusive radiation therapy showed that involved-fields and a dose of 35-40 Gy (daily fraction of 1.8 Gy, 5 days a week) are the optimal schedule. The interest of radiotherapy in the treatment of advanced-stage aggressive lymphoma is yet to be proven. Further studies had to stratify localized stages according to the factors of the International Prognostic Index. For easy-stage low-grade lymphoma, radiotherapy remains the standard treatment. However, the appropriate technique to use is controversial. Involved-field irradiation at a dose of 35 Gy seems to be the optimal schedule, providing a 10 year disease-free survival rate of 50 % and no major toxicity. There is no standard indication of radiotherapy in the treatment advanced-stage low-grade lymphoma. For 'new' nodal lymphoma's types, the indication of radiotherapy cannot be established (mantle-zone lymphoma, marginal zone B-cell lymphoma) or must take into account the natural history (Burkitt's lymphoma, peripheral T-cell lymphoma) and the sensibility to others therapeutic methods. (authors)
Extra-nodal lymphoma. A survey of Japan lymphoma radiation therapy group
International Nuclear Information System (INIS)
Oguchi, Masahiko; Ikeda, Hiroshi; Nakamura, Shigeo
2002-01-01
The purpose of this study was to examine, retrospectively, national-wide clinical data of patients with localized extranodal non-Hodgkin's lymphoma (NHL) who were treated by radiation therapy with or without chemotherapy. The survey was carried out at 25 radiation oncology institutions in Japan in 1998. In 1999, according to the Revised European American Lymphoma (REAL) classification, central pathological review conducted at Aichi cancer center was carried out for the data from 7 radiation oncology institutions. The 5-year progression free survival rates (PFS) were calculated to identify prognostic factors. Survey: Data from 1, 141 patients with stage I and II NHL were recruited from 1988 through 1992. Of them, 787 patients, who were treated using definitive radiotherapy with or without chemotherapy for intermediate and high-grade lymphomas in Working Formulation, constituted the core of this study. Primary tumors arose mainly from extra-nodal organs (71%) in the head and neck (Waldeyer's ring: 41%, thyroid gland: 7%, nasal cavities: 5%, oral cavities: 4%, sinus: 3%, orbital structures: 3%, skin: 2% and etc.). The median age of 60 years for patients with extra-nodal NHL was higher than that of 56 years for patients with nodal NHL (p<0.01). Female were dominant in incidence of extra-nodal NHL arising from the thyroid gland, skin and gastrointestinal tract. The percentage of stage I to the extra-nodal NHL from orbit, sino-nasal presentation was higher than that of other NHLs. The percentage of stage II to the extra-nodal NHL from Waldeyer's ring and thyroid gland was higher than that of other NHLs. Central pathological review was carried out for pathological data from 79 patients (Waldeyer's ring: 45, thyroid gland: 19, sinonasal cavities: 15). Of these, diffuse large B cell lymphoma (DLBCL) composed 63% of all patients, mucosa associated lyumphoid tissue lymphoma (MALT-L): 16%, Natural Killer/T cell lymphoma (NK/T-L): 11%, and mantle cell lymphoma: 5% in REAL
Torsionfree Sheaves over a Nodal Curve of Arithmetic Genus One
Indian Academy of Sciences (India)
We classify all isomorphism classes of stable torsionfree sheaves on an irreducible nodal curve of arithmetic genus one defined over C C . Let be a nodal curve of arithmetic genus one defined over R R , with exactly one node, such that does not have any real points apart from the node. We classify all isomorphism ...
Three-dimensional static and dynamic reactor calculations by the nodal expansion method
International Nuclear Information System (INIS)
Christensen, B.
1985-05-01
This report reviews various method for the calculation of the neutron-flux- and power distribution in an nuclear reactor. The nodal expansion method (NEM) is especially described in much detail. The nodal expansion method solves the diffusion equation. In this method the reactor core is divided into nodes, typically 10 to 20 cm in each direction, and the average flux in each node is calculated. To obtain the coupling between the nodes the local flux inside each node is expressed by use of a polynomial expansion. The expansion is one-dimensional, so inside each node such three expansions occur. To calculate the expansion coefficients it is necessary that the polynomial expansion is a solution to the one-dimensional diffusion equation. When the one-dimensional diffusion equation is established a term with the transversal leakage occur, and this term is expanded after the same polynomials. The resulting equation system with the expansion coefficients as the unknowns is solved with weigthed residual technique. The nodal expansion method is built into a computer program (also called NEM), which is divided into two parts, one part for steady-state calculations and one part for dynamic calculations. It is possible to take advantage of symmetry properties of the reactor core. The program is very flexible with regard to the number of energy groups, the node size, the flux expansion order and the transverse leakage expansion order. The boundary of the core is described by albedos. The program and input to it are described. The program is tested on a number of examples extending from small theoretical one up to realistic reactor cores. Many calculations are done on the wellknown IAEA benchmark case. The calculations have tested the accuracy and the computing time for various node sizes and polynomial expansions. In the dynamic examples various strategies for variation of the time step-length have been tested. (author)
A nodalization study of steam separator in real time simulation
International Nuclear Information System (INIS)
Horugshyang, Lein; Luh, R.T.J.; Zen-Yow, Wang
1999-01-01
The motive of this paper is to investigate the influence of steam separator nodalization on reactor thermohydraulics in terms of stability and level response. Three different nodalizations of steam separator are studied by using THEATRE and REMARK Code in a BWR simulator. The first nodalization is the traditional one with two nodes for steam separator. In this nodalization, the steam separation is modeled in the outer node, i.e., upper downcomer. Separated steam enters the Steen dome node and the liquid goes to the feedwater node. The second nodalization is similar to the first one with the steam separation modeled in the inner node. There is one additional junction connecting steam dome node and the inner node. The liquid fallback junction connects the inner node and feedwater node. The third nodalization is a combination of the former two with an integrated node for steam separator. Boundary conditions in this study are provided by a simplified feedwater and main steam driver. For comparison purpose, three tests including full power steady state initialisation, recirculation pumps runback and reactor scram are conducted. Major parameters such as reactor pressure, reactor level, void fractions, neutronic power and junction flows are recorded for analysis. Test results clearly show that the first nodalization is stable for steady state initialisation. However it has too responsive level performance in core flow reduction transients. The second nodalization is the closest representation of real plant structure, but not the performance. Test results show that an instability occurs in the separator region for both steady state initialisation and transients. This instability is caused by an unbalanced momentum in the dual loop configuration. The magnitude of the oscillation reduces as the power decreases. No superiority to the other nodalizations is shown in the test results. The third nodalization shows both stability and responsiveness in the tests. (author)
International Nuclear Information System (INIS)
Dorning, J.J.
1991-01-01
A simultaneous pin lattice cell and fuel bundle homogenization theory has been developed for use with nodal diffusion calculations of practical reactors. The theoretical development of the homogenization theory, which is based on multiple-scales asymptotic expansion methods carried out through fourth order in a small parameter, starts from the transport equation and systematically yields: a cell-homogenized bundled diffusion equation with self-consistent expressions for the cell-homogenized cross sections and diffusion tensor elements; and a bundle-homogenized global reactor diffusion equation with self-consistent expressions for the bundle-homogenized cross sections and diffusion tensor elements. The continuity of the angular flux at cell and bundle interfaces also systematically yields jump conditions for the scaler flux or so-called flux discontinuity factors on the cell and bundle interfaces in terms of the two adjacent cell or bundle eigenfunctions. The expressions required for the reconstruction of the angular flux or the 'de-homogenization' theory were obtained as an integral part of the development; hence the leading order transport theory angular flux is easily reconstructed throughout the reactor including the regions in the interior of the fuel bundles or computational nodes and in the interiors of the pin lattice cells. The theoretical development shows that the exact transport theory angular flux is obtained to first order from the whole-reactor nodal diffusion calculations, done using the homogenized nuclear data and discontinuity factors, is a product of three computed quantities: a ''cell shape function''; a ''bundle shape function''; and a ''global shape function''. 10 refs
Topological surface states in nodal superconductors
International Nuclear Information System (INIS)
Schnyder, Andreas P; Brydon, Philip M R
2015-01-01
Topological superconductors have become a subject of intense research due to their potential use for technical applications in device fabrication and quantum information. Besides fully gapped superconductors, unconventional superconductors with point or line nodes in their order parameter can also exhibit nontrivial topological characteristics. This article reviews recent progress in the theoretical understanding of nodal topological superconductors, with a focus on Weyl and noncentrosymmetric superconductors and their protected surface states. Using selected examples, we review the bulk topological properties of these systems, study different types of topological surface states, and examine their unusual properties. Furthermore, we survey some candidate materials for topological superconductivity and discuss different experimental signatures of topological surface states. (topical review)
Nodal aberration theory applied to freeform surfaces
Fuerschbach, Kyle; Rolland, Jannick P.; Thompson, Kevin P.
2014-12-01
When new three-dimensional packages are developed for imaging optical systems, the rotational symmetry of the optical system is often broken, changing its imaging behavior and making the optical performance worse. A method to restore the performance is to use freeform optical surfaces that compensate directly the aberrations introduced from tilting and decentering the optical surfaces. In order to effectively optimize the shape of a freeform surface to restore optical functionality, it is helpful to understand the aberration effect the surface may induce. Using nodal aberration theory the aberration fields induced by a freeform surface in an optical system are explored. These theoretical predications are experimentally validated with the design and implementation of an aberration generating telescope.
Disrupted Nodal and Hub Organization Account for Brain Network Abnormalities in Parkinson's Disease.
Koshimori, Yuko; Cho, Sang-Soo; Criaud, Marion; Christopher, Leigh; Jacobs, Mark; Ghadery, Christine; Coakeley, Sarah; Harris, Madeleine; Mizrahi, Romina; Hamani, Clement; Lang, Anthony E; Houle, Sylvain; Strafella, Antonio P
2016-01-01
The recent application of graph theory to brain networks promises to shed light on complex diseases such as Parkinson's disease (PD). This study aimed to investigate functional changes in sensorimotor and cognitive networks in Parkinsonian patients, with a focus on inter- and intra-connectivity organization in the disease-associated nodal and hub regions using the graph theoretical analyses. Resting-state functional MRI data of a total of 65 participants, including 23 healthy controls (HCs) and 42 patients, were investigated in 120 nodes for local efficiency, betweenness centrality, and degree. Hub regions were identified in the HC and patient groups. We found nodal and hub changes in patients compared with HCs, including the right pre-supplementary motor area (SMA), left anterior insula, bilateral mid-insula, bilateral dorsolateral prefrontal cortex (DLPFC), and right caudate nucleus. In general, nodal regions within the sensorimotor network (i.e., right pre-SMA and right mid-insula) displayed weakened connectivity, with the former node associated with more severe bradykinesia, and impaired integration with default mode network regions. The left mid-insula also lost its hub properties in patients. Within the executive networks, the left anterior insular cortex lost its hub properties in patients, while a new hub region was identified in the right caudate nucleus, paralleled by an increased level of inter- and intra-connectivity in the bilateral DLPFC possibly representing compensatory mechanisms. These findings highlight the diffuse changes in nodal organization and regional hub disruption accounting for the distributed abnormalities across brain networks and the clinical manifestations of PD.
Disrupted nodal and hub organization account for brain network abnormalities in Parkinson’s disease
Directory of Open Access Journals (Sweden)
Yuko Koshimori
2016-11-01
Full Text Available The recent application of graph theory to brain networks promises to shed light on complex diseases such as Parkinson’s disease. This study aimed to investigate functional changes in sensorimotor and cognitive networks in parkinsonian patients, with a focus on inter- and intra-connectivity organization in the disease-associated nodal and hub regions using the graph theoretical analyses. Resting-state functional MRI data of a total of 65 participants, including 23 healthy controls and 42 patients, were investigated in 120 nodes for local efficiency, betweenness centrality, and degree. Hub regions were identified in the healthy control and patient groups. We found nodal and hub changes in patients compared with healthy controls, including the right pre-supplementary motor area, left anterior insula, bilateral mid-insula, bilateral dorsolateral prefrontal cortex, and right caudate nucleus. In general, nodal regions within the sensorimotor network (i.e. right pre-supplementary motor area and right mid-insula displayed weakened connectivity, with the former node associated with more severe bradykinesia, and impaired integration with default mode network regions. The left mid-insula also lost its hub properties in patients. Within the executive networks, the left anterior insular cortex lost its hub properties in patients, while a new hub region was identified in the right caudate nucleus, paralleled by an increased level of inter- and intra-connectivity in the bilateral dorsolateral prefrontal cortex possibly representing compensatory mechanisms. These findings highlight the diffuse changes in nodal organization and regional hub disruption accounting for the distributed abnormalities across brain networks and the clinical manifestations of Parkinson’s disease.
International Nuclear Information System (INIS)
Khericha, Soli T.
2000-01-01
One-energy group, two-dimensional computer code was developed to calculate the response of a detector to a vibrating absorber in a reactor core. A concept of local/global components, based on the frequency dependent detector adjoint function, and a nodalization technique were utilized. The frequency dependent detector adjoint functions presented by complex equations were expanded into real and imaginary parts. In the nodalization technique, the flux is expanded into polynomials about the center point of each node. The phase angle and the magnitude of the one-energy group detector adjoint function were calculated for a detector located in the center of a 200x200 cm reactor using a two-dimensional nodalization technique, the computer code EXTERMINATOR, and the analytical solution. The purpose of this research was to investigate the applicability of a polynomial nodal model technique to the calculations of the real and the imaginary parts of the detector adjoint function for one-energy group two-dimensional polynomial nodal model technique. From the results as discussed earlier, it is concluded that the nodal model technique can be used to calculate the detector adjoint function and the phase angle. Using the computer code developed for nodal model technique, the magnitude of one energy group frequency dependent detector adjoint function and the phase angle were calculated for the detector located in the center of a 200x200 cm homogenous reactor. The real part of the detector adjoint function was compared with the results obtained from the EXTERMINATOR computer code as well as the analytical solution based on a double sine series expansion using the classical Green's Function solution. The values were found to be less than 1% greater at 20 cm away from the source region and about 3% greater closer to the source compared to the values obtained from the analytical solution and the EXTERMINATOR code. The currents at the node interface matched within 1% of the average
Modifying nodal pricing method considering market participants optimality and reliability
Directory of Open Access Journals (Sweden)
A. R. Soofiabadi
2015-06-01
Full Text Available This paper develops a method for nodal pricing and market clearing mechanism considering reliability of the system. The effects of components reliability on electricity price, market participants’ profit and system social welfare is considered. This paper considers reliability both for evaluation of market participant’s optimality as well as for fair pricing and market clearing mechanism. To achieve fair pricing, nodal price has been obtained through a two stage optimization problem and to achieve fair market clearing mechanism, comprehensive criteria has been introduced for optimality evaluation of market participant. Social welfare of the system and system efficiency are increased under proposed modified nodal pricing method.
International Nuclear Information System (INIS)
Couto, Nozimar do
2003-01-01
Diffusion theory is traditionally applied to nuclear reactor global calculations. Based on the good results generated by the one-dimensional spectral nodal diffusion (SND) method for benchmark problems, we offer the SND method for nuclear reactor global calculations in X,Y geometry. In this method, the continuity equation and Flick law are transverse integrated in each spatial direction leading to a system of two 'one-dimensional' equations coupled by the transverse leakage terms. We then apply the SND method to numerically solve this system with constant approximations for the transverse leakage terms. We perform a spectral analysis to determine the local general solution of each 'one-dimensional' nodal equation with flat approximation for the transverse leakages. We used special auxiliary equations with parameters that are to be determined in order to preserve the analytical general solutions in the numerical algorithm. By considering continuity conditions at the node interfaces and appropriate boundary conditions, we obtain a solvable system of discretized equations involving the node-edge average scalar fluxes at each estimate of the dominant eigenvalue (k eff ) in the outer power iterations. As we considered approximations to the transverse leakages, the SND method is not free of spatial truncation errors. Nevertheless, it generated good results for the typical model problems that we considered. (author)
International Nuclear Information System (INIS)
Munoz-Cobo, J. L.; Merino, R.; Escriva, A.; Melara, J.; Concejal, A.
2014-01-01
We have developed a 3D code with two energy groups and diffusion theory that is capable of calculating eigenvalues lambda of a BWR reactor using nodal methods and boundary conditions that calculates ALBEDO NODAL-LAMBDA from the properties of the reflector code itself. The code calculates the sub-criticality of the first harmonic, which is involved in the stability against oscillations reactor out of phase, and which is needed for calculating the decay rate for data out of phase oscillations. The code is very fast and in a few seconds is able to make a calculation of the first eigenvalues and eigenvectors, discretized solving the problem with different matrix elements zero. The code uses the LAPACK and ARPACK libraries. It was necessary to modify the LAPACK library to perform various operations with five non-diagonal matrices simultaneously in order to reduce the number of calls to bookstores and simplify the procedure for calculating the matrices in compressed format CSR. The code is validated by comparing it with the results for SIMULATE different cases and making 3D BENCHMAR of the IAEA. (Author)
CT simulation in nodal positive breast cancer
International Nuclear Information System (INIS)
Horst, E.; Schuck, A.; Moustakis, C.; Schaefer, U.; Micke, O.; Kronholz, H.L.; Willich, N.
2001-01-01
Background: A variety of solutions are used to match tangential fields and opposed lymph node fields in irradiation of nodal positive breast cancer. The choice is depending on the technical equipment which is available and the clinical situation. The CT simulation of a non-monoisocentric technique was evaluated in terms of accuracy and reproducibility. Patients, Material and Methods: The field match parameters were adjusted virtually at CT simulation and were compared with parameters derived mathematically. The coordinate transfer from the CT simulator to the conventional simulator was analyzed in 25 consecutive patients. Results: The angles adjusted virtually for a geometrically exact coplanar field match corresponded with the angles calculated for each set-up. The mean isocenter displacement was 5.7 mm and the total uncertainty of the coordinate transfer was 6.7 mm (1 SD). Limitations in the patient set-up became obvious because of the steep arm abduction necessary to fit the 70 cm CT gantry aperture. Required modifications of the arm position and coordinate transfer errors led to a significant shift of the marked matchline of >1.0 cm in eight of 25 patients (32%). Conclusion: The virtual CT simulation allows a precise and graphic definition of the field match parameters. However, modifications of the virtual set-up basically due to technical limitations were required in a total of 32% of cases, so that a hybrid technique was adapted at present that combines virtual adjustment of the ideal field alignment parameters with conventional simulation. (orig.) [de
Present Status of GNF New Nodal Simulator
International Nuclear Information System (INIS)
Iwamoto, T.; Tamitani, M.; Moore, B.
2001-01-01
This paper presents core simulator consolidation work done at Global Nuclear Fuel (GNF). The unified simulator needs to supercede the capabilities of past simulator packages from the original GNF partners: GE, Hitachi, and Toshiba. At the same time, an effort is being made to produce a simulation package that will be a state-of-the-art analysis tool when released, in terms of the physics solution methodology and functionality. The core simulator will be capable and qualified for (a) high-energy cycles in the U.S. markets, (b) mixed-oxide (MOX) introduction in Japan, and (c) high-power density plants in Europe, etc. The unification of the lattice physics code is also in progress based on a transport model with collision probability methods. The AETNA core simulator is built upon the PANAC11 software base. The goal is to essentially replace the 1.5-energy-group model with a higher-order multigroup nonlinear nodal solution capable of the required modeling fidelity, while keeping highly automated library generation as well as functionality. All required interfaces to PANAC11 will be preserved, which minimizes the impact on users and process automation. Preliminary results show statistical accuracy improvement over the 1.5-group model
BEACON: An application of nodal methods for operational support
International Nuclear Information System (INIS)
Boyd, W.A.; Nguyen, T.Q.
1992-01-01
A practical application of nodal methods is on-line plant operational support. However, to enable plant personnel to take full advantage of a nodal model to support plant operations, (a) a core nodal model must always be up to date with the current core history and conditions, (b) the nodal methods must be fast enough to allow numerous core calculations to be performed in minutes to support engineering decisions, and (c) the system must be easily accessible to engineering personnel at the reactor, their offices, or any other location considered appropriate. A core operational support package developed by Westinghouse called BEACON (best estimate analysis of core operations - nuclear) has been installed at several plants. Results from these plants and numerous in-core flux maps analyzed have demonstrated the accuracy of the model and the effectiveness of the methodology
Aircraft Nodal Data Acquisition System (ANDAS), Phase II
National Aeronautics and Space Administration — Development of an Aircraft Nodal Data Acquisition System (ANDAS) based upon the short haul Zigbee networking standard is proposed. It employs a very thin (135 um)...
Hybrid nodal loop metal: Unconventional magnetoresponse and material realization
Zhang, Xiaoming; Yu, Zhi-Ming; Lu, Yunhao; Sheng, Xian-Lei; Yang, Hui Ying; Yang, Shengyuan A.
2018-03-01
A nodal loop is formed by a band crossing along a one-dimensional closed manifold, with each point on the loop a linear nodal point in the transverse dimensions, and can be classified as type I or type II depending on the band dispersion. Here, we propose a class of nodal loops composed of both type-I and type-II points, which are hence termed as hybrid nodal loops. Based on first-principles calculations, we predict the realization of such loops in the existing electride material Ca2As . For a hybrid loop, the Fermi surface consists of coexisting electron and hole pockets that touch at isolated points for an extended range of Fermi energies, without the need for fine-tuning. This leads to unconventional magnetic responses, including the zero-field magnetic breakdown and the momentum-space Klein tunneling observable in the magnetic quantum oscillations, as well as the peculiar anisotropy in the cyclotron resonance.
A nodal method based on matrix-response method
International Nuclear Information System (INIS)
Rocamora Junior, F.D.; Menezes, A.
1982-01-01
A nodal method based in the matrix-response method, is presented, and its application to spatial gradient problems, such as those that exist in fast reactors, near the core - blanket interface, is investigated. (E.G.) [pt
Nodal prices determination with wind integration for radial ...
African Journals Online (AJOL)
With competitive electricity market operation, open access to the transmission and distribution network is essential ... The results have been obtained for IEEE 33 ...... The value of intermittent wind DG under nodal prices and amp – mile tariffs.
Nodal aberration theory for wild-filed asymmetric optical systems
Chen, Yang; Cheng, Xuemin; Hao, Qun
2016-10-01
Nodal Aberration Theory (NAT) was used to calculate the zero field position in Full Field Display (FFD) for the given aberration term. Aiming at wide-filed non-rotational symmetric decentered optical systems, we have presented the nodal geography behavior of the family of third-order and fifth-order aberrations. Meanwhile, we have calculated the wavefront aberration expressions when one optical element in the system is tilted, which was not at the entrance pupil. By using a three-piece-cellphone lens example in optical design software CodeV, the nodal geography is testified under several situations; and the wavefront aberrations are calculated when the optical element is tilted. The properties of the nodal aberrations are analyzed by using Fringe Zernike coefficients, which are directly related with the wavefront aberration terms and usually obtained by real ray trace and wavefront surface fitting.
The ADO-nodal method for solving two-dimensional discrete ordinates transport problems
International Nuclear Information System (INIS)
Barichello, L.B.; Picoloto, C.B.; Cunha, R.D. da
2017-01-01
Highlights: • Two-dimensional discrete ordinates neutron transport. • Analytical Discrete Ordinates (ADO) nodal method. • Heterogeneous media fixed source problems. • Local solutions. - Abstract: In this work, recent results on the solution of fixed-source two-dimensional transport problems, in Cartesian geometry, are reported. Homogeneous and heterogeneous media problems are considered in order to incorporate the idea of arbitrary number of domain division into regions (nodes) when applying the ADO method, which is a method of analytical features, to those problems. The ADO-nodal formulation is developed, for each node, following previous work devoted to heterogeneous media problem. Here, however, the numerical procedure is extended to higher number of domain divisions. Such extension leads, in some cases, to the use of an iterative method for solving the general linear system which defines the arbitrary constants of the general solution. In addition to solve alternative heterogeneous media configurations than reported in previous works, the present approach allows comparisons with results provided by other metodologies generated with refined meshes. Numerical results indicate the ADO solution may achieve a prescribed accuracy using coarser meshes than other schemes.
Uniqueness Theorem for the Inverse Aftereffect Problem and Representation the Nodal Points Form
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A. Neamaty
2015-03-01
Full Text Available In this paper, we consider a boundary value problem with aftereffect on a finite interval. Then, the asymptotic behavior of the solutions, eigenvalues, the nodal points and the associated nodal length are studied. We also calculate the numerical values of the nodal points and the nodal length. Finally, we prove the uniqueness theorem for the inverse aftereffect problem by applying any dense subset of the nodal points.
Uniqueness Theorem for the Inverse Aftereffect Problem and Representation the Nodal Points Form
A. Neamaty; Sh. Akbarpoor; A. Dabbaghian
2015-01-01
In this paper, we consider a boundary value problem with aftereffect on a finite interval. Then, the asymptotic behavior of the solutions, eigenvalues, the nodal points and the associated nodal length are studied. We also calculate the numerical values of the nodal points and the nodal length. Finally, we prove the uniqueness theorem for the inverse aftereffect problem by applying any dense subset of the nodal points.
Interface discontinuity factors in the modal Eigenspace of the multigroup diffusion matrix
International Nuclear Information System (INIS)
Garcia-Herranz, N.; Herrero, J.J.; Cuervo, D.; Ahnert, C.
2011-01-01
Interface discontinuity factors based on the Generalized Equivalence Theory are commonly used in nodal homogenized diffusion calculations so that diffusion average values approximate heterogeneous higher order solutions. In this paper, an additional form of interface correction factors is presented in the frame of the Analytic Coarse Mesh Finite Difference Method (ACMFD), based on a correction of the modal fluxes instead of the physical fluxes. In the ACMFD formulation, implemented in COBAYA3 code, the coupled multigroup diffusion equations inside a homogenized region are reduced to a set of uncoupled modal equations through diagonalization of the multigroup diffusion matrix. Then, physical fluxes are transformed into modal fluxes in the Eigenspace of the diffusion matrix. It is possible to introduce interface flux discontinuity jumps as the difference of heterogeneous and homogeneous modal fluxes instead of introducing interface discontinuity factors as the ratio of heterogeneous and homogeneous physical fluxes. The formulation in the modal space has been implemented in COBAYA3 code and assessed by comparison with solutions using classical interface discontinuity factors in the physical space. (author)
International Nuclear Information System (INIS)
O'Dell, R.D.; Stepanek, J.; Wagner, M.R.
1983-01-01
The aim of the present work is to compare and discuss the three of the most advanced two dimensional transport methods, the finite difference and nodal discrete ordinates and surface flux method, incorporated into the transport codes TWODANT, TWOTRAN-NODAL, MULTIMEDIUM and SURCU. For intercomparison the eigenvalue and the neutron flux distribution are calculated using these codes in the LWR pool reactor benchmark problem. Additionally the results are compared with some results obtained by French collision probability transport codes MARSYAS and TRIDENT. Because the transport solution of this benchmark problem is close to its diffusion solution some results obtained by the finite element diffusion code FINELM and the finite difference diffusion code DIFF-2D are included
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Mohammadnia Meysam
2013-01-01
Full Text Available The flux expansion nodal method is a suitable method for considering nodalization effects in node corners. In this paper we used this method to solve the intra-nodal flux analytically. Then, a computer code, named MA.CODE, was developed using the C# programming language. The code is capable of reactor core calculations for hexagonal geometries in two energy groups and three dimensions. The MA.CODE imports two group constants from the WIMS code and calculates the effective multiplication factor, thermal and fast neutron flux in three dimensions, power density, reactivity, and the power peaking factor of each fuel assembly. Some of the code's merits are low calculation time and a user friendly interface. MA.CODE results showed good agreement with IAEA benchmarks, i. e. AER-FCM-101 and AER-FCM-001.
Implications of inaccurate clinical nodal staging in pancreatic adenocarcinoma.
Swords, Douglas S; Firpo, Matthew A; Johnson, Kirsten M; Boucher, Kenneth M; Scaife, Courtney L; Mulvihill, Sean J
2017-07-01
Many patients with stage I-II pancreatic adenocarcinoma do not undergo resection. We hypothesized that (1) clinical staging underestimates nodal involvement, causing stage IIB to have a greater percent of resected patients and (2) this stage-shift causes discrepancies in observed survival. The Surveillance, Epidemiology, and End Results (SEER) research database was used to evaluate cause-specific survival in patients with pancreatic adenocarcinoma from 2004-2012. Survival was compared using the log-rank test. Single-center data on 105 patients who underwent resection of pancreatic adenocarcinoma without neoadjuvant treatment were used to compare clinical and pathologic nodal staging. In SEER data, medium-term survival in stage IIB was superior to IB and IIA, with median cause-specific survival of 14, 9, and 11 months, respectively (P < .001). Seventy-two percent of stage IIB patients underwent resection vs 28% in IB and 36% in IIA (P < .001). In our institutional data, 12.4% of patients had clinical evidence of nodal involvement vs 69.5% by pathologic staging (P < .001). Among clinical stage IA-IIA patients, 71.6% had nodal involvement by pathologic staging. Both SEER and institutional data support substantial underestimation of nodal involvement by clinical staging. This finding has implications in decisions regarding neoadjuvant therapy and analysis of outcomes in the absence of pathologic staging. Copyright © 2017 Elsevier Inc. All rights reserved.
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A. Lagra
2018-01-01
Full Text Available Combined Soret and Dufour effects on thermosolutal convection induced in a horizontal layer filled with a binary fluid and subject to constant heat and mass fluxes are investigated analytically and numerically. The thresholds marking the onset of supercritical and subcritical convection are predicted analytically and explicitly versus the governing parameters. The present investigation shows that different regions exist in the N-Du plane corresponding to different parallel flow regimes. The number, the extent, and the locations of these regions depend on whether SrDu>-(1+Le2/2Le2=f(Le or SrDu<-(1+Le2/2Le2. Conjugate effects of cross-phenomena on thresholds of fluid flow and heat and mass transfer characteristics are illustrated and discussed.
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Tristan Guillaume
2016-01-01
Full Text Available This paper shows how to value multiasset options analytically in a modeling framework that combines both continuous and discontinuous variations in the underlying equity or foreign exchange processes and a stochastic, two-factor yield curve. All correlations are taken into account, between the factors driving the yield curve, between fixed income and equity as asset classes, and between the individual equity assets themselves. The valuation method is applied to three of the most popular two-asset options.
On the Nodal Lines of Eisenstein Series on Schottky Surfaces
Jakobson, Dmitry; Naud, Frédéric
2017-04-01
On convex co-compact hyperbolic surfaces {X=Γ backslash H2}, we investigate the behavior of nodal curves of real valued Eisenstein series {F_λ(z,ξ)}, where {λ} is the spectral parameter, {ξ} the direction at infinity. Eisenstein series are (non-{L^2}) eigenfunctions of the Laplacian {Δ_X} satisfying {Δ_X F_λ=(1/4+λ^2)F_λ}. As {λ} goes to infinity (the high energy limit), we show that, for generic {ξ}, the number of intersections of nodal lines with any compact segment of geodesic grows like {λ}, up to multiplicative constants. Applications to the number of nodal domains inside the convex core of the surface are then derived.
A computational study of nodal-based tetrahedral element behavior.
Energy Technology Data Exchange (ETDEWEB)
Gullerud, Arne S.
2010-09-01
This report explores the behavior of nodal-based tetrahedral elements on six sample problems, and compares their solution to that of a corresponding hexahedral mesh. The problems demonstrate that while certain aspects of the solution field for the nodal-based tetrahedrons provide good quality results, the pressure field tends to be of poor quality. Results appear to be strongly affected by the connectivity of the tetrahedral elements. Simulations that rely on the pressure field, such as those which use material models that are dependent on the pressure (e.g. equation-of-state models), can generate erroneous results. Remeshing can also be strongly affected by these issues. The nodal-based test elements as they currently stand need to be used with caution to ensure that their numerical deficiencies do not adversely affect critical values of interest.
A nodal method of calculating power distributions for LWR-type reactors with square fuel lattices
International Nuclear Information System (INIS)
Hoeglund, Randolph.
1980-06-01
A nodal model is developed for calculating the power distribution in the core of a light water reactor with a square fuel lattice. The reactor core is divided into a number of more or less cubic nodes and a nodal coupling equation, which gives the thermal power density in one node as a function of the power densities in the neighbour nodes, is derived from the neutron diffusion equations for two energy groups. The three-dimensional power distribution can be computed iteratively using this coupling equation, for example following the point Jacobi, the Gauss-Seidel or the point successive overrelaxation scheme. The method has been included as the neutronic model in a reactor core simulation computer code BOREAS, where it is combined with a thermal-hydraulic model in order to make a simultaneous computation of the interdependent power and void distributions in a boiling water reactor possible. Also described in this report are a method for temporary one-dimensional iteration developed in order to accelerate the iterative solution of the problem and the Haling principle which is widely used in the planning of reloading operations for BWR reactors. (author)
NODAL3 Sensitivity Analysis for NEACRP 3D LWR Core Transient Benchmark (PWR
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Surian Pinem
2016-01-01
Full Text Available This paper reports the results of sensitivity analysis of the multidimension, multigroup neutron diffusion NODAL3 code for the NEACRP 3D LWR core transient benchmarks (PWR. The code input parameters covered in the sensitivity analysis are the radial and axial node sizes (the number of radial node per fuel assembly and the number of axial layers, heat conduction node size in the fuel pellet and cladding, and the maximum time step. The output parameters considered in this analysis followed the above-mentioned core transient benchmarks, that is, power peak, time of power peak, power, averaged Doppler temperature, maximum fuel centerline temperature, and coolant outlet temperature at the end of simulation (5 s. The sensitivity analysis results showed that the radial node size and maximum time step give a significant effect on the transient parameters, especially the time of power peak, for the HZP and HFP conditions. The number of ring divisions for fuel pellet and cladding gives negligible effect on the transient solutions. For productive work of the PWR transient analysis, based on the present sensitivity analysis results, we recommend NODAL3 users to use 2×2 radial nodes per assembly, 1×18 axial layers per assembly, the maximum time step of 10 ms, and 9 and 1 ring divisions for fuel pellet and cladding, respectively.
Oddness of least energy nodal solutions on radial domains
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Christopher Grumiau
2010-07-01
Full Text Available In this article, we consider the Lane-Emden problem $$displaylines{ Delta u(x + |{u(x}mathclose|^{p-2}u(x=0, quad hbox{for } xinOmega,cr u(x=0, quad hbox{for } xinpartialOmega, }$$ where $2 < p < 2^{*}$ and $Omega$ is a ball or an annulus in $mathbb{R}^{N}$, $Ngeq 2$. We show that, for p close to 2, least energy nodal solutions are odd with respect to an hyperplane -- which is their nodal surface. The proof ingredients are a constrained implicit function theorem and the fact that the second eigenvalue is simple up to rotations.
Regional Nodal Irradiation in Early-Stage Breast Cancer.
Whelan, Timothy J; Olivotto, Ivo A; Parulekar, Wendy R; Ackerman, Ida; Chua, Boon H; Nabid, Abdenour; Vallis, Katherine A; White, Julia R; Rousseau, Pierre; Fortin, Andre; Pierce, Lori J; Manchul, Lee; Chafe, Susan; Nolan, Maureen C; Craighead, Peter; Bowen, Julie; McCready, David R; Pritchard, Kathleen I; Gelmon, Karen; Murray, Yvonne; Chapman, Judy-Anne W; Chen, Bingshu E; Levine, Mark N
2015-07-23
Most women with breast cancer who undergo breast-conserving surgery receive whole-breast irradiation. We examined whether the addition of regional nodal irradiation to whole-breast irradiation improved outcomes. We randomly assigned women with node-positive or high-risk node-negative breast cancer who were treated with breast-conserving surgery and adjuvant systemic therapy to undergo either whole-breast irradiation plus regional nodal irradiation (including internal mammary, supraclavicular, and axillary lymph nodes) (nodal-irradiation group) or whole-breast irradiation alone (control group). The primary outcome was overall survival. Secondary outcomes were disease-free survival, isolated locoregional disease-free survival, and distant disease-free survival. Between March 2000 and February 2007, a total of 1832 women were assigned to the nodal-irradiation group or the control group (916 women in each group). The median follow-up was 9.5 years. At the 10-year follow-up, there was no significant between-group difference in survival, with a rate of 82.8% in the nodal-irradiation group and 81.8% in the control group (hazard ratio, 0.91; 95% confidence interval [CI], 0.72 to 1.13; P=0.38). The rates of disease-free survival were 82.0% in the nodal-irradiation group and 77.0% in the control group (hazard ratio, 0.76; 95% CI, 0.61 to 0.94; P=0.01). Patients in the nodal-irradiation group had higher rates of grade 2 or greater acute pneumonitis (1.2% vs. 0.2%, P=0.01) and lymphedema (8.4% vs. 4.5%, P=0.001). Among women with node-positive or high-risk node-negative breast cancer, the addition of regional nodal irradiation to whole-breast irradiation did not improve overall survival but reduced the rate of breast-cancer recurrence. (Funded by the Canadian Cancer Society Research Institute and others; MA.20 ClinicalTrials.gov number, NCT00005957.).
Discontinuous nodal schemes applied to the bidimensional neutron transport equation
International Nuclear Information System (INIS)
Delfin L, A.; Valle G, E. Del; Hennart B, J.P.
1996-01-01
In this paper several strong discontinuous nodal schemes are described, starting from the one that has only two interpolation parameters per cell to the one having ten. Their application to the spatial discretization of the neutron transport equation in X-Y geometry is also described, giving, for each one of the nodal schemes, the approximation for the angular neutron flux that includes the set of interpolation parameters and the corresponding polynomial space. Numerical results were obtained for several test problems presenting here the problem with the highest degree of difficulty and their comparison with published results 1,2 . (Author)
International Nuclear Information System (INIS)
Dieperink, C.; Brand, I.; Vermeulen, W.
2004-01-01
The need to improve eco-efficiency is indisputable, and the way forward is through widespread application of environmental innovations. Yet research into the dissemination of such innovations in the Netherlands has been limited in scope. Most studies tend to focus on the feasibility of a particular technology. Few try to explain how technology spreads throughout society. The explanatory factors discerned in these studies are often not related to each other. In this contribution the authors try to integrate different partial explanations for the diffusion of energy-saving technologies in industry and the built environment into one conceptual framework. This integration is based on a secondary analysis of relatively well-elaborated studies dealing with the diffusion of heat pumps, combined heat and power and condensing boilers in industry and the built environment. Core of the framework is the decision-making process of the potentially adapting actor. Characteristics of the actor and the networks in which the actor participates (government, market, society) could have impact on this decision-making process. Technological and economic characteristics of the innovation and more general context factors are also relevant as factors that influence the considerations made in the decision-making process. This conceptual framework can be used both in more elaborate research projects and in brainstorming projects to improve policymaking
Diffusing diffusivity: Rotational diffusion in two and three dimensions
Jain, Rohit; Sebastian, K. L.
2017-06-01
We consider the problem of calculating the probability distribution function (pdf) of angular displacement for rotational diffusion in a crowded, rearranging medium. We use the diffusing diffusivity model and following our previous work on translational diffusion [R. Jain and K. L. Sebastian, J. Phys. Chem. B 120, 3988 (2016)], we show that the problem can be reduced to that of calculating the survival probability of a particle undergoing Brownian motion, in the presence of a sink. We use the approach to calculate the pdf for the rotational motion in two and three dimensions. We also propose new dimensionless, time dependent parameters, αr o t ,2 D and αr o t ,3 D, which can be used to analyze the experimental/simulation data to find the extent of deviation from the normal behavior, i.e., constant diffusivity, and obtain explicit analytical expressions for them, within our model.
Development of a New core/reflector model for coarse-mesh nodal methods
International Nuclear Information System (INIS)
Pogosbekyan, Leonid; Cho, Jin Young; Kim, Young Il; Kim, Young Jin; Joo, Hyung Kuk; Chang, Moon Hee.
1997-10-01
This work presents two approaches for reflector simulation in coarse-mesh nodal methods. The first approach is called Interface Matrix Technique (IMT), which simulates the baffle as a banishingly thin layer having the property of reflection and transmission. We applied this technique within the frame of AFEN (Analytic Function Expansion Nodal) method, and developed the AFEN-IM (Interface Matrix) method. AFEN-IM method shows 1.24% and 0.42 % in maximum and RMS (Root Mean Square) assemblywise power error for ZION-1 benchmark problem. The second approach is L-shaped reflector homogenization method. This method is based on the integral response conservation along the L-shaped core-reflector interface. The reference reflector response is calculated from 2-dimensional spectral calculation and the response of the homogenized reflector is derived from the one-node 2-dimensional AFEN problem solution. This method shows 5 times better accuracy than the 1-dimensional homogenization technique in the assemblywise power. Also, the concept of shroud/reflector homogenization for hexagonal core have been developed. The 1-dimensional spectral calculation was used for the determination of 2 group cross sections. The essence of homogenization concept consists in the calculation of equivalent shroud width, which preserve albedo for the fast neutrons in 2-dimensional reflector. This method shows a relative error less than 0.42% in assemblywise power and a difference of 9x10 -5 in multiplication factor for full-core model. (author). 9 refs., 3 tabs., 28 figs
International Nuclear Information System (INIS)
Premuda, F.
1983-01-01
Two lines in improved neutron diffusion theory extending the efficiency of finite-difference diffusion codes to the field of optically small systems, are here reviewed. The firs involves the nodal solution for tensorial diffusion equation in slab geometry and tensorial formulation in parallelepiped and cylindrical gemometry; the dependence of critical eigenvalue from small slab thicknesses is also analitically investigated and finally a regularized tensorial diffusion equation is derived for slab. The other line refer to diffusion models formally unchanged with respect to the classical one, but where new size-dependent RTGB definitions for diffusion parameters are adopted, requiring that they allow to reproduce, in diffusion approach, the terms of neutron transport global balance; the trascendental equation for the buckling, arising in slab, sphere and parallelepiped geometry from the above requirement, are reported and the sizedependence of the new diffusion coefficient and extrapolated end point is investigated
Application of the HGPT methodology of reactor operation problems with a nodal mixed method
International Nuclear Information System (INIS)
Baudron, A.M.; Bruna, G.B.; Gandini, A.; Lautard, J.J.; Monti, S.; Pizzigati, G.
1998-01-01
The heuristically based generalized perturbation theory (HGPT), to first and higher order, applied to the neutron field of a reactor system, is discussed in relation to quasistatic problems. This methodology is of particular interest in reactor operation. In this application it may allow an on-line appraisal of the main physical responses of the reactor system when subject to alterations relevant to normal system exploitation, e.g. control rod movement, and/or soluble boron concentration changes to be introduced, for instance, for compensating power level variations following electrical network demands. In this paper, after describing the main features of the theory, its implementation into the diffusion, 3D mixed dual nodal code MINOS of the SAPHYR system is presented. The results from a small scale investigation performed on a simplified PWR system corroborate the validity of the methodology proposed
Pellet by pellet neutron flux calculations coupled with nodal expansion method
International Nuclear Information System (INIS)
Aldo, Dall'Osso
2003-01-01
We present a technique whose aim is to replace 2-dimensional pin by pin de-homogenization, currently done in core reactor calculations with the nodal expansion method (NEM), by a 3-dimensional finite difference diffusion calculation. This fine calculation is performed as a zoom in each node taking as boundary conditions the results of the NEM calculations. The size of fine mesh is of the order of a fuel pellet. The coupling between fine and NEM calculations is realised by an albedo like boundary condition. Some examples are presented showing fine neutron flux shape near control rods or assembly grids. Other fine flux behaviour as the thermal flux rise in the fuel near the reflector is emphasised. In general the results show the interest of the method in conditions where the separability of radial and axial directions is not granted. (author)
Extension of the linear nodal method to large concrete building calculations
International Nuclear Information System (INIS)
Childs, R.L.; Rhoades, W.A.
1985-01-01
The implementation of the linear nodal method in the TORT code is described, and the results of a mesh refinement study to test the effectiveness of the linear nodal and weighted diamond difference methods available in TORT are presented
Rationale of chemotherapy for Nodal Disease
International Nuclear Information System (INIS)
Zwelling, L.A.; Silberman, L.; Estey, E.
1987-01-01
Defining biochemical differences between malignant and normal cells or between drug-sensitive and drug-resistant cells may lead to the discovery of pharmacologically exploitable pathways by which to treat human cancer. Systems in which active antineoplastic agents display different cytotoxic effects allow biochemical study of the basis for these differences. The interaction between topoisomerase II and active, anti-neoplastic DNA intercalating agents may be the way these active drugs kill cells. Details of the biochemical mechanisms and their effects on cellular events await precise description, but the principles learned in studies of this unique drug-protein-DNA interaction may be applicable to the treatment of locally advanced and diffusely disseminated human malignancies
Transport equivalent diffusion constants for reflector region in PWRs
International Nuclear Information System (INIS)
Tahara, Yoshihisa; Sekimoto, Hiroshi
2002-01-01
The diffusion-theory-based nodal method is widely used in PWR core designs for reason of its high computing speed in three-dimensional calculations. The baffle/reflector (B/R) constants used in nodal calculations are usually calculated based on a one-dimensional transport calculation. However, to achieve high accuracy of assembly power prediction, two-dimensional model is needed. For this reason, the method for calculating transport equivalent diffusion constants of reflector material was developed so that the neutron currents on the material boundaries could be calculated exactly in diffusion calculations. Two-dimensional B/R constants were calculated using the transport equivalent diffusion constants in the two-dimensional diffusion calculation whose geometry reflected the actual material configuration in the reflector region. The two-dimensional B/R constants enabled us to predict assembly power within an error of 1.5% at hot full power conditions. (author)
Analysis of 2D reactor core using linear perturbation theory and nodal finite element methods
International Nuclear Information System (INIS)
Adrian Mugica; Edmundo del Valle
2005-01-01
In this work the multigroup steady state neutron diffusion equations are solved using the nodal finite element method (NFEM) and the Linear Perturbation Theory (LPT) for XY geometry. The NFEM used corresponds to the Raviart-Thomas schemes RT0 and RT1, interpolating 5 and 12 parameters respectively in each node of the space discretization. The accuracy of these methods is related with the dimension of the space approximation and the mesh size. Therefore, using fine meshes and the RT0 or RT1 nodal methods leads to a large an interesting eigenvalue problem. The finite element method used to discretize the weak formulation of the diffusion equations is the Galerkin one. The algebraic structure of the discrete eigenvalue problem is obtained and solved using the Wielandt technique and the BGSTAB iterative method using the SPARSKIT package developed by Yousef Saad. The results obtained with LPT show good agreement with the results obtained directly for the perturbed problem. In fact, the cpu time to solve a single problem, the unperturbed and the perturbed one, is practically the same but when one is focused in shuffling many times two different assemblies in the core then the LPT technique becomes quite useful to get good approximations in a short time. This particular problem was solved for one quarter-core with NFEM. Thus, the computer program based on LPT can be used to perform like an analysis tool in the fuel reload optimization or combinatory analysis to get reload patterns in nuclear power plants once that it had been incorporated with the thermohydraulic aspects needed to simulate accurately a real problem. The maximum differences between the NFEM and LPT for the three LWR reactor cores are about 250 pcm. This quantity is considered an acceptable value for this kind of analysis. (authors)
The Nodal Location of Metastases in Melanoma Sentinel Lymph Nodes
DEFF Research Database (Denmark)
Riber-Hansen, Rikke; Nyengaard, Jens; Hamilton-Dutoit, Stephen
2009-01-01
BACKGROUND: The design of melanoma sentinel lymph node (SLN) histologic protocols is based on the premise that most metastases are found in the central parts of the nodes, but the evidence for this belief has never been thoroughly tested. METHODS: The nodal location of melanoma metastases in 149...
Real-time control of power systems using nodal prices
Jokic, A.; Lazar, M.; Bosch, van den P.P.J.
2009-01-01
This article presents a novel control scheme for achieving optimal power balancing and congestion management in electrical power systems via nodal prices. We develop a dynamic controller that guarantees economically optimal steady-state operation while respecting all line flow constraints in
Topological transport in Dirac nodal-line semimetals
Rui, W. B.; Zhao, Y. X.; Schnyder, Andreas P.
2018-04-01
Topological nodal-line semimetals are characterized by one-dimensional Dirac nodal rings that are protected by the combined symmetry of inversion P and time-reversal T . The stability of these Dirac rings is guaranteed by a quantized ±π Berry phase and their low-energy physics is described by a one-parameter family of (2+1)-dimensional quantum field theories exhibiting the parity anomaly. Here we study the Berry-phase supported topological transport of P T -invariant nodal-line semimetals. We find that small inversion breaking allows for an electric-field-induced anomalous transverse current, whose universal component originates from the parity anomaly. Due to this Hall-like current, carriers at opposite sides of the Dirac nodal ring flow to opposite surfaces when an electric field is applied. To detect the topological currents, we propose a dumbbell device, which uses surface states to filter charges based on their momenta. Suggestions for experiments and device applications are discussed.
Hyoid bone chondrosarcoma with cervical nodal metastasis: A case ...
African Journals Online (AJOL)
Background: Hyoid bone chondrosarcoma is a very rare condition. This study presents a case report of low-grade chondrosarcoma of hyoid bone with cervical nodal metastasis. The study also presents preoperative radiological investigations, pathological examination and the follow-up of the case. Case presentation: A 42 ...
Note on the nodal line of the p-Laplacian
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Abdel R. El Amrouss
2006-09-01
Full Text Available In this paper, we prove that the length of the nodal line of the eigenfunctions associated to the second eigenvalue of the problem $$ -Delta_p u = lambda ho (x |u|^{p-2}u quad hbox{in } Omega $$ with the Dirichlet conditions is not bounded uniformly with respect to the weight.
A nodal method based on the response-matrix method
International Nuclear Information System (INIS)
Cunha Menezes Filho, A. da; Rocamora Junior, F.D.
1983-02-01
A nodal approach based on the Response-Matrix method is presented with the purpose of investigating the possibility of mixing two different allocations in the same problem. It is found that the use of allocation of albedo combined with allocation of direct reflection produces good results for homogeneous fast reactor configurations. (Author) [pt
CRY 1AB trangenic cowpea obtained by nodal electroporation ...
African Journals Online (AJOL)
Electroporation-mediated genetic transformation was used to introduce Cry 1 Ab insecticidal gene into cowpea. Nodal buds were electroporated in planta with a plasmid carrying the Cry 1Ab and antibiotic resistance npt II genes driven by a 35S CaMV promoter. T1 seeds derived from electroporated branches were selected ...
Energy Technology Data Exchange (ETDEWEB)
Kromar, M; Trkov, A [Institut Jozef Stefan, Ljubljana (Yugoslavia); Pregl, G [Tehnishka Fakulteta Maribor Univ. (Yugoslavia)
1988-07-01
Nodal expansion method (NEM) is one of the advanced coarse-mesh methods based on integral form of few-group diffusion equation. NEM can be characterized by high accuracy and computational efficiency. Method was tested by development of computer code NEXT. Validation of the code was performed by calculation of 2-D and 3-D IAEA benchmark problem. NEXT was compared with codes based on other methods (finite differences, finite elements) and has been found to be accurate as well as fast. (author)
47 CFR 101.503 - Digital Electronic Message Service Nodal Stations.
2010-10-01
... Service § 101.503 Digital Electronic Message Service Nodal Stations. 10.6 GHz DEMS Nodal Stations may be... 47 Telecommunication 5 2010-10-01 2010-10-01 false Digital Electronic Message Service Nodal Stations. 101.503 Section 101.503 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY...
EPA’s Web Analytics Program collects, analyzes, and provides reports on traffic, quality assurance, and customer satisfaction metrics for EPA’s website. The program uses a variety of analytics tools, including Google Analytics and CrazyEgg.
Energy Technology Data Exchange (ETDEWEB)
Schmocker, U
1980-07-01
Repositories in geological formations are planned for the final disposal of radioactive wastes produced by nuclear power. Generally, water entry leading to leaching of the waste matrix is considered as the critical process which can result in release of radionuclides from a waste repository. In risk analyses for waste repositories the migration of radionuclides through the geosphere is usually described mathematically by a one-dimensional transport model. On the other hand the hydrological calculational models used for determining the critical migration paths are invariably two- or three-dimensional. A one-dimensional transport calculation always gives conservative results for a specific migration path because the influence of the transverse dispersion/diffusion effect is neglected. This effect results in an additional decrease of the nuclide concentration along the migration path. On the other hand radionuclides can spread to adjacent geological formations which are not taken into account in a one-dimensional model. If the water velocities in these formations are higher than along the original (one-dimensional) migration path or if the distance to the biosphere (e.g. lake, river or well) is shorter, then the process of the transverse diffusion/dispersion can represent an additional risk. The present work deals with the influence of the transverse diffusion/dispersion effect on the migration of radionuclides through the geosphere. We restrict ourselves to migration in porous media which is the standard approach of most existing transport models. For modelling the transport of radionuclides in fissured systems there exist only a few preliminary calculational approaches to date. We are mainly interested in analytically soluble problems which take into account the transverse diffusion/dispersion effect. This procedure permits investigation of the most important effects in a simple and direct manner. 17 refs., 36 figs., 2 tabs.
New procedure for criticality search using coarse mesh nodal methods
International Nuclear Information System (INIS)
Pereira, Wanderson F.; Silva, Fernando C. da; Martinez, Aquilino S.
2011-01-01
The coarse mesh nodal methods have as their primary goal to calculate the neutron flux inside the reactor core. Many computer systems use a specific form of calculation, which is called nodal method. In classical computing systems that use the criticality search is made after the complete convergence of the iterative process of calculating the neutron flux. In this paper, we proposed a new method for the calculation of criticality, condition which will be over very iterative process of calculating the neutron flux. Thus, the processing time for calculating the neutron flux was reduced by half compared with the procedure developed by the Nuclear Engineering Program of COPPE/UFRJ (PEN/COPPE/UFRJ). (author)
New procedure for criticality search using coarse mesh nodal methods
Energy Technology Data Exchange (ETDEWEB)
Pereira, Wanderson F.; Silva, Fernando C. da; Martinez, Aquilino S., E-mail: wneto@con.ufrj.b, E-mail: fernando@con.ufrj.b, E-mail: Aquilino@lmp.ufrj.b [Coordenacao dos Programas de Pos-Graduacao de Engenharia (PEN/COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear
2011-07-01
The coarse mesh nodal methods have as their primary goal to calculate the neutron flux inside the reactor core. Many computer systems use a specific form of calculation, which is called nodal method. In classical computing systems that use the criticality search is made after the complete convergence of the iterative process of calculating the neutron flux. In this paper, we proposed a new method for the calculation of criticality, condition which will be over very iterative process of calculating the neutron flux. Thus, the processing time for calculating the neutron flux was reduced by half compared with the procedure developed by the Nuclear Engineering Program of COPPE/UFRJ (PEN/COPPE/UFRJ). (author)
The variational nodal method: history and recent accomplishments
International Nuclear Information System (INIS)
Lewis, E.E.
2004-01-01
The variational nodal method combines spherical harmonics expansions in angle with hybrid finite element techniques is space to obtain multigroup transport response matrix algorithms applicable to both deep penetration and reactor core physics problems. This survey briefly recounts the method's history and reviews its capabilities. The variational basis for the approach is presented and two methods for obtaining discretized equations in the form of response matrices are detailed. The first is that contained the widely used VARIANT code, while the second incorporates newly developed integral transport techniques into the variational nodal framework. The two approaches are combined with a finite sub element formulation to treat heterogeneous nodes. Applications are presented for both a deep penetration problem and to an OECD benchmark consisting of LWR MOX fuel assemblies. Ongoing work is discussed. (Author)
Radiological signs of extra nodal abdominal involvements in lymphoma
International Nuclear Information System (INIS)
Carro, A.I.; Alegre, N.; Cervera, J.L.; Montero, A.I.
1998-01-01
To assess abdominal CT images in lymphoma patients for the study of extra nodal abdominal involvement. Ninety-two patients diagnosed as having lymphoma were studied retrospectively. All the patients underwent abdominopelvic CT with oral and intravenous contrast (except in one patient who was allergic). In every case, the diagnosis was confirmed by biopsy or radiological follow-up after treatment had been completed. Fifty-two patients (56.5%) presented infiltration of extra nodal organs. The organs most frequently involved were liver and spleen, followed by the gastrointestinal tract, the musculoskeletal system and the genitourinary tract. The findings in this study coincide with those reported elsewhere with the exception of the splenic involvement the incidence of which was lower in the present series. (Author) 17 refs
On the nodal structure of atomic and molecular Wigner functions
International Nuclear Information System (INIS)
Dahl, J.P.; Schmider, H.
1996-01-01
In previous work on the phase-space representation of quantum mechanics, we have presented detailed pictures of the electronic one-particle reduced Wigner function for atoms and small molecules. In this communication, we focus upon the nodal structure of the function. On the basis of the simplest systems, we present an expression which relates the oscillatory decay of the Wigner function solely to the dot product of the position and momentum vector, if both arguments are large. We then demonstrate the regular behavior of nodal patterns for the larger systems. For the molecular systems, an argument analogous to the open-quotes bond-oscillatory principleclose quotes for momentum densities links the nuclear framework to an additional oscillatory term in momenta parallel to bonds. It is shown that these are visible in the Wigner function in terms of characteristic nodes
Topological and trivial magnetic oscillations in nodal loop semimetals
Oroszlány, László; Dóra, Balázs; Cserti, József; Cortijo, Alberto
2018-05-01
Nodal loop semimetals are close descendants of Weyl semimetals and possess a topologically dressed band structure. We argue by combining the conventional theory of magnetic oscillation with topological arguments that nodal loop semimetals host coexisting topological and trivial magnetic oscillations. These originate from mapping the topological properties of the extremal Fermi surface cross sections onto the physics of two dimensional semi-Dirac systems, stemming from merging two massless Dirac cones. By tuning the chemical potential and the direction of magnetic field, a sharp transition is identified from purely trivial oscillations, arising from the Landau levels of a normal two dimensional (2D) electron gas, to a phase where oscillations of topological and trivial origin coexist, originating from 2D massless Dirac and semi-Dirac points, respectively. These could in principle be directly identified in current experiments.
Ischemic stroke associated with radio frequency ablation for nodal reentry
International Nuclear Information System (INIS)
Diaz M, Juan C; Duran R, Carlos E; Perafan B, Pablo; Pava M, Luis F
2010-01-01
Atrioventricular nodal reentry tachycardia is the most common type of paroxysmal supraventricular tachycardia. In those patients in whom drug therapy is not effective or not desired, radio frequency ablation is an excellent therapeutic method. Although overall these procedures are fast and safe, several complications among which ischemic stroke stands out, have been reported. We present the case of a 41 year old female patient with repetitive episodes of tachycardia due to nodal reentry who was treated with radiofrequency ablation. Immediately after the procedure she presented focal neurologic deficit consistent with ischemic stroke in the right medial cerebral artery territory. Angiography with angioplastia and abxicimab was performed and then tissue plasminogen activator (rtPA) was locally infused, with appropriate clinical and angiographic outcome.
RELAP 4/MOD 6 boiling water nodalization study
International Nuclear Information System (INIS)
Sonneck, G.; Pfau, H.
1985-09-01
The risk of nuclear steam supply systems is dominated by the core melt accidents. The first step to a realistic assessment of these sequences is the successful prediction of a loss of coolant event in a test loop. One of the codes for that is RELAP 4/MOD 6 and one of the important options in this code is the nodalization. The base of this work is the test LOCA No. 1 FIX II in Studsvik (Sweden) which also served as the OECD International Standard Problem 15. This report discusses the influence of different nodalizations, of different distributions of pressure, water and structural heat as well as of different bubble rise options, break flow coefficients, and heat transfer time steps. The most important result is that a simple RELAP 4/MOD6 model with less than 10 volumes is able to predict an experiment as LOCA No. 1 in FIX II successfully using only a fraction of the usual computing time. (Author)
A nodal model for the simulation of a PWR core
International Nuclear Information System (INIS)
Souza Pinto, R. de.
1981-06-01
A computer program FORTRAN language was developed to simulate the neutronic and thermal-hydraulic transient behaviour of a PWR reactor core. The reator power is calculated using a point kinectics model with six groups of delayed neutron precursors. The fission product decay heat was considered assuming three effective decay heat groups. A nodal model was employed for the treatment of heat transfer in the fuel rod, with integration of the heat equation by the lumped parameter technique. Axial conduction was neglected. A single-channel nodal model was developed for the thermo-hydrodynamic simulation using mass and energy conservation equations for the control volumes. The effect of the axial pressure variation was neglected. The computer program was tested, with good results, through the simulation of the transient behaviour of postulated accidents in a typical PWR. (Author) [pt
The variational nodal method: some history and recent activity
International Nuclear Information System (INIS)
Lewis, E.E.; Smith, M.A.; Palmiotti, G.
2005-01-01
The variational nodal method combines spherical harmonics expansions in angle with hybrid finite element techniques in space to obtain multigroup transport response matrix algorithms applicable to a wide variety of reactor physics problems. This survey briefly recounts the method's history and reviews its capabilities. Two methods for obtaining discretized equations in the form of response matrices are compared. The first is that contained the widely used VARIANT code, while the second incorporates more recently developed integral transport techniques into the variational nodal framework. The two approaches are combined with a finite sub-element formulation to treat heterogeneous nodes. Results are presented for application to a deep penetration problem and to an OECD benchmark consisting of LWR Mox fuel assemblies. Ongoing work is discussed. (authors)
The simplified P3 approach on a trigonal geometry in the nodal reactor code DYN3D
International Nuclear Information System (INIS)
Duerigen, S.; Fridman, E.
2011-01-01
DYN3D is a three-dimensional nodal diffusion code for steady-state and transient analyses of Light-Water Reactors with square and hexagonal fuel assembly geometries. Currently, several versions of the DYN3D code are available including a multi-group diffusion and a simplified P 3 (SP 3 ) neutron transport option. In this work, the multi-group SP 3 method based on trigonal-z geometry was developed. The method is applicable to the analysis of reactor cores with hexagonal fuel assemblies and allows flexible mesh refinement, which is of particular importance for WWER-type Pressurized Water Reactors as well as for innovative reactor concepts including block type High-Temperature Reactors and Sodium Fast Reactors. In this paper, the theoretical background for the trigonal SP 3 methodology is outlined and the results of a preliminary verification analysis are presented by means of a simplified WWER-440 core test example. The accordant cross sections and reference solutions were produced by the Monte Carlo code SERPENT. The DYN3D results are in good agreement with the reference solutions. The average deviation in the nodal power distribution is about 1%. (Authors)
Flow-based market coupling. Stepping stone towards nodal pricing?
International Nuclear Information System (INIS)
Van der Welle, A.J.
2012-07-01
For achieving one internal energy market for electricity by 2014, market coupling is deployed to integrate national markets into regional markets and ultimately one European electricity market. The extent to which markets can be coupled depends on the available transmission capacities between countries. Since interconnections are congested from time to time, congestion management methods are deployed to divide the scarce available transmission capacities over market participants. For further optimization of the use of available transmission capacities while maintaining current security of supply levels, flow-based market coupling (FBMC) will be implemented in the CWE region by 2013. Although this is an important step forward, important hurdles for efficient congestion management remain. Hence, flow based market coupling is compared to nodal pricing, which is often considered as the most optimal solution from theoretical perspective. In the context of decarbonised power systems it is concluded that advantages of nodal pricing are likely to exceed its disadvantages, warranting further development of FBMC in the direction of nodal pricing.
Non-linear triangle-based polynomial expansion nodal method for hexagonal core analysis
International Nuclear Information System (INIS)
Cho, Jin Young; Cho, Byung Oh; Joo, Han Gyu; Zee, Sung Qunn; Park, Sang Yong
2000-09-01
This report is for the implementation of triangle-based polynomial expansion nodal (TPEN) method to MASTER code in conjunction with the coarse mesh finite difference(CMFD) framework for hexagonal core design and analysis. The TPEN method is a variation of the higher order polynomial expansion nodal (HOPEN) method that solves the multi-group neutron diffusion equation in the hexagonal-z geometry. In contrast with the HOPEN method, only two-dimensional intranodal expansion is considered in the TPEN method for a triangular domain. The axial dependence of the intranodal flux is incorporated separately here and it is determined by the nodal expansion method (NEM) for a hexagonal node. For the consistency of node geometry of the MASTER code which is based on hexagon, TPEN solver is coded to solve one hexagonal node which is composed of 6 triangular nodes directly with Gauss elimination scheme. To solve the CMFD linear system efficiently, stabilized bi-conjugate gradient(BiCG) algorithm and Wielandt eigenvalue shift method are adopted. And for the construction of the efficient preconditioner of BiCG algorithm, the incomplete LU(ILU) factorization scheme which has been widely used in two-dimensional problems is used. To apply the ILU factorization scheme to three-dimensional problem, a symmetric Gauss-Seidel Factorization scheme is used. In order to examine the accuracy of the TPEN solution, several eigenvalue benchmark problems and two transient problems, i.e., a realistic VVER1000 and VVER440 rod ejection benchmark problems, were solved and compared with respective references. The results of eigenvalue benchmark problems indicate that non-linear TPEN method is very accurate showing less than 15 pcm of eigenvalue errors and 1% of maximum power errors, and fast enough to solve the three-dimensional VVER-440 problem within 5 seconds on 733MHz PENTIUM-III. In the case of the transient problems, the non-linear TPEN method also shows good results within a few minute of
Belkacemi, Y.; Kaidar-Person, O.; Poortmans, P.; Ozsahin, M.; Valli, M.-C.; Russell, N.; Kunkler, I.; Hermans, J.; Kuten, A.; van Tienhoven, G.; Westenberg, H.
2015-01-01
Predicting outcome of breast cancer (BC) patients based on sentinel lymph node (SLN) status without axillary lymph node dissection (ALND) is an area of uncertainty. It influences the decision-making for regional nodal irradiation (RNI). The aim of the NORA (NOdal RAdiotherapy) survey was to examine
Immunoarchitectural patterns in nodal marginal zone B-cell lymphoma: a study of 51 cases.
Salama, Mohamed E; Lossos, Izidore S; Warnke, Roger A; Natkunam, Yasodha
2009-07-01
Nodal marginal zone lymphoma (NMZL) represents a rare and heterogeneous group that lacks markers specific for the diagnosis. We evaluated morphologic and immunoarchitectural features of 51 NMZLs, and the following immunostains were performed: CD20, CD21, CD23, CD5, CD3, CD43, CD10, Ki-67, BCL1, BCL2, BCL6, HGAL, and LMO2. Four immunoarchitectural patterns were evident: diffuse (38 [75%]), well-formed nodular/follicular (5 [10%]), interfollicular (7 [14%]), and perifollicular (1 [2%]). Additional features included a monocytoid component (36 [71%]), admixed large cells (20 [39%]), plasma cells (24 [47%]), compartmentalizing stromal sclerosis (13 [25%]), and prominent blood vessel sclerosis (10 [20%]). CD21 highlighted disrupted follicular dendritic cell meshwork in 35 (71%) of 49 cases, and CD43 coexpression was present in 10 (24%) of 42 cases. A panel of germinal center-associated markers was helpful in eliminating cases of diffuse follicle center lymphoma. Our results highlight the histologic and immunoarchitectural spectrum of NMZL and the usefulness of immunohistochemical analysis for CD43, CD23, CD21, BCL6, HGAL, and LMO2 in the diagnosis of NMZL.
Multigrid solution of diffusion equations on distributed memory multiprocessor systems
International Nuclear Information System (INIS)
Finnemann, H.
1988-01-01
The subject is the solution of partial differential equations for simulation of the reactor core on high-performance computers. The parallelization and implementation of nodal multigrid diffusion algorithms on array and ring configurations of the DIRMU multiprocessor system is outlined. The particular iteration scheme employed in the nodal expansion method appears similarly efficient in serial and parallel environments. The combination of modern multi-level techniques with innovative hardware (vector-multiprocessor systems) provides powerful tools needed for real time simulation of physical systems. The parallel efficiencies range from 70 to 90%. The same performance is estimated for large problems on large multiprocessor systems being designed at present. (orig.) [de
Energy Technology Data Exchange (ETDEWEB)
Silva, Davi Jose M.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: davijmsilva@yahoo.com.br, E-mail: halves@iprj.uerj.br, E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Programa de Pos-Graduacao em Modelagem Computacional
2015-07-01
A spectral nodal method is developed for multigroup x,y-geometry discrete ordinates (S{sub N}) eigenvalue problems for nuclear reactor global calculations. This method uses the conventional multigroup SN discretized spatial balance nodal equations with two non-standard auxiliary equations: the spectral diamond (SD) auxiliary equations for the discretization nodes inside the fuel regions, and the spectral Green's function (SGF) auxiliary equations for the non-multiplying regions, such as the baffle and the reactor. This spectral nodal method is derived from the analytical general solution of the SN transverse integrated nodal equations with constant approximations for the transverse leakage terms within each discretization node. The SD and SGF auxiliary equations have parameters, which are determined to preserve the homogeneous and the particular components of these local general solutions. Therefore, we refer to the offered method as the hybrid SD-SGF-Constant Nodal (SD-SGF-CN) method. The S{sub N} discretized spatial balance equations, together with the SD and the SGF auxiliary equations form the SD-SGF-CN equations. We solve the SD-SGF-CN equations by using the one-node block inversion inner iterations (NBI), wherein the most recent estimates for the incoming group node-edge average or prescribed boundary conditions are used to evaluate the outgoing group node-edge average fluxes in the directions of the S{sub N} transport sweeps, for each estimate of the dominant eigenvalue in the conventional Power outer iterations. We show in numerical calculations that the SD-SGF-CN method is very accurate for coarse-mesh multigroup S{sub N} eigenvalue problems, even though the transverse leakage terms are approximated rather simply. (author)
International Nuclear Information System (INIS)
Silva, Davi Jose M.; Alves Filho, Hermes; Barros, Ricardo C.
2015-01-01
A spectral nodal method is developed for multigroup x,y-geometry discrete ordinates (S N ) eigenvalue problems for nuclear reactor global calculations. This method uses the conventional multigroup SN discretized spatial balance nodal equations with two non-standard auxiliary equations: the spectral diamond (SD) auxiliary equations for the discretization nodes inside the fuel regions, and the spectral Green's function (SGF) auxiliary equations for the non-multiplying regions, such as the baffle and the reactor. This spectral nodal method is derived from the analytical general solution of the SN transverse integrated nodal equations with constant approximations for the transverse leakage terms within each discretization node. The SD and SGF auxiliary equations have parameters, which are determined to preserve the homogeneous and the particular components of these local general solutions. Therefore, we refer to the offered method as the hybrid SD-SGF-Constant Nodal (SD-SGF-CN) method. The S N discretized spatial balance equations, together with the SD and the SGF auxiliary equations form the SD-SGF-CN equations. We solve the SD-SGF-CN equations by using the one-node block inversion inner iterations (NBI), wherein the most recent estimates for the incoming group node-edge average or prescribed boundary conditions are used to evaluate the outgoing group node-edge average fluxes in the directions of the S N transport sweeps, for each estimate of the dominant eigenvalue in the conventional Power outer iterations. We show in numerical calculations that the SD-SGF-CN method is very accurate for coarse-mesh multigroup S N eigenvalue problems, even though the transverse leakage terms are approximated rather simply. (author)
Radiotherapy studies and extra-nodal non-Hodgkin lymphomas, progress and challenges
DEFF Research Database (Denmark)
Specht, L
2012-01-01
Extra-nodal lymphomas may arise in any organ, and different histological subtypes occur in distinct patterns. Prognosis and treatment depend not only on the histological subtype and disease extent, but also on the particular involved extra-nodal organ. The clinical course and response to treatment...... for the more common extra-nodal organs, e.g. stomach, Waldeyer's ring, skin and brain, are fairly well known and show significant variation. A few randomised trials have been carried out testing the role of radiotherapy in these lymphomas. However, for most extra-nodal lymphomas, randomised trials have...... not been carried out, and treatment decisions are made on small patient series and extrapolations from nodal lymphomas. Hopefully, wide international collaboration will make controlled clinical trials possible in the less common extra-nodal lymphomas. Modern highly conformal radiotherapy allows better...
Solution and study of nodal neutron transport equation applying the LTSN-DiagExp method
International Nuclear Information System (INIS)
Hauser, Eliete Biasotto; Pazos, Ruben Panta; Vilhena, Marco Tullio de; Barros, Ricardo Carvalho de
2003-01-01
In this paper we report advances about the three-dimensional nodal discrete-ordinates approximations of neutron transport equation for Cartesian geometry. We use the combined collocation method of the angular variables and nodal approach for the spatial variables. By nodal approach we mean the iterated transverse integration of the S N equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTS N method, first applying the Laplace transform to the set of the nodal S N equations and then obtained the solution by symbolic computation. We include the LTS N method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTS N approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation. (author)
A Nodal-independent and tissue-intrinsic mechanism controls heart-looping chirality
Noël, Emily S.; Verhoeven, Manon; Lagendijk, Anne Karine; Tessadori, Federico; Smith, Kelly; Choorapoikayil, Suma; den Hertog, Jeroen; Bakkers, Jeroen
2013-11-01
Breaking left-right symmetry in bilateria is a major event during embryo development that is required for asymmetric organ position, directional organ looping and lateralized organ function in the adult. Asymmetric expression of Nodal-related genes is hypothesized to be the driving force behind regulation of organ laterality. Here we identify a Nodal-independent mechanism that drives asymmetric heart looping in zebrafish embryos. In a unique mutant defective for the Nodal-related southpaw gene, preferential dextral looping in the heart is maintained, whereas gut and brain asymmetries are randomized. As genetic and pharmacological inhibition of Nodal signalling does not abolish heart asymmetry, a yet undiscovered mechanism controls heart chirality. This mechanism is tissue intrinsic, as explanted hearts maintain ex vivo retain chiral looping behaviour and require actin polymerization and myosin II activity. We find that Nodal signalling regulates actin gene expression, supporting a model in which Nodal signalling amplifies this tissue-intrinsic mechanism of heart looping.
Park, C B; Dufort, D
2011-03-01
Nodal, a secreted signaling protein in the transforming growth factor-beta (TGF-β) superfamily, has established roles in vertebrate development. However, components of the Nodal signaling pathway are also expressed at the maternal-fetal interface and have been implicated in many processes of mammalian reproduction. Emerging evidence indicates that Nodal and its extracellular inhibitor Lefty are expressed in the uterus and complex interactions between the two proteins mediate menstruation, decidualization and embryo implantation. Furthermore, several studies have shown that Nodal from both fetal and maternal sources may regulate trophoblast cell fate and facilitate placentation as both embryonic and uterine-specific Nodal knockout mouse strains exhibit disrupted placenta morphology. Here we review the established and prospective roles of Nodal signaling in facilitating successful pregnancy, including recent evidence supporting a potential link to parturition and preterm birth. Copyright © 2011 Elsevier Ltd. All rights reserved.
Nodal wear model: corrosion in carbon blast furnace hearths
International Nuclear Information System (INIS)
Verdeja, L. F.; Gonzalez, R.; Alfonso, A.; Barbes, M. F.
2003-01-01
Criteria developed for the Nodal Wear Model (NWM) were applied to estimate the shape of the corrosion profiles that a blast furnace hearth may acquire during its campaign. Taking into account design of the hearth, the boundary conditions, the characteristics of the refractory materials used and the operation conditions of the blast furnace, simulation of wear profiles with central well, mushroom and elephant foot shape were accomplished. The foundations of the NWM are constructed considering that the corrosion of the refractory is a function of the temperature present at each point (node) of the liquid metal-refractory interface and the corresponding physical and chemical characteristics of the corrosive fluid. (Author) 31 refs
Mechanism of polyuria and natriuresis in atrioventricular nodal tachycardia.
Canepa-Anson, R; Williams, M; Marshall, J; Mitsuoka, T; Lightman, S; Sutton, R
1984-01-01
A woman with tachycardia associated with polyuria was investigated. Electrophysiological analysis showed that the tachycardia was an atrioventricular nodal re-entrant tachycardia. Programmed stimulation was then used to provoke and sustain the tachycardia for 40 minutes. Polyuria, with an appreciable increase in free water clearance, was observed. This was associated with reduction in plasma and urinary arginine vasopressin concentrations. Appreciable natriuresis also developed. These results support the hypothesis that the polyuria with increased free water clearance and the natriuresis occurring during sustained tachycardia in man are due to inhibition of secretion of vasopressin and the release of natriuretic factor. PMID:6434116
Approximate Schur complement preconditioning of the lowest order nodal discretizations
Energy Technology Data Exchange (ETDEWEB)
Moulton, J.D.; Ascher, U.M. [Univ. of British Columbia, Vancouver, British Columbia (Canada); Morel, J.E. [Los Alamos National Lab., NM (United States)
1996-12-31
Particular classes of nodal methods and mixed hybrid finite element methods lead to equivalent, robust and accurate discretizations of 2nd order elliptic PDEs. However, widespread popularity of these discretizations has been hindered by the awkward linear systems which result. The present work exploits this awkwardness, which provides a natural partitioning of the linear system, by defining two optimal preconditioners based on approximate Schur complements. Central to the optimal performance of these preconditioners is their sparsity structure which is compatible with Dendy`s black box multigrid code.
Evaluation of the use of nodal methods for MTR neutronic analysis
Energy Technology Data Exchange (ETDEWEB)
Reitsma, F.; Mueller, E.Z.
1997-08-01
Although modern nodal methods are used extensively in the nuclear power industry, their use for research reactor analysis has been very limited. The suitability of nodal methods for material testing reactor analysis is investigated with the emphasis on the modelling of the core region (fuel assemblies). The nodal approach`s performance is compared with that of the traditional finite-difference fine mesh approach. The advantages of using nodal methods coupled with integrated cross section generation systems are highlighted, especially with respect to data preparation, simplicity of use and the possibility of performing a great variety of reactor calculations subject to strict time limitations such as are required for the RERTR program.
Nodal line optimization and its application to violin top plate design
Yu, Yonggyun; Jang, In Gwun; Kim, In Kyum; Kwak, Byung Man
2010-10-01
In the literature, most problems of structural vibration have been formulated to adjust a specific natural frequency: for example, to maximize the first natural frequency. In musical instruments like a violin; however, mode shapes are equally important because they are related to sound quality in the way that natural frequencies are related to the octave. The shapes of nodal lines, which represent the natural mode shapes, are generally known to have a unique feature for good violins. Among the few studies on mode shape optimization, one typical study addresses the optimization of nodal point location for reducing vibration in a one-dimensional beam structure. However, nodal line optimization, which is required in violin plate design, has not yet been considered. In this paper, the central idea of controlling the shape of the nodal lines is proposed and then applied to violin top plate design. Finite element model for a violin top plate was constructed using shell elements. Then, optimization was performed to minimize the square sum of the displacement of selected nodes located along the target nodal lines by varying the thicknesses of the top plate. We conducted nodal line optimization for the second and the fifth modes together at the same time, and the results showed that the nodal lines obtained match well with the target nodal lines. The information on plate thickness distribution from nodal line optimization would be valuable for tailored trimming of a violin top plate for the given performances.
Time-dependent patterning of the mesoderm and endoderm by Nodal signals in zebrafish
Directory of Open Access Journals (Sweden)
Dougan Scott T
2007-03-01
Full Text Available Abstract Background The vertebrate body plan is generated during gastrulation with the formation of the three germ layers. Members of the Nodal-related subclass of the TGF-β superfamily induce and pattern the mesoderm and endoderm in all vertebrates. In zebrafish, two nodal-related genes, called squint and cyclops, are required in a dosage-dependent manner for the formation of all derivatives of the mesoderm and endoderm. These genes are expressed dynamically during the blastula stages and may have different roles at different times. This question has been difficult to address because conditions that alter the timing of nodal-related gene expression also change Nodal levels. We utilized a pharmacological approach to conditionally inactivate the ALK 4, 5 and 7 receptors during the blastula stages without disturbing earlier signaling activity. This permitted us to directly examine when Nodal signals specify cell types independently of dosage effects. Results We show that two drugs, SB-431542 and SB-505124, completely block the response to Nodal signals when added to embryos after the mid-blastula transition. By blocking Nodal receptor activity at later stages, we demonstrate that Nodal signaling is required from the mid-to-late blastula period to specify sequentially, the somites, notochord, blood, Kupffer's vesicle, hatching gland, heart, and endoderm. Blocking Nodal signaling at late times prevents specification of cell types derived from the embryo margin, but not those from more animal regions. This suggests a linkage between cell fate and length of exposure to Nodal signals. Confirming this, cells exposed to a uniform Nodal dose adopt progressively more marginal fates with increasing lengths of exposure. Finally, cell fate specification is delayed in squint mutants and accelerated when Nodal levels are elevated. Conclusion We conclude that (1 Nodal signals are most active during the mid-to-late blastula stages, when nodal-related gene
Energy Technology Data Exchange (ETDEWEB)
Couto, Nozimar do
2003-07-01
Diffusion theory is traditionally applied to nuclear reactor global calculations. Based on the good results generated by the one-dimensional spectral nodal diffusion (SND) method for benchmark problems, we offer the SND method for nuclear reactor global calculations in X,Y geometry. In this method, the continuity equation and Flick law are transverse integrated in each spatial direction leading to a system of two 'one-dimensional' equations coupled by the transverse leakage terms. We then apply the SND method to numerically solve this system with constant approximations for the transverse leakage terms. We perform a spectral analysis to determine the local general solution of each 'one-dimensional' nodal equation with flat approximation for the transverse leakages. We used special auxiliary equations with parameters that are to be determined in order to preserve the analytical general solutions in the numerical algorithm. By considering continuity conditions at the node interfaces and appropriate boundary conditions, we obtain a solvable system of discretized equations involving the node-edge average scalar fluxes at each estimate of the dominant eigenvalue (k{sub eff}) in the outer power iterations. As we considered approximations to the transverse leakages, the SND method is not free of spatial truncation errors. Nevertheless, it generated good results for the typical model problems that we considered. (author)
Energy Technology Data Exchange (ETDEWEB)
Couto, Nozimar do
2003-07-01
Diffusion theory is traditionally applied to nuclear reactor global calculations. Based on the good results generated by the one-dimensional spectral nodal diffusion (SND) method for benchmark problems, we offer the SND method for nuclear reactor global calculations in X,Y geometry. In this method, the continuity equation and Flick law are transverse integrated in each spatial direction leading to a system of two 'one-dimensional' equations coupled by the transverse leakage terms. We then apply the SND method to numerically solve this system with constant approximations for the transverse leakage terms. We perform a spectral analysis to determine the local general solution of each 'one-dimensional' nodal equation with flat approximation for the transverse leakages. We used special auxiliary equations with parameters that are to be determined in order to preserve the analytical general solutions in the numerical algorithm. By considering continuity conditions at the node interfaces and appropriate boundary conditions, we obtain a solvable system of discretized equations involving the node-edge average scalar fluxes at each estimate of the dominant eigenvalue (k{sub eff}) in the outer power iterations. As we considered approximations to the transverse leakages, the SND method is not free of spatial truncation errors. Nevertheless, it generated good results for the typical model problems that we considered. (author)
Bruce, William J; Maxwell, E A; Sneddon, I N
1963-01-01
Analytic Trigonometry details the fundamental concepts and underlying principle of analytic geometry. The title aims to address the shortcomings in the instruction of trigonometry by considering basic theories of learning and pedagogy. The text first covers the essential elements from elementary algebra, plane geometry, and analytic geometry. Next, the selection tackles the trigonometric functions of angles in general, basic identities, and solutions of equations. The text also deals with the trigonometric functions of real numbers. The fifth chapter details the inverse trigonometric functions
Exact boundary controllability of nodal profile for quasilinear hyperbolic systems
Li, Tatsien; Gu, Qilong
2016-01-01
This book provides a comprehensive overview of the exact boundary controllability of nodal profile, a new kind of exact boundary controllability stimulated by some practical applications. This kind of controllability is useful in practice as it does not require any precisely given final state to be attained at a suitable time t=T by means of boundary controls, instead it requires the state to exactly fit any given demand (profile) on one or more nodes after a suitable time t=T by means of boundary controls. In this book we present a general discussion of this kind of controllability for general 1-D first order quasilinear hyperbolic systems and for general 1-D quasilinear wave equations on an interval as well as on a tree-like network using a modular-structure construtive method, suggested in LI Tatsien's monograph "Controllability and Observability for Quasilinear Hyperbolic Systems"(2010), and we establish a complete theory on the local exact boundary controllability of nodal profile for 1-D quasilinear hyp...
Hereditary bone dysplasia with pathological fractures and nodal osteoarthropathy
International Nuclear Information System (INIS)
Arendse, Regan; Brink, Paul; Beighton, Peter
2009-01-01
A father and daughter both had multiple pathological fractures and nodal osteoarthropathy. The father, aged 50 years, had at least 20 healed fractures of the axial and appendicular skeleton, sustained by minor trauma over his 50-year lifespan, many of which had been surgically fixed prior to his first presentation to us. Fractures of the clavicles, thoracic cage and long bones of the arms and legs, had healed with malalignment and deformity. Healed fractures were complicated by ankylosis of the cervical vertebrae and both elbows. He also had osteoarthritis of the hands, with exuberant osteophytosis, and profound perceptive deafness. His general health was good, his intellect and facies were normal, and his sclerae were white. The daughter, aged 27 years, had sustained at least seven fractures of the axial and appendicular skeleton following trivial injuries, in distribution similar to those of the father. She had also experienced painful swelling of the fingers, which preceded progressive development of nodal osteoarthropathy. Her hearing was normal. In both individuals, biochemical and immunological investigations yielded normal results. It was not possible for molecular studies to be undertaken. Pedigree data were consistent with autosomal dominant transmission, and this disorder appeared to be a previously undocumented heritable skeletal dysplasia. (orig.)
Hereditary bone dysplasia with pathological fractures and nodal osteoarthropathy
Energy Technology Data Exchange (ETDEWEB)
Arendse, Regan [University of Stellenbosch, Department of Medicine, Tygerberg Hospital, Stellenbosch (South Africa); University of Cape Town, Division of Rheumatology, Groote Schuur Hospital, Cape Town (South Africa); Brink, Paul [University of Stellenbosch, Department of Medicine, Tygerberg Hospital, Stellenbosch (South Africa); Beighton, Peter [University of Cape Town, Division of Human Genetics, Faculty of Health Sciences, Cape Town (South Africa)
2009-12-15
A father and daughter both had multiple pathological fractures and nodal osteoarthropathy. The father, aged 50 years, had at least 20 healed fractures of the axial and appendicular skeleton, sustained by minor trauma over his 50-year lifespan, many of which had been surgically fixed prior to his first presentation to us. Fractures of the clavicles, thoracic cage and long bones of the arms and legs, had healed with malalignment and deformity. Healed fractures were complicated by ankylosis of the cervical vertebrae and both elbows. He also had osteoarthritis of the hands, with exuberant osteophytosis, and profound perceptive deafness. His general health was good, his intellect and facies were normal, and his sclerae were white. The daughter, aged 27 years, had sustained at least seven fractures of the axial and appendicular skeleton following trivial injuries, in distribution similar to those of the father. She had also experienced painful swelling of the fingers, which preceded progressive development of nodal osteoarthropathy. Her hearing was normal. In both individuals, biochemical and immunological investigations yielded normal results. It was not possible for molecular studies to be undertaken. Pedigree data were consistent with autosomal dominant transmission, and this disorder appeared to be a previously undocumented heritable skeletal dysplasia. (orig.)
Dirac Magnon Nodal Loops in Quasi-2D Quantum Magnets.
Owerre, S A
2017-07-31
In this report, we propose a new concept of one-dimensional (1D) closed lines of Dirac magnon nodes in two-dimensional (2D) momentum space of quasi-2D quantum magnetic systems. They are termed "2D Dirac magnon nodal-line loops". We utilize the bilayer honeycomb ferromagnets with intralayer coupling J and interlayer coupling J L , which is realizable in the honeycomb chromium compounds CrX 3 (X ≡ Br, Cl, and I). However, our results can also exist in other layered quasi-2D quantum magnetic systems. Here, we show that the magnon bands of the bilayer honeycomb ferromagnets overlap for J L ≠ 0 and form 1D closed lines of Dirac magnon nodes in 2D momentum space. The 2D Dirac magnon nodal-line loops are topologically protected by inversion and time-reversal symmetry. Furthermore, we show that they are robust against weak Dzyaloshinskii-Moriya interaction Δ DM magnon edge modes.
Federal Laboratory Consortium — The Analytical Labspecializes in Oil and Hydraulic Fluid Analysis, Identification of Unknown Materials, Engineering Investigations, Qualification Testing (to support...
Energy Technology Data Exchange (ETDEWEB)
Tres, Anderson [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada; Becker Picoloto, Camila [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Prolo Filho, Joao Francisco [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Inst de Matematica, Estatistica e Fisica; Dias da Cunha, Rudnei; Basso Barichello, Liliane [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Inst de Matematica
2014-04-15
In this work a study of two-dimensional fixed-source neutron transport problems, in Cartesian geometry, is reported. The approach reduces the complexity of the multidimensional problem using a combination of nodal schemes and the Analytical Discrete Ordinates Method (ADO). The unknown leakage terms on the boundaries that appear from the use of the derivation of the nodal scheme are incorporated to the problem source term, such as to couple the one-dimensional integrated solutions, made explicit in terms of the x and y spatial variables. The formulation leads to a considerable reduction of the order of the associated eigenvalue problems when combined with the usual symmetric quadratures, thereby providing solutions that have a higher degree of computational efficiency. Reflective-type boundary conditions are introduced to represent the domain on a simpler form than that previously considered in connection with the ADO method. Numerical results obtained with the technique are provided and compared to those present in the literature. (orig.)
International Nuclear Information System (INIS)
Kim, Kyung-O; Jeong, Hae Sun; Jo, Daeseong
2017-01-01
Highlights: • Employing the Radial Point Interpolation Method (RPIM) in numerical analysis of multi-group neutron-diffusion equation. • Establishing mathematical formation of modified multi-group neutron-diffusion equation by RPIM. • Performing the numerical analysis for 2D critical problem. - Abstract: A mesh-free method is introduced to overcome the drawbacks (e.g., mesh generation and connectivity definition between the meshes) of mesh-based (nodal) methods such as the finite-element method and finite-difference method. In particular, the Point Interpolation Method (PIM) using a radial basis function is employed in the numerical analysis for the multi-group neutron-diffusion equation. The benchmark calculations are performed for the 2D homogeneous and heterogeneous problems, and the Multiquadrics (MQ) and Gaussian (EXP) functions are employed to analyze the effect of the radial basis function on the numerical solution. Additionally, the effect of the dimensionless shape parameter in those functions on the calculation accuracy is evaluated. According to the results, the radial PIM (RPIM) can provide a highly accurate solution for the multiplication eigenvalue and the neutron flux distribution, and the numerical solution with the MQ radial basis function exhibits the stable accuracy with respect to the reference solutions compared with the other solution. The dimensionless shape parameter directly affects the calculation accuracy and computing time. Values between 1.87 and 3.0 for the benchmark problems considered in this study lead to the most accurate solution. The difference between the analytical and numerical results for the neutron flux is significantly increased in the edge of the problem geometry, even though the maximum difference is lower than 4%. This phenomenon seems to arise from the derivative boundary condition at (x,0) and (0,y) positions, and it may be necessary to introduce additional strategy (e.g., the method using fictitious points and
Reactivity Coefficient Calculation for AP1000 Reactor Using the NODAL3 Code
Pinem, Surian; Malem Sembiring, Tagor; Tukiran; Deswandri; Sunaryo, Geni Rina
2018-02-01
The reactivity coefficient is a very important parameter for inherent safety and stability of nuclear reactors operation. To provide the safety analysis of the reactor, the calculation of changes in reactivity caused by temperature is necessary because it is related to the reactor operation. In this paper, the temperature reactivity coefficients of fuel and moderator of the AP1000 core are calculated, as well as the moderator density and boron concentration. All of these coefficients are calculated at the hot full power condition (HFP). All neutron diffusion constant as a function of temperature, water density and boron concentration were generated by the SRAC2006 code. The core calculations for determination of the reactivity coefficient parameter are done by using NODAL3 code. The calculation results show that the fuel temperature, moderator temperature and boron reactivity coefficients are in the range between -2.613 pcm/°C to -4.657pcm/°C, -1.00518 pcm/°C to 1.00649 pcm/°C and -9.11361 pcm/ppm to -8.0751 pcm/ppm, respectively. For the water density reactivity coefficients, the positive reactivity occurs at the water temperature less than 190 °C. The calculation results show that the reactivity coefficients are accurate because the results have a very good agreement with the design value.
Benchmarking of the PHOENIX-P/ANC [Advanced Nodal Code] advanced nuclear design system
International Nuclear Information System (INIS)
Nguyen, T.Q.; Liu, Y.S.; Durston, C.; Casadei, A.L.
1988-01-01
At Westinghouse, an advanced neutronic methods program was designed to improve the quality of the predictions, enhance flexibility in designing advanced fuel and related products, and improve design lead time. Extensive benchmarking data is presented to demonstrate the accuracy of the Advanced Nodal Code (ANC) and the PHOENIX-P advanced lattice code. Qualification data to demonstrate the accuracy of ANC include comparison of key physics parameters against a fine-mesh diffusion theory code, TORTISE. Benchmarking data to demonstrate the validity of the PHOENIX-P methodologies include comparison of physics predictions against critical experiments, isotopics measurements and measured power distributions from spatial criticals. The accuracy of the PHOENIX-P/ANC Advanced Design System is demonstrated by comparing predictions of hot zero power physics parameters and hot full power core follow against measured data from operating reactors. The excellent performance of this system for a broad range of comparisons establishes the basis for implementation of these tools for core design, licensing and operational follow of PWR [pressurized water reactor] cores at Westinghouse
Assessment of Effect on LBLOCA PCT for Change in Upper Head Nodalization
International Nuclear Information System (INIS)
Kang, Dong Gu; Huh, Byung Gil; Yoo, Seung Hun; Bang, Youngseok; Seul, Kwangwon; Cho, Daehyung
2014-01-01
In this study, the best estimate plus uncertainty (BEPU) analysis of LBLOCA for original and modified nodalizations was performed, and the effect on LBLOCA PCT for change in upper head nodalization was assessed. In this study, the best estimate plus uncertainty (BEPU) analysis of LBLOCA for original and modified nodalizations was performed, and the effect on LBLOCA PCT for change in upper head nodalization was assessed. It is confirmed that modification of upper head nodalization influences PCT behavior, especially in the reflood phase. In conclusions, the modification of nodalization to reflect design characteristic of upper head temperature should be done to predict PCT behavior accurately in LBLOCA analysis. In the best estimate (BE) method with the uncertainty evaluation, the system nodalization is determined by the comparative studies of the experimental data. Up to now, it was assumed that the temperature of the upper dome in OPR-1000 was close to that of the cold leg. However, it was found that the temperature of the upper head/dome might be a little lower than or similar to that of the hot leg through the evaluation of the detailed design data. Since the higher upper head temperature affects blowdown quenching and peak cladding temperature in the reflood phase, the nodalization for upper head should be modified
Diffusion Influenced Adsorption Kinetics.
Miura, Toshiaki; Seki, Kazuhiko
2015-08-27
When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.
Opposing nodal and BMP signals regulate left-right asymmetry in the sea urchin larva.
Directory of Open Access Journals (Sweden)
Yi-Jyun Luo
Full Text Available Nodal and BMP signals are important for establishing left-right (LR asymmetry in vertebrates. In sea urchins, Nodal signaling prevents the formation of the rudiment on the right side. However, the opposing pathway to Nodal signaling during LR axis establishment is not clear. Here, we revealed that BMP signaling is activated in the left coelomic pouch, specifically in the veg2 lineage, but not in the small micromeres. By perturbing BMP activities, we demonstrated that BMP signaling is required for activating the expression of the left-sided genes and the formation of the left-sided structures. On the other hand, Nodal signals on the right side inhibit BMP signaling and control LR asymmetric separation and apoptosis of the small micromeres. Our findings show that BMP signaling is the positive signal for left-sided development in sea urchins, suggesting that the opposing roles of Nodal and BMP signals in establishing LR asymmetry are conserved in deuterostomes.
Directory of Open Access Journals (Sweden)
Bhalaghuru Chokkalingam Mani, MD
2014-01-01
Full Text Available More than half a century has passed since the concept of dual atrioventricular (AV nodal pathways physiology was conceived. Dual AV nodal pathways have been shown to be responsible for many clinical arrhythmia syndromes, most notably AV nodal reentrant tachycardia. Although there has been a considerable amount of research on this topic, the subject of dual AV nodal pathways physiology remains heavily debated and discussed. Despite advances in understanding arrhythmia mechanisms and the widespread use of invasive electrophysiologic studies, there is still disagreement on the anatomy and physiology of the AV node that is the basis of discontinuous antegrade AV conduction. The purpose of this paper is to review the concept of dual AV nodal pathways physiology and its varied electrocardiographic manifestations.
Lambrecht, L.; Lamert, A.; Friederich, W.; Möller, T.; Boxberg, M. S.
2018-03-01
A nodal discontinuous Galerkin (NDG) approach is developed and implemented for the computation of viscoelastic wavefields in complex geological media. The NDG approach combines unstructured tetrahedral meshes with an element-wise, high-order spatial interpolation of the wavefield based on Lagrange polynomials. Numerical fluxes are computed from an exact solution of the heterogeneous Riemann problem. Our implementation offers capabilities for modelling viscoelastic wave propagation in 1-D, 2-D and 3-D settings of very different spatial scale with little logistical overhead. It allows the import of external tetrahedral meshes provided by independent meshing software and can be run in a parallel computing environment. Computation of adjoint wavefields and an interface for the computation of waveform sensitivity kernels are offered. The method is validated in 2-D and 3-D by comparison to analytical solutions and results from a spectral element method. The capabilities of the NDG method are demonstrated through a 3-D example case taken from tunnel seismics which considers high-frequency elastic wave propagation around a curved underground tunnel cutting through inclined and faulted sedimentary strata. The NDG method was coded into the open-source software package NEXD and is available from GitHub.
Diffusion effects in undulator radiation
Directory of Open Access Journals (Sweden)
Ilya Agapov
2014-11-01
Full Text Available Quantum diffusion effects in undulator radiation in semiclassical approximation are considered. Short-term effects on the electron beam motion are discussed and it is shown that approaches based on diffusion approximation with drift-diffusion coefficients derived from undulator or bending magnet radiation spectrum, and on Poisson statistics with radiation spectrum defined by the local beding field, all lead to similar results in terms of electron energy spread for cases of practical interest. An analytical estimate of the influence of quantum diffusion on the undulator radiation spectrum is derived.
Burdette, A C
1971-01-01
Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st
An integral nodal variational method for multigroup criticality calculations
International Nuclear Information System (INIS)
Lewis, E.E.; Tsoulfanidis, N.
2003-01-01
An integral formulation of the variational nodal method is presented and applied to a series of benchmark critically problems. The method combines an integral transport treatment of the even-parity flux within the spatial node with an odd-parity spherical harmonics expansion of the Lagrange multipliers at the node interfaces. The response matrices that result from this formulation are compatible with those in the VARIANT code at Argonne National Laboratory. Either homogeneous or heterogeneous nodes may be employed. In general, for calculations requiring higher-order angular approximations, the integral method yields solutions with comparable accuracy while requiring substantially less CPU time and memory than the standard spherical harmonics expansion using the same spatial approximations. (author)
On-line application of the PANTHER advanced nodal code
International Nuclear Information System (INIS)
Hutt, P.K.; Knight, M.P.
1992-01-01
Over the last few years, Nuclear Electric has developed an integrated core performance code package for both light water reactors (LWRs) and advanced gas-cooled reactors (AGRs) that can perform a comprehensive range of calculations for fuel cycle design, safety analysis, and on-line operational support for such plants. The package consists of the following codes: WIMS for lattice physics, PANTHER whole reactor nodal flux and AGR thermal hydraulics, VIPRE for LWR thermal hydraulics, and ENIGMA for fuel performance. These codes are integrated within a UNIX-based interactive system called the Reactor Physics Workbench (RPW), which provides an interactive graphic user interface and quality assurance records/data management. The RPW can also control calculational sequences and data flows. The package has been designed to run both off-line and on-line accessing plant data through the RPW
Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems
Leuschner, Matthias; Fritzen, Felix
2017-11-01
Fourier-based homogenization schemes are useful to analyze heterogeneous microstructures represented by 2D or 3D image data. These iterative schemes involve discrete periodic convolutions with global ansatz functions (mostly fundamental solutions). The convolutions are efficiently computed using the fast Fourier transform. FANS operates on nodal variables on regular grids and converges to finite element solutions. Compared to established Fourier-based methods, the number of convolutions is reduced by FANS. Additionally, fast iterations are possible by assembling the stiffness matrix. Due to the related memory requirement, the method is best suited for medium-sized problems. A comparative study involving established Fourier-based homogenization schemes is conducted for a thermal benchmark problem with a closed-form solution. Detailed technical and algorithmic descriptions are given for all methods considered in the comparison. Furthermore, many numerical examples focusing on convergence properties for both thermal and mechanical problems, including also plasticity, are presented.
Nodal domains on isospectral quantum graphs: the resolution of isospectrality?
International Nuclear Information System (INIS)
Band, Ram; Shapira, Talia; Smilansky, Uzy
2006-01-01
We present and discuss isospectral quantum graphs which are not isometric. These graphs are the analogues of the isospectral domains in R 2 which were introduced recently in Gordon et al (1992 Bull. Am. Math. Soc. 27 134-8), Chapman (1995 Am. Math. Mon. 102 124), Buser et al (1994 Int. Math. Res. Not. 9 391-400), Okada and Shudo (2001 J. Phys. A: Math. Gen. 34 5911-22), Jakobson et al (2006 J. Comput. Appl. Math. 194 141-55) and Levitin et al (2006 J. Phys. A: Math. Gen. 39 2073-82)) all based on Sunada's construction of isospectral domains (Sunada T 1985 Ann. Math. 121 196-86). After presenting some of the properties of these graphs, we discuss a few examples which support the conjecture that by counting the nodal domains of the corresponding eigenfunctions one can resolve the isospectral ambiguity
INTERMITTENT ANTIARYTHMIC THERAPY OF ARIOVENTICULAR NODAL REENTRY TACHYCARDIA IN CHILDREN
Directory of Open Access Journals (Sweden)
Boris Djindjic
2008-04-01
Full Text Available Until recent advances in pharmacology and clinical cardiology regarding farmacodynamics of antiarrhythmic drugs and their efficiency in patients with refractory paroxysmal supraventricular tachycardia, chronic prophylactic therapy was the only treatment option for patients refusing catheter ablation. Another treatment option, also known by eponym “pill in pocket” have been shown to be equally useful and efficacious.The aim of our study was prospective examination of children with refractory atrioventricular nodal reentry tachycardia (AVNRT who were withdrawn from chronic antiarrhythmic prophylactic therapy and started with intermittent oral beta blocker treatment (propranolol at dosage 1 mg/kg - max 80 mg.Twelve children (8 boys and 4 girls with AVNRT were included in the study. Four children did not have arrhythmia during first six months after withdrawal and 7 were successfully treated without complication.Intermittent antiarrhythmic therapy in children with AVNRT could be very efficacious and useful treatment option which significantly improves their quality of life.
CAISO flicks switch on nodal scheme and lights stay on
Energy Technology Data Exchange (ETDEWEB)
NONE
2009-06-15
In 2000-01, two years after introducing a competitive wholesale power auction in California - with a separate day-ahead zonal market operated by the California Power Exchange and a zonal market for ancillary services and balancing energy operated by the California Independent System Operator (CAISO) - the California market collapsed from exorbitant prices, flagrant gaming, and abuse of market power. Nine years later, CAISO introduced a nodal pricing auction for the wholesale market in April, replacing the zonal scheme, which was among many causes of the original market's demise. With nearly 3,000 nodes on the network, high prices in one region do not affect prices everywhere on the system. After investing some $200 million to upgrade the software, countless delays, and 18 months of market simulation and testing, the new auction was introduced and nothing unusual happened.
Ultrasound beam characteristics of a symmetric nodal origami based array
Bilgunde, Prathamesh N.; Bond, Leonard J.
2018-04-01
Origami-the ancient art of paper folding-is being explored in acoustics for effective focusing of sound. In this short communication, we present a numerical investigation of beam characteristics for an origami based ultrasound array. A spatial re-configuration of array elements is performed based upon the symmetric nodal origami. The effect of fold angle on the ultrasound beam is evaluated using frequency domain and transient finite element analysis. It was found that increase in the fold angle reduces near field length by 58% and also doubles the beam intensity as compared to the linear array. Transient analysis also indicated 80% reduction in the -6dB beam width, which can improve the lateral resolution of phased array. Such a spatially re-configurable array could potentially be used in the future to reduce the cost of electronics in the phased array instrumentation.
Space-angle approximations in the variational nodal method
International Nuclear Information System (INIS)
Lewis, E. E.; Palmiotti, G.; Taiwo, T.
1999-01-01
The variational nodal method is formulated such that the angular and spatial approximations maybe examined separately. Spherical harmonic, simplified spherical harmonic, and discrete ordinate approximations are coupled to the primal hybrid finite element treatment of the spatial variables. Within this framework, two classes of spatial trial functions are presented: (1) orthogonal polynomials for the treatment of homogeneous nodes and (2) bilinear finite subelement trial functions for the treatment of fuel assembly sized nodes in which fuel-pin cell cross sections are represented explicitly. Polynomial and subelement trial functions are applied to benchmark water-reactor problems containing MOX fuel using spherical harmonic and simplified spherical harmonic approximations. The resulting accuracy and computing costs are compared
Comparison of PANTHER nodal solutions in hexagonal-z geometry
International Nuclear Information System (INIS)
Knight, M.; Hutt, P.; Lewis, I.
1995-01-01
The reactor physics code PANTHER has been extended to hexagonal geometries. Steady-state, depletion, and transient calculations with feedback can all be performed. Two hexagonal nodal flux solutions have been developed. In the first method, transverse integration is performed exactly as in the rectangular case. The resulting transverse integrated equation has singular terms, which are simply ignored. The second approach applies a conformal mapping that transforms the hexagon onto a rectangle. Pin power reconstruction has also been developed with both methods. For a benchmark VVER-1000 reactor depletion problem, both methods give accurate results for standard depletion calculations. In the more extreme situation with all rods inserted, the simpler method breaks down. However, the accuracy of the conformal solution was found to be excellent in all cases studied
Contemporary Management of Recurrent Nodal Disease in Differentiated Thyroid Carcinoma
Na’ara, Shorook; Amit, Moran; Fridman, Eran; Gil, Ziv
2016-01-01
Differentiated thyroid carcinoma (DTC) comprises over 90% of thyroid tumors and includes papillary and follicular carcinomas. Patients with DTC have an excellent prognosis, with a 10-year survival rate of over 90%. However, the risk of recurrent tumor ranges between 5% and 30% within 10 years of the initial diagnosis. Cervical lymph node disease accounts for the majority of recurrences and in most cases is detected during follow-up by ultrasound or elevated levels of serum thyroglobulin. Recurrent disease is accompanied by increased morbidity. The mainstay of treatment of nodal recurrence is surgical management. We provide an overview of the literature addressing surgical management of recurrent or persistent lymph node disease in patients with DTC. PMID:26886954
Error Estimation and Accuracy Improvements in Nodal Transport Methods
International Nuclear Information System (INIS)
Zamonsky, O.M.
2000-01-01
The accuracy of the solutions produced by the Discrete Ordinates neutron transport nodal methods is analyzed.The obtained new numerical methodologies increase the accuracy of the analyzed scheems and give a POSTERIORI error estimators. The accuracy improvement is obtained with new equations that make the numerical procedure free of truncation errors and proposing spatial reconstructions of the angular fluxes that are more accurate than those used until present. An a POSTERIORI error estimator is rigurously obtained for one dimensional systems that, in certain type of problems, allows to quantify the accuracy of the solutions. From comparisons with the one dimensional results, an a POSTERIORI error estimator is also obtained for multidimensional systems. LOCAL indicators, which quantify the spatial distribution of the errors, are obtained by the decomposition of the menctioned estimators. This makes the proposed methodology suitable to perform adaptive calculations. Some numerical examples are presented to validate the theoretical developements and to illustrate the ranges where the proposed approximations are valid
Nodal wear model: corrosion in carbon blast furnace hearths
Directory of Open Access Journals (Sweden)
Verdeja, L. F.
2003-06-01
Full Text Available Criterions developed for the Nodal Wear Model (NWM were applied to estimate the shape of the corrosion profiles that a blast furnace hearth may acquire during its campaign. Taking into account design of the hearth, the boundary conditions, the characteristics of the refractory materials used and the operation conditions of the blast furnace, simulation of wear profiles with central well, mushroom and elephant foot shape were accomplished. The foundations of the NWM are constructed considering that the corrosion of the refractory is a function of the temperature present at each point (node of the liquid metal-refractory interface and the corresponding physical and chemical characteristics of the corrosive fluid.
Se aplican los criterios del Modelo de Desgaste Nodal (MDN para la estimación de los perfiles de corrosión que podría ir adquiriendo el crisol de un homo alto durante su campaña. Atendiendo al propio diseño del crisol, a las condiciones límites de contorno, a las características del material refractario utilizado y a las condiciones de operación del horno, se consiguen simular perfiles de desgaste con "pozo central", con "forma de seta" ó de "pie de elefante". Los fundamentos del MDN se apoyan en la idea de considerar que la corrosión del refractario es función de la temperatura que el sistema pueda presentar en cada punto (nodo de la intercara refractario-fundido y de las correspondientes características físico-químicas del fluido corrosivo.
Energy Technology Data Exchange (ETDEWEB)
Chae, Myeong Hu; Lee, Hu Jun; Kim, Ha Seok
1989-02-15
This book give explanations on analytical chemistry with ten chapters, which deal with development of analytical chemistry, the theory of error with definition and classification, sample and treatment gravimetry on general process of gravimetry in aqueous solution and non-aqueous solution, precipitation titration about precipitation reaction and types, complexometry with summary and complex compound, oxidation-reduction equilibrium on electrode potential and potentiometric titration, solvent extraction and chromatograph and experiment with basic operation for chemical experiment.
International Nuclear Information System (INIS)
Chae, Myeong Hu; Lee, Hu Jun; Kim, Ha Seok
1989-02-01
This book give explanations on analytical chemistry with ten chapters, which deal with development of analytical chemistry, the theory of error with definition and classification, sample and treatment gravimetry on general process of gravimetry in aqueous solution and non-aqueous solution, precipitation titration about precipitation reaction and types, complexometry with summary and complex compound, oxidation-reduction equilibrium on electrode potential and potentiometric titration, solvent extraction and chromatograph and experiment with basic operation for chemical experiment.
Strong Stationary Duality for Diffusion Processes
Fill, James Allen; Lyzinski, Vince
2014-01-01
We develop the theory of strong stationary duality for diffusion processes on compact intervals. We analytically derive the generator and boundary behavior of the dual process and recover a central tenet of the classical Markov chain theory in the diffusion setting by linking the separation distance in the primal diffusion to the absorption time in the dual diffusion. We also exhibit our strong stationary dual as the natural limiting process of the strong stationary dual sequence of a well ch...
A simple nodal force distribution method in refined finite element meshes
Energy Technology Data Exchange (ETDEWEB)
Park, Jai Hak [Chungbuk National University, Chungju (Korea, Republic of); Shin, Kyu In [Gentec Co., Daejeon (Korea, Republic of); Lee, Dong Won [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Cho, Seungyon [National Fusion Research Institute, Daejeon (Korea, Republic of)
2017-05-15
In finite element analyses, mesh refinement is frequently performed to obtain accurate stress or strain values or to accurately define the geometry. After mesh refinement, equivalent nodal forces should be calculated at the nodes in the refined mesh. If field variables and material properties are available at the integration points in each element, then the accurate equivalent nodal forces can be calculated using an adequate numerical integration. However, in certain circumstances, equivalent nodal forces cannot be calculated because field variable data are not available. In this study, a very simple nodal force distribution method was proposed. Nodal forces of the original finite element mesh are distributed to the nodes of refined meshes to satisfy the equilibrium conditions. The effect of element size should also be considered in determining the magnitude of the distributing nodal forces. A program was developed based on the proposed method, and several example problems were solved to verify the accuracy and effectiveness of the proposed method. From the results, accurate stress field can be recognized to be obtained from refined meshes using the proposed nodal force distribution method. In example problems, the difference between the obtained maximum stress and target stress value was less than 6 % in models with 8-node hexahedral elements and less than 1 % in models with 20-node hexahedral elements or 10-node tetrahedral elements.
International Nuclear Information System (INIS)
Goel, L.; Wu, Qiuwei; Wang, Peng
2008-01-01
With the development of restructured power systems, the conventional 'same for all customers' electricity price is getting replaced by nodal prices. Electricity prices will fluctuate with time and nodes. In restructured power systems, electricity demands will interact mutually with prices. Customers may shift some of their electricity consumption from time slots of high electricity prices to those of low electricity prices if there is a commensurate price incentive. The demand side load shift will influence nodal prices in return. This interaction between demand and price can be depicted using demand-price elasticity. This paper proposes an evaluation technique incorporating the impact of the demand-price elasticity on nodal prices, system reliability and nodal reliabilities of restructured power systems. In this technique, demand and price correlations are represented using the demand-price elasticity matrix which consists of self/cross-elasticity coefficients. Nodal prices are determined using optimal power flow (OPF). The OPF and customer damage functions (CDFs) are combined in the proposed reliability evaluation technique to assess the reliability enhancement of restructured power systems considering demand-price elasticity. The IEEE reliability test system (RTS) is simulated to illustrate the developed techniques. The simulation results show that demand-price elasticity reduces the nodal price volatility and improves both the system reliability and nodal reliabilities of restructured power systems. Demand-price elasticity can therefore be utilized as a possible efficient tool to reduce price volatility and to enhance the reliability of restructured power systems. (author)
Type-I and type-II topological nodal superconductors with s -wave interaction
Huang, Beibing; Yang, Xiaosen; Xu, Ning; Gong, Ming
2018-01-01
Topological nodal superconductors with protected gapless points in momentum space are generally realized based on unconventional pairings. In this work we propose a minimal model to realize these topological nodal phases with only s -wave interaction. In our model the linear and quadratic spin-orbit couplings along the two orthogonal directions introduce anisotropic effective unconventional pairings in momentum space. This model may support different nodal superconducting phases characterized by either an integer winding number in BDI class or a Z2 index in D class at the particle-hole invariant axes. In the vicinity of the nodal points the effective Hamiltonian can be described by either type-I or type-II Dirac equations, and the Lifshitz transition from type-I nodal phases to type-II nodal phases can be driven by external in-plane magnetic fields. We show that these nodal phases are robust against weak impurities, which only slightly renormalizes the momentum-independent parameters in the impurity-averaged Hamiltonian, thus these phases are possible to be realized in experiments with real semi-Dirac materials. The smoking-gun evidences to verify these phases based on scanning tunneling spectroscopy method are also briefly discussed.
Directory of Open Access Journals (Sweden)
Christopher E Slagle
2011-05-01
Full Text Available Vertebrate mesendoderm specification requires the Nodal signaling pathway and its transcriptional effector FoxH1. However, loss of FoxH1 in several species does not reliably cause the full range of loss-of-Nodal phenotypes, indicating that Nodal signals through additional transcription factors during early development. We investigated the FoxH1-dependent and -independent roles of Nodal signaling during mesendoderm patterning using a novel recessive zebrafish FoxH1 mutation called midway, which produces a C-terminally truncated FoxH1 protein lacking the Smad-interaction domain but retaining DNA-binding capability. Using a combination of gel shift assays, Nodal overexpression experiments, and genetic epistasis analyses, we demonstrate that midway more accurately represents a complete loss of FoxH1-dependent Nodal signaling than the existing zebrafish FoxH1 mutant schmalspur. Maternal-zygotic midway mutants lack notochords, in agreement with FoxH1 loss in other organisms, but retain near wild-type expression of markers of endoderm and various nonaxial mesoderm fates, including paraxial and intermediate mesoderm and blood precursors. We found that the activity of the T-box transcription factor Eomesodermin accounts for specification of these tissues in midway embryos. Inhibition of Eomesodermin in midway mutants severely reduces the specification of these tissues and effectively phenocopies the defects seen upon complete loss of Nodal signaling. Our results indicate that the specific combinations of transcription factors available for signal transduction play critical and separable roles in determining Nodal pathway output during mesendoderm patterning. Our findings also offer novel insights into the co-evolution of the Nodal signaling pathway, the notochord specification program, and the chordate branch of the deuterostome family of animals.
Face centered cubic SnSe as a Z2 trivial Dirac nodal line material
Tateishi, Ikuma; Matsuura, Hiroyasu
2018-01-01
The presence of Dirac nodal line in the time-reversal and inversion symmetric system is dictated by Z2 index when spin-orbit interaction is absent. With the first principles calculation, we show that the Dirac nodal line can emerge in Z2 trivial material by calculating the band structure of SnSe of face centered cubic lattice as an example and it becomes a topological crystalline insulator when spin-orbit interaction is taken into account. We clarify the origin of the Dirac nodal line by obta...
NUMERICAL SOLUTION OF SINGULAR INVERSE NODAL PROBLEM BY USING CHEBYSHEV POLYNOMIALS
NEAMATY, ABDOLALI; YILMAZ, EMRAH; AKBARPOOR, SHAHRBANOO; DABBAGHIAN, ABDOLHADI
2017-01-01
In this study, we consider Sturm-Liouville problem in two cases: the first case having no singularity and the second case having a singularity at zero. Then, we calculate the eigenvalues and the nodal points and present the uniqueness theorem for the solution of the inverse problem by using a dense subset of the nodal points in two given cases. Also, we use Chebyshev polynomials of the first kind for calculating the approximate solution of the inverse nodal problem in these cases. Finally, we...
[Method for optimal sensor placement in water distribution systems with nodal demand uncertainties].
Liu, Shu-Ming; Wu, Xue; Ouyang, Le-Yan
2013-08-01
The notion of identification fitness was proposed for optimizing sensor placement in water distribution systems. Nondominated Sorting Genetic Algorithm II was used to find the Pareto front between minimum overlap of possible detection times of two events and the best probability of detection, taking nodal demand uncertainties into account. This methodology was applied to an example network. The solutions show that the probability of detection and the number of possible locations are not remarkably affected by nodal demand uncertainties, but the sources identification accuracy declines with nodal demand uncertainties.
Lemos, Nivaldo A
2018-01-01
Analytical mechanics is the foundation of many areas of theoretical physics including quantum theory and statistical mechanics, and has wide-ranging applications in engineering and celestial mechanics. This introduction to the basic principles and methods of analytical mechanics covers Lagrangian and Hamiltonian dynamics, rigid bodies, small oscillations, canonical transformations and Hamilton–Jacobi theory. This fully up-to-date textbook includes detailed mathematical appendices and addresses a number of advanced topics, some of them of a geometric or topological character. These include Bertrand's theorem, proof that action is least, spontaneous symmetry breakdown, constrained Hamiltonian systems, non-integrability criteria, KAM theory, classical field theory, Lyapunov functions, geometric phases and Poisson manifolds. Providing worked examples, end-of-chapter problems, and discussion of ongoing research in the field, it is suitable for advanced undergraduate students and graduate students studying analyt...
Regional nodal relapse in surgically staged Merkel cell carcinoma
Energy Technology Data Exchange (ETDEWEB)
Hoeller, Ulrike; Mueller, Thomas; Schubert, Tina; Budach, Volker; Ghadjar, Pirus [Charite Universitaetsmedizin Berlin, Department of Radiation Oncology, Berlin (Germany); Brenner, Winfried [Charite Universitaetsmedizin Berlin, Department of Nuclear Medicine, Berlin (Germany); Kiecker, Felix [Charite Universitaetsmedizin Berlin, Department of Dermatology, Berlin (Germany); Schicke, Bernd [Tumor Center Berlin, Berlin (Germany); Haase, Oliver [Charite Universitaetsmedizin Berlin, Department of Surgery, Berlin (Germany)
2014-10-08
The nodal relapse pattern of surgically staged Merkel cell carcinoma (MCC) with/without elective nodal radiotherapy (RT) was studied in a single institution. A total of 51 patients with MCC, 33 % UICC stage I, 14 % II, 53 % III (4 lymph node metastases of unknown primary) were eligible. All patients had surgical staging: 23 patients sentinel node biopsy (SNB), 22 patients SNB followed by lymphadenectomy (LAD) and 6 patients LAD. In all, 94 % of the primary tumors (PT) were completely resected; 57 % of patients received RT, 51 % of known PT sites, 33 % (8/24 patients) regional RT to snN0 nodes and 68 % (17/27 patients) to pN+ nodes, mean reference dose 51.5 and 50 Gy, respectively. Mean follow-up was 6 years (range 2-14 years). A total of 22 % (11/51) patients developed regional relapses (RR); the 5-year RR rate was 27 %. In snN0 sites (stage I/II), relapse occurred in 5 of 14 nonirradiated vs. none of 8 irradiated sites (p = 0.054), resulting in a 5-year RR rate of 33 % versus 0 % (p = 0.16). The crude RR rate was lower in stage I (12 %, 2/17 patients) than for stage II (43 %, 3/7 patients). In stage III (pN+), RR appeared to be less frequent in irradiated sites (18 %, 3/14 patients) compared with nonirradiated sites (33 %, 3/10 patients, p = 0.45) with 5-year RR rates of 23 % vs. 34 %, respectively. Our data suggest that adjuvant nodal RT plays a major role even if the sentinel nodes were negative. Adjuvant RT of the lymph nodes in patients with stage IIa tumors and RT after LAD in stage III tumors is proposed and should be evaluated prospectively. (orig.) [German] Untersucht wurde das regionaere Rezidivmuster des Merkelzell-Karzinoms (MCC) nach chirurgischem Staging und stadienadaptierter Therapie. Eingeschlossen wurden 51 Patienten mit lokalisiertem MCC: 33 % hatten UICC-Stadium-I-, 14 % -II-, 53 % -III-Tumoren (davon 4 Lymphknotenmetastasen eines unbekannten Primaertumors). Alle Patienten erhielten ein chirurgisches Staging: 23 Waechterlymphknotenbiopsien (SNB
Application of finite Fourier transformation for the solution of the diffusion equation
International Nuclear Information System (INIS)
Kobayashi, Keisuke
1991-01-01
The application of the finite Fourier transformation to the solution of the neutron diffusion equation in one dimension, two dimensional x-y and triangular geometries is discussed. It can be shown that the equation obtained by the Nodal Green's function method in Cartesian coordinates can be derived as a special case of the finite Fourier transformation method. (author)
Spain, Barry; Ulam, S; Stark, M
1960-01-01
Analytical Quadrics focuses on the analytical geometry of three dimensions. The book first discusses the theory of the plane, sphere, cone, cylinder, straight line, and central quadrics in their standard forms. The idea of the plane at infinity is introduced through the homogenous Cartesian coordinates and applied to the nature of the intersection of three planes and to the circular sections of quadrics. The text also focuses on paraboloid, including polar properties, center of a section, axes of plane section, and generators of hyperbolic paraboloid. The book also touches on homogenous coordi
International Nuclear Information System (INIS)
Jacqmin, R.P.
1991-01-01
The safety and optimal performance of large, commercial, light-water reactors require the knowledge at all time of the neutron-flux distribution in the core. In principle, this information can be obtained by solving the time-dependent neutron diffusion equations. However, this approach is complicated and very expensive. Sufficiently accurate, real-time calculations (time scale of approximately one second) are not yet possible on desktop computers, even with fast-running, nodal kinetics codes. A semi-experimental, nodal synthesis method which avoids the solution of the time-dependent, neutron diffusion equations is described. The essential idea of this method is to approximate instantaneous nodal group-fluxes by a linear combination of K, precomputed, three-dimensional, static expansion-functions. The time-dependent coefficients of the combination are found from the requirement that the reconstructed flux-distribution agree in a least-squares sense with the readings of J (≥K) fixed, prompt-responding neutron-detectors. Possible numerical difficulties with the least-squares solution of the ill-conditioned, J-by-K system of equations are brought under complete control by the use of a singular-value-decomposition technique. This procedure amounts to the rearrangement of the original, linear combination of K expansion functions into an equivalent more convenient, linear combination of R (≤K) orthogonalized ''modes'' of decreasing magnitude. Exceedingly small modes are zeroed to eliminate any risk of roundoff-error amplification, and to assure consistency with the limited accuracy of the data. Additional modes are zeroed when it is desirable to limit the sensitivity of the results to measurement noise
Energy Technology Data Exchange (ETDEWEB)
Jacqmin, Robert P. [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
1991-12-10
The safety and optimal performance of large, commercial, light-water reactors require the knowledge at all time of the neutron-flux distribution in the core. In principle, this information can be obtained by solving the time-dependent neutron diffusion equations. However, this approach is complicated and very expensive. Sufficiently accurate, real-time calculations (time scale of approximately one second) are not yet possible on desktop computers, even with fast-running, nodal kinetics codes. A semi-experimental, nodal synthesis method which avoids the solution of the time-dependent, neutron diffusion equations is described. The essential idea of this method is to approximate instantaneous nodal group-fluxes by a linear combination of K, precomputed, three-dimensional, static expansion-functions. The time-dependent coefficients of the combination are found from the requirement that the reconstructed flux-distribution agree in a least-squares sense with the readings of J (≥K) fixed, prompt-responding neutron-detectors. Possible numerical difficulties with the least-squares solution of the ill-conditioned, J-by-K system of equations are brought under complete control by the use of a singular-value-decomposition technique. This procedure amounts to the rearrangement of the original, linear combination of K expansion functions into an equivalent more convenient, linear combination of R (≤K) orthogonalized ``modes`` of decreasing magnitude. Exceedingly small modes are zeroed to eliminate any risk of roundoff-error amplification, and to assure consistency with the limited accuracy of the data. Additional modes are zeroed when it is desirable to limit the sensitivity of the results to measurement noise.
Energy Technology Data Exchange (ETDEWEB)
Jacqmin, R.P.
1991-12-10
The safety and optimal performance of large, commercial, light-water reactors require the knowledge at all time of the neutron-flux distribution in the core. In principle, this information can be obtained by solving the time-dependent neutron diffusion equations. However, this approach is complicated and very expensive. Sufficiently accurate, real-time calculations (time scale of approximately one second) are not yet possible on desktop computers, even with fast-running, nodal kinetics codes. A semi-experimental, nodal synthesis method which avoids the solution of the time-dependent, neutron diffusion equations is described. The essential idea of this method is to approximate instantaneous nodal group-fluxes by a linear combination of K, precomputed, three-dimensional, static expansion-functions. The time-dependent coefficients of the combination are found from the requirement that the reconstructed flux-distribution agree in a least-squares sense with the readings of J ({ge}K) fixed, prompt-responding neutron-detectors. Possible numerical difficulties with the least-squares solution of the ill-conditioned, J-by-K system of equations are brought under complete control by the use of a singular-value-decomposition technique. This procedure amounts to the rearrangement of the original, linear combination of K expansion functions into an equivalent more convenient, linear combination of R ({le}K) orthogonalized modes'' of decreasing magnitude. Exceedingly small modes are zeroed to eliminate any risk of roundoff-error amplification, and to assure consistency with the limited accuracy of the data. Additional modes are zeroed when it is desirable to limit the sensitivity of the results to measurement noise.
2016-04-30
Warfare, Naval Sea Systems Command Acquisition Cycle Time : Defining the Problem David Tate, Institute for Defense Analyses Schedule Analytics Jennifer...research was comprised of the following high- level steps : Identify and review primary data sources 1...research. However, detailed reviews of the OMB IT Dashboard data revealed that schedule data is highly aggregated. Program start date and program end date
Molecular pathogenesis of splenic and nodal marginal zone lymphoma.
Spina, Valeria; Rossi, Davide
Genomic studies have improved our understanding of the biological basis of splenic (SMZL) and nodal (NMZL) marginal zone lymphoma by providing a comprehensive and unbiased view of the genes/pathways that are deregulated in these diseases. Consistent with the physiological involvement of NOTCH, NF-κB, B-cell receptor and toll-like receptor signaling in mature B-cells differentiation into the marginal zone B-cells, many oncogenic mutations of genes involved in these pathways have been identified in SMZL and NMZL. Beside genetic lesions, also epigenetic and post-transcriptional modifications contribute to the deregulation of marginal zone B-cell differentiation pathways in SMZL and NMZL. This review describes the progress in understanding the molecular mechanism underlying SMZL and NMZL, including molecular and post-transcriptional modifications, and discusses how information gained from these efforts has provided new insights on potential targets of diagnostic, prognostic and therapeutic relevance in SMZL and NMZL. Copyright © 2016 Elsevier Ltd. All rights reserved.
Micropropagation of Calophyllum brasiliense (Cambess.) from nodal segments.
Silveira, S S; Cordeiro-Silva, R; Degenhardt-Goldbach, J; Quoirin, M
2016-05-03
Micropropagation of Calophyllum brasiliense Cambess. (Clusiaceae) is a way to overcome difficulties in achieving large-scale plant production, given the recalcitrant nature of the seeds, irregular fructification and absence of natural vegetative propagation of the species. Cultures were established using nodal segments 2 cm in length, obtained from 1-2 year old seedlings, maintained in a greenhouse. Mercury chloride and Plant Preservative Mixture™ were used in the surface sterilizing stage, better results being achieved with Plant Preservative Mixture™ incorporation in culture medium, at any concentration. Polyvinylpyrrolidone, activated charcoal, cysteine, ascorbic acid or citric acid were added to the culture medium to avoid oxidation. After 30 days of culture, polyvinylpirrolidone and ascorbic acid gave better results, eliminating oxidation in most explants. For shoot multiplication, benzylaminopurine was used in concentrations of 4.4 and 8.8 µM in Woody Plant Medium, resulting in an average of 4.43 and 4.68 shoots per explant, respectively, after 90 days. Indole-3-butyric acid and α-naphthalene acetic acid were used to induce root formation, reaching a maximum rooting rate of 24% with 20µM α-naphthalene acetic acid. For acclimatization. the rooted plants were transferred to Plantmax® substrate and cultured in a greenhouse, reaching 79% of survival after 30 days and 60% after one year.
Relevance of regional nodal management in multimodality esophageal cancer treatment
International Nuclear Information System (INIS)
Wong, J.; Perez-Tamayo, C.; Takasugi, B.; Orringer, M.B.; Flint, A.; Lichter, A.S.
1986-01-01
A prospective study has been undertaken at the University of Michigan Hospital, where patients with distal esophageal carcinoma receive concurrent radiation therapy (3,750 cGy delivered in 15 fractions) and systemic chemotherapy (cisplatin, Velban, 5-FU), followed by blunt esophagectomy with exploration and lymph node sampling. Strict pathologic screening and handling of nodal tissue and esophagectomy specimens were analyzed. Eighteen patients with distal esophageal lesions ranging from 5 to 12 cm (average, 7 cm) detected on the initial barium swallow study have been seen to date. In three of these patients celiac axis involvement has been demonstrated on CT. All primary lesions were confirmed by biopsy. Five were found to be squamous cell carcinoma and thirteen were adenocarcinomas. One of 15 of the presently evaluable patients (5%) had microscopic involvement of a celiac node at surgery. Celiac, lesser curvature, and superior gastric nodes where all encompassed in the radiation therapy portals to the aforementioned dose. CT scan planning was done in all patients. This added volume was well tolerated by the patients without morbidity
Topological Nodal Cooper Pairing in Doped Weyl Metals
Li, Yi; Haldane, F. D. M.
2018-02-01
We generalize the concept of Berry connection of the single-electron band structure to that of a two-particle Cooper pairing state between two Fermi surfaces with opposite Chern numbers. Because of underlying Fermi surface topology, the pairing Berry phase acquires nontrivial monopole structure. Consequently, pairing gap functions have topologically protected nodal structure as vortices in the momentum space with the total vorticity solely determined by the pair monopole charge qp. The nodes of gap function behave as the Weyl-Majorana points of the Bogoliubov-de Gennes pairing Hamiltonian. Their relation with the connection patterns of the surface modes from the Weyl band structure and the Majorana surface modes inside the pairing gap is also discussed. Under the approximation of spherical Fermi surfaces, the pairing symmetry are represented by monopole harmonic functions. The lowest possible pairing channel carries angular momentum number j =|qp|, and the corresponding gap functions are holomorphic or antiholomorphic functions on Fermi surfaces. After projected on the Fermi surfaces with nontrivial topology, all the partial-wave channels of pairing interactions acquire the monopole charge qp independent of concrete pairing mechanism.
Directory of Open Access Journals (Sweden)
Huiqing Fang
2016-01-01
Full Text Available Based on geometrically exact beam theory, a hybrid interpolation is proposed for geometric nonlinear spatial Euler-Bernoulli beam elements. First, the Hermitian interpolation of the beam centerline was used for calculating nodal curvatures for two ends. Then, internal curvatures of the beam were interpolated with a second interpolation. At this point, C1 continuity was satisfied and nodal strain measures could be consistently derived from nodal displacement and rotation parameters. The explicit expression of nodal force without integration, as a function of global parameters, was founded by using the hybrid interpolation. Furthermore, the proposed beam element can be degenerated into linear beam element under the condition of small deformation. Objectivity of strain measures and patch tests are also discussed. Finally, four numerical examples are discussed to prove the validity and effectivity of the proposed beam element.
Pang, Changlee S; Grier, David D; Beaty, Michael W
2011-03-01
Sinus histiocytosis with massive lymphadenopathy (SHML), also known as Rosai-Dorfman disease, is a rare self-limiting disorder of histiocytes with unknown etiology. Sinus histiocytosis with massive lymphadenopathy is most common in children and young adults and is characterized by painless lymphadenopathy. Histologically there is a proliferation of sinus histiocytes with lymphophagocytosis or emperipolesis. On rare occasions, SHML has been associated with lymphoma, usually involving different anatomic sites and developing at different times. We report a case of concomitant SHML and nodal marginal zone lymphoma involving the same lymph node without involvement of other nodal or extranodal sites. The presence of concomitant SHML within the lymph node involved by nodal marginal zone lymphoma may represent the responsiveness of SHML histiocytes to B-cell-derived cytokines in lymphoproliferative disorders. To our knowledge, this is the first description of concomitant occurrence of SHML and nodal marginal zone lymphoma.
Directory of Open Access Journals (Sweden)
Cox James D
2009-01-01
Full Text Available Abstract Background Controversy still exists regarding the long-term outcome of patients whose uninvolved lymph node stations are not prophylactically irradiated for non-small cell lung cancer (NSCLC treated with definitive radiotherapy. To determine the frequency of elective nodal failure (ENF and in-field failure (IFF, we examined a large cohort of patients with NSCLC staged with positron emission tomography (PET/computed tomography (CT and treated with 3-dimensional conformal radiotherapy (3D-CRT that excluded uninvolved lymph node stations. Methods We retrospectively reviewed the records of 115 patients with non-small cell lung cancer treated at our institution with definitive radiation therapy with or without concurrent chemotherapy (CHT. All patients were treated with 3D-CRT, including nodal regions determined by CT or PET to be disease involved. Concurrent platinum-based CHT was administered for locally advanced disease. Patients were analyzed in follow-up for survival, local regional recurrence, and distant metastases (DM. Results The median follow-up time was 18 months (3 to 44 months among all patients and 27 months (6 to 44 months among survivors. The median overall survival, 2-year actuarial overall survival and disease-free survival were 19 months, 38%, and 28%, respectively. The majority of patients died from DM, the overall rate of which was 36%. Of the 31 patients with local regional failure, 26 (22.6% had IFF, 5 (4.3% had ENF and 2 (1.7% had isolated ENF. For 88 patients with stage IIIA/B, the frequencies of IFF, any ENF, isolated ENF, and DM were 23 (26%, 3 (9%, 1 (1.1% and 36 (40.9%, respectively. The comparable rates for the 22 patients with early stage node-negative disease (stage IA/IB were 3 (13.6%, 1(4.5%, 0 (0%, and 5 (22.7%, respectively. Conclusion We observed only a 4.3% recurrence of any ENF and a 1.7% recurrence of isolated ENF in patients with NSCLC treated with definitive 3D-CRT without prophylactic irradiation of
International Nuclear Information System (INIS)
Sulman, Erik P; Komaki, Ritsuko; Klopp, Ann H; Cox, James D; Chang, Joe Y
2009-01-01
Controversy still exists regarding the long-term outcome of patients whose uninvolved lymph node stations are not prophylactically irradiated for non-small cell lung cancer (NSCLC) treated with definitive radiotherapy. To determine the frequency of elective nodal failure (ENF) and in-field failure (IFF), we examined a large cohort of patients with NSCLC staged with positron emission tomography (PET)/computed tomography (CT) and treated with 3-dimensional conformal radiotherapy (3D-CRT) that excluded uninvolved lymph node stations. We retrospectively reviewed the records of 115 patients with non-small cell lung cancer treated at our institution with definitive radiation therapy with or without concurrent chemotherapy (CHT). All patients were treated with 3D-CRT, including nodal regions determined by CT or PET to be disease involved. Concurrent platinum-based CHT was administered for locally advanced disease. Patients were analyzed in follow-up for survival, local regional recurrence, and distant metastases (DM). The median follow-up time was 18 months (3 to 44 months) among all patients and 27 months (6 to 44 months) among survivors. The median overall survival, 2-year actuarial overall survival and disease-free survival were 19 months, 38%, and 28%, respectively. The majority of patients died from DM, the overall rate of which was 36%. Of the 31 patients with local regional failure, 26 (22.6%) had IFF, 5 (4.3%) had ENF and 2 (1.7%) had isolated ENF. For 88 patients with stage IIIA/B, the frequencies of IFF, any ENF, isolated ENF, and DM were 23 (26%), 3 (9%), 1 (1.1%) and 36 (40.9%), respectively. The comparable rates for the 22 patients with early stage node-negative disease (stage IA/IB) were 3 (13.6%), 1(4.5%), 0 (0%), and 5 (22.7%), respectively. We observed only a 4.3% recurrence of any ENF and a 1.7% recurrence of isolated ENF in patients with NSCLC treated with definitive 3D-CRT without prophylactic irradiation of uninvolved lymph node stations. Thus
International Nuclear Information System (INIS)
Menezes, Welton Alves de
2009-01-01
In this dissertation the spectral nodal method SD-SGF-CN, cf. spectral diamond - spectral Green's function - constant nodal, is used to determine the angular fluxes averaged along the edges of the homogenized nodes in heterogeneous domains. Using these results, we developed an algorithm for the reconstruction of the node-edge average angular fluxes within the nodes of the spatial grid set up on the domain, since more localized numerical solutions are not generated by coarse-mesh numerical methods. Numerical results are presented to illustrate the accuracy of the algorithm we offer. (author)
International Nuclear Information System (INIS)
Carlen, E.A.
1984-01-01
In Nelson's stochastic mechanics, quantum phenomena are described in terms of diffusions instead of wave functions. These diffusions are formally given by stochastic differential equations with extremely singular coefficients. Using PDE methods, we prove the existence of solutions. This reult provides a rigorous basis for stochastic mechanics. (orig.)
International Nuclear Information System (INIS)
Delfin L, A.; Alonso V, G.; Valle G, E. del
2003-01-01
In this work two nodal schemes of finite element are presented, one of second and the other of third order of accurate that allow to determine the radial distribution of power starting from the corresponding reactivities.The schemes here developed were obtained taking as starting point the equation developed by Driscoll et al, the one which is based on the diffusion approach of 1-1/2 energy groups. This equation relates the power fraction of an assemble with their reactivity and with the power fractions and reactivities of the assemblies that its surround it. Driscoll and collaborators they solve in form approximate such equation supposing that the reactivity of each assemble it is but a lineal function of the burnt one of the fuel. The spatial approach carries out it with the classic technique of finite differences centered in mesh. Nevertheless that the algebraic system to which its arrive it can be solved without more considerations introduce some additional suppositions and adjustment parameters that it allows them to predict results comparable to those contributed by three dimensions analysis and this way to reduce the one obtained error when its compare their results with those of a production code like CASMO. Also in the two schemes that here are presented the same approaches of Driscoll were used being obtained errors of the one 10% and of 5% for the second schemes and third order respectively for a test case that it was built starting from data of the Cycle 1 of the Unit 1 of the Laguna Verde Nucleo electric plant. These errors its were obtained when comparing with a computer program based on the matrix response method. It is sought to have this way a quick and efficient tool for the multicycle analysis in the fuel management. However, this model presents problems in the appropriate prediction of the average burnt of the nucleus and of the burnt one by lot. (Author)
Canine nodal marginal zone lymphoma: Descriptive insight into the biological behaviour.
Cozzi, M; Marconato, L; Martini, V; Aresu, L; Riondato, F; Rossi, F; Stefanello, D; Comazzi, S
2018-06-01
Canine nodal marginal zone lymphoma (nMZL) is classified as an indolent lymphoma. Such lymphomas are typified by low mitotic rate and slow clinical progression. While the clinical behaviour of canine splenic MZL has been described, characterized by an indolent course and a good prognosis following splenectomy, there are no studies specifically describing nMZL. The aim of this study was to describe the clinical features of and outcome for canine nMZL. Dogs with histologically confirmed nMZL undergoing a complete staging work-up (including blood analysis, flow cytometry [FC] on lymph node [LN], peripheral blood and bone marrow, imaging, histology and immunohistochemistry on a surgically removed peripheral LN) were retrospectively enrolled. Treatment consisted of chemotherapy or chemo-immunotherapy. Endpoints were response rate (RR), time to progression (TTP) and lymphoma-specific survival (LSS). A total of 35 cases were enrolled. At diagnosis, all dogs showed generalized lymphadenopathy. One-third was systemically unwell. All dogs had stage V disease; one-third also had extranodal involvement. The LN population was mainly composed of medium-sized CD21+ cells with scant resident normal lymphocytes. Histology revealed diffuse LN involvement, referring to "late-stage" MZL. Median TTP and LSS were 149 and 259 days, respectively. Increased LDH activity and substage b were significantly associated with a shorter LSS. Dogs with nMZL may show generalized lymphadenopathy and an advanced disease stage. Overall, the outcome is poor, despite the "indolent" designation. The best treatment option still needs to be defined. © 2017 John Wiley & Sons Ltd.
A study of the literature on nodal methods in reactor physics calculations
International Nuclear Information System (INIS)
Van de Wetering, T.F.H.
1993-01-01
During the last few decades several calculation methods have been developed for the three-dimensional analysis of a reactor core. A literature survey was carried out to gain insights in the starting points and method of operation of the advanced nodal methods. These methods are applied in reactor core analyses of large nuclear power reactors, because of their high computing speed. The so-called Nodal-Expansion method is described in detail
Cilia are required for asymmetric nodal induction in the sea urchin embryo.
Tisler, Matthias; Wetzel, Franziska; Mantino, Sabrina; Kremnyov, Stanislav; Thumberger, Thomas; Schweickert, Axel; Blum, Martin; Vick, Philipp
2016-08-23
Left-right (LR) organ asymmetries are a common feature of metazoan animals. In many cases, laterality is established by a conserved asymmetric Nodal signaling cascade during embryogenesis. In most vertebrates, asymmetric nodal induction results from a cilia-driven leftward fluid flow at the left-right organizer (LRO), a ciliated epithelium present during gastrula/neurula stages. Conservation of LRO and flow beyond the vertebrates has not been reported yet. Here we study sea urchin embryos, which use nodal to establish larval LR asymmetry as well. Cilia were found in the archenteron of embryos undergoing gastrulation. Expression of foxj1 and dnah9 suggested that archenteron cilia were motile. Cilia were polarized to the posterior pole of cells, a prerequisite of directed flow. High-speed videography revealed rotating cilia in the archenteron slightly before asymmetric nodal induction. Removal of cilia through brief high salt treatments resulted in aberrant patterns of nodal expression. Our data demonstrate that cilia - like in vertebrates - are required for asymmetric nodal induction in sea urchin embryos. Based on these results we argue that the anterior archenteron represents a bona fide LRO and propose that cilia-based symmetry breakage is a synapomorphy of the deuterostomes.
Advances in the solution of three-dimensional nodal neutron transport equation
International Nuclear Information System (INIS)
Pazos, Ruben Panta; Hauser, Eliete Biasotto; Vilhena, Marco Tullio de
2003-01-01
In this paper we study the three-dimensional nodal discrete-ordinates approximations of neutron transport equation in a convex domain with piecewise smooth boundaries. We use the combined collocation method of the angular variables and nodal approach for the spatial variables. By nodal approach we mean the iterated transverse integration of the S N equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTS N method, first applying the Laplace transform to the set of the nodal S N equations and then obtaining the solution by symbolic computation. We include the LTS N method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTS N approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation. We give numerical results obtained with an algebraic computer system (for N up to 8) and with a code for higher values of N. We compare our results for the geometry of a box with a source in a vertex and a leakage zone in the opposite with others techniques used in this problem. (author)
Directory of Open Access Journals (Sweden)
M. Ghayeni
2010-12-01
Full Text Available This paper proposes an algorithm for transmission cost allocation (TCA in a large power system based on nodal pricing approach using the multi-area scheme. The nodal pricing approach is introduced to allocate the transmission costs by the control of nodal prices in a single area network. As the number of equations is dependent on the number of buses and generators, this method will be very time consuming for large power systems. To solve this problem, the present paper proposes a new algorithm based on multi-area approach for regulating the nodal prices, so that the simulation time is greatly reduced and therefore the TCA problem with nodal pricing approach will be applicable for large power systems. In addition, in this method the transmission costs are allocated to users more equitable. Since the higher transmission costs in an area having a higher reliability are paid only by users of that area in contrast with the single area method, in which these costs are allocated to all users regardless of their locations. The proposed method is implemented on the IEEE 118 bus test system which comprises three areas. Results show that with application of multi-area approach, the simulation time is greatly reduced and the transmission costs are also allocated to users with less variation in new nodal prices with respect to the single area approach.
Shapourian, Hassan; Wang, Yuxuan; Ryu, Shinsei
2018-03-01
We study the intrinsic fully gapped odd-parity superconducting order in doped nodal-loop materials with a torus-shaped Fermi surface. We show that the mirror symmetry, which protects the nodal loop in the normal state, also protects the superconducting state as a topological crystalline superconductor. As a result, the surfaces preserving the mirror symmetry host gapless Majorana cones. Moreover, for a Weyl-loop system (twofold degenerate at the nodal loop), the surfaces that break the mirror symmetry (those parallel to the bulk nodal loop) contribute a Chern (winding) number to the quasi-two-dimensional system in a slab geometry, which leads to a quantized thermal Hall effect and a single Majorana zero mode bound at a vortex line penetrating the system. This Chern number can be viewed as a higher-order topological invariant, which supports hinge modes in a cubic sample when mirror symmetry is broken. For a Dirac-loop system (fourfold degenerate at the nodal loop), the fully gapped odd-parity state can be either time-reversal symmetry-breaking or symmetric, similar to the A and B phases of 3He. In a slab geometry, the A phase has a Chern number two, while the B phase carries a nontrivial Z2 invariant. We discuss the experimental relevance of our results to nodal-loop materials such as CaAgAs.
Energy Technology Data Exchange (ETDEWEB)
Choi, Jae Seong
1993-02-15
This book is comprised of nineteen chapters, which describes introduction of analytical chemistry, experimental error and statistics, chemistry equilibrium and solubility, gravimetric analysis with mechanism of precipitation, range and calculation of the result, volume analysis on general principle, sedimentation method on types and titration curve, acid base balance, acid base titration curve, complex and firing reaction, introduction of chemical electro analysis, acid-base titration curve, electrode and potentiometry, electrolysis and conductometry, voltammetry and polarographic spectrophotometry, atomic spectrometry, solvent extraction, chromatograph and experiments.
International Nuclear Information System (INIS)
Choi, Jae Seong
1993-02-01
This book is comprised of nineteen chapters, which describes introduction of analytical chemistry, experimental error and statistics, chemistry equilibrium and solubility, gravimetric analysis with mechanism of precipitation, range and calculation of the result, volume analysis on general principle, sedimentation method on types and titration curve, acid base balance, acid base titration curve, complex and firing reaction, introduction of chemical electro analysis, acid-base titration curve, electrode and potentiometry, electrolysis and conductometry, voltammetry and polarographic spectrophotometry, atomic spectrometry, solvent extraction, chromatograph and experiments.
International Nuclear Information System (INIS)
Anon.
1985-01-01
The division for Analytical Chemistry continued to try and develope an accurate method for the separation of trace amounts from mixtures which, contain various other elements. Ion exchange chromatography is of special importance in this regard. New separation techniques were tried on certain trace amounts in South African standard rock materials and special ceramics. Methods were also tested for the separation of carrier-free radioisotopes from irradiated cyclotron discs
TGF-β promotes glioma cell growth via activating Nodal expression through Smad and ERK1/2 pathways
International Nuclear Information System (INIS)
Sun, Jing; Liu, Su-zhi; Lin, Yan; Cao, Xiao-pan; Liu, Jia-ming
2014-01-01
Highlights: •TGF-β promoted Nodal expression in glioma cells. •TGF-β promoted Nodal expression via activating Smad and ERK1/2 pathways. •TGF-β promotes glioma cell growth via activating Nodal expression. -- Abstract: While there were certain studies focusing on the mechanism of TGF-β promoting the growth of glioma cells, the present work revealed another novel mechanism that TGF-β may promote glioma cell growth via enhancing Nodal expression. Our results showed that Nodal expression was significantly upregulated in glioma cells when TGF-β was added, whereas the TGF-β-induced Nodal expression was evidently inhibited by transfection Smad2 or Smad3 siRNAs, and the suppression was especially significant when the Smad3 was downregulated. Another, the attenuation of TGF-β-induced Nodal expression was observed with blockade of the ERK1/2 pathway also. Further detection of the proliferation, apoptosis, and invasion of glioma cells indicated that Nodal overexpression promoted the proliferation and invasion of tumor cells and inhibited their apoptosis, resembling the effect of TGF-β addition. Downregulation of Nodal expression via transfection Nodal-specific siRNA in the presence of TGF-β weakened the promoting effect of the latter on glioma cells growth, and transfecting Nodal siRNA alone in the absence of exogenous TGF-β more profoundly inhibited the growth of glioma cells. These results demonstrated that while both TGF-β and Nodal promoted glioma cells growth, the former might exert such effect by enhancing Nodal expression, which may form a new target for glioma therapy
Reissmann, Eva; Jörnvall, Henrik; Blokzijl, Andries; Andersson, Olov; Chang, Chenbei; Minchiotti, Gabriella; Persico, M. Graziella; Ibáñez, Carlos F.; Brivanlou, Ali H.
2001-01-01
Nodal proteins have crucial roles in mesendoderm formation and left–right patterning during vertebrate development. The molecular mechanisms of signal transduction by Nodal and related ligands, however, are not fully understood. In this paper, we present biochemical and functional evidence that the orphan type I serine/threonine kinase receptor ALK7 acts as a receptor for mouse Nodal and Xenopus Nodal-related 1 (Xnr1). Receptor reconstitution experiments indicate that ALK7 collaborates with ActRIIB to confer responsiveness to Xnr1 and Nodal. Both receptors can independently bind Xnr1. In addition, Cripto, an extracellular protein genetically implicated in Nodal signaling, can independently interact with both Xnr1 and ALK7, and its expression greatly enhances the ability of ALK7 and ActRIIB to respond to Nodal ligands. The Activin receptor ALK4 is also able to mediate Nodal signaling but only in the presence of Cripto, with which it can also interact directly. A constitutively activated form of ALK7 mimics the mesendoderm-inducing activity of Xnr1 in Xenopus embryos, whereas a dominant-negative ALK7 specifically blocks the activities of Nodal and Xnr1 but has little effect on other related ligands. In contrast, a dominant-negative ALK4 blocks all mesoderm-inducing ligands tested, including Nodal, Xnr1, Xnr2, Xnr4, and Activin. In agreement with a role in Nodal signaling, ALK7 mRNA is localized to the ectodermal and organizer regions of Xenopus gastrula embryos and is expressed during early stages of mouse embryonic development. Therefore, our results indicate that both ALK4 and ALK7 can mediate signal transduction by Nodal proteins, although ALK7 appears to be a receptor more specifically dedicated to Nodal signaling. PMID:11485994
Drug diffusion across skin with diffusivity spatially modulated
Montoya Arroyave, Isabel
2014-05-01
A diffusion and delivery model of a drug across the skin with diffusivity spatially modulated is formulated and solved analytically using computer algebra. The model is developed using one-dimensional diffusion equation with a diffusivity which is a function of position in the skin; with an initial condition which is describing that the drug is initially contained inside a therapeutic patch; with a boundary condition according to which the change in concentration in the patch is minimal, such that assumption of zero flux at the patch-skin interface is valid; and with other boundary condition according to which the microcirculation in the capillaries just below the dermis carries the drug molecules away from the site at a very fast rate, maintaining the inner concentration at 0. The model is solved analytically by the method of the Laplace transform, with Bromwich integral and residue theorem. The concentration profile of the drug in the skin is expressed as an infinite series of Bessel functions. The corresponding total amount of delivered drug is expressed as an infinite series of decreasing exponentials. Also, the corresponding effective time for the therapeutic patch is determined. All computations were performed using computer algebra software, specifically Maple. The analytical results obtained are important for understanding and improving currentapplications of therapeutic patches. For future research it is interesting to consider more general models of spatial modulation of the diffusivity and the possible application of other computer algebra software such as Mathematica and Maxima.
Churchill regulates cell movement and mesoderm specification by repressing Nodal signaling
Directory of Open Access Journals (Sweden)
Mentzer Laura
2007-11-01
Full Text Available Abstract Background Cell movements are essential to the determination of cell fates during development. The zinc-finger transcription factor, Churchill (ChCh has been proposed to regulate cell fate by regulating cell movements during gastrulation in the chick. However, the mechanism of action of ChCh is not understood. Results We demonstrate that ChCh acts to repress the response to Nodal-related signals in zebrafish. When ChCh function is abrogated the expression of mesodermal markers is enhanced while ectodermal markers are expressed at decreased levels. In cell transplant assays, we observed that ChCh-deficient cells are more motile than wild-type cells. When placed in wild-type hosts, ChCh-deficient cells often leave the epiblast, migrate to the germ ring and are later found in mesodermal structures. We demonstrate that both movement of ChCh-compromised cells to the germ ring and acquisition of mesodermal character depend on the ability of the donor cells to respond to Nodal signals. Blocking Nodal signaling in the donor cells at the levels of Oep, Alk receptors or Fast1 inhibited migration to the germ ring and mesodermal fate change in the donor cells. We also detect additional unusual movements of transplanted ChCh-deficient cells which suggests that movement and acquisition of mesodermal character can be uncoupled. Finally, we demonstrate that ChCh is required to limit the transcriptional response to Nodal. Conclusion These data establish a broad role for ChCh in regulating both cell movement and Nodal signaling during early zebrafish development. We show that chch is required to limit mesodermal gene expression, inhibit Nodal-dependant movement of presumptive ectodermal cells and repress the transcriptional response to Nodal signaling. These findings reveal a dynamic role for chch in regulating cell movement and fate during early development.
Seol, Ki Ho; Lee, Jeong Eun
2016-03-01
To evaluate the patterns of nodal failure after radiotherapy (RT) with the reduced volume approach for elective neck nodal irradiation (ENI) in nasopharyngeal carcinoma (NPC). Fifty-six NPC patients who underwent definitive chemoradiotherapy with the reduced volume approach for ENI were reviewed. The ENI included retropharyngeal and level II lymph nodes, and only encompassed the echelon inferior to the involved level to eliminate the entire neck irradiation. Patients received either moderate hypofractionated intensity-modulated RT for a total of 72.6 Gy (49.5 Gy to elective nodal areas) or a conventional fractionated three-dimensional conformal RT for a total of 68.4-72 Gy (39.6-45 Gy to elective nodal areas). Patterns of failure, locoregional control, and survival were analyzed. The median follow-up was 38 months (range, 3 to 80 months). The out-of-field nodal failure when omitting ENI was none. Three patients developed neck recurrences (one in-field recurrence in the 72.6 Gy irradiated nodal area and two in the elective irradiated region of 39.6 Gy). Overall disease failure at any site developed in 11 patients (19.6%). Among these, there were six local failures (10.7%), three regional failures (5.4%), and five distant metastases (8.9%). The 3-year locoregional control rate was 87.1%, and the distant failure-free rate was 90.4%; disease-free survival and overall survival at 3 years was 80% and 86.8%, respectively. No patient developed nodal failure in the omitted ENI site. Our investigation has demonstrated that the reduced volume approach for ENI appears to be a safe treatment approach in NPC.
Energy Technology Data Exchange (ETDEWEB)
Seol, Ki Ho; Lee, Jeong Eun [Dept. of Radiation Oncology, Kyungpook National University School of Medicine, Daegu (Korea, Republic of)
2016-03-15
To evaluate the patterns of nodal failure after radiotherapy (RT) with the reduced volume approach for elective neck nodal irradiation (ENI) in nasopharyngeal carcinoma (NPC). Fifty-six NPC patients who underwent definitive chemoradiotherapy with the reduced volume approach for ENI were reviewed. The ENI included retropharyngeal and level II lymph nodes, and only encompassed the echelon inferior to the involved level to eliminate the entire neck irradiation. Patients received either moderate hypofractionated intensity-modulated RT for a total of 72.6 Gy (49.5 Gy to elective nodal areas) or a conventional fractionated three-dimensional conformal RT for a total of 68.4-72 Gy (39.6-45 Gy to elective nodal areas). Patterns of failure, locoregional control, and survival were analyzed. The median follow-up was 38 months (range, 3 to 80 months). The out-of-field nodal failure when omitting ENI was none. Three patients developed neck recurrences (one in-field recurrence in the 72.6 Gy irradiated nodal area and two in the elective irradiated region of 39.6 Gy). Overall disease failure at any site developed in 11 patients (19.6%). Among these, there were six local failures (10.7%), three regional failures (5.4%), and five distant metastases (8.9%). The 3-year locoregional control rate was 87.1%, and the distant failure-free rate was 90.4%; disease-free survival and overall survival at 3 years was 80% and 86.8%, respectively. No patient developed nodal failure in the omitted ENI site. Our investigation has demonstrated that the reduced volume approach for ENI appears to be a safe treatment approach in NPC.
International Nuclear Information System (INIS)
Seol, Ki Ho; Lee, Jeong Eun
2016-01-01
To evaluate the patterns of nodal failure after radiotherapy (RT) with the reduced volume approach for elective neck nodal irradiation (ENI) in nasopharyngeal carcinoma (NPC). Fifty-six NPC patients who underwent definitive chemoradiotherapy with the reduced volume approach for ENI were reviewed. The ENI included retropharyngeal and level II lymph nodes, and only encompassed the echelon inferior to the involved level to eliminate the entire neck irradiation. Patients received either moderate hypofractionated intensity-modulated RT for a total of 72.6 Gy (49.5 Gy to elective nodal areas) or a conventional fractionated three-dimensional conformal RT for a total of 68.4-72 Gy (39.6-45 Gy to elective nodal areas). Patterns of failure, locoregional control, and survival were analyzed. The median follow-up was 38 months (range, 3 to 80 months). The out-of-field nodal failure when omitting ENI was none. Three patients developed neck recurrences (one in-field recurrence in the 72.6 Gy irradiated nodal area and two in the elective irradiated region of 39.6 Gy). Overall disease failure at any site developed in 11 patients (19.6%). Among these, there were six local failures (10.7%), three regional failures (5.4%), and five distant metastases (8.9%). The 3-year locoregional control rate was 87.1%, and the distant failure-free rate was 90.4%; disease-free survival and overall survival at 3 years was 80% and 86.8%, respectively. No patient developed nodal failure in the omitted ENI site. Our investigation has demonstrated that the reduced volume approach for ENI appears to be a safe treatment approach in NPC
Ultrasound-guided core biopsy: an effective method of detecting axillary nodal metastases.
LENUS (Irish Health Repository)
Solon, Jacqueline G
2012-02-01
BACKGROUND: Axillary nodal status is an important prognostic predictor in patients with breast cancer. This study evaluated the sensitivity and specificity of ultrasound-guided core biopsy (Ax US-CB) at detecting axillary nodal metastases in patients with primary breast cancer, thereby determining how often sentinel lymph node biopsy could be avoided in node positive patients. STUDY DESIGN: Records of patients presenting to a breast unit between January 2007 and June 2010 were reviewed retrospectively. Patients who underwent axillary ultrasonography with or without preoperative core biopsy were identified. Sensitivity, specificity, positive predictive value, and negative predictive value for ultrasonography and percutaneous biopsy were evaluated. RESULTS: Records of 718 patients were reviewed, with 445 fulfilling inclusion criteria. Forty-seven percent (n = 210\\/445) had nodal metastases, with 110 detected by Ax US-CB (sensitivity 52.4%, specificity 100%, positive predictive value 100%, negative predictive value 70.1%). Axillary ultrasonography without biopsy had sensitivity and specificity of 54.3% and 97%, respectively. Lymphovascular invasion was an independent predictor of nodal metastases (sensitivity 60.8%, specificity 80%). Ultrasound-guided core biopsy detected more than half of all nodal metastases, sparing more than one-quarter of all breast cancer patients an unnecessary sentinel lymph node biopsy. CONCLUSIONS: Axillary ultrasonography, when combined with core biopsy, is a valuable component of the management of patients with primary breast cancer. Its ability to definitively identify nodal metastases before surgical intervention can greatly facilitate a patient\\'s preoperative integrated treatment plan. In this regard, we believe our study adds considerably to the increasing data, which indicate the benefit of Ax US-CB in the preoperative detection of nodal metastases.
International Nuclear Information System (INIS)
Kang, Dong Gu
2017-01-01
Highlights: • The nodalization of APR-1400 was modified to reflect the characteristic of upper region temperature. • The effect of nodalization and temperature of reactor upper region on LBLOCA consequence was evaluated. • The modification of nodalization is an essential prerequisite in APR-1400 LBLOCA analysis. - Abstract: In best estimate (BE) calculation, the definition of system nodalization is important step influencing the prediction accuracy for specific thermal-hydraulic phenomena. The upper region of reactor is defined as the region of the upper guide structure (UGS) and upper dome. It has been assumed that the temperature of upper region is close to average temperature in most large break loss of coolant accident (LBLOCA) analysis cases. However, it was recently found that the temperature of upper region of APR-1400 reactor might be little lower than or similar to hot leg temperature through the review of detailed design data. In this study, the nodalization of APR-1400 was modified to reflect the characteristic of upper region temperature, and the effect of nodalization and temperature of reactor upper region on LBLOCA consequence was evaluated by sensitivity analysis including best estimate plus uncertainty (BEPU) calculation. In basecase calculation, in case of modified version, the peak cladding temperature (PCT) in blowdown phase became higher and the blowdown quenching (or cooling) was significantly deteriorated as compared to original case, and as a result, the cladding temperature in reflood phase became higher and the final quenching was also delayed. In addition, thermal-hydraulic parameters were compared and analyzed to investigate the effect of change of upper region on cladding temperature. In BEPU analysis, the 95 percentile PCT used in current regulatory practice was increased due to the modification of upper region nodalization, and it occurred in the reflood phase unlike original case.
Extra-nodal extension is a significant prognostic factor in lymph node positive breast cancer.
Directory of Open Access Journals (Sweden)
Sura Aziz
Full Text Available Presence of lymph node (LN metastasis is a strong prognostic factor in breast cancer, whereas the importance of extra-nodal extension and other nodal tumor features have not yet been fully recognized. Here, we examined microscopic features of lymph node metastases and their prognostic value in a population-based cohort of node positive breast cancer (n = 218, as part of the prospective Norwegian Breast Cancer Screening Program NBCSP (1996-2009. Sections were reviewed for the largest metastatic tumor diameter (TD-MET, nodal afferent and efferent vascular invasion (AVI and EVI, extra-nodal extension (ENE, number of ENE foci, as well as circumferential (CD-ENE and perpendicular (PD-ENE diameter of extra-nodal growth. Number of positive lymph nodes, EVI, and PD-ENE were significantly increased with larger primary tumor (PT diameter. Univariate survival analysis showed that several features of nodal metastases were associated with disease-free (DFS or breast cancer specific survival (BCSS. Multivariate analysis demonstrated an independent prognostic value of PD-ENE (with 3 mm as cut-off value in predicting DFS and BCSS, along with number of positive nodes and histologic grade of the primary tumor (for DFS: P = 0.01, P = 0.02, P = 0.01, respectively; for BCSS: P = 0.02, P = 0.008, P = 0.02, respectively. To conclude, the extent of ENE by its perpendicular diameter was independently prognostic and should be considered in line with nodal tumor burden in treatment decisions of node positive breast cancer.
International Nuclear Information System (INIS)
Noh, J. M.; Yoo, J. W.; Joo, H. K.
2004-01-01
In this study, we invented a method of component decomposition to derive the systematic inter-nodal coupled equations of the refined AFEN method and developed an object oriented nodal code to solve the derived coupled equations. The method of component decomposition decomposes the intra-nodal flux expansion of a nodal method into even and odd components in three dimensions to reduce the large coupled linear system equation into several small single equations. This method requires no additional technique to accelerate the iteration process to solve the inter-nodal coupled equations, since the derived equations can automatically act as the coarse mesh re-balance equations. By utilizing the object oriented programming concepts such as abstraction, encapsulation, inheritance and polymorphism, dynamic memory allocation, and operator overloading, we developed an object oriented nodal code that can facilitate the input/output and the dynamic control of the memories, and can make the maintenance easy. (authors)
Analytical Estimates of the Dispersion Curve in Planar Ionization Fronts
International Nuclear Information System (INIS)
Arrayas, Manuel; Trueba, Jose L.; Betelu, Santiago; Fontelos, Marco A.
2009-01-01
Fingers from ionization fronts for a hydrodynamic plasma model result from a balance between impact ionization and electron diffusion in a non-attaching gas. An analytical estimation of the size of the fingers and its dependence on both the electric field and electron diffusion coefficient can be done when the diffusion is low and the electric field is strong.
Energy Technology Data Exchange (ETDEWEB)
Najera H, M.C
2003-07-01
As they have gone being managed complex systems that fulfill tasks inside industrial or nuclear processes, it becomes necessary the development of technical novel of control, in which can incorporate heuristic knowledge of operation without to necessarily use the theories of classic control based mainly in mathematical models. One of the control techniques that allows to carry out this is the control based on diffuse logic. For the case of a model of the nuclear research reactor Triga Mark III of the National Institute of Nuclear Research have been developed diverse algorithms of diffuse control that have as objective the regulation of the neutron power in the nucleus. The aggregation stages and desdifussification in these algorithms discretize the universe of values of the control variable, being required a high number of operations for their execution. With the purpose of reducing this number of operations and to obtain results more exact in the generation of the aggregated group in each cycle of control and in the determination of the center of gravity of this added group, it is presented the development of an analytical method for these calculations. The main objectives outlined in this entitled thesis {sup D}esign of an analytical aggregate of a diffuse controller rules and their application in the pattern of a nuclear research reactor{sup ,} they are: to improve the behavior of control systems in closed knot based on diffuse logic by means of the development of an analytical method that determines an aggregated group resultant of the activation of rules in the diffuse controller and the obtaining of the exit variable using an exact solution of the technique of the center of gravity; and to compare the operation of these methods with those traditionally used ones that consider the discretization of the universe of the exit variable so much for the aggregation like for the desdiffusification. The chapters 1 and 2 present an introduction at two fundamental
Directory of Open Access Journals (Sweden)
Jun Zhou
Full Text Available OBJECTIVE: To investigate the accuracy of preoperative computed tomography (CT, magnetic resonance (MR imaging and diffusion-weighted imaging with background body signal suppression (DWIBS in the prediction of nodal involvement in primary rectal carcinoma patients in the absence of tumor invasion into pelvic structures. METHODS AND MATERIALS: Fifty-two subjects with primary rectal cancer were preoperatively assessed by CT and MRI at 1.5 T with a phased-array coil. Preoperative lymph node staging with imaging modalities (CT, MRI, and DWIBS were compared with the final histological findings. RESULTS: The accuracy of CT, MRI, and DWIBS were 57.7%, 63.5%, and 40.4%. The accuracy of DWIBS with higher sensitivity and negative predictive value for evaluating primary rectal cancer patients was lower than that of CT and MRI. Nodal staging agreement between imaging and pathology was fairly strong for CT and MRI (Kappa value = 0.331 and 0.348, P<0.01 but was relatively weaker for DWIBS (Kappa value = 0.174, P<0.05. The accuracy was 57.7% and 59.6%, respectively, for CT and MRI when the lymph node border information was used as the criteria, and was 57.7% and 61.5%, respectively, for enhanced CT and MRI when the lymph node enhancement pattern was used as the criteria. CONCLUSION: MRI is more accurate than CT in predicting nodal involvement in primary rectal carcinoma patients in the absence of tumor invasion into pelvic structures. DWIBS has a great diagnostic value in differentiating small malignant from benign lymph nodes.
Fractional Diffusion Equations and Anomalous Diffusion
Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin
2018-01-01
Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.
Recognizing nodal marginal zone lymphoma: recent advances and pitfalls. A systematic review
van den Brand, Michiel; van Krieken, J. Han J.M.
2013-01-01
The diagnosis of nodal marginal zone lymphoma is one of the remaining problem areas in hematopathology. Because no established positive markers exist for this lymphoma, it is frequently a diagnosis of exclusion, making distinction from other low-grade B-cell lymphomas difficult or even impossible. This systematic review summarizes and discusses the current knowledge on nodal marginal zone lymphoma, including clinical features, epidemiology and etiology, histology, and cytogenetic and molecular features. In particular, recent advances in diagnostics and pathogenesis are discussed. New immunohistochemical markers have become available that could be used as positive markers for nodal marginal zone lymphoma. These markers could be used to ensure more homogeneous study groups in future research. Also, recent gene expression studies and studies describing specific gene mutations have provided clues to the pathogenesis of nodal marginal zone lymphoma, suggesting deregulation of the nuclear factor kappa B pathway. Nevertheless, nodal marginal zone lymphoma remains an enigmatic entity, requiring further study to define its pathogenesis to allow an accurate diagnosis and tailored treatment. However, recent data indicate that it is not related to splenic or extranodal lymphoma, and that it is also not related to lymphoplasmacytic lymphoma. Thus, even though the diagnosis is not always easy, it is clearly a separate entity. PMID:23813646
Interplay between short-range correlated disorder and Coulomb interaction in nodal-line semimetals
Wang, Yuxuan; Nandkishore, Rahul M.
2017-09-01
In nodal-line semimetals, Coulomb interactions and short-range correlated disorder are both marginal perturbations to the clean noninteracting Hamiltonian. We analyze their interplay using a weak-coupling renormalization group approach. In the clean case, the Coulomb interaction has been found to be marginally irrelevant, leading to Fermi liquid behavior. We extend the analysis to incorporate the effects of disorder. The nodal line structure gives rise to kinematical constraints similar to that for a two-dimensional Fermi surface, which plays a crucial role in the one-loop renormalization of the disorder couplings. For a twofold degenerate nodal loop (Weyl loop), we show that disorder flows to strong coupling along a unique fixed trajectory in the space of symmetry inequivalent disorder couplings. Along this fixed trajectory, all symmetry inequivalent disorder strengths become equal. For a fourfold degenerate nodal loop (Dirac loop), disorder also flows to strong coupling, however, the strengths of symmetry inequivalent disorder couplings remain different. We show that feedback from disorder reverses the sign of the beta function for the Coulomb interaction, causing the Coulomb interaction to flow to strong coupling as well. However, the Coulomb interaction flows to strong coupling asymptotically more slowly than disorder. Extrapolating our results to strong coupling, we conjecture that at low energies nodal line semimetals should be described by a noninteracting nonlinear sigma model. We discuss the relation of our results with possible many-body localization at zero temperatures in such materials.
Tumor microvessel density–associated mast cells in canine nodal lymphoma
Directory of Open Access Journals (Sweden)
Moges Woldemeskel
2014-11-01
Full Text Available Objective: Mast cells are associated in angiogenesis in various human and animal neoplasms. However, association of mast cells with tumor microvessel density in canine lymphoma was not previously documented. The objective of the study is to determine if mast cells are increased in canine nodal lymphomas and to evaluate their correlation with tumor microvessel density and grading of lymphomas. Methods: Nodal lymphomas from 33 dogs were studied and compared with nonneoplastic lymph nodes from 6 dogs as control. Mast cell count was made on Toluidine blue stained sections. Immunohistochemistry using antibody against Factor VIII was employed to visualize and determine microvessel density. Results: The mast cell count in lymphoma (2.95 ± 2.4 was significantly higher (p < 0.05 than that in the control (0.83 ± 0.3 and was positively correlated with tumor microvessel density (r = 0.44, p = 0.009. Significant difference was not observed in mast cell count and tumor microvessel density among different gradings of lymphomas. Conclusions: Mast cells are associated with tumor microvessel density in canine nodal lymphoma with no significant difference among gradings of lymphomas. Mast cells may play an important role in development of canine nodal lymphomas. Further detailed investigation on the role of mast cells as important part of tumor microenvironment in canine nodal lymphomas is recommended.
Sensitivity analysis of MIDAS tests using SPACE code. Effect of nodalization
International Nuclear Information System (INIS)
Eom, Shin; Oh, Seung-Jong; Diab, Aya
2018-01-01
The nodalization sensitivity analysis for the ECCS (Emergency Core Cooling System) bypass phe�nomena was performed using the SPACE (Safety and Performance Analysis CodE) thermal hydraulic analysis computer code. The results of MIDAS (Multi-�dimensional Investigation in Downcomer Annulus Simulation) test were used. The MIDAS test was conducted by the KAERI (Korea Atomic Energy Research Institute) for the performance evaluation of the ECC (Emergency Core Cooling) bypass phenomenon in the DVI (Direct Vessel Injection) system. The main aim of this study is to examine the sensitivity of the SPACE code results to the number of thermal hydraulic channels used to model the annulus region in the MIDAS experiment. The numerical model involves three nodalization cases (4, 6, and 12 channels) and the result show that the effect of nodalization on the bypass fraction for the high steam flow rate MIDAS tests is minimal. For computational efficiency, a 4 channel representation is recommended for the SPACE code nodalization. For the low steam flow rate tests, the SPACE code over-�predicts the bypass fraction irrespective of the nodalization finesse. The over-�prediction at low steam flow may be attributed to the difficulty to accurately represent the flow regime in the vicinity of the broken cold leg.
Nodalization effects on RELAP5 results related to MTR research reactor transient scenarios
Directory of Open Access Journals (Sweden)
Khedr Ahmed
2005-01-01
Full Text Available The present work deals with the anal y sis of RELAP5 results obtained from the evaluation study of the total loss of flow transient with the deficiency of the heat removal system in a research reactor using two different nodalizations. It focuses on the effect of nodalization on the thermal-hydraulic evaluation of the re search reactor. The analysis of RELAP5 results has shown that nodalization has a big effect on the predicted scenario of the postulated transient. There fore, great care should be taken during the nodalization of the reactor, especially when the avail able experimental or measured data are insufficient for making a complete qualification of the nodalization. Our analysis also shows that the research reactor pool simulation has a great effect on the evaluation of natural circulation flow and on other thermal-hydraulic parameters during the loss of flow transient. For example, the on set time of core boiling changes from less than 2000 s to 15000 s, starting from the beginning of the transient. This occurs if the pool is simulated by two vertical volumes in stead of one vertical volume.
Tumor microvessel density–associated mast cells in canine nodal lymphoma
Mann, Elizabeth; Whittington, Lisa
2014-01-01
Objective: Mast cells are associated in angiogenesis in various human and animal neoplasms. However, association of mast cells with tumor microvessel density in canine lymphoma was not previously documented. The objective of the study is to determine if mast cells are increased in canine nodal lymphomas and to evaluate their correlation with tumor microvessel density and grading of lymphomas. Methods: Nodal lymphomas from 33 dogs were studied and compared with nonneoplastic lymph nodes from 6 dogs as control. Mast cell count was made on Toluidine blue stained sections. Immunohistochemistry using antibody against Factor VIII was employed to visualize and determine microvessel density. Results: The mast cell count in lymphoma (2.95 ± 2.4) was significantly higher (p < 0.05) than that in the control (0.83 ± 0.3) and was positively correlated with tumor microvessel density (r = 0.44, p = 0.009). Significant difference was not observed in mast cell count and tumor microvessel density among different gradings of lymphomas. Conclusions: Mast cells are associated with tumor microvessel density in canine nodal lymphoma with no significant difference among gradings of lymphomas. Mast cells may play an important role in development of canine nodal lymphomas. Further detailed investigation on the role of mast cells as important part of tumor microenvironment in canine nodal lymphomas is recommended. PMID:26770752
Sensitivity analysis of MIDAS tests using SPACE code. Effect of nodalization
Energy Technology Data Exchange (ETDEWEB)
Eom, Shin; Oh, Seung-Jong; Diab, Aya [KEPCO International Nuclear Graduate School (KINGS), Ulsan (Korea, Republic of). Dept. of NPP Engineering
2018-02-15
The nodalization sensitivity analysis for the ECCS (Emergency Core Cooling System) bypass phe�nomena was performed using the SPACE (Safety and Performance Analysis CodE) thermal hydraulic analysis computer code. The results of MIDAS (Multi-�dimensional Investigation in Downcomer Annulus Simulation) test were used. The MIDAS test was conducted by the KAERI (Korea Atomic Energy Research Institute) for the performance evaluation of the ECC (Emergency Core Cooling) bypass phenomenon in the DVI (Direct Vessel Injection) system. The main aim of this study is to examine the sensitivity of the SPACE code results to the number of thermal hydraulic channels used to model the annulus region in the MIDAS experiment. The numerical model involves three nodalization cases (4, 6, and 12 channels) and the result show that the effect of nodalization on the bypass fraction for the high steam flow rate MIDAS tests is minimal. For computational efficiency, a 4 channel representation is recommended for the SPACE code nodalization. For the low steam flow rate tests, the SPACE code over-�predicts the bypass fraction irrespective of the nodalization finesse. The over-�prediction at low steam flow may be attributed to the difficulty to accurately represent the flow regime in the vicinity of the broken cold leg.
Helrich, Carl S
2017-01-01
This advanced undergraduate textbook begins with the Lagrangian formulation of Analytical Mechanics and then passes directly to the Hamiltonian formulation and the canonical equations, with constraints incorporated through Lagrange multipliers. Hamilton's Principle and the canonical equations remain the basis of the remainder of the text. Topics considered for applications include small oscillations, motion in electric and magnetic fields, and rigid body dynamics. The Hamilton-Jacobi approach is developed with special attention to the canonical transformation in order to provide a smooth and logical transition into the study of complex and chaotic systems. Finally the text has a careful treatment of relativistic mechanics and the requirement of Lorentz invariance. The text is enriched with an outline of the history of mechanics, which particularly outlines the importance of the work of Euler, Lagrange, Hamilton and Jacobi. Numerous exercises with solutions support the exceptionally clear and concise treatment...
Cryopreservation of in vitro grown nodal segments of Rauvolfia serpentina by PVS2 vitrification.
Ray, Avik; Bhattacharya, Sabita
2008-01-01
This paper describes the cryopreservation by PVS2 vitrification of Rauvolfia serpentina (L.) Benth ex kurz, an important tropical medicinal plant. The effects of type and size of explants, sucrose preculture (duration and concentration) and vitrification treatment were tested. Preliminary experiments with PVS1, 2 and 3 produced shoot growth only for PVS2. When optimizing the PVS2 vitrification of nodal segments, those of 0.31 - 0.39 cm in size were better than other nodal sizes and or apices. Sucrose preculture had a positive role in survival and subsequent regrowth of the cryopreserved explants. Seven days on 0.5 M sucrose solution significantly improved the viability of nodal segments. PVS2 incubation for 45 minutes combined with a 7-day preculture gave the optimum result of 66 percent. Plantlets derived after cryopreservation resumed growth and regenerated normally.
Isospectral discrete and quantum graphs with the same flip counts and nodal counts
Juul, Jonas S.; Joyner, Christopher H.
2018-06-01
The existence of non-isomorphic graphs which share the same Laplace spectrum (to be referred to as isospectral graphs) leads naturally to the following question: what additional information is required in order to resolve isospectral graphs? It was suggested by Band, Shapira and Smilansky that this might be achieved by either counting the number of nodal domains or the number of times the eigenfunctions change sign (the so-called flip count) (Band et al 2006 J. Phys. A: Math. Gen. 39 13999–4014 Band and Smilansky 2007 Eur. Phys. J. Spec. Top. 145 171–9). Recent examples of (discrete) isospectral graphs with the same flip count and nodal count have been constructed by Ammann by utilising Godsil–McKay switching (Ammann private communication). Here, we provide a simple alternative mechanism that produces systematic examples of both discrete and quantum isospectral graphs with the same flip and nodal counts.
Discrete rod burnup analysis capability in the Westinghouse advanced nodal code
International Nuclear Information System (INIS)
Buechel, R.J.; Fetterman, R.J.; Petrunyak, M.A.
1992-01-01
Core design analysis in the last several years has evolved toward the adoption of nodal-based methods to replace traditional fine-mesh models as the standard neutronic tool for first core and reload design applications throughout the nuclear industry. The accuracy, speed, and reduction in computation requirements associated with the nodal methods have made three-dimensional modeling the preferred approach to obtain the most realistic core model. These methods incorporate detailed rod power reconstruction as well. Certain design applications such as confirmation of fuel rod design limits and fuel reconstitution considerations, for example, require knowledge of the rodwise burnup distribution to avoid unnecessary conservatism in design analyses. The Westinghouse Advanced Nodal Code (ANC) incorporates the capability to generate the intra-assembly pin burnup distribution using an efficient algorithm
International Nuclear Information System (INIS)
Colombo, V; Ghedini, E; Gherardi, M; Sanibondi, P; Shigeta, M
2012-01-01
Nano-particle synthesis by means of inductively coupled plasma torches is a material process of large technological interest. Numerous parameters are involved in the optimization of this process; hence the development of numerical models for the prediction of thermal and magneto-fluid dynamics fields, precursor powder trajectories and thermal history, as well as nano-particle formation and growth, is necessary for the up-scaling of these devices from laboratory batch production to an industrial continuous process. In this work, a two-dimensional (2D) discrete-type model (nodal model) for the analysis of nano-powder nucleation and growth is presented, taking into account convection, diffusion and turbulent effects on particle formation. Discrete-type models feature high precision and reveal a great deal of information useful for clarifying the nano-particle formation process. Using Si as the precursor material, 2D simulations of a nano-particle synthesis RF plasma apparatus with a reaction chamber are carried out. Good agreement is found when comparing results obtained with this model with those coming from a well-established nucleation-coupled moment method. Moreover, the extended amount of obtainable information that characterizes the nodal model is underlined. (paper)
Application of the RT-0 nodal methods and NRMPO matrix-response to the cycles 1 and 2 of the LVC
International Nuclear Information System (INIS)
Delfin L, A.; Hernandez L, H.; Alonso V, G.
2005-01-01
The nodal methods the same as that of matrix-response are used to develop numeric calculations, so much in static as dynamics of reactors, in one, two and three dimensions. The topic of this work is to apply the equations modeled in the RPM0 program, obtained when using the nodal scheme RT-0 (Raviart-Thomas index zero) in the neutron diffusion equation in stationary state X Y geometry, applying finite differences centered in mesh and lineal reactivity; also, to use those equations captured in the NRMPO program developed by E. Malambu that uses the matrix-response method in X Y geometry. The numeric results of the radial distribution of power by fuel assembly of the unit 1, in the cycles 1 and 2 of the CLV obtained by both methods, they are compared with the calculations obtained with the CM-PRESTO code that is a neutronic-thermo hydraulic simulator in three dimensions. The comparison of the radial distribution of power in the cycles 1 and 2 of the CLV with the CM-PRESTO code, it presents for RPM0 maximum errors of 8.2% and 12.4% and for NRMPO 31.2% and 61.3% respectively. The results show that it can be feasible to use the program RPM0 like a quick and efficient tool in the multicycle analysis in the fuel management. (Author)
A transient, Hex-Z nodal code corrected by discontinuity factors
International Nuclear Information System (INIS)
Shatilla, Y.A.M.; Henry, A.F.
1993-01-01
This document constitutes Volume 1 of the Final Report of a three-year study supported by the special Research Grant Program for Nuclear Energy Research set up by the US Department of Energy. The original motivation for the work was to provide a fast and accurate computer program for the analysis of transients in heavy water or graphite-moderated reactors being considered as candidates for the New Production Reactor. Thus, part of the funding was by way of pass-through money from the Savannah River Laboratory. With this intent in mind, a three-dimensional (Hex-Z), general-energy-group transient, nodal code was created, programmed, and tested. In order to improve accuracy, correction terms, called open-quotes discontinuity factors,close quotes were incorporated into the nodal equations. Ideal values of these factors force the nodal equations to provide node-integrated reaction rates and leakage rates across nodal surfaces that match exactly those edited from a more exact reference calculation. Since the exact reference solution is needed to compute the ideal discontinuity factors, the fact that they result in exact nodal equations would be of little practical interest were it not that approximate discontinuity factors, found at a greatly reduced cost, often yield very accurate results. For example, for light-water reactors, discontinuity factors found from two-dimensional, fine-mesh, multigroup transport solutions for two-dimensional cuts of a fuel assembly provide very accurate predictions of three-dimensional, full-core power distributions. The present document (volume 1) deals primarily with the specification, programming and testing of the three-dimensional, Hex-Z computer program. The program solves both the static (eigenvalue) and transient, general-energy-group, nodal equations corrected by user-supplied discontinuity factors
Fluorine-18-Fluorodeoxyglucose PET in the mediastinal nodal staging of bronchogenic carcinoma.
Energy Technology Data Exchange (ETDEWEB)
Berlangieri, S.U.; Scott, A.M.; Knight, S.; Pointon, O.; Thomas, D.L.; O``Keefe, G.; Chan, J.G.; Egen, G.F.; Tochon-Danguy, H.J.; Clarke, C.P.; McKay, W.J. [Austin Hospital, Melbourne, VIC (Australia). Centre for Positron Emission Tomography and the Departments of Nuclear Medicine and Thoracic Surgery
1998-03-01
Full text: Non-invasive methods of pre-operative staging of non-small cell bronchogenic carcinoma are inaccurate. To determine the clinical role of positron emission tomography (PET) in the mediastinal staging of lung carcinoma, {sup 18}F-fluorodeoxyglucose (FDG) studies were performed in 25 patients with suspected non-small cell bronchogenic carcinoma and correlated with pathology. The patients comprised 20 men and 5 women (mean age 63; range 43-78 y). All patients had proven non-small cell lung carcinoma, except two, one patient with benign inflammatory disease and the other with small cell carcinoma. The FDG PET studies were acquired on a Siemens 951131R body tomography over 2-3 bed positions to include the thorax and mediastinum. The PET images were interpreted for tumour involvement of mediastinal nodes according to the American Thoracic Society classification and scored for confidence of tumour presence on a 5 point scale. The intensity of glucose metabolism was compared to mediastinal blood pool activity and graded on a 4 point scale. FDG PET correctly excluded ipsilateral mediastinal nodal (N2) disease in 16 of 16 patients. Six of nine patients with N2 disease were correctly identified by FDG PET. Of the three patients with N2 nodal involvement not detected by PET, each had single station nodal disease, and in two patients the primary lesions abutted the involved nodal group. A total of 104 nodal stations were sampled or examined at surgery. FDG PET correctly excluded disease in 83/83 (100% specificity) negative nodal stations. FDG PET is a promising non-invasive functional imaging modality for the mediastinal staging of bronchogenic carcinoma.
On the treatment of nonlinear local feedbacks within advanced nodal generalized perturbation theory
International Nuclear Information System (INIS)
Maldonado, G.I.; Turinsky, P.J.; Kropaczek, D.J.
1993-01-01
Recent efforts to upgrade the underlying neutronics formulations within the in-core nuclear fuel management optimization code FORMOSA (Ref. 1) have produced two important developments; first, a computationally efficient and second-order-accurate advanced nodal generalized perturbation theory (GPT) model [derived from the nonlinear iterative nodal expansion method (NEM)] for evaluating core attributes (i.e., k eff and power distribution versus cycle burnup), and second, an equally efficient and accurate treatment of local thermal-hydraulic and fission product feedbacks embedded within NEM GPT. The latter development is the focus of this paper
Segregated nodal domains of two-dimensional multispecies Bose-Einstein condensates
Chang, Shu-Ming; Lin, Chang-Shou; Lin, Tai-Chia; Lin, Wen-Wei
2004-09-01
In this paper, we study the distribution of m segregated nodal domains of the m-mixture of Bose-Einstein condensates under positive and large repulsive scattering lengths. It is shown that components of positive bound states may repel each other and form segregated nodal domains as the repulsive scattering lengths go to infinity. Efficient numerical schemes are created to confirm our theoretical results and discover a new phenomenon called verticillate multiplying, i.e., the generation of multiple verticillate structures. In addition, our proposed Gauss-Seidel-type iteration method is very effective in that it converges linearly in 10-20 steps.
Riou, O; Bourgier, C; Fenoglietto, P; Azria, D
2015-06-01
Treatment volume is a major risk factor of radiation-induced toxicity. As nodal irradiation increases treatment volume, radiation toxicity should be greater. Nevertheless, scientific randomised data do not support this fact. However, a radiation-induced toxicity is possible outside tangential fields in the nodal volumes not related to breast-only treatment. Treatment should not be adapted only to the disease but personalized to the individual risk of toxicity for each patient. Copyright © 2015 Société française de radiothérapie oncologique (SFRO). Published by Elsevier SAS. All rights reserved.
Nodal signals mediate interactions between the extra-embryonic and embryonic tissues in zebrafish
Xiang, Fan; Hagos, Engda G.; Xu, Bo; Sias, Christina; Kawakami, Koichi; Burdine, Rebecca D.; Dougan, Scott T.
2007-01-01
In many vertebrates, extra-embryonic tissues are important signaling centers that induce and pattern the germ layers. In teleosts, the mechanism by which the extra-embryonic yolk syncytial layer (YSL) patterns the embryo is not understood. Although the Nodal-related protein Squint is expressed in the YSL, its role in this tissue is not known. We generated a series of stable transgenic lines with GFP under the control of squint genomic sequences. In all species, nodal-related genes induce thei...
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Lao, Louis [Department of Radiation Oncology, Princess Margaret Cancer Centre, University of Toronto, Toronto, Ontario (Canada); Department of Radiation Oncology, Auckland City Hospital, Auckland (New Zealand); Hope, Andrew J. [Department of Radiation Oncology, Princess Margaret Cancer Centre, University of Toronto, Toronto, Ontario (Canada); Maganti, Manjula [Department of Biostatistics, Princess Margaret Cancer Centre, University of Toronto, Toronto, Ontario (Canada); Brade, Anthony; Bezjak, Andrea; Saibishkumar, Elantholi P.; Giuliani, Meredith; Sun, Alexander [Department of Radiation Oncology, Princess Margaret Cancer Centre, University of Toronto, Toronto, Ontario (Canada); Cho, B. C. John, E-mail: john.cho@rmp.uhn.on.ca [Department of Radiation Oncology, Princess Margaret Cancer Centre, University of Toronto, Toronto, Ontario (Canada)
2014-09-01
Purpose: Reported rates of non-small cell lung cancer (NSCLC) nodal failure following stereotactic body radiation therapy (SBRT) are lower than those reported in the surgical series when matched for stage. We hypothesized that this effect was due to incidental prophylactic nodal irradiation. Methods and Materials: A prospectively collected group of medically inoperable early stage NSCLC patients from 2004 to 2010 was used to identify cases with nodal relapses. Controls were matched to cases, 2:1, controlling for tumor volume (ie, same or greater) and tumor location (ie, same lobe). Reference (normalized to equivalent dose for 2-Gy fractions [EQD2]) point doses at the ipsilateral hilum and carina, demographic data, and clinical outcomes were extracted from the medical records. Univariate conditional logistical regression analyses were performed with variables of interest. Results: Cases and controls were well matched except for size. The controls, as expected, had larger gross tumor volumes (P=.02). The mean ipsilateral hilar doses were 9.6 Gy and 22.4 Gy for cases and controls, respectively (P=.014). The mean carinal doses were 7.0 Gy and 9.2 Gy, respectively (P=.13). Mediastinal nodal relapses, with and without ipsilateral hilar relapse, were associated with mean ipsilateral hilar doses of 3.6 Gy and 19.8 Gy, respectively (P=.01). The conditional density plot appears to demonstrate an inverse dose-effect relationship between ipsilateral hilar normalized total dose and risk of ipsilateral hilar relapse. Conclusions: Incidental hilar dose greater than 20 Gy is significantly associated with fewer ipsilateral hilar relapses in inoperable early stage NSCLC patients treated with SBRT.
International Nuclear Information System (INIS)
Lao, Louis; Hope, Andrew J.; Maganti, Manjula; Brade, Anthony; Bezjak, Andrea; Saibishkumar, Elantholi P.; Giuliani, Meredith; Sun, Alexander; Cho, B. C. John
2014-01-01
Purpose: Reported rates of non-small cell lung cancer (NSCLC) nodal failure following stereotactic body radiation therapy (SBRT) are lower than those reported in the surgical series when matched for stage. We hypothesized that this effect was due to incidental prophylactic nodal irradiation. Methods and Materials: A prospectively collected group of medically inoperable early stage NSCLC patients from 2004 to 2010 was used to identify cases with nodal relapses. Controls were matched to cases, 2:1, controlling for tumor volume (ie, same or greater) and tumor location (ie, same lobe). Reference (normalized to equivalent dose for 2-Gy fractions [EQD2]) point doses at the ipsilateral hilum and carina, demographic data, and clinical outcomes were extracted from the medical records. Univariate conditional logistical regression analyses were performed with variables of interest. Results: Cases and controls were well matched except for size. The controls, as expected, had larger gross tumor volumes (P=.02). The mean ipsilateral hilar doses were 9.6 Gy and 22.4 Gy for cases and controls, respectively (P=.014). The mean carinal doses were 7.0 Gy and 9.2 Gy, respectively (P=.13). Mediastinal nodal relapses, with and without ipsilateral hilar relapse, were associated with mean ipsilateral hilar doses of 3.6 Gy and 19.8 Gy, respectively (P=.01). The conditional density plot appears to demonstrate an inverse dose-effect relationship between ipsilateral hilar normalized total dose and risk of ipsilateral hilar relapse. Conclusions: Incidental hilar dose greater than 20 Gy is significantly associated with fewer ipsilateral hilar relapses in inoperable early stage NSCLC patients treated with SBRT
Energy Technology Data Exchange (ETDEWEB)
Akherraz, B.; Lautard, J.J. [CEA Saclay, Dept. Modelisation de Systemes et Structures, Serv. d' Etudes des Reacteurs et de Modelisation Avancee (DMSS/SERMA), 91 - Gif sur Yvette (France); Erhard, P. [Electricite de France (EDF), Dir. de Recherche et Developpement, Dept. Sinetics, 92 - Clamart (France)
2003-07-01
In this paper we present two applications of the Nodal finite elements developed by Hennart and del Valle, first to three-dimensional Cartesian meshes and then to two-dimensional Hexagonal meshes. This work has been achieved within the framework of the DESCARTES project, which is a co-development effort by the 'Commissariat a l'Energie Atomique' (CEA) and 'Electricite de France' (EDF) for the development of a toolbox for reactor core calculations based on object oriented programming. The general structure of this project is based on the object oriented method. By using a mapping technique proposed in Schneider's thesis and del Valle, Mund, we show how this structuration allows us an easy implementation of the hexagonal case from the Cartesian case. The main attractiveness of this methodology is the possibility of a pin-by-pin representation by division of each lozenge into smaller ones. Furthermore, we will explore the use of non structured quadrangles to treat the circular geometry within a hexagon. It remains nevertheless, in the hexagonal case, the implementation of the acceleration of the internal iterations by the DSA (Diffusion Synthetic Acceleration) or the TSA. (authors)
International Nuclear Information System (INIS)
Toreja, Allen J.; Uddin, Rizwan
2002-01-01
An existing implementation of the nodal integral method for the time-dependent convection-diffusion equation is modified to incorporate various PETSc (Portable, Extensible Tool-kit for Scientific Computation) solver and pre-conditioner routines. In the modified implementation, the default iterative Gauss-Seidel solver is replaced with one of the following PETSc iterative linear solver routines: Generalized Minimal Residuals, Stabilized Bi-conjugate Gradients, or Transpose-Free Quasi-Minimal Residuals. For each solver, a Jacobi or a Successive Over-Relaxation pre-conditioner is used. Two sample problems, one with a low Peclet number and one with a high Peclet number, are solved using the new implementation. In all the cases tested, the new implementation with the PETSc solver routines outperforms the original Gauss-Seidel implementation. Moreover, the PETSc Stabilized Bi-conjugate Gradients routine performs the best on the two sample problems leading to CPU times that are less than half the CPU times of the original implementation. (authors)
Noorlag, Rob; Boeve, Koos; Witjes, Max J H; Koole, Ronald; Peeters, Ton L M; Schuuring, Ed; Willems, Stefan M; van Es, Robert J J
2017-02-01
Accurate nodal staging is pivotal for treatment planning in early (stage I-II) oral cancer. Unfortunately, current imaging modalities lack sensitivity to detect occult nodal metastases. Chromosomal region 11q13, including genes CCND1, Fas-associated death domain (FADD), and CTTN, is often amplified in oral cancer with nodal metastases. However, evidence in predicting occult nodal metastases is limited. In 158 patients with early tongue and floor of mouth (FOM) squamous cell carcinomas, both CCND1 amplification and cyclin D1, FADD, and cortactin protein expression were correlated with occult nodal metastases. CCND1 amplification and cyclin D1 expression correlated with occult nodal metastases. Cyclin D1 expression was validated in an independent multicenter cohort, confirming the correlation with occult nodal metastases in early FOM cancers. Cyclin D1 is a predictive biomarker for occult nodal metastases in early FOM cancers. Prospective research on biopsy material should confirm these results before implementing its use in routine clinical practice. © 2016 Wiley Periodicals, Inc. Head Neck 39: 326-333, 2017. © 2016 Wiley Periodicals, Inc.
International Nuclear Information System (INIS)
Anderson, R.C.
1976-01-01
A method is described for joining beryllium to beryllium by diffusion bonding. At least one surface portion of at least two beryllium pieces is coated with nickel. A coated surface portion is positioned in a contiguous relationship with another surface portion and subjected to an environment having an atmosphere at a pressure lower than ambient pressure. A force is applied on the beryllium pieces for causing the contiguous surface portions to abut against each other. The contiguous surface portions are heated to a maximum temperature less than the melting temperature of the beryllium, and the applied force is decreased while increasing the temperature after attaining a temperature substantially above room temperature. A portion of the applied force is maintained at a temperature corresponding to about maximum temperature for a duration sufficient to effect the diffusion bond between the contiguous surface portions
van den Brand, Michiel; van der Velden, Walter J F M; Diets, Illja J; Ector, Geneviève I C G; de Haan, Anton F J; Stevens, Wendy B C; Hebeda, Konnie M; Groenen, Patricia J T A; van Krieken, Han J M
2016-07-01
Nodal marginal zone lymphoma (NMZL) is a rare type of B-cell non-Hodgkin lymphoma. This study assessed the clinical features of 56 patients with NMZL in comparison to 46 patients with follicular lymphoma (FL). Patients with NMZL and FL had a largely similar clinical presentation, but patients with FL had a higher disease stage at presentation, more frequent abdominal lymphadenopathy and bone marrow involvement, and showed more common transformation into diffuse large B-cell lymphoma (DLBCL) during the course of disease. Overall survival and event-free survival were similar for patients with NMZL and FL, but factors associated with worse prognosis differed between the two groups. Transformation into DLBCL was associated with a significantly poorer outcome in both groups, but the phenotypes were different: DLBCL arising in FL was mainly of germinal center B-cell phenotype, whereas DLBCL arising in NMZL was mainly of non-germinal center B-cell phenotype.
Diffusion in Deterministic Interacting Lattice Systems
Medenjak, Marko; Klobas, Katja; Prosen, Tomaž
2017-09-01
We study reversible deterministic dynamics of classical charged particles on a lattice with hard-core interaction. It is rigorously shown that the system exhibits three types of transport phenomena, ranging from ballistic, through diffusive to insulating. By obtaining an exact expressions for the current time-autocorrelation function we are able to calculate the linear response transport coefficients, such as the diffusion constant and the Drude weight. Additionally, we calculate the long-time charge profile after an inhomogeneous quench and obtain diffusive profilewith the Green-Kubo diffusion constant. Exact analytical results are corroborated by Monte Carlo simulations.
International Nuclear Information System (INIS)
Lalis, A.; Rouviere, R.; Simon, G.
1976-01-01
A multipassage diffuser having 2p passages comprises a leak-tight cylindrical enclosure closed by a top cover and a bottom end-wall, parallel porous tubes which are rigidly assembled in sectors between tube plates and through which the gas mixture flows, the tube sectors being disposed at uniform intervals on the periphery of the enclosure. The top tube plates are rigidly fixed to an annular header having the shape of a half-torus and adapted to communicate with the tubes of the corresponding sector. Each passage is constituted by a plurality of juxtaposed sectors in which the mixture circulates in the same direction, the header being divided into p portions limited by radial partition-walls and each constituting two adjacent passages. The diffuser is provided beneath the bottom end-wall with p-1 leak-tight chambers each adapted to open into two different portions of the header, and with two collector-chambers each fitted with a nozzle for introducing the gas mixture and discharging the fraction of the undiffused mixture. By means of a central orifice formed in the bottom end-wall the enclosure communicates with a shaft for discharging the diffused fraction of the gas mixture
Energy Technology Data Exchange (ETDEWEB)
Oliva, Amaury M.; Filho, Hermes A.; Silva, Davi M.; Garcia, Carlos R., E-mail: aoliva@iprj.uerj.br, E-mail: halves@iprj.uerj.br, E-mail: davijmsilva@yahoo.com.br, E-mail: cgh@instec.cu [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Instituto Politecnico. Departamento de Modelagem Computacional; Instituto Superior de Tecnologias y Ciencias Aplicadas (InSTEC), La Habana (Cuba)
2017-07-01
In this paper, we propose a numerical methodology for the development of a method of the spectral nodal class that will generate numerical solutions free from spatial truncation errors. This method, denominated Spectral Deterministic Method (SDM), is tested as an initial study of the solutions (spectral analysis) of neutron transport equations in the discrete ordinates (S{sub N}) formulation, in one-dimensional slab geometry, multigroup approximation, with linearly anisotropic scattering, considering homogeneous and heterogeneous domains with fixed source. The unknowns in the methodology are the cell-edge, and cell average angular fluxes, the numerical values calculated for these quantities coincide with the analytic solution of the equations. These numerical results are shown and compared with the traditional ne- mesh method Diamond Difference (DD) and the coarse-mesh method spectral Green's function (SGF) to illustrate the method's accuracy and stability. The solution algorithms problems are implemented in a computer simulator made in C++ language, the same that was used to generate the results of the reference work. (author)
Nodal involvement in Hodgkin disease and non-Hodgkin lymphoma assessed by magnetic resonance
International Nuclear Information System (INIS)
Tesoro Tess, J.D.; Balzarini, L.; Ceglia, E.; Petrillo, R.; Musumeci, R.
1990-01-01
Magnetic Resonance Imaging (MRI) demonstrates a good capability in distinguishing nodal involvement in hodgkin disease and nonhodgkin lymphoma both in the chest and in the retroperitoneal areas the initial presentation of the disease. However CT and lymphangiography demonstrated comparable or superior values of accuracy and sensitivity. (H.W.) 4 refs.; 2 tabs
A nodal Grean's function method of reactor core fuel management code, NGCFM2D
International Nuclear Information System (INIS)
Li Dongsheng; Yao Dong.
1987-01-01
This paper presents the mathematical model and program structure of the nodal Green's function method of reactor core fuel management code, NGCFM2D. Computing results of some reactor cores by NGCFM2D are analysed and compared with other codes
Unbounded planar domains whose second nodal line does not touch the boundary
Czech Academy of Sciences Publication Activity Database
Freitas, P.; Krejčiřík, David
2007-01-01
Roč. 14, č. 1 (2007), s. 107-111 ISSN 1073-2780 R&D Projects: GA MŠk LC06002 Institutional research plan: CEZ:AV0Z10480505 Keywords : Dirichlet Laplacian * eigenfunctions * nodal line Subject RIV: BA - General Mathematics Impact factor: 0.702, year: 2007
Computation of Steady State Nodal Voltages for Fast Security Assessment in Power Systems
DEFF Research Database (Denmark)
Møller, Jakob Glarbo; Jóhannsson, Hjörtur; Østergaard, Jacob
2014-01-01
Development of a method for real-time assess-ment of post-contingency nodal voltages is introduced. Linear network theory is applied in an algorithm that utilizes Thevenin equivalent representation of power systems as seen from every voltage-controlled node in a network. The method is evaluated b...
Moran, Jean M.; Balter, James M.; Ben-David, Merav A.; Marsh, Robin B.; van Herk, Marcel; Pierce, Lori J.
2007-01-01
PURPOSE: The short-term displacement and reproducibility of the breast or chest wall, and the internal mammary (IM), infraclavicular (ICV), and supraclavicular (SCV) nodal regions have been assessed as a function of breath-hold state using an active breathing control (ABC) device for patients
An error bound estimate and convergence of the Nodal-LTS N solution in a rectangle
International Nuclear Information System (INIS)
Hauser, Eliete Biasotto; Pazos, Ruben Panta; Tullio de Vilhena, Marco
2005-01-01
In this work, we report the mathematical analysis concerning error bound estimate and convergence of the Nodal-LTS N solution in a rectangle. For such we present an efficient algorithm, called LTS N 2D-Diag solution for Cartesian geometry
Lymphoma no Hodgkin extra nodal in head and neck: value of CT
International Nuclear Information System (INIS)
Ramos Aguilar, A.; Romance Garcia, A.; Fuentes Lupianez, J.J.; Sanchez Lafuente, J.; Rodriguez Sanpedro, F.
1994-01-01
The head and neck regions is one of the most common sites of extra nodal non-Hodgkin's lymphoma (NHL). We studied 7 cases of NHL of head and neck using CT enhanced with intravenous contrast medium, analyzing the important role it plays in diagnosis, treatment planning and evaluation of the recurrence of these tumors. (Author)
Encapsulation of nodal cuttings and shoot tips for storage and exchange of cassava germplasm.
Danso, K E; Ford-Lloyd, B V
2003-04-01
We report the encapsulation of in vitro-derived nodal cuttings or shoot tips of cassava in 3% calcium alginate for storage and germplasm exchange purposes. Shoot regrowth was not significantly affected by the concentration of sucrose in the alginate matrix while root formation was. In contrast, increasing the sucrose concentration in the calcium chloride polymerisation medium significantly reduced regrowth from encapsulated nodal cuttings of accession TME 60444. Supplementing the alginate matrix with increased concentrations of 6-benzylaminopurine and alpha-naphthaleneacetic acid enhanced complete plant regrowth within 2 weeks. Furthermore, plant regrowth by encapsulated nodal cuttings and shoot tips was significantly affected by the duration of the storage period as shoot recovery decreased from almost 100% to 73.3% for encapsulated nodal cuttings and 94.4% to 60% for shoot tips after 28 days of storage. The high frequency of plant regrowth from alginate-coated micropropagules coupled with high viability percentage after 28 days of storage is highly encouraging for the exchange of cassava genetic resources. Such encapsulated micropropagules could be used as an alternative to synthetic seeds derived from somatic embryos.
GDF3 is a BMP inhibitor that can activate Nodal signaling only at very high doses
Levine, Ariel J.; Levine, Zachary J.; Brivanlou, Ali H.
2013-01-01
Within the TGF-β superfamily, there are approximately forty ligands divided into two major branches: the TGF-β/Activin/Nodal ligands and the BMP/GDF ligands. We studied the ligand GDF3 and found that it inhibits signaling by its co-family members, the BMPs; however, GDF3 has been described by others to have Nodal-like activity. Here, we show that GDF3 can activate Nodal signaling, but only at very high doses and only upon mRNA over-expression. In contrast, GDF3 inhibits BMP signaling upon over-expression of GDF3 mRNA, as recombinant protein, and regardless of its dose. We therefore further characterized the mechanism through which GDF3 protein acts as a specific BMP inhibitor and found that the BMP inhibitory activity of GDF3 resides redundantly in the unprocessed, predominant form and in the mature form of the protein. These results confirm and extend the activity that we described for GDF3 and illuminate the experimental basis for the different observations of others. We suggest that GDF3 is either a bi-functional TGF-β ligand, or, more likely, that it is a BMP inhibitor that can artificially activate Nodal signaling under non-physiological conditions. PMID:18823971
Katritsis, Demosthenes G.; Ellenbogen, Kenneth A.; Becker, Anton E.
2006-01-01
Detailed right and left septal mapping of retrograde atrial activation during typical atrioventricular nodal reentrant tachycardia (AVNRT) has not been undertaken and may provide insight into the complex physiology of AVNRT, especially the anatomic localization of the fast and slow pathways. The