Nodal Diffusion & Transport Theory
Energy Science and Technology Software Center (ESTSC)
1992-02-19
DIF3D solves multigroup diffusion theory eigenvalue, adjoint, fixed source, and criticality (concentration, buckling, and dimension search) problems in 1, 2, and 3-space dimensions for orthogonal (rectangular or cylindrical), triangular, and hexagonal geometries. Anisotropic diffusion theory coefficients are permitted. Flux and power density maps by mesh cell and regionwise balance integrals are provided. Although primarily designed for fast reactor problems, upscattering and internal black boundary conditions are also treated.
The AN neutron transport by nodal diffusion
Barbarino, A.; Tomatis, D.
2013-07-01
The two group diffusion model combined to a nodal approach in space is the preferred scheme for the industrial simulation of nuclear water reactors. The main selling point is the speed of computation, allowing a large number of parametric studies. Anyway, the drawbacks of the underlying diffusion equation may arise with highly heterogeneous interfaces, often encountered in modern UO{sub 2} and MO{sub x} fuel loading patterns, and boron less controlled systems. This paper aims at showing how the simplified AN transport model, equivalent to the well known SPN, can be implemented in standard diffusion codes with minor modifications. Some numerical results are illustrated. (authors)
NASA Technical Reports Server (NTRS)
Harvey, Jason; Moore, Michael
2013-01-01
The General-Use Nodal Network Solver (GUNNS) is a modeling software package that combines nodal analysis and the hydraulic-electric analogy to simulate fluid, electrical, and thermal flow systems. GUNNS is developed by L-3 Communications under the TS21 (Training Systems for the 21st Century) project for NASA Johnson Space Center (JSC), primarily for use in space vehicle training simulators at JSC. It has sufficient compactness and fidelity to model the fluid, electrical, and thermal aspects of space vehicles in real-time simulations running on commodity workstations, for vehicle crew and flight controller training. It has a reusable and flexible component and system design, and a Graphical User Interface (GUI), providing capability for rapid GUI-based simulator development, ease of maintenance, and associated cost savings. GUNNS is optimized for NASA's Trick simulation environment, but can be run independently of Trick.
Diffusion of Zonal Variables Using Node-Centered Diffusion Solver
Yang, T B
2007-08-06
Tom Kaiser [1] has done some preliminary work to use the node-centered diffusion solver (originally developed by T. Palmer [2]) in Kull for diffusion of zonal variables such as electron temperature. To avoid numerical diffusion, Tom used a scheme developed by Shestakov et al. [3] and found their scheme could, in the vicinity of steep gradients, decouple nearest-neighbor zonal sub-meshes leading to 'alternating-zone' (red-black mode) errors. Tom extended their scheme to couple the sub-meshes with appropriate chosen artificial diffusion and thereby solved the 'alternating-zone' problem. Because the choice of the artificial diffusion coefficient could be very delicate, it is desirable to use a scheme that does not require the artificial diffusion but still able to avoid both numerical diffusion and the 'alternating-zone' problem. In this document we present such a scheme.
Differential diffusivity of Nodal and Lefty underlies a reaction-diffusion patterning system
Müller, Patrick; Rogers, Katherine W.; Jordan, Ben M.; Lee, Joon S.; Robson, Drew; Ramanathan, Sharad; Schier, Alexander F.
2012-01-01
Biological systems involving short-range activators and long-range inhibitors can generate complex patterns. Reaction-diffusion models postulate that differences in signaling range are caused by differential diffusivity of inhibitor and activator. Other models suggest that differential clearance underlies different signaling ranges. To test these models, we measured the biophysical properties of the Nodal/Lefty activator/inhibitor system during zebrafish embryogenesis. Analysis of Nodal and Lefty gradients reveals that Nodals have a shorter range than Lefty proteins. Pulse-labelinganalysis indicates that Nodals and Leftys have similar clearance kinetics, whereas fluorescence recovery assays reveal that Leftys have a higher effective diffusion coefficient than Nodals. These results indicate that differential diffusivity is the major determinant of the differences in Nodal/Lefty range and provide biophysical support for reaction-diffusion models of activator/inhibitor-mediated patterning. PMID:22499809
Fisher, A. C.; Bailey, D. S.; Kaiser, T. B.; Eder, D. C.; Gunney, B. T. N.; Masters, N. D.; Koniges, A. E.; Anderson, R. W.
2015-02-01
Here, we present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L_{2} norm.
Nodal Diffusion Burnable Poison Treatment for Prismatic Reactor Cores
A. M. Ougouag; R. M. Ferrer
2010-10-01
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.
ANOVA-HDMR structure of the higher order nodal diffusion solution
Bokov, P. M.; Prinsloo, R. H.; Tomasevic, D. I.
2013-07-01
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)
Advanced Nodal P_{3}/SP_{3} Axial Transport Solvers for the MPACT 2D/1D Scheme
Stimpson, Shane G; Collins, Benjamin S
2015-01-01
As part of its initiative to provide multiphysics simulations of nuclear reactor cores, the Consortium for Advanced Simulation of Light Water Reactors (CASL) is developing the Virtual Environment for Reactor Applications Core Simulator (VERA-CS). The MPACT code, which is the primary neutron transport solver of VERA-CS, employs the two-dimensional/one-dimensional (2D/1D) method to solve 3-dimensional neutron transport problems and provide sub-pin-level resolution of the power distribution. While 2D method of characteristics is used to solve for the transport effects within each plane, 1D-nodal methods are used axially. There have been extensive studies of the 2D/1D method with a variety nodal methods, and the P_{3}/SP_{3} solver has proved to be an effective method of providing higher-fidelity solutions while maintaining a low computational burden.The current implementation in MPACT wraps a one-node nodal expansion method (NEM) kernel for each moment, iterating between them and performing multiple sweeps to resolve flux distributions. However, it has been observed that this approach is more sensitive to convergence problems. This paper documents the theory and application two new nodal P_{3}/SP_{3} approaches to be used within the 2D/1D method in MPACT. These two approaches aim to provide enhanced stability compared with the pre-existing one-node approach. Results from the HY-NEM-SP_{3} solver show that the accuracy is consistent with the one-node formulations and provides improved convergence for some problems; but the solver has issues with cases in thin planes. Although the 2N-SENM-SP_{3} solver is still under development, it is intended to resolve the issues with HY-NEM-SP_{3} but it will incur some additional computational burden by necessitating an additional 1D-CMFD-P_{3} solver to generate the second moment cell-averaged scalar flux.
Errors associated with standard nodal diffusion methods as applied to mixed oxide fuel problems
Brantley, P. S., LLNL
1998-07-24
The evaluation of the disposition of plutonium using light water reactors is receiving increased attention. However, mixed-oxide (MOX) fuel assemblies possess much higher absorption and fission cross- sections when compared to standard UO2 assemblies. Those properties yield very high thermal flux gradients at the interfaces between MOX and UO2 assemblies. It has already been reported that standard flux reconstruction methods (that recover the homogeneous intranodal flux shape using the converged nodal solution) yield large errors in the presence of MOX assemblies. In an accompanying paper, we compare diffusion and simplified PN calculations of a mixed-oxide benchmark problem to a reference transport calculation. In this paper, we examine the errors associated with standard nodal diffusion methods when applied to the same benchmark problem. Our results show that a large portion of the error is associated with the quadratic leakage approximation (QLA) that is commonly used in the standard nodal codes.
Transport Corrections in Nodal Diffusion Codes for HTR Modeling
Abderrafi M. Ougouag; Frederick N. Gleicher
2010-08-01
The cores and reflectors of High Temperature Reactors (HTRs) of the Next Generation Nuclear Plant (NGNP) type are dominantly diffusive media from the point of view of behavior of the neutrons and their migration between the various structures of the reactor. This means that neutron diffusion theory is sufficient for modeling most features of such reactors and transport theory may not be needed for most applications. Of course, the above statement assumes the availability of homogenized diffusion theory data. The statement is true for most situations but not all. Two features of NGNP-type HTRs require that the diffusion theory-based solution be corrected for local transport effects. These two cases are the treatment of burnable poisons (BP) in the case of the prismatic block reactors and, for both pebble bed reactor (PBR) and prismatic block reactor (PMR) designs, that of control rods (CR) embedded in non-multiplying regions near the interface between fueled zones and said non-multiplying zones. The need for transport correction arises because diffusion theory-based solutions appear not to provide sufficient fidelity in these situations.
Green's Function Nodal Algorithm for the Diffusion Equation.
Energy Science and Technology Software Center (ESTSC)
1989-12-04
Version 00 GRENADE is a coarse-mesh program designed for neutronic flux and power calculations in nuclear reactors. It solves the static diffusion equation for neutrons in multidimensional problems, assuming Cartesian Geometry. The program yields flux and power distributions and the effective neutron multiplication factor .
High-Speed Three-Dimensional Nodal Diffusion Code System.
Energy Science and Technology Software Center (ESTSC)
2001-03-21
Version 00 MOSRA-Light is a three-dimensional diffusion calculation code for X-Y-Z geometry. It can be used in: validation of discontinuity factor for adjoint problem; benchmark on discontinuity factor (forward & adjoint cal.); DVP BWR Benchmark (2D,2G calculation); and void reactivity effect benchmark; etc. A utility code called More-MOSRA provides many useful functions with the file produced by MOSRA-Light.
Advanced nodal neutron diffusion method with space-dependent cross sections: ILLICO-VX
Rajic, H.L.; Ougouag, A.M.
1987-01-01
Advanced transverse integrated nodal methods for neutron diffusion developed since the 1970s require that node- or assembly-homogenized cross sections be known. The underlying structural heterogeneity can be accurately accounted for in homogenization procedures by the use of heterogeneity or discontinuity factors. Other (milder) types of heterogeneity, burnup-induced or due to thermal-hydraulic feedback, can be resolved by explicitly accounting for the spatial variations of material properties. This can be done during the nodal computations via nonlinear iterations. The new method has been implemented in the code ILLICO-VX (ILLICO variable cross-section method). Numerous numerical tests were performed. As expected, the convergence rate of ILLICO-VX is lower than that of ILLICO, requiring approx. 30% more outer iterations per k/sub eff/ computation. The methodology has also been implemented as the NOMAD-VX option of the NOMAD, multicycle, multigroup, two- and three-dimensional nodal diffusion depletion code. The burnup-induced heterogeneities (space dependence of cross sections) are calculated during the burnup steps.
Advanced computational methods for nodal diffusion, Monte Carlo, and S[sub N] problems
Martin, W.R.
1993-01-01
This document describes progress on five efforts for improving effectiveness of computational methods for particle diffusion and transport problems in nuclear engineering: (1) Multigrid methods for obtaining rapidly converging solutions of nodal diffusion problems. A alternative line relaxation scheme is being implemented into a nodal diffusion code. Simplified P2 has been implemented into this code. (2) Local Exponential Transform method for variance reduction in Monte Carlo neutron transport calculations. This work yielded predictions for both 1-D and 2-D x-y geometry better than conventional Monte Carlo with splitting and Russian Roulette. (3) Asymptotic Diffusion Synthetic Acceleration methods for obtaining accurate, rapidly converging solutions of multidimensional SN problems. New transport differencing schemes have been obtained that allow solution by the conjugate gradient method, and the convergence of this approach is rapid. (4) Quasidiffusion (QD) methods for obtaining accurate, rapidly converging solutions of multidimensional SN Problems on irregular spatial grids. A symmetrized QD method has been developed in a form that results in a system of two self-adjoint equations that are readily discretized and efficiently solved. (5) Response history method for speeding up the Monte Carlo calculation of electron transport problems. This method was implemented into the MCNP Monte Carlo code. In addition, we have developed and implemented a parallel time-dependent Monte Carlo code on two massively parallel processors.
Advanced computational methods for nodal diffusion, Monte Carlo, and S(sub N) problems
NASA Astrophysics Data System (ADS)
Martin, W. R.
1993-01-01
This document describes progress on five efforts for improving effectiveness of computational methods for particle diffusion and transport problems in nuclear engineering: (1) Multigrid methods for obtaining rapidly converging solutions of nodal diffusion problems. An alternative line relaxation scheme is being implemented into a nodal diffusion code. Simplified P2 has been implemented into this code. (2) Local Exponential Transform method for variance reduction in Monte Carlo neutron transport calculations. This work yielded predictions for both 1-D and 2-D x-y geometry better than conventional Monte Carlo with splitting and Russian Roulette. (3) Asymptotic Diffusion Synthetic Acceleration methods for obtaining accurate, rapidly converging solutions of multidimensional SN problems. New transport differencing schemes have been obtained that allow solution by the conjugate gradient method, and the convergence of this approach is rapid. (4) Quasidiffusion (QD) methods for obtaining accurate, rapidly converging solutions of multidimensional SN Problems on irregular spatial grids. A symmetrized QD method has been developed in a form that results in a system of two self-adjoint equations that are readily discretized and efficiently solved. (5) Response history method for speeding up the Monte Carlo calculation of electron transport problems. This method was implemented into the MCNP Monte Carlo code. In addition, we have developed and implemented a parallel time-dependent Monte Carlo code on two massively parallel processors.
A coarse-mesh nodal method-diffusive-mesh finite difference method
Joo, H.; Nichols, W.R.
1994-05-01
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.
NASA Astrophysics Data System (ADS)
Jia, Jingfei; Kim, Hyun K.; Hielscher, Andreas H.
2015-12-01
It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in an all-at-once manner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta-Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5-3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners.
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.
NASA Astrophysics Data System (ADS)
Valeau, Vincent; Sakout, Anas; Li, Feng; Picaut, Judicael
2002-11-01
Over the last years, some publications [e.g., Picaut, Simon, and Hardy, J. Acoust. Soc. Am. 106, 2638-2645 (1999)] showed that the acoustic energy density in closed or semiclosed spaces is the solution of a diffusion equation. This approach allows the nonuniform repartition of energy, and is especially relevant in room acoustics for complex spaces or long rooms. In this work, the 3-D diffusion equation is solved directly by using a finite element solver, for a set of long rooms and absorbing rooms. The stationary equation is first solved. A constant-power acoustic source is modelized by setting appropriate boundary conditions. The time-dependent problem is also solved to simulate the sound decay, with an impulse source defined in a subregion with relevant initial conditions. Results concerning sound attenuation and reverberation times match satisfactorily with other theoretical and numerical models. An application is also given for two coupled rooms.
Nonlinear Solver Approaches for the Diffusive Wave Approximation to the Shallow Water Equations
NASA Astrophysics Data System (ADS)
Collier, N.; Knepley, M.
2015-12-01
The diffusive wave approximation to the shallow water equations (DSW) is a doubly-degenerate, nonlinear, parabolic partial differential equation used to model overland flows. Despite its challenges, the DSW equation has been extensively used to model the overland flow component of various integrated surface/subsurface models. The equation's complications become increasingly problematic when ponding occurs, a feature which becomes pervasive when solving on large domains with realistic terrain. In this talk I discuss the various forms and regularizations of the DSW equation and highlight their effect on the solvability of the nonlinear system. In addition to this analysis, I present results of a numerical study which tests the applicability of a class of composable nonlinear algebraic solvers recently added to the Portable, Extensible, Toolkit for Scientific Computation (PETSc).
BioFVM: an efficient, parallelized diffusive transport solver for 3-D biological simulations
Ghaffarizadeh, Ahmadreza; Friedman, Samuel H.; Macklin, Paul
2016-01-01
Motivation: Computational models of multicellular systems require solving systems of PDEs for release, uptake, decay and diffusion of multiple substrates in 3D, particularly when incorporating the impact of drugs, growth substrates and signaling factors on cell receptors and subcellular systems biology. Results: We introduce BioFVM, a diffusive transport solver tailored to biological problems. BioFVM can simulate release and uptake of many substrates by cell and bulk sources, diffusion and decay in large 3D domains. It has been parallelized with OpenMP, allowing efficient simulations on desktop workstations or single supercomputer nodes. The code is stable even for large time steps, with linear computational cost scalings. Solutions are first-order accurate in time and second-order accurate in space. The code can be run by itself or as part of a larger simulator. Availability and implementation: BioFVM is written in C ++ with parallelization in OpenMP. It is maintained and available for download at http://BioFVM.MathCancer.org and http://BioFVM.sf.net under the Apache License (v2.0). Contact: paul.macklin@usc.edu. Supplementary information: Supplementary data are available at Bioinformatics online. PMID:26656933
Gorpas, Dimitris; Andersson-Engels, Stefan
2012-12-01
The solution of the forward problem in fluorescence molecular imaging strongly influences the successful convergence of the fluorophore reconstruction. The most common approach to meeting this problem has been to apply the diffusion approximation. However, this model is a first-order angular approximation of the radiative transfer equation, and thus is subject to some well-known limitations. This manuscript proposes a methodology that confronts these limitations by applying the radiative transfer equation in spatial regions in which the diffusion approximation gives decreased accuracy. The explicit integro differential equations that formulate this model were solved by applying the Galerkin finite element approximation. The required spatial discretization of the investigated domain was implemented through the Delaunay triangulation, while the azimuthal discretization scheme was used for the angular space. This model has been evaluated on two simulation geometries and the results were compared with results from an independent Monte Carlo method and the radiative transfer equation by calculating the absolute values of the relative errors between these models. The results show that the proposed forward solver can approximate the radiative transfer equation and the Monte Carlo method with better than 95% accuracy, while the accuracy of the diffusion approximation is approximately 10% lower. PMID:23208221
Dirix, Piet; Vandecaveye, Vincent; De Keyzer, Frederik; Op de beeck, Katya; Poorten, Vincent Vander; Delaere, Pierre; Verbeken, Eric; Hermans, Robert; Nuyts, Sandra
2010-03-01
Purpose: To evaluate the use of diffusion-weighted magnetic resonance imaging (DW-MRI) for nodal staging and its impact on radiotherapy (RT) planning. Methods and Materials: Twenty-two patients with locally advanced head and neck squamous cell carcinoma underwent contrast-enhanced computed tomography (CT), as well as MRI (with routine and DW sequences) prior to neck dissection. After topographic correlation, lymph nodes were evaluated microscopically with prekeratin immunostaining. Pathology results were correlated with imaging findings and an RT planning study was performed for these surgically treated patients. One set of target volumes was based on conventional imaging only, and another set was based on the corresponding DW-MRI images. A third reference set was contoured based solely on pathology results. Results: A sensitivity of 89% and a specificity of 97% per lymph node were found for DW-MRI. Nodal staging agreement between imaging and pathology was significantly stronger for DW-MRI (kappa = 0.97; 95% confidence interval [CI], 0.84-1.00) than for conventional imaging (kappa = 0.56; 95% CI, 0.16-0.96; p = 0.019, by McNemar's test). For both imaging modalities, the absolute differences between RT volumes and those obtained by pathology were calculated. Using an exact paired Wilcoxon test, the observed difference was significantly larger for conventional imaging than for DW-MRI for nodal gross tumor volume (p = 0.0013), as well as for nodal clinical target volume (p = 0.0415) delineation. Conclusions: These results suggest that DW-MRI is superior to conventional imaging for preradiotherapy nodal staging of head and neck squamous cell carcinoma, and provides a potential impact on organsparing and tumor control.
Three-Dimensional, Nodal, Neutron Diffusion Criticality Code System in Hex-Z Geometry.
Energy Science and Technology Software Center (ESTSC)
1992-07-27
Version: 00 SIXTUS-3 is a 3D extention of SIXTUS-2 and is based on a response matrix nodal model. The code offers a fast and accurate analysis of critical systems in the regular hex-z geometry with the multigroup cross section representation including arbitrary upscattering.
Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model
NASA Astrophysics Data System (ADS)
Baudron, Anne-Marie; Lautard, Jean-Jacques; Maday, Yvon; Riahi, Mohamed Kamel; Salomon, Julien
2014-12-01
In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a θ-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity of the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch-Maurer-Werner benchmark.
Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model
Baudron, Anne-Marie; Riahi, Mohamed Kamel; Salomon, Julien
2014-12-15
In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a θ-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity of the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch–Maurer–Werner benchmark.
Gutiérrez-García, Gonzalo; Colomo, Lluis; Villamor, Neus; Arenillas, Leonor; Martínez, Antonio; Cardesa, Teresa; García-Herrera, Adriana; Setoain, Xavier; Rodríguez, Sonia; Ghita, Gabriela; Abrisqueta, Pau; Giné, Eva; Bosch, Francesc; Campo, Elías; Montserrat, Emilio; López-Guillermo, Armando
2010-07-01
To study the main clinico-biological characteristics and the outcome of patients with diffuse large B-cell lymphoma (DLBCL) according to the primary site (nodal vs. extranodal), we included 262 patients consecutively diagnosed with DLBCL in a single institution, 5 years before and after immunochemotherapy was considered as the standard treatment. Altogether 116 patients received CHOP (cyclophosphamide, adriamycin, vincristine, and prednisone) and 146 rituximab plus CHOP (R-CHOP). The primary site was the lymph node in 140 patients (53%), Waldeyer's ring (WR) in 22, gastrointestinal (GI) in 33, and other extranodal in 67. The addition of rituximab significantly improved the CR rate in nodal, but not in extranodal, lymphomas. Patients receiving R-CHOP showed higher OS than those treated with CHOP alone (5-year OS: 71% vs. 48%). This difference was maintained in primary nodal (5-year OS: 69% vs. 37%, p < 0.0001), but was not observed in primary extranodal (75% vs. 65%, p = 0.45) lymphomas. The IPI, treatment, and primary site were the main variables for OS in multivariate analysis. In nodal cases, IPI and treatment maintained value, whereas only IPI predicted OS in extranodal cases. In conclusion, immunochemotherapy treatment dramatically improved the outcome of patients with nodal DLBCL; however, its effect was less in primary extranodal cases, so the prognosis of patients with nodal and extranodal lymphomas has been equalized in the rituximab era. PMID:20497002
Multigroup 3-Dimensional Neutron Diffusion Nodal Code System with Thermohydraulic Feedbacks.
Energy Science and Technology Software Center (ESTSC)
1994-02-07
Version 01 GNOMER is a program which solves the multigroup neutron diffusion equation on coarse mesh in 1D, 2D, and 3D Cartesian geometry. The program is designed to calculate the global core power distributions (with thermohydraulic feedbacks) as well as power distributions and homogenized cross sections over a fuel assembly.
NASA Astrophysics Data System (ADS)
Mena, Andres; Ferrero, Jose M.; Rodriguez Matas, Jose F.
2015-11-01
Solving the electric activity of the heart possess a big challenge, not only because of the structural complexities inherent to the heart tissue, but also because of the complex electric behaviour of the cardiac cells. The multi-scale nature of the electrophysiology problem makes difficult its numerical solution, requiring temporal and spatial resolutions of 0.1 ms and 0.2 mm respectively for accurate simulations, leading to models with millions degrees of freedom that need to be solved for thousand time steps. Solution of this problem requires the use of algorithms with higher level of parallelism in multi-core platforms. In this regard the newer programmable graphic processing units (GPU) has become a valid alternative due to their tremendous computational horsepower. This paper presents results obtained with a novel electrophysiology simulation software entirely developed in Compute Unified Device Architecture (CUDA). The software implements fully explicit and semi-implicit solvers for the monodomain model, using operator splitting. Performance is compared with classical multi-core MPI based solvers operating on dedicated high-performance computer clusters. Results obtained with the GPU based solver show enormous potential for this technology with accelerations over 50 × for three-dimensional problems.
Ougouag, Abderrafi Mohammed-El-Ami; Terry, William Knox
2002-04-01
The usual strategy for solving the neutron diffusion equation in two or three dimensions by nodal methods is to reduce the multidimensional partial differential equation to a set of ordinary differential equations (ODEs) in the separate spatial coordinates. This reduction is accomplished by “transverse integration” of the equation.1 For example, in three-dimensional Cartesian coordinates, the three-dimensional equation is first integrated over x and y to obtain an ODE in z, then over x and z to obtain an ODE in y, and finally over y and z to obtain an ODE in x. Then the ODEs are solved to obtain onedimensional solutions for the neutron fluxes averaged over the other two dimensions. These solutions are found in regions (“nodes”) small enough for the material properties and cross sections in them to be adequately represented by average values. Because the solution in each node is an exact analytical solution, the nodes can be much larger than the mesh elements used in finite-difference solutions. Then the solutions in the different nodes are coupled by applying interface conditions, ultimately fixing the solutions to the external boundary conditions.
NASA Technical Reports Server (NTRS)
Fletcher, Michael J.; Won, Mark J.; Cosentino, Gary B.; Te, Alexander
1993-01-01
Subsonic inlet ducts for advanced, high-performance aircraft are evolving towards complex three-dimensional shapes for reasons of overall integration and weight. These factors lead to diffuser geometries that may sacrifice inlet performance, unless careful attention to design details and boundary layer management techniques are employed. The ability of viscous computational fluid dynamic (CFD) analysis of such geometries to aid the aircraft configurator in this complex design problem is herein examined. The RANS-3D Reynolds-Averaged Navier-Stokes solver is applied to model the complex flowfield occurring in a representative diffuser geometry and the solutions are compared to experimental results from a static test of the inlet duct. The computational results are shown to compare very favorably with experimental results over a range of mass flow rates, including those involving large amounts of separation in the diffuser. In addition, a novel grid topology is presented, and two turbulence models are evaluated in this study as part of the RANS-3D code.
Martin, W.R.
1993-01-01
This document describes progress on five efforts for improving effectiveness of computational methods for particle diffusion and transport problems in nuclear engineering: (1) Multigrid methods for obtaining rapidly converging solutions of nodal diffusion problems. A alternative line relaxation scheme is being implemented into a nodal diffusion code. Simplified P2 has been implemented into this code. (2) Local Exponential Transform method for variance reduction in Monte Carlo neutron transport calculations. This work yielded predictions for both 1-D and 2-D x-y geometry better than conventional Monte Carlo with splitting and Russian Roulette. (3) Asymptotic Diffusion Synthetic Acceleration methods for obtaining accurate, rapidly converging solutions of multidimensional SN problems. New transport differencing schemes have been obtained that allow solution by the conjugate gradient method, and the convergence of this approach is rapid. (4) Quasidiffusion (QD) methods for obtaining accurate, rapidly converging solutions of multidimensional SN Problems on irregular spatial grids. A symmetrized QD method has been developed in a form that results in a system of two self-adjoint equations that are readily discretized and efficiently solved. (5) Response history method for speeding up the Monte Carlo calculation of electron transport problems. This method was implemented into the MCNP Monte Carlo code. In addition, we have developed and implemented a parallel time-dependent Monte Carlo code on two massively parallel processors.
Dai, William W. Scannapieco, Anthony J.
2015-01-15
A numerical scheme is developed for two- and three-dimensional time-dependent diffusion equations in numerical simulations involving mixed cells. The focus of the development is on the formulations for both transient and steady states, the property for large time steps, second-order accuracy in both space and time, the correct treatment of the discontinuity in material properties, and the handling of mixed cells. For a mixed cell, interfaces between materials are reconstructed within the cell so that each of resulting sub-cells contains only one material and the material properties of each sub-cell are known. Diffusion equations are solved on the resulting polyhedral mesh even if the original mesh is structured. The discontinuity of material properties between different materials is correctly treated based on governing physics principles. The treatment is exact for arbitrarily strong discontinuity. The formulae for effective diffusion coefficients across interfaces between materials are derived for general polyhedral meshes. The scheme is general in two and three dimensions. Since the scheme to be developed in this paper is intended for multi-physics code with adaptive mesh refinement (AMR), we present the scheme on mesh generated from AMR. The correctness and features of the scheme are demonstrated for transient problems and steady states in one-, two-, and three-dimensional simulations for heat conduction and radiation heat transfer. The test problems involve dramatically different materials.
Siddiqi, Imran N; Friedman, Julia; Barry-Holson, Keegan Q; Ma, Charles; Thodima, Venkata; Kang, Irene; Padmanabhan, Raghavendra; Dias, Lizalynn M; Kelly, Kevin R; Brynes, Russell K; Kamalakaran, Sitharthan; Houldsworth, Jane
2016-06-01
A predominantly diffuse growth pattern and CD23 co-expression are uncommon findings in nodal follicular lymphoma and can create diagnostic challenges. A single case series in 2009 (Katzenberger et al) proposed a unique morphologic variant of nodal follicular lymphoma, characterized by a predominantly diffuse architecture, lack of the t(14;18) IGH/BCL2 translocation, presence of 1p36 deletion, frequent inguinal lymph node involvement, CD23 co-expression, and low clinical stage. Other studies on CD23+ follicular lymphoma, while associating inguinal location, have not specifically described this architecture. In addition, no follow-up studies have correlated the histopathologic and cytogenetic/molecular features of these cases, and they remain a diagnostic problem. We identified 11 cases of diffuse, CD23+ follicular lymphoma with histopathologic features similar to those described by Katzenberger et al. Along with pertinent clinical information, we detail their histopathology, IGH/BCL2 translocation status, lymphoma-associated chromosomal gains/losses, and assessment of mutations in 220 lymphoma-associated genes by massively parallel sequencing. All cases showed a diffuse growth pattern around well- to ill-defined residual germinal centers, uniform CD23 expression, mixed centrocytic/centroblastic cytology, and expression of at least one germinal center marker. Ten of 11 involved inguinal lymph nodes, 5 solely. By fluorescence in situ hybridization analysis, the vast majority lacked IGH/BCL2 translocation (9/11). Deletion of 1p36 was observed in five cases and included TNFRSF14. Of the six cases lacking 1p36 deletion, TNFRSF14 mutations were identified in three, highlighting the strong association of 1p36/TNFRSF14 abnormalities with this follicular lymphoma variant. In addition, 9 of the 11 cases tested (82%) had STAT6 mutations and nuclear P-STAT6 expression was detectable in the mutated cases by immunohistochemistry. The proportion of STAT6 mutations is higher than
Gill DF
2007-04-17
The objective of this work is to investigate the thick diffusion limit of various spatial discretizations of the one-dimensional, steady-state, monoenergetic, discrete ordinates neutron transport equation. This work specifically addresses the two lowest order nodal methods, AHOT-N0 and AHOT-N1, as well as reconsiders the asymptotic limit of the Diamond Difference method. The asymptotic analyses of the AHOT-N0 and AHOT-N1 nodal methods show that AHOT-N0 does not possess the thick diffusion limit for cell edge or cell average fluxes except under very limiting conditions, which is to be expected considering the AHOT-N0 method limits to the Step method in the thick diffusion limit. The AHOT-N1 method, which uses a linear in-cell representation of the flux, was shown to possess the thick diffusion limit for both cell average and cell edge fluxes. The thick diffusion limit of the DD method, including the boundary conditions, was derived entirely in terms of cell average scalar fluxes. It was shown that, for vacuum boundaries, only when {sigma}{sub t}, h, and Q are constant and {sigma}{sub a} = 0 is the asymptotic limit of the DD method close to the finite-differenced diffusion equation in the system interior, and that the boundary conditions between the systems will only agree in the absence of an external source. For a homogeneous medium an effective diffusion coefficient was shown to be present, which was responsible for causing numeric diffusion in certain cases. A technique was presented to correct the numeric diffusion in the interior by altering certain problem parameters. Numerical errors introduced by the boundary conditions and material interfaces were also explored for a two-region problem using the Diamond Difference method. A discrete diffusion solution which exactly solves the one-dimensional diffusion equation in a homogeneous region with constant cross sections and a uniform external source was also developed and shown to be equal to the finite
Gualco, Gabriela; Weiss, Lawrence M.; Harrington, William J.; Bacchi, Carlos E.
2009-01-01
Diffuse large B-cell lymphoma (DLBCL) is a very infrequent neoplasm in the pediatric age group; therefore there are very few studies on the immunophenotype or genetics of these cases. We studied a series of 16 patients with nodal DLBCL occurring in patients between 10 and 18 years of age. The cases were classified according to the 2008 World Health Organization classification criteria, with application of immunohistochemistry for the detection of CD10, BCL-6 and MUM1 proteins to divide the lymphomas into germinal center and non-germinal center types. In addition, TCL1, BCL-2 expression, and the Ki-67 proliferation index were evaluated by immunohistochemistry, and c-MYC and BCL-2 translocations were evaluated by FISH. All these parameters were correlated with clinical features and outcome. Our study revealed that centroblastic morphology and the germinal center type of DLBCL are more prevalent in these young patients (63%), with 37% containing a c-MYC translocation. Only one case showed a BCL-2 translocation, reflecting a double-hit case with features intermediate between DLBCL and Burkitt lymphoma. We found a higher frequency of BCL-2 expression than previously reported, with no direct influence on the outcome of the disease in univariate or multivariate analysis. The expression of TCL1 has not been specifically studied in nodal pediatric DLBCL before; we found a 31% incidence of TCL1 expression. MUM1 expression was observed in 44% of the cases and these positive cases showed a significant negative impact on clinical outcome. TCL1 is directly and significantly associated with the presence of c-MYC and a high proliferative index. The germinal center and non-germinal center subtypes showed significant differences for both overall survival and disease-free interval. C-MYC translocation was found in 37% of patients, and had a favorable impact on clinical outcome. We conclude that nodal pediatric and adolescent DLBCL are mainly of the germinal center type, with a
Gualco, Gabriela; Weiss, Lawrence M; Barber, Glen N; Bacchi, Carlos E
2010-09-01
The physiologic expression of the product of the proto-oncogene TCL1 (T-cell leukemia 1) is primarily restricted to early embryonic cells. In nonneoplastic B cells, the expression of TCL1 is determined by the differentiation step with silencing at the germinal center stage. TCL1 protein is overexpressed in a wide variety of human diseases. It has been shown that TCL1 is a powerful B-cell oncogene, which has been implicated in the pathogenesis of various types of mature B-cell lymphomas. There is no comparative information in the literature addressing the expression of TCL1 in pediatric and adult nodal diffuse large B-cell lymphoma or primary mediastinal large B-cell lymphoma. We studied 55 cases of adult and pediatric diffuse large B-cell lymphoma and primary mediastinal large B-cell lymphoma to analyze the phenotypic profile of these lymphomas, including TCL1 expression, and its relationship with clinical outcome in different age groups. The cases were analyzed by immunohistochemistry for the expression of TCL1, CD10, BCL-2, BCL-6, and MUM1. We also evaluated c-MYC translocation by fluorescence in situ hybridization. TCL1 was observed in 11 cases, 5 pediatric and 6 adult cases, all but one diffuse large B-cell lymphoma. Pediatric cases showed a significant association between TCL1 expression, high proliferative index, and presence of c-MYC translocation. TCL1 positivity was predominantly found in germinal center phenotype diffuse large B-cell lymphoma. Overall survival was worse in adult TCL1-positive cases than pediatric ones. Primary mediastinal large B-cell lymphomas infrequently expressed TCL1 in both age groups. PMID:20382409
Gualco, Gabriela; Bacchi, Lívia M; Domeny-Duarte, Pollyanna; Natkunam, Yasodha; Bacchi, Carlos E
2012-11-01
Diffuse large B-cell lymphoma can be subclassified into at least two molecular subgroups by gene expression profiling: germinal center B-cell like and activated B-cell like diffuse large B-cell lymphoma. Several immunohistological algorithms have been proposed as surrogates to gene expression profiling at the level of protein expression, but their reliability has been an issue of controversy. Furthermore, the proportion of misclassified cases of germinal center B-cell subgroup by immunohistochemistry, in all reported algorithms, is higher compared with germinal center B-cell cases defined by gene expression profiling. We analyzed 424 cases of nodal diffuse large B-cell lymphoma with the panel of markers included in the three previously described algorithms: Hans, Choi, and Tally. To test whether the sensitivity of detecting germinal center B-cell cases could be improved, the germinal center B-cell marker HGAL/GCET2 was also added to all three algorithms. Our results show that the inclusion of HGAL/GCET2 significantly increased the detection of germinal center B-cell cases in all three algorithms (P<0.001). The proportions of germinal center B-cell cases in the original algorithms were 27%, 34%, and 19% for Hans, Choi, and Tally, respectively. In the modified algorithms, with the inclusion of HGAL/GCET2, the frequencies of germinal center B-cell cases were increased to 38%, 48%, and 35%, respectively. Therefore, HGAL/GCET2 protein expression may function as a marker for germinal center B-cell type diffuse large B-cell lymphoma. Consideration should be given to the inclusion of HGAL/GCET2 analysis in algorithms to better predict the cell of origin. These findings bear further validation, from comparison to gene expression profiles and from clinical/therapeutic data. PMID:22743653
NASA Astrophysics Data System (ADS)
Nuttin, A.; Capellan, N.; David, S.; Doligez, X.; El Mhari, C.; Méplan, O.
2014-06-01
Safety analysis of innovative reactor designs requires three dimensional modeling to ensure a sufficiently realistic description, starting from steady state. Actual Monte Carlo (MC) neutron transport codes are suitable candidates to simulate large complex geometries, with eventual innovative fuel. But if local values such as power densities over small regions are needed, reliable results get more difficult to obtain within an acceptable computation time. In this scope, NEA has proposed a performance test of full PWR core calculations based on Monte Carlo neutron transport, which we have used to define an optimal detail level for convergence of steady state coupled neutronics. Coupling between MCNP for neutronics and the subchannel code COBRA for thermal-hydraulics has been performed using the C++ tool MURE, developed for about ten years at LPSC and IPNO. In parallel with this study and within the same MURE framework, a simplified code of nodal kinetics based on two-group and few-point diffusion equations has been developed and validated on a typical CANDU LOCA. Methods for the computation of necessary diffusion data have been defined and applied to NU (Nat. U) and Th fuel CANDU after assembly evolutions by MURE. Simplicity of CANDU LOCA model has made possible a comparison of these two fuel behaviours during such a transient.
Time-domain Raman analytical forward solvers.
Martelli, Fabrizio; Binzoni, Tiziano; Sekar, Sanathana Konugolu Venkata; Farina, Andrea; Cavalieri, Stefano; Pifferi, Antonio
2016-09-01
A set of time-domain analytical forward solvers for Raman signals detected from homogeneous diffusive media is presented. The time-domain solvers have been developed for two geometries: the parallelepiped and the finite cylinder. The potential presence of a background fluorescence emission, contaminating the Raman signal, has also been taken into account. All the solvers have been obtained as solutions of the time dependent diffusion equation. The validation of the solvers has been performed by means of comparisons with the results of "gold standard" Monte Carlo simulations. These forward solvers provide an accurate tool to explore the information content encoded in the time-resolved Raman measurements. PMID:27607645
Heterogeneous treatment in the variational nodal method
Fanning, T.H.; Palmiotti, G.
1995-06-01
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.
Fuerer, Christophe; Nostro, M. Cristina; Constam, Daniel B.
2014-01-01
The TGFβ family member Nodal is central to control pluripotent stem cell fate, but its use as a stem cell differentiation factor is limited by low specific activity. During development, Nodal depends on growth and differentiation factor (Gdf)-1 and on the shared co-receptor Cryptic to specify visceral left-right axis asymmetry. We therefore asked whether the functionality of Nodal can be augmented by Gdf1. Because Nodal and Gdf1 coimmunoprecipitate each other, they were predicted to form heterodimers, possibly to facilitate diffusion or to increase the affinity for signaling receptors. Here, we report that Gdf1 suppresses an unexpected dependence of Nodal on serum proteins and that it is critically required for non-autonomous signaling in cells expressing Cryptic. Nodal, Gdf1, and their cleaved propeptides copurified as a heterodimeric low molecular weight complex that stimulated Activin receptor (Acvr) signaling far more potently than Nodal alone. Although heterodimerization with Gdf1 did not increase binding of Nodal to Fc fusions of co-receptors or Acvr extracellular domains, it was essential for soluble Acvr2 to inhibit Nodal signaling. This implies that Gdf1 potentiates Nodal activity by stabilizing a low molecular weight fraction that is susceptible to neutralization by soluble Acvr2. Finally, in differentiating human ES cells, endodermal markers were more efficiently induced by Nodal·Gdf1 than by Nodal, suggesting that Nodal·Gdf1 is an attractive new reagent to direct stem cell differentiation. PMID:24798330
Shestakov, Aleksei I. Offner, Stella S.R.
2008-01-10
We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with Adaptive Mesh Refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate 'level-solve' packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation ({psi}tc). We analyze the magnitude of the {psi}tc parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichlet boundary data at the coarse-fine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the sync-solve (SS), is required in order to enforce conservation. The MGD SS reduces to an elliptic solve on a combined grid for a system of G equations, where G is the number of groups. We adapt the 'partial temperature' scheme for the SS; hence, we reuse the infrastructure developed for scalar equations. Results are presented. We consider a multigroup test problem with a known analytic solution. We demonstrate utility of {psi}tc by running with increasingly larger timesteps. Lastly, we simulate the sudden release of energy Y inside an Al sphere (r = 15 cm) suspended in air at STP. For Y = 11 kT, we find that gray radiation diffusion and MGD produce similar results. However, if Y = 1 MT, the two packages yield different results. Our large Y simulation contradicts a long-standing theory and demonstrates
Shestakov, A I; Offner, S R
2007-03-02
We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate 'level-solve' packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation ({Psi}tc). We analyze the magnitude of the {Psi}tc parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichet boundary data at the coarse-fine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the sync-solve (SS), is required in order to enforce conservation. The MGD SS reduces to an elliptic solve on a combined grid for a system of G equations, where G is the number of groups. We adapt the 'partial temperature' scheme for the SS; hence, we reuse the infrastructure developed for scalar equations. Results are presented. We consider a multigroup test problem with a known analytic solution. We demonstrate utility of {Psi}tc by running with increasingly larger timesteps. Lastly, we simulate the sudden release of energy Y inside an Al sphere (r = 15 cm) suspended in air at STP. For Y = 11 kT, we find that gray radiation diffusion and MGD produce similar results. However, if Y = 1 MT, the two packages yield different results. Our large Y simulation contradicts a long-standing theory and demonstrates
NASA Astrophysics Data System (ADS)
Shestakov, Aleksei I.; Offner, Stella S. R.
2008-01-01
We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with Adaptive Mesh Refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate "level-solve" packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation (Ψtc). We analyze the magnitude of the Ψtc parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichlet boundary data at the coarse-fine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the sync-solve (SS), is required in order to enforce conservation. The MGD SS reduces to an elliptic solve on a combined grid for a system of G equations, where G is the number of groups. We adapt the "partial temperature" scheme for the SS; hence, we reuse the infrastructure developed for scalar equations. Results are presented. We consider a multigroup test problem with a known analytic solution. We demonstrate utility of Ψtc by running with increasingly larger timesteps. Lastly, we simulate the sudden release of energy Y inside an Al sphere (r = 15 cm) suspended in air at STP. For Y = 11 kT, we find that gray radiation diffusion and MGD produce similar results. However, if Y = 1 MT, the two packages yield different results. Our large Y simulation contradicts a long-standing theory and demonstrates the
Shestakov, A I; Offner, S R
2006-09-21
We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate 'level-solve' packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation ({Psi}tc). We analyze the magnitude of the {Psi}tc parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichet boundary data at the coarse-fine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the sync-solve (SS), is required in order to enforce conservation. The MGD SS reduces to an elliptic solve on a combined grid for a system of G equations, where G is the number of groups. We adapt the 'partial temperature' scheme for the SS; hence, we reuse the infrastructure developed for scalar equations. Results are presented. We consider a multigroup test problem with a known analytic solution. We demonstrate utility of {Psi}tc by running with increasingly larger timesteps. Lastly, we simulate the sudden release of energy Y inside an Al sphere (r = 15 cm) suspended in air at STP. For Y = 11 kT, we find that gray radiation diffusion and MGD produce similar results. However, if Y = 1 MT, the two packages yield different results. Our large Y simulation contradicts a long-standing theory and demonstrates
Druskin, V.; Knizhnerman, L.
1994-12-31
The authors solve the Cauchy problem for an ODE system Au + {partial_derivative}u/{partial_derivative}t = 0, u{vert_bar}{sub t=0} = {var_phi}, where A is a square real nonnegative definite symmetric matrix of the order N, {var_phi} is a vector from R{sup N}. The stiffness matrix A is obtained due to semi-discretization of a parabolic equation or system with time-independent coefficients. The authors are particularly interested in large stiff 3-D problems for the scalar diffusion and vectorial Maxwell`s equations. First they consider an explicit method in which the solution on a whole time interval is projected on a Krylov subspace originated by A. Then they suggest another Krylov subspace with better approximating properties using powers of an implicit transition operator. These Krylov subspace methods generate optimal in a spectral sense polynomial approximations for the solution of the ODE, similar to CG for SLE.
Extracellular interactions and ligand degradation shape the nodal morphogen gradient
Wang, Yin; Wang, Xi; Wohland, Thorsten; Sampath, Karuna
2016-01-01
The correct distribution and activity of secreted signaling proteins called morphogens is required for many developmental processes. Nodal morphogens play critical roles in embryonic axis formation in many organisms. Models proposed to generate the Nodal gradient include diffusivity, ligand processing, and a temporal activation window. But how the Nodal morphogen gradient forms in vivo remains unclear. Here, we have measured in vivo for the first time, the binding affinity of Nodal ligands to their major cell surface receptor, Acvr2b, and to the Nodal inhibitor, Lefty, by fluorescence cross-correlation spectroscopy. We examined the diffusion coefficient of Nodal ligands and Lefty inhibitors in live zebrafish embryos by fluorescence correlation spectroscopy. We also investigated the contribution of ligand degradation to the Nodal gradient. We show that ligand clearance via degradation shapes the Nodal gradient and correlates with its signaling range. By computational simulations of gradient formation, we demonstrate that diffusivity, extra-cellular interactions, and selective ligand destruction collectively shape the Nodal morphogen gradient. DOI: http://dx.doi.org/10.7554/eLife.13879.001 PMID:27101364
Stanley, Vendall S.; Heroux, Michael A.; Hoekstra, Robert J.; Sala, Marzio
2004-03-01
Amesos is the Direct Sparse Solver Package in Trilinos. The goal of Amesos is to make AX=S as easy as it sounds, at least for direct methods. Amesos provides interfaces to a number of third party sparse direct solvers, including SuperLU, SuperLU MPI, DSCPACK, UMFPACK and KLU. Amesos provides a common object oriented interface to the best sparse direct solvers in the world. A sparse direct solver solves for x in Ax = b. where A is a matrix and x and b are vectors (or multi-vectors). A sparse direct solver flrst factors A into trinagular matrices L and U such that A = LU via gaussian elimination and then solves LU x = b. Switching amongst solvers in Amesos roquires a change to a single parameter. Yet, no solver needs to be linked it, unless it is used. All conversions between the matrices provided by the user and the format required by the underlying solver is performed by Amesos. As new sparse direct solvers are created, they will be incorporated into Amesos, allowing the user to simpty link with the new solver, change a single parameter in the calling sequence, and use the new solver. Amesos allows users to specify whether the matrix has changed. Amesos can be used anywhere that any sparse direct solver is needed.
Energy Science and Technology Software Center (ESTSC)
2004-03-01
Amesos is the Direct Sparse Solver Package in Trilinos. The goal of Amesos is to make AX=S as easy as it sounds, at least for direct methods. Amesos provides interfaces to a number of third party sparse direct solvers, including SuperLU, SuperLU MPI, DSCPACK, UMFPACK and KLU. Amesos provides a common object oriented interface to the best sparse direct solvers in the world. A sparse direct solver solves for x in Ax = b. wheremore » A is a matrix and x and b are vectors (or multi-vectors). A sparse direct solver flrst factors A into trinagular matrices L and U such that A = LU via gaussian elimination and then solves LU x = b. Switching amongst solvers in Amesos roquires a change to a single parameter. Yet, no solver needs to be linked it, unless it is used. All conversions between the matrices provided by the user and the format required by the underlying solver is performed by Amesos. As new sparse direct solvers are created, they will be incorporated into Amesos, allowing the user to simpty link with the new solver, change a single parameter in the calling sequence, and use the new solver. Amesos allows users to specify whether the matrix has changed. Amesos can be used anywhere that any sparse direct solver is needed.« less
Aykul, Senem; Ni, Wendi; Mutatu, Washington; Martinez-Hackert, Erik
2015-01-01
The Transforming Growth Factor-ß (TGFß) family ligand Nodal is an essential embryonic morphogen that is associated with progression of breast and other cancers. It has therefore been suggested that Nodal inhibitors could be used to treat breast cancers where Nodal plays a defined role. As secreted antagonists, such as Cerberus, tightly regulate Nodal signaling during embryonic development, we undertook to produce human Cerberus, characterize its biochemical activities, and determine its effect on human breast cancer cells. Using quantitative methods, we investigated the mechanism of Nodal signaling, we evaluated binding of human Cerberus to Nodal and other TGFß family ligands, and we characterized the mechanism of Nodal inhibition by Cerberus. Using cancer cell assays, we examined the ability of Cerberus to suppress aggressive breast cancer cell phenotypes. We found that human Cerberus binds Nodal with high affinity and specificity, blocks binding of Nodal to its signaling partners, and inhibits Nodal signaling. Moreover, we showed that Cerberus profoundly suppresses migration, invasion, and colony forming ability of Nodal expressing and Nodal supplemented breast cancer cells. Taken together, our studies provide mechanistic insights into Nodal signaling and Nodal inhibition with Cerberus and highlight the potential value of Cerberus as anti-Nodal therapeutic. PMID:25603319
NASA Astrophysics Data System (ADS)
Zamani, K.; Bombardelli, F.
2011-12-01
Almost all natural phenomena on Earth are highly nonlinear. Even simplifications to the equations describing nature usually end up being nonlinear partial differential equations. Transport (ADR) equation is a pivotal equation in atmospheric sciences and water quality. This nonlinear equation needs to be solved numerically for practical purposes so academicians and engineers thoroughly rely on the assistance of numerical codes. Thus, numerical codes require verification before they are utilized for multiple applications in science and engineering. Model verification is a mathematical procedure whereby a numerical code is checked to assure the governing equation is properly solved as it is described in the design document. CFD verification is not a straightforward and well-defined course. Only a complete test suite can uncover all the limitations and bugs. Results are needed to be assessed to make a distinction between bug-induced-defect and innate limitation of a numerical scheme. As Roache (2009) said, numerical verification is a state-of-the-art procedure. Sometimes novel tricks work out. This study conveys the synopsis of the experiences we gained during a comprehensive verification process which was done for a transport solver. A test suite was designed including unit tests and algorithmic tests. Tests were layered in complexity in several dimensions from simple to complex. Acceptance criteria defined for the desirable capabilities of the transport code such as order of accuracy, mass conservation, handling stiff source term, spurious oscillation, and initial shape preservation. At the begining, mesh convergence study which is the main craft of the verification is performed. To that end, analytical solution of ADR equation gathered. Also a new solution was derived. In the more general cases, lack of analytical solution could be overcome through Richardson Extrapolation and Manufactured Solution. Then, two bugs which were concealed during the mesh convergence
Wave pinning and spatial patterning in a mathematical model of Antivin/Lefty-Nodal signalling.
Middleton, A M; King, J R; Loose, M
2013-12-01
Nodal signals are key regulators of mesoderm and endoderm development in vertebrate embryos. It has been observed experimentally that in Xenopus embryos the spatial range of Nodal signals is restricted by the signal Antivin (also known as Lefty). Nodal signals can activate both Nodal and Antivin, whereas Antivin is thought to antagonise Nodal by binding either directly to it or to its receptor. In this paper we develop a mathematical model of this signalling network in a line of cells. We consider the heterodimer and receptor-mediated inhibition mechanisms separately and find that, in both cases, the restriction by Antivin to the range of Nodal signals corresponds to wave pinning in the model. Our analysis indicates that, provided Antivin diffuses faster than Nodal, either mechanism can robustly account for the experimental data. We argue that, in the case of Xenopus development, it is wave pinning, rather than Turing-type patterning, that is underlying Nodal-Antivin dynamics. This leads to several experimentally testable predictions, which are discussed. Furthermore, for heterodimer-mediated inhibition to prevent waves of Nodal expression from propagating, the Nodal-Antivin complex must be turned over, and diffusivity of the complex must be negligible. In the absence of molecular mechanisms regulating these, we suggest that Antivin restricts Nodal signals via receptor-mediated, and not heterodimer-mediated, inhibition. PMID:23070212
Farzad Rahnema; Dingkang Zhang; Abderrafi Ougouag; Frederick Gleicher
2011-04-04
The main objective of this research is to develop an integrated diffusion/transport (IDT) method to substantially improve the accuracy of nodal diffusion methods for the design and analysis of Very High Temperature Reactors (VHTR). Because of the presence of control rods in the reflector regions in the Pebble Bed Reactor (PBR-VHTR), traditional nodal diffusion methods do not accurately model these regions, within which diffusion theory breaks down in the vicinity of high neutron absorption and steep flux gradients. The IDT method uses a local transport solver based on a new incident flux response expansion method in the controlled nodes. Diffusion theory is used in the rest of the core. This approach improves the accuracy of the core solution by generating transport solutions of controlled nodes while maintaining computational efficiency by using diffusion solutions in nodes where such a treatment is sufficient. The transport method is initially developed and coupled to the reformulated 3-D nodal diffusion model in the CYNOD code for PBR core design and fuel cycle analysis. This method is also extended to the prismatic VHTR. The new method accurately captures transport effects in highly heterogeneous regions with steep flux gradients. The calculations of these nodes with transport theory avoid errors associated with spatial homogenization commonly used in diffusion methods in reactor core simulators
Energy Science and Technology Software Center (ESTSC)
2004-04-21
Version 04 NESTLE solves the few-group neutron diffusion equation utilizing the NEM. The NESTLE code can solve the eigenvalue (criticality), eigenvalue adjoint, external fixed-source steady-state, and external fixed-source or eigenvalue initiated transient problems. 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- ormore » four-energy groups can be utilized, with all energy groups being thermal groups (i.e., upscatter exits) if desired. Core geometries modeled include Cartesian and hexagonal. Three-, two-, and one-dimensional models can be utilized with various symmetries. The thermal conditions predicted by the thermal-hydraulic model of the core are used to correct cross sections for temperature and density effects. Cross sections are parameterized by color, control rod state (i.e., in or out), and burnup, allowing fuel depletion to be modeled. Either a macroscopic or microscopic model may be employed.« less
Nodal Promotes Glioblastoma Cell Growth
De Silva, Tanya; Ye, Gang; Liang, Yao-Yun; Fu, Guodong; Xu, Guoxiong; Peng, Chun
2012-01-01
Nodal is a member of the transforming growth factor-β (TGF-β) superfamily that plays critical roles during embryogenesis. Recent studies in ovarian, breast, prostate, and skin cancer cells suggest that Nodal also regulates cell proliferation, apoptosis, and invasion in cancer cells. However, it appears to exert both tumor-suppressing and tumor-promoting effects, depending on the cell type. To further understand the role of Nodal in tumorigenesis, we examined the effect of Nodal in glioblastoma cell growth and spheroid formation using U87 cell line. Treatment of U87 with recombinant Nodal significantly increased U87 cell growth. In U87 cells stably transfected with the plasmid encoding Nodal, Smad2 phosphorylation was strongly induced and cell growth was significantly enhanced. Overexpression of Nodal also resulted in tight spheroid formation. On the other hand, the cells stably transfected with Nodal siRNA formed loose spheroids. Nodal is known to signal through activin receptor-like kinase 4 (ALK4) and ALK7 and the Smad2/3 pathway. To determine which receptor and Smad mediate the growth promoting effect of Nodal, we transfected siRNAs targeting ALK4, ALK7, Smad2, or Smad3 into Nodal-overexpressing cells and observed that cell growth was significantly inhibited by ALK4, ALK7, and Smad3 siRNAs. Taken together, these findings suggest that Nodal may have tumor-promoting effects on glioblastoma cells and these effects are mediated by ALK4, ALK7, and Smad3. PMID:22645523
Off-diagonal Jacobian support for Nodal BCs
Peterson, John W.; Andrs, David; Gaston, Derek R.; Permann, Cody J.; Slaughter, Andrew E.
2015-01-01
In this brief note, we describe the implementation of o-diagonal Jacobian computations for nodal boundary conditions in the Multiphysics Object Oriented Simulation Environment (MOOSE) [1] framework. There are presently a number of applications [2{5] based on the MOOSE framework that solve complicated physical systems of partial dierential equations whose boundary conditions are often highly nonlinear. Accurately computing the on- and o-diagonal Jacobian and preconditioner entries associated to these constraints is crucial for enabling ecient numerical solvers in these applications. Two key ingredients are required for properly specifying the Jacobian contributions of nonlinear nodal boundary conditions in MOOSE and nite element codes in general: 1. The ability to zero out entire Jacobian matrix rows after \
Shindoh, M; Takami, T; Arisue, M; Yamashita, T; Saito, T; Kohgo, T; Notani, K; Totsuka, Y; Amemiya, A
1997-07-01
Fifty-two cases of non-Hodgkin's lymphoma (NHL) in the oral and maxillofacial region, comprising 31 submucosal (extra-nodal) and 21 cervical node NHLs, were investigated. The patients' ages ranged from 5 to 86 years, with a bimodal age distribution among young people below 12 years of age (average 8 years) and in those aged 30 years or older (average 60.3 years). The male-to-female gender difference ratio was 1.3:1. Patients presented with swelling as the major symptom. Histologically, diffuse, large cell malignant lymphoma was the most frequent type and 67.9% of lymphomas were of intermediate malignancy as defined by the Working Formulation for Clinical Usage. All submucosal lymphomas showed diffuse proliferation patterns, although follicular proliferation was identified in 5 of the 21 nodal lymphomas. Immunohistochemistry showed that the B-cell type was predominant, especially in nodal lymphomas. PMID:9234189
Parallel Multigrid Equation Solver
Energy Science and Technology Software Center (ESTSC)
2001-09-07
Prometheus is a fully parallel multigrid equation solver for matrices that arise in unstructured grid finite element applications. It includes a geometric and an algebraic multigrid method and has solved problems of up to 76 mullion degrees of feedom, problems in linear elasticity on the ASCI blue pacific and ASCI red machines.
A Temporal Window for Signal Activation Dictates the Dimensions of a Nodal Signaling Domain
van Boxtel, Antonius L.; Chesebro, John E.; Heliot, Claire; Ramel, Marie-Christine; Stone, Richard K.; Hill, Caroline S.
2015-01-01
Summary Morphogen signaling is critical for the growth and patterning of tissues in embryos and adults, but how morphogen signaling gradients are generated in tissues remains controversial. The morphogen Nodal was proposed to form a long-range signaling gradient via a reaction-diffusion system, on the basis of differential diffusion rates of Nodal and its antagonist Lefty. Here we use a specific zebrafish Nodal biosensor combined with immunofluorescence for phosphorylated Smad2 to demonstrate that endogenous Nodal is unlikely to diffuse over a long range. Instead, short-range Nodal signaling activation in a temporal window is sufficient to determine the dimensions of the Nodal signaling domain. The size of this temporal window is set by the differentially timed production of Nodal and Lefty, which arises mainly from repression of Lefty translation by the microRNA miR-430. Thus, temporal information is transformed into spatial information to define the dimensions of the Nodal signaling domain and, consequently, to specify mesendoderm. PMID:26506307
A Temporal Window for Signal Activation Dictates the Dimensions of a Nodal Signaling Domain.
van Boxtel, Antonius L; Chesebro, John E; Heliot, Claire; Ramel, Marie-Christine; Stone, Richard K; Hill, Caroline S
2015-10-26
Morphogen signaling is critical for the growth and patterning of tissues in embryos and adults, but how morphogen signaling gradients are generated in tissues remains controversial. The morphogen Nodal was proposed to form a long-range signaling gradient via a reaction-diffusion system, on the basis of differential diffusion rates of Nodal and its antagonist Lefty. Here we use a specific zebrafish Nodal biosensor combined with immunofluorescence for phosphorylated Smad2 to demonstrate that endogenous Nodal is unlikely to diffuse over a long range. Instead, short-range Nodal signaling activation in a temporal window is sufficient to determine the dimensions of the Nodal signaling domain. The size of this temporal window is set by the differentially timed production of Nodal and Lefty, which arises mainly from repression of Lefty translation by the microRNA miR-430. Thus, temporal information is transformed into spatial information to define the dimensions of the Nodal signaling domain and, consequently, to specify mesendoderm. PMID:26506307
Super-nodal methods for space-time kinetics
NASA Astrophysics Data System (ADS)
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
Handling Vacuum Regions in a Hybrid Plasma Solver
NASA Astrophysics Data System (ADS)
Holmström, M.
2013-04-01
In a hybrid plasma solver (particle ions, fluid mass-less electrons) regions of vacuum, or very low charge density, can cause problems since the evaluation of the electric field involves division by charge density. This causes large electric fields in low density regions that can lead to numerical instabilities. Here we propose a self consistent handling of vacuum regions for hybrid solvers. Vacuum regions can be considered having infinite resistivity, and in this limit Faraday's law approaches a magnetic diffusion equation. We describe an algorithm that solves such a diffusion equation in regions with charge density below a threshold value. We also present an implementation of this algorithm in a hybrid plasma solver, and an application to the interaction between the Moon and the solar wind. We also discuss the implementation of hyperresistivity for smoothing the electric field in a PIC solver.
Topological semimetals and nodal superconductors
NASA Astrophysics Data System (ADS)
Chang, Po-Yao
Besides topological band insulators, which have a full bulk gap, there are also gapless phases of matter that belong to the broad class of topological materials, such as topological semimetals and nodal superconductors. We systematically study these gapless topological phases described by the Bloch and Bogoliubov-de Gennes Hamiltonians. We discuss a generalized bulk-boundary correspondence, which relates the topological properties in the bulk of gapless topological phases and the protected zero-energy states at the boundary. We study examples of gapless topological phases, focusing in particular on nodal superconductors, such as nodal noncentrosymmetric superconductors (NCSs). We compute the surface density of states of nodal NCSs and interpret experimental measurements of surface states. In addition, we investigate Majorana vortex-bound states in both nodal and fully gapped NCSs using numerical and analytical methods. We show that different topological properties of the bulk Bogoliubov-quasiparticle wave functions reflect themselves in different types of zero-energy vortex-bound states. In particular, in the case of NCSs with tetragonal point-group symmetry, we find that the stability of these Majorana zero modes is guaranteed by a combination of reflection, time-reversal, and particle-hole symmetries. Finally, by using K-theory arguments and a dimensional reduction procedure from higher-dimensional topological insulators and superconductors, we derive a classification of topologically stable Fermi surfaces in semimetals and nodal lines in superconductors.
NASA Astrophysics Data System (ADS)
Gazdallah, Moncef; Feldheim, Véronique; Claramunt, Kilian; Hirsch, Charles
2012-06-01
This paper presents the implementation of the finite volume method to solve the radiative transfer equation in a commercial code. The particularity of this work is that the method applied on unstructured hexahedral meshes does not need a pre-processing step establishing a particular marching order to visit all the control volumes. The solver simply visits the faces of the control volumes as numbered in the hexahedral unstructured mesh. A cell centred mesh and a spatial differencing step scheme to relate facial radiative intensities to nodal intensities is used. The developed computer code based on FVM has been integrated in the CFD solver FINE™/Open from NUMECA Int. Radiative heat transfer can be evaluated within systems containing uniform, grey, emitting, absorbing and/or isotropically or linear anisotropically scattering medium bounded by diffuse grey walls. This code has been validated for three test cases. The first one is a three dimensional rectangular enclosure filled with emitting, absorbing and anisotropically scattering media. The second is the differentially heated cubic cavity. The third one is the L-shaped enclosure. For these three test cases a good agreement has been observed when temperature and heat fluxes predictions are compared with references taken, from literature.
Kotulski, Joseph D.; Womble, David E.; Greenberg, David; Driessen, Brian
2004-03-01
PLIRIS is an object-oriented solver built on top of a previous matrix solver used in a number of application codes. Puns solves a linear system directly via LU factorization with partial pivoting. The user provides the linear system in terms of Epetra Objects including a matrix and right-hand-sides. The user can then factor the matrix and perform the forward and back solve at a later time or solve for multiple right-hand-sides at once. This package is used when dense matrices are obtained in the problem formulation. These dense matrices occur whenever boundary element techniques are chosen for the solution procedure. This has been used in electromagnetics for both static and frequency domain problems.
Energy Science and Technology Software Center (ESTSC)
2004-03-01
PLIRIS is an object-oriented solver built on top of a previous matrix solver used in a number of application codes. Puns solves a linear system directly via LU factorization with partial pivoting. The user provides the linear system in terms of Epetra Objects including a matrix and right-hand-sides. The user can then factor the matrix and perform the forward and back solve at a later time or solve for multiple right-hand-sides at once. This packagemore » is used when dense matrices are obtained in the problem formulation. These dense matrices occur whenever boundary element techniques are chosen for the solution procedure. This has been used in electromagnetics for both static and frequency domain problems.« less
Dmitriy Y. Anistratov; Marvin L. Adams; Todd S. Palmer; Kord S. Smith; Kevin Clarno; Hikaru Hiruta; Razvan Nes
2003-08-04
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.
Energy Science and Technology Software Center (ESTSC)
2007-03-01
HPCCG is a simple PDE application and preconditioned conjugate gradient solver that solves a linear system on a beam-shaped domain. Although it does not address many performance issues present in real engineering applications, such as load imbalance and preconditioner scalability, it can serve as a first "sanity test" of new processor design choices, inter-connect network design choices and the scalability of a new computer system. Because it is self-contained, easy to compile and easily scaledmore » to 100s or 1000s of porcessors, it can be an attractive study code for computer system designers.« less
Parallel tridiagonal equation solvers
NASA Technical Reports Server (NTRS)
Stone, H. S.
1974-01-01
Three parallel algorithms were compared for the direct solution of tridiagonal linear systems of equations. The algorithms are suitable for computers such as ILLIAC 4 and CDC STAR. For array computers similar to ILLIAC 4, cyclic odd-even reduction has the least operation count for highly structured sets of equations, and recursive doubling has the least count for relatively unstructured sets of equations. Since the difference in operation counts for these two algorithms is not substantial, their relative running times may be more related to overhead operations, which are not measured in this paper. The third algorithm, based on Buneman's Poisson solver, has more arithmetic operations than the others, and appears to be the least favorable. For pipeline computers similar to CDC STAR, cyclic odd-even reduction appears to be the most preferable algorithm for all cases.
Amesos2 Templated Direct Sparse Solver Package
Energy Science and Technology Software Center (ESTSC)
2011-05-24
Amesos2 is a templated direct sparse solver package. Amesos2 provides interfaces to direct sparse solvers, rather than providing native solver capabilities. Amesos2 is a derivative work of the Trilinos package Amesos.
Nodal-mediated epigenesis requires dynamin-mediated endocytosis
Ertl, Robin P.; Robertson, Anthony J.; Saunders, Diane; Coffman, James A.
2011-01-01
Nodal proteins are diffusible morphogens that drive pattern formation via short-range feedback activation coupled to long-range Lefty-mediated inhibition. In the sea urchin embryo, specification of the secondary (oral-aboral) axis occurs via zygotic expression of nodal, which is localized to the prospective oral ectoderm at early blastula stage. In mid-blastula stage embryos treated with low micromolar nickel or zinc, nodal expression expands progressively beyond the confines of this localized domain to encompass the entire equatorial circumference of the embryo, producing radialized embryos lacking an oral-aboral axis. RNAseq analysis of embryos treated with nickel, zinc or cadmium (which does not radialize embryos) showed that several genes involved in endocytosis were similarly perturbed by nickel and zinc but not cadmium. Inhibiting dynamin, a GTPase required for receptor-mediated endocytosis, phenocopies the effects of nickel and zinc, suggesting that dynamin-mediated endocytosis is required as a sink to limit the range of Nodal signaling. PMID:21337468
NASA Technical Reports Server (NTRS)
Ilin, Andrew V.
2006-01-01
The Magnetic Field Solver computer program calculates the magnetic field generated by a group of collinear, cylindrical axisymmetric electromagnet coils. Given the current flowing in, and the number of turns, axial position, and axial and radial dimensions of each coil, the program calculates matrix coefficients for a finite-difference system of equations that approximates a two-dimensional partial differential equation for the magnetic potential contributed by the coil. The program iteratively solves these finite-difference equations by use of the modified incomplete Cholesky preconditioned-conjugate-gradient method. The total magnetic potential as a function of axial (z) and radial (r) position is then calculated as a sum of the magnetic potentials of the individual coils, using a high-accuracy interpolation scheme. Then the r and z components of the magnetic field as functions of r and z are calculated from the total magnetic potential by use of a high-accuracy finite-difference scheme. Notably, for the finite-difference calculations, the program generates nonuniform two-dimensional computational meshes from nonuniform one-dimensional meshes. Each mesh is generated in such a way as to minimize the numerical error for a benchmark one-dimensional magnetostatic problem.
Sherlock Holmes, Master Problem Solver.
ERIC Educational Resources Information Center
Ballew, Hunter
1994-01-01
Shows the connections between Sherlock Holmes's investigative methods and mathematical problem solving, including observations, characteristics of the problem solver, importance of data, questioning the obvious, learning from experience, learning from errors, and indirect proof. (MKR)
MILAMIN 2 - Fast MATLAB FEM solver
NASA Astrophysics Data System (ADS)
Dabrowski, Marcin; Krotkiewski, Marcin; Schmid, Daniel W.
2013-04-01
MILAMIN is a free and efficient MATLAB-based two-dimensional FEM solver utilizing unstructured meshes [Dabrowski et al., G-cubed (2008)]. The code consists of steady-state thermal diffusion and incompressible Stokes flow solvers implemented in approximately 200 lines of native MATLAB code. The brevity makes the code easily customizable. An important quality of MILAMIN is speed - it can handle millions of nodes within minutes on one CPU core of a standard desktop computer, and is faster than many commercial solutions. The new MILAMIN 2 allows three-dimensional modeling. It is designed as a set of functional modules that can be used as building blocks for efficient FEM simulations using MATLAB. The utilities are largely implemented as native MATLAB functions. For performance critical parts we use MUTILS - a suite of compiled MEX functions optimized for shared memory multi-core computers. The most important features of MILAMIN 2 are: 1. Modular approach to defining, tracking, and discretizing the geometry of the model 2. Interfaces to external mesh generators (e.g., Triangle, Fade2d, T3D) and mesh utilities (e.g., element type conversion, fast point location, boundary extraction) 3. Efficient computation of the stiffness matrix for a wide range of element types, anisotropic materials and three-dimensional problems 4. Fast global matrix assembly using a dedicated MEX function 5. Automatic integration rules 6. Flexible prescription (spatial, temporal, and field functions) and efficient application of Dirichlet, Neuman, and periodic boundary conditions 7. Treatment of transient and non-linear problems 8. Various iterative and multi-level solution strategies 9. Post-processing tools (e.g., numerical integration) 10. Visualization primitives using MATLAB, and VTK export functions We provide a large number of examples that show how to implement a custom FEM solver using the MILAMIN 2 framework. The examples are MATLAB scripts of increasing complexity that address a given
A New Stabilized Nodal Integration Approach
Puso, M; Zywicz, E; Chen, J S
2006-02-08
A new stabilized nodal integration scheme is proposed and implemented. In this work, focus is on the natural neighbor meshless interpolation schemes. The approach is a modification of the stabilized conforming nodal integration (SCNI) scheme and is shown to perform well in several benchmark problems.
On code verification of RANS solvers
NASA Astrophysics Data System (ADS)
Eça, L.; Klaij, C. M.; Vaz, G.; Hoekstra, M.; Pereira, F. S.
2016-04-01
This article discusses Code Verification of Reynolds-Averaged Navier Stokes (RANS) solvers that rely on face based finite volume discretizations for volumes of arbitrary shape. The study includes test cases with known analytical solutions (generated with the method of manufactured solutions) corresponding to laminar and turbulent flow, with the latter using eddy-viscosity turbulence models. The procedure to perform Code Verification based on grid refinement studies is discussed and the requirements for its correct application are illustrated in a simple one-dimensional problem. It is shown that geometrically similar grids are recommended for proper Code Verification and so the data should not have scatter making the use of least square fits unnecessary. Results show that it may be advantageous to determine the extrapolated error to cell size/time step zero instead of assuming that it is zero, especially when it is hard to determine the asymptotic order of grid convergence. In the RANS examples, several of the features of the ReFRESCO solver are checked including the effects of the available turbulence models in the convergence properties of the code. It is shown that it is required to account for non-orthogonality effects in the discretization of the diffusion terms and that the turbulence quantities transport equations can deteriorate the order of grid convergence of mean flow quantities.
Self-correcting Multigrid Solver
Jerome L.V. Lewandowski
2004-06-29
A new multigrid algorithm based on the method of self-correction for the solution of elliptic problems is described. The method exploits information contained in the residual to dynamically modify the source term (right-hand side) of the elliptic problem. It is shown that the self-correcting solver is more efficient at damping the short wavelength modes of the algebraic error than its standard equivalent. When used in conjunction with a multigrid method, the resulting solver displays an improved convergence rate with no additional computational work.
Scalable Parallel Algebraic Multigrid Solvers
Bank, R; Lu, S; Tong, C; Vassilevski, P
2005-03-23
The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.
General complex polynomial root solver
NASA Astrophysics Data System (ADS)
Skowron, J.; Gould, A.
2012-12-01
This general complex polynomial root solver, implemented in Fortran and further optimized for binary microlenses, uses a new algorithm to solve polynomial equations and is 1.6-3 times faster than the ZROOTS subroutine that is commercially available from Numerical Recipes, depending on application. The largest improvement, when compared to naive solvers, comes from a fail-safe procedure that permits skipping the majority of the calculations in the great majority of cases, without risking catastrophic failure in the few cases that these are actually required.
Nodal equivalence theory for hexagonal geometry, thermal reactor analysis
Zika, M.; Downar, T. )
1992-01-01
An important aspect of advanced nodal methods is the determination of equivalent few-group parameters for the relatively large homogenized regions used in the nodal flux solution. The theoretical foundation for light water reactor (LWR) assembly homogenization methods has been clearly established, and during the last several years, its successes have secured its position in the stable of dependable LWR analysis methods. Groupwise discontinuity factors that correct for assembly homogenization errors are routinely generated along with the group constants during lattice physics analysis. During the last several years, there has been interest in applying equivalence theory to other reactor types and other geometries. A notable effort has been the work at Argonne National Laboratory to incorporate nodal equivalence theory (NET) for hexagonal lattices into the nodal diffusion option of the DIF3D code. This work was originally intended to improve the neutronics methods used for the analysis of the Experimental Breeder Reactor II (EBR-II), and Ref. 4 discusses the success of that application. More recently, however, attempts were made to apply NET to advanced, thermal reactor designs such as the modular high-temperature gas reactor (MHTGR) and the new production heavy water reactor (NPR/HWR). The same methods that were successful for EBR-II have encountered problems for these reactors. Our preliminary analysis indicates that the sharp global flux gradients in these cores requires large discontinuity factors (greater than 4 or 5) to reproduce the reference solution. This disrupts the convergence of the iterative methods used to solve for the node-wise flux moments and partial currents. Several attempts to remedy the problem have been made over the last few years, including bounding the discontinuity factors and providing improved initial guesses for the flux solution, but nothing has been satisfactory.
A quasi-static polynomial nodal method for nuclear reactor analysis
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.
Optical conductivity of nodal metals
NASA Astrophysics Data System (ADS)
Homes, C. C.; Gu, G. D.; Tu, J. J.; Li, J.; Akrap, A.
2014-03-01
Fermi liquid theory is remarkably successful in describing the transport and optical properties of metals; at frequencies higher than the scattering rate, the optical conductivity adopts the well-known power law behavior σ1(ω) ~ω-2 . We have observed an unusual non-Fermi liquid response σ1(ω) ~ω - 1 +/- 0 . 2 in the ground states of several quasi two-dimensional cuprate (optimally doped Bi2Sr2CaCu2O8+δ, optimally and underdoped YBa2Cu3O7-δ) and iron-based materials (AFe2As2, A = Ba, Ca) which undergo electronic or magnetic phase transitions resulting in dramatically reduced or nodal Fermi surfaces. The identification of an inverse (or fractional) power-law behavior in the residual optical conductivity now permits the removal of this contribution, revealing the direct transitions across the gap and allowing the nature of the electron-boson coupling to be probed. The non-Fermi liquid behavior in these systems may be the result of a common Fermi surface topology of Dirac cone-like features in the electronic dispersion. Supported by the DOE under Contract No. DE-AC02-98CH10886.
Optical conductivity of nodal metals
Homes, C. C.; Tu, J. J.; Li, J.; Gu, G. D.; Akrap, A.
2013-01-01
Fermi liquid theory is remarkably successful in describing the transport and optical properties of metals; at frequencies higher than the scattering rate, the optical conductivity adopts the well-known power law behavior σ1(ω) ∝ ω−2. We have observed an unusual non-Fermi liquid response σ1(ω) ∝ ω−1±0.2 in the ground states of several cuprate and iron-based materials which undergo electronic or magnetic phase transitions resulting in dramatically reduced or nodal Fermi surfaces. The identification of an inverse (or fractional) power-law behavior in the residual optical conductivity now permits the removal of this contribution, revealing the direct transitions across the gap and allowing the nature of the electron-boson coupling to be probed. The non-Fermi liquid behavior in these systems may be the result of a common Fermi surface topology of Dirac cone-like features in the electronic dispersion. PMID:24336241
Nodal network generator for CAVE3
NASA Technical Reports Server (NTRS)
Palmieri, J. V.; Rathjen, K. A.
1982-01-01
A new extension of CAVE3 code was developed that automates the creation of a finite difference math model in digital form ready for input to the CAVE3 code. The new software, Nodal Network Generator, is broken into two segments. One segment generates the model geometry using a Tektronix Tablet Digitizer and the other generates the actual finite difference model and allows for graphic verification using Tektronix 4014 Graphic Scope. Use of the Nodal Network Generator is described.
Nodal signalling determines biradial asymmetry in Hydra.
Watanabe, Hiroshi; Schmidt, Heiko A; Kuhn, Anne; Höger, Stefanie K; Kocagöz, Yigit; Laumann-Lipp, Nico; Ozbek, Suat; Holstein, Thomas W
2014-11-01
In bilaterians, three orthogonal body axes define the animal form, with distinct anterior-posterior, dorsal-ventral and left-right asymmetries. The key signalling factors are Wnt family proteins for the anterior-posterior axis, Bmp family proteins for the dorsal-ventral axis and Nodal for the left-right axis. Cnidarians, the sister group to bilaterians, are characterized by one oral-aboral body axis, which exhibits a distinct biradiality of unknown molecular nature. Here we analysed the biradial growth pattern in the radially symmetrical cnidarian polyp Hydra, and we report evidence of Nodal in a pre-bilaterian clade. We identified a Nodal-related gene (Ndr) in Hydra magnipapillata, and this gene is essential for setting up an axial asymmetry along the main body axis. This asymmetry defines a lateral signalling centre, inducing a new body axis of a budding polyp orthogonal to the mother polyp's axis. Ndr is expressed exclusively in the lateral bud anlage and induces Pitx, which encodes an evolutionarily conserved transcription factor that functions downstream of Nodal. Reminiscent of its function in vertebrates, Nodal acts downstream of β-Catenin signalling. Our data support an evolutionary scenario in which a 'core-signalling cassette' consisting of β-Catenin, Nodal and Pitx pre-dated the cnidarian-bilaterian split. We presume that this cassette was co-opted for various modes of axial patterning: for example, for lateral branching in cnidarians and left-right patterning in bilaterians. PMID:25156256
Primary extra nodal non-Hodgkin's lymphoma of the oral cavity in a young girl
Vinoth, Ponnurangam N.; Selvan, Sathyamoorthi Muthamil; Sahni, Latika; Krishnaratnam, Kannan; Rajendiran, Swaminathan; Anand, Chidambaram Vishwanath; Scott, Julius X.
2012-01-01
Primary Non Hodgkin s Lymphoma (NHL) usually arises within the lymphnodes, but 20-30% account for extra nodal sites. Oral cavity, as a primary extra nodal site for NHL, is relatively rare and diverse in presentation, response to therapy and prognosis. We report a 14 year old adolescent girl who presented with multiple gingival swellings, the most prominent one being in the right anterior maxilla. Gingival biopsy showed NHL- diffuse large B cell type. Child was completely cured with chemotherapy and now she is in complete remission and under regular follow up. PMID:23833495
NASA Astrophysics Data System (ADS)
Pelanti, Marica; Bouchut, François; Mangeney, Anne
2011-02-01
We present a Riemann solver derived by a relaxation technique for classical single-phase shallow flow equations and for a two-phase shallow flow model describing a mixture of solid granular material and fluid. Our primary interest is the numerical approximation of this two-phase solid/fluid model, whose complexity poses numerical difficulties that cannot be efficiently addressed by existing solvers. In particular, we are concerned with ensuring a robust treatment of dry bed states. The relaxation system used by the proposed solver is formulated by introducing auxiliary variables that replace the momenta in the spatial gradients of the original model systems. The resulting relaxation solver is related to Roe solver in that its Riemann solution for the flow height and relaxation variables is formally computed as Roe's Riemann solution. The relaxation solver has the advantage of a certain degree of freedom in the specification of the wave structure through the choice of the relaxation parameters. This flexibility can be exploited to handle robustly vacuum states, which is a well known difficulty of standard Roe's method, while maintaining Roe's low diffusivity. For the single-phase model positivity of flow height is rigorously preserved. For the two-phase model positivity of volume fractions in general is not ensured, and a suitable restriction on the CFL number might be needed. Nonetheless, numerical experiments suggest that the proposed two-phase flow solver efficiently models wet/dry fronts and vacuum formation for a large range of flow conditions. As a corollary of our study, we show that for single-phase shallow flow equations the relaxation solver is formally equivalent to the VFRoe solver with conservative variables of Gallouët and Masella [T. Gallouët, J.-M. Masella, Un schéma de Godunov approché C.R. Acad. Sci. Paris, Série I, 323 (1996) 77-84]. The relaxation interpretation allows establishing positivity conditions for this VFRoe method.
A generalized gyrokinetic Poisson solver
Lin, Z.; Lee, W.W.
1995-03-01
A generalized gyrokinetic Poisson solver has been developed, which employs local operations in the configuration space to compute the polarization density response. The new technique is based on the actual physical process of gyrophase-averaging. It is useful for nonlocal simulations using general geometry equilibrium. Since it utilizes local operations rather than the global ones such as FFT, the new method is most amenable to massively parallel algorithms.
On unstructured grids and solvers
NASA Technical Reports Server (NTRS)
Barth, T. J.
1990-01-01
The fundamentals and the state-of-the-art technology for unstructured grids and solvers are highlighted. Algorithms and techniques pertinent to mesh generation are discussed. It is shown that grid generation and grid manipulation schemes rely on fast multidimensional searching. Flow solution techniques for the Euler equations, which can be derived from the integral form of the equations are discussed. Sample calculations are also provided.
NASA Technical Reports Server (NTRS)
Padovan, J.; Lackney, J.
1986-01-01
The current paper develops a constrained hierarchical least square nonlinear equation solver. The procedure can handle the response behavior of systems which possess indefinite tangent stiffness characteristics. Due to the generality of the scheme, this can be achieved at various hierarchical application levels. For instance, in the case of finite element simulations, various combinations of either degree of freedom, nodal, elemental, substructural, and global level iterations are possible. Overall, this enables a solution methodology which is highly stable and storage efficient. To demonstrate the capability of the constrained hierarchical least square methodology, benchmarking examples are presented which treat structure exhibiting highly nonlinear pre- and postbuckling behavior wherein several indefinite stiffness transitions occur.
An investigation of nodal structures and the construction of trial wave functions
NASA Astrophysics Data System (ADS)
Bressanini, Dario; Morosi, Gabriele; Tarasco, Silvia
2005-11-01
The factors influencing the quality of the nodal surfaces, namely, the atomic basis set, the single-particle orbitals, and the configurations included in the wave-function expansion, are examined for a few atomic and molecular systems. The following empirical rules are found: the atomic basis set must be fairly large, complete active space and natural orbitals are usually better than Hartree-Fock orbitals, multiconfiguration expansions perform better than single-determinant wave functions, but only few configurations are effective and their choice is suggested by symmetry considerations, while too long determinantal expansions spoil the nodal surfaces. These rules allow us to reduce the nodal error and to compute the best fixed node-diffusion Monte Carlo energies for a series of dimers of first-row atoms.
Harms, Paul W.; Chang, Chenbei
2003-01-01
Transforming growth factor β (TGF-β) signals regulate multiple processes during development and in adult. We recently showed that tomoregulin-1 (TMEFF1), a transmembrane protein, selectively inhibits nodal but not activin in early Xenopus embryos. Here we report that TMEFF1 binds to the nodal coreceptor Cripto, but does not associate with either nodal or the type I ALK (activin receptor-like kinase) 4 receptor in coimmunoprecipitation assays. The inhibition of the nodal signaling by TMEFF1 in Xenopus ectodermal explants is rescued with wild-type but not mutant forms of Cripto. Furthermore, we show that the Cripto-FRL1-Cryptic (CFC) domain in Cripto, which is essential for its binding to ALK4, is also important for its interaction with TMEFF1. Our results demonstrate for the first time that nodal signaling can be regulated by a novel mechanism of blocking the Cripto coreceptor. PMID:14563676
Keeping a lid on nodal: transcriptional and translational repression of nodal signalling
Robertson, Elizabeth J.
2016-01-01
Nodal is an evolutionarily conserved member of the transforming growth factor-β (TGF-β) superfamily of secreted signalling factors. Nodal factors are known to play key roles in embryonic development and asymmetry in a variety of organisms ranging from hydra and sea urchins to fish, mice and humans. In addition to embryonic patterning, Nodal signalling is required for maintenance of human embryonic stem cell pluripotency and mis-regulated Nodal signalling has been found associated with tumour metastases. Therefore, precise and timely regulation of this pathway is essential. Here, we discuss recent evidence from sea urchins, frogs, fish, mice and humans that show a role for transcriptional and translational repression of Nodal signalling during early development. PMID:26791244
Nodal Quasiparticle in Pseudogapped Colossal Magnetoresistive Manganites
Mannella, N.
2010-06-02
A characteristic feature of the copper oxide high-temperature superconductors is the dichotomy between the electronic excitations along the nodal (diagonal) and antinodal (parallel to the Cu-O bonds) directions in momentum space, generally assumed to be linked to the d-wave symmetry of the superconducting state. Angle-resolved photoemission measurements in the superconducting state have revealed a quasiparticle spectrum with a d-wave gap structure that exhibits a maximum along the antinodal direction and vanishes along the nodal direction. Subsequent measurements have shown that, at low doping levels, this gap structure persists even in the high-temperature metallic state, although the nodal points of the superconducting state spread out in finite Fermi arcs. This is the so-called pseudogap phase, and it has been assumed that it is closely linked to the superconducting state, either by assigning it to fluctuating superconductivity or by invoking orders which are natural competitors of d-wave superconductors. Here we report experimental evidence that a very similar pseudogap state with a nodal-antinodal dichotomous character exists in a system that is markedly different from a superconductor: the ferromagnetic metallic groundstate of the colossal magnetoresistive bilayer manganite La{sub 1.2}Sr{sub 1.8}Mn{sub 2}O{sub 7}. Our findings therefore cast doubt on the assumption that the pseudogap state in the copper oxides and the nodal-antinodal dichotomy are hallmarks of the superconductivity state.
A Parallelized 3D Particle-In-Cell Method With Magnetostatic Field Solver And Its Applications
NASA Astrophysics Data System (ADS)
Hsu, Kuo-Hsien; Chen, Yen-Sen; Wu, Men-Zan Bill; Wu, Jong-Shinn
2008-10-01
A parallelized 3D self-consistent electrostatic particle-in-cell finite element (PIC-FEM) code using an unstructured tetrahedral mesh was developed. For simulating some applications with external permanent magnet set, the distribution of the magnetostatic field usually also need to be considered and determined accurately. In this paper, we will firstly present the development of a 3D magnetostatic field solver with an unstructured mesh for the flexibility of modeling objects with complex geometry. The vector Poisson equation for magnetostatic field is formulated using the Galerkin nodal finite element method and the resulting matrix is solved by parallel conjugate gradient method. A parallel adaptive mesh refinement module is coupled to this solver for better resolution. Completed solver is then verified by simulating a permanent magnet array with results comparable to previous experimental observations and simulations. By taking the advantage of the same unstructured grid format of this solver, the developed PIC-FEM code could directly and easily read the magnetostatic field for particle simulation. In the upcoming conference, magnetron is simulated and presented for demonstrating the capability of this code.
CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. II. GRAY RADIATION HYDRODYNAMICS
Zhang, W.; Almgren, A.; Bell, J.; Howell, L.; Burrows, A.
2011-10-01
We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation hydrodynamics. In our approach, the system is split into two parts, one part that couples the radiation and fluid in a hyperbolic subsystem, and another parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem is solved explicitly with a high-order Godunov scheme, whereas the parabolic part is solved implicitly with a first-order backward Euler method.
Finite Element Interface to Linear Solvers
Williams, Alan
2005-03-18
Sparse systems of linear equations arise in many engineering applications, including finite elements, finite volumes, and others. The solution of linear systems is often the most computationally intensive portion of the application. Depending on the complexity of problems addressed by the application, there may be no single solver capable of solving all of the linear systems that arise. This motivates the desire to switch an application from one solver librwy to another, depending on the problem being solved. The interfaces provided by solver libraries differ greatly, making it difficult to switch an application code from one library to another. The amount of library-specific code in an application Can be greatly reduced by having an abstraction layer between solver libraries and the application, putting a common "face" on various solver libraries. One such abstraction layer is the Finite Element Interface to Linear Solvers (EEl), which has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory.
Nodal analysis of two-phase instabilities
Lahey, R.T. Jr.; Garea, V.P.
1995-10-01
Nodal models having moving nodal boundaries have been developed for the analysis of two-phase flow instabilities in a boiling channel. The first model, which was based on a Galerkin method for the discretization, has been found to be accurate in the prediction of the onset of instabilities as well as the frequency of oscillations. This model however, had some problems with the prediction of chaotic phenomena and did not allow for flow reversal in the channel. A second nodal model, based on a finite difference approach, has been found to perform better for the prediction of non-linear response and it also allows for flow reversal. Both models are numerically more efficient than the existing fixed grid models for instabilities analysis.
Analysis Tools for CFD Multigrid Solvers
NASA Technical Reports Server (NTRS)
Mineck, Raymond E.; Thomas, James L.; Diskin, Boris
2004-01-01
Analysis tools are needed to guide the development and evaluate the performance of multigrid solvers for the fluid flow equations. Classical analysis tools, such as local mode analysis, often fail to accurately predict performance. Two-grid analysis tools, herein referred to as Idealized Coarse Grid and Idealized Relaxation iterations, have been developed and evaluated within a pilot multigrid solver. These new tools are applicable to general systems of equations and/or discretizations and point to problem areas within an existing multigrid solver. Idealized Relaxation and Idealized Coarse Grid are applied in developing textbook-efficient multigrid solvers for incompressible stagnation flow problems.
Enthalpy Diffusion in Multicomponent Flows
Cook, A W
2009-01-20
The conclusions of this paper are: (1) Enthalpy diffusion preserves the second law. (2) Euler solvers will not produce correct temperatures in mixing regions. (3) Navier-Stokes solvers will only produce correct temperatures if q{sub d} is included. (4) Errors from neglecting enthalpy diffusion are most severe when differences in molecular weights are large. (5) In addition to temperature, enthalpy diffusion affects density, dilatation and other fields in subtle ways. (6) Reacting flow simulations that neglect the term are a dubious proposition. (7) Turbulence models for RANS and LES closures should preserve consistency between energy and species diffusion.
A lymph nodal capillary-cavernous hemangioma.
Dellachà, A; Fulcheri, E; Campisi, C
1999-09-01
A capillary-cavernous hemangioma in an obturator lymph node was found incidentally in a 64 year-old woman who had undergone unilateral salpingo-oophorectomy and lymphadenectomy for an ovarian neoplasm. Vascular tumors of lymph nodes are briefly reviewed including eight previously described nodal capillary-cavernous hemangiomas. The association with other splanchnic hemangiomas is pointed out and the likelihood that the lesion is a hamartoma rather than a true neoplasm is addressed. Despite its rarity, this entity needs to be recognized by lymphologists who image lymph nodes by lymphangiography as well as by lymph nodal pathologists. PMID:10494525
NOKIN1D: one-dimensional neutron kinetics based on a nodal collocation method
NASA Astrophysics Data System (ADS)
Verdú, G.; Ginestar, D.; Miró, R.; Jambrina, A.; Barrachina, T.; Soler, Amparo; Concejal, Alberto
2014-06-01
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.
A.A. Bingham; R.M. Ferrer; A.M. ougouag
2009-09-01
An accurate and computationally efficient two or three-dimensional neutron diffusion model will be necessary for the development, safety parameters computation, and fuel cycle analysis of a prismatic Very High Temperature Reactor (VHTR) design under Next Generation Nuclear Plant Project (NGNP). For this purpose, an analytical nodal Green’s function solution for the transverse integrated neutron diffusion equation is developed in two and three-dimensional hexagonal geometry. This scheme is incorporated into HEXPEDITE, a code first developed by Fitzpatrick and Ougouag. HEXPEDITE neglects non-physical discontinuity terms that arise in the transverse leakage due to the transverse integration procedure application to hexagonal geometry and cannot account for the effects of burnable poisons across nodal boundaries. The test code being developed for this document accounts for these terms by maintaining an inventory of neutrons by using the nodal balance equation as a constraint of the neutron flux equation. The method developed in this report is intended to restore neutron conservation and increase the accuracy of the code by adding these terms to the transverse integrated flux solution and applying the nodal Green’s function solution to the resulting equation to derive a semi-analytical solution.
NASA Astrophysics Data System (ADS)
Dutta, Vimala
1993-07-01
An implicit finite volume nodal point scheme has been developed for solving the two-dimensional compressible Navier-Stokes equations. The numerical scheme is evolved by efficiently combining the basic ideas of the implicit finite-difference scheme of Beam and Warming (1978) with those of nodal point schemes due to Hall (1985) and Ni (1982). The 2-D Navier-Stokes solver is implemented for steady, laminar/turbulent flows past airfoils by using C-type grids. Turbulence closure is achieved by employing the algebraic eddy-viscosity model of Baldwin and Lomax (1978). Results are presented for the NACA-0012 and RAE-2822 airfoil sections. Comparison of the aerodynamic coefficients with experimental results for the different test cases presented here establishes the validity and efficiency of the method.
Network and Nodal Accessibility Teaching Exercise.
ERIC Educational Resources Information Center
Wheeler, James O.
1988-01-01
Presents an exercise, for use in college-level economic geography courses, which teaches the concept of nodal and network accessibility with an application to manufacturing locations. Intended to guide students to think spatially and to generalize from numeric data, this out-of-class activity teaches students to discover results, to do simple…
Benchmarking transport solvers for fracture flow problems
NASA Astrophysics Data System (ADS)
Olkiewicz, Piotr; Dabrowski, Marcin
2015-04-01
Fracture flow may dominate in rocks with low porosity and it can accompany both industrial and natural processes. Typical examples of such processes are natural flows in crystalline rocks and industrial flows in geothermal systems or hydraulic fracturing. Fracture flow provides an important mechanism for transporting mass and energy. For example, geothermal energy is primarily transported by the flow of the heated water or steam rather than by the thermal diffusion. The geometry of the fracture network and the distribution of the mean apertures of individual fractures are the key parameters with regard to the fracture network transmissivity. Transport in fractures can occur through the combination of advection and diffusion processes like in the case of dissolved chemical components. The local distribution of the fracture aperture may play an important role for both flow and transport processes. In this work, we benchmark various numerical solvers for flow and transport processes in a single fracture in 2D and 3D. Fracture aperture distributions are generated by a number of synthetic methods. We examine a single-phase flow of an incompressible viscous Newtonian fluid in the low Reynolds number limit. Periodic boundary conditions are used and a pressure difference is imposed in the background. The velocity field is primarly found using the Stokes equations. We systematically compare the obtained velocity field to the results obtained by solving the Reynolds equation. This allows us to examine the impact of the aperture distribution on the permeability of the medium and the local velocity distribution for two different mathematical descriptions of the fracture flow. Furthermore, we analyse the impact of aperture distribution on the front characteristics such as the standard deviation and the fractal dimension for systems in 2D and 3D.
MACSYMA's symbolic ordinary differential equation solver
NASA Technical Reports Server (NTRS)
Golden, J. P.
1977-01-01
The MACSYMA's symbolic ordinary differential equation solver ODE2 is described. The code for this routine is delineated, which is of interest because it is written in top-level MACSYMA language, and may serve as a good example of programming in that language. Other symbolic ordinary differential equation solvers are mentioned.
KLU2 Direct Linear Solver Package
Energy Science and Technology Software Center (ESTSC)
2012-01-04
KLU2 is a direct sparse solver for solving unsymmetric linear systems. It is related to the existing KLU solver, (in Amesos package and also as a stand-alone package from University of Florida) but provides template support for scalar and ordinal types. It uses a left looking LU factorization method.
Improving Resource-Unaware SAT Solvers
NASA Astrophysics Data System (ADS)
Hölldobler, Steffen; Manthey, Norbert; Saptawijaya, Ari
The paper discusses cache utilization in state-of-the-art SAT solvers. The aim of the study is to show how a resource-unaware SAT solver can be improved by utilizing the cache sensibly. The analysis is performed on a CDCL-based SAT solver using a subset of the industrial SAT Competition 2009 benchmark. For the analysis, the total cycles, the resource stall cycles, the L2 cache hits and the L2 cache misses are traced using sample based profiling. Based on the analysis, several techniques - some of which have not been used in SAT solvers so far - are proposed resulting in a combined speedup up to 83% without affecting the search path of the solver. The average speedup on the benchmark is 60%. The new techniques are also applied to MiniSAT2.0 improving its runtime by 20% on average.
Belos Block Linear Solvers Package
Energy Science and Technology Software Center (ESTSC)
2004-03-01
Belos is an extensible and interoperable framework for large-scale, iterative methods for solving systems of linear equations with multiple right-hand sides. The motivation for this framework is to provide a generic interface to a collection of algorithms for solving large-scale linear systems. Belos is interoperable because both the matrix and vectors are considered to be opaque objects--only knowledge of the matrix and vectors via elementary operations is necessary. An implementation of Balos is accomplished viamore » the use of interfaces. One of the goals of Belos is to allow the user flexibility in specifying the data representation for the matrix and vectors and so leverage any existing software investment. The algorithms that will be included in package are Krylov-based linear solvers, like Block GMRES (Generalized Minimal RESidual) and Block CG (Conjugate-Gradient).« less
EXTENSION OF THE 1D FOUR-GROUP ANALYTIC NODAL METHOD TO FULL MULTIGROUP
B. D. Ganapol; D. W. Nigg
2008-09-01
In the mid 80’s, a four-group/two-region, entirely analytical 1D nodal benchmark appeared. It was readily acknowledged that this special case was as far as one could go in terms of group number and still achieve an analytical solution. In this work, we show that by decomposing the solution to the multigroup diffusion equation into homogeneous and particular solutions, extension to any number of groups is a relatively straightforward exercise using the mathematics of linear algebra.
Nodal and Lefty signaling regulates the growth of pancreatic cells
Zhang, You-Qing; Sterling, Lori; Stotland, Aleksandr; Hua, Hong; Kritzik, Marcie; Sarvetnick, Nora
2014-01-01
Nodal and its antagonist, Lefty, are important mediators specifying the laterality of the organs during embryogenesis. Nodal signals through activin receptors in the presence of its co-receptor, Cripto. In the present study, we investigated the possible roles of Nodal and Lefty signaling during islet development and regeneration. We found that both Nodal and Lefty are expressed in the pancreas during embryogenesis and islet regeneration. In vitro studies demonstrated that Nodal inhibits, whereas Lefty enhances, the proliferation of a pancreatic cell line. In addition, we showed that Lefty-1 activates MAPK and Akt phosphorylation in these cells. In vivo blockade of endogenous Lefty using neutralizing Lefty-1 monoclonal antibody results in a significantly decreased proliferation of duct epithelial cells during islet regeneration. This is the first study to decipher the expression and function of Nodal and Lefty in pancreatic growth. Importantly, our results highlight a novel function of Nodal-Lefty signaling in the regulation of expansion of pancreatic cells. PMID:18393305
ALPS - A LINEAR PROGRAM SOLVER
NASA Technical Reports Server (NTRS)
Viterna, L. A.
1994-01-01
Linear programming is a widely-used engineering and management tool. Scheduling, resource allocation, and production planning are all well-known applications of linear programs (LP's). Most LP's are too large to be solved by hand, so over the decades many computer codes for solving LP's have been developed. ALPS, A Linear Program Solver, is a full-featured LP analysis program. ALPS can solve plain linear programs as well as more complicated mixed integer and pure integer programs. ALPS also contains an efficient solution technique for pure binary (0-1 integer) programs. One of the many weaknesses of LP solvers is the lack of interaction with the user. ALPS is a menu-driven program with no special commands or keywords to learn. In addition, ALPS contains a full-screen editor to enter and maintain the LP formulation. These formulations can be written to and read from plain ASCII files for portability. For those less experienced in LP formulation, ALPS contains a problem "parser" which checks the formulation for errors. ALPS creates fully formatted, readable reports that can be sent to a printer or output file. ALPS is written entirely in IBM's APL2/PC product, Version 1.01. The APL2 workspace containing all the ALPS code can be run on any APL2/PC system (AT or 386). On a 32-bit system, this configuration can take advantage of all extended memory. The user can also examine and modify the ALPS code. The APL2 workspace has also been "packed" to be run on any DOS system (without APL2) as a stand-alone "EXE" file, but has limited memory capacity on a 640K system. A numeric coprocessor (80X87) is optional but recommended. The standard distribution medium for ALPS is a 5.25 inch 360K MS-DOS format diskette. IBM, IBM PC and IBM APL2 are registered trademarks of International Business Machines Corporation. MS-DOS is a registered trademark of Microsoft Corporation.
GARDNER, P.R.
2006-04-01
Sudoku, also known as Number Place, is a logic-based placement puzzle. The aim of the puzzle is to enter a numerical digit from 1 through 9 in each cell of a 9 x 9 grid made up of 3 x 3 subgrids (called ''regions''), starting with various digits given in some cells (the ''givens''). Each row, column, and region must contain only one instance of each numeral. Completing the puzzle requires patience and logical ability. Although first published in a U.S. puzzle magazine in 1979, Sudoku initially caught on in Japan in 1986 and attained international popularity in 2005. Last fall, after noticing Sudoku puzzles in some newspapers and magazines, I attempted a few just to see how hard they were. Of course, the difficulties varied considerably. ''Obviously'' one could use Trial and Error but all the advice was to ''Use Logic''. Thinking to flex, and strengthen, those powers, I began to tackle the puzzles systematically. That is, when I discovered a new tactical rule, I would write it down, eventually generating a list of ten or so, with some having overlap. They served pretty well except for the more difficult puzzles, but even then I managed to develop an additional three rules that covered all of them until I hit the Oregonian puzzle shown. With all of my rules, I could not seem to solve that puzzle. Initially putting my failure down to rapid mental fatigue (being unable to hold a sufficient quantity of information in my mind at one time), I decided to write a program to implement my rules and see what I had failed to notice earlier. The solver, too, failed. That is, my rules were insufficient to solve that particular puzzle. I happened across a book written by a fellow who constructs such puzzles and who claimed that, sometimes, the only tactic left was trial and error. With a trial and error routine implemented, my solver successfully completed the Oregonian puzzle, and has successfully solved every puzzle submitted to it since.
SIERRA framework version 4 : solver services.
Williams, Alan B.
2005-02-01
Several SIERRA applications make use of third-party libraries to solve systems of linear and nonlinear equations, and to solve eigenproblems. The classes and interfaces in the SIERRA framework that provide linear system assembly services and access to solver libraries are collectively referred to as solver services. This paper provides an overview of SIERRA's solver services including the design goals that drove the development, and relationships and interactions among the various classes. The process of assembling and manipulating linear systems will be described, as well as access to solution methods and other operations.
A scalable 2-D parallel sparse solver
Kothari, S.C.; Mitra, S.
1995-12-01
Scalability beyond a small number of processors, typically 32 or less, is known to be a problem for existing parallel general sparse (PGS) direct solvers. This paper presents a parallel general sparse PGS direct solver for general sparse linear systems on distributed memory machines. The algorithm is based on the well-known sequential sparse algorithm Y12M. To achieve efficient parallelization, a 2-D scattered decomposition of the sparse matrix is used. The proposed algorithm is more scalable than existing parallel sparse direct solvers. Its scalability is evaluated on a 256 processor nCUBE2s machine using Boeing/Harwell benchmark matrices.
Nodal resonance in a strong standing wave
NASA Astrophysics Data System (ADS)
Fernández C., David J.; Mielnik, Bogdan
1990-06-01
The motion of charged particles in a standing electromagnetic wave is considered. For amplitudes that are not too high, the wave causes an effect of attraction of particles to the nodal points, resembling the channeling effect reported by Salomon, Dalibard, Aspect, Metcalf, and Cohen-Tannoudji [Phys. Rev. Lett. 59, 1659 (1987)] consistent with the ``high-frequency potential'' of Kapitza [Zh. Eksp. Teor. Fiz. 21, 588 (1951)]. For high-field intensities, however, the nodal points undergo a qualitative metamorphosis, converting themselves from particle attractors into resonant centers. Some chaotic phenomena arise and the description of the oscillating field in terms of an ``effective potential'' becomes inappropriate. The question of a correct Floquet Hamiltonian that could describe the standing wave within this amplitude and frequency regime is open.
NASA Technical Reports Server (NTRS)
Ferencz, Donald C.; Viterna, Larry A.
1991-01-01
ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.
Euler solvers for transonic applications
NASA Technical Reports Server (NTRS)
Vanleer, Bram
1989-01-01
The 1980s may well be called the Euler era of applied aerodynamics. Computer codes based on discrete approximations of the Euler equations are now routinely used to obtain solutions of transonic flow problems in which the effects of entropy and vorticity production are significant. Such codes can even predict separation from a sharp edge, owing to the inclusion of artificial dissipation, intended to lend numerical stability to the calculation but at the same time enforcing the Kutta condition. One effect not correctly predictable by Euler codes is the separation from a smooth surface, and neither is viscous drag; for these some form of the Navier-Stokes equation is needed. It, therefore, comes as no surprise to observe that the Navier-Stokes has already begun before Euler solutions were fully exploited. Moreover, most numerical developments for the Euler equations are now constrained by the requirement that the techniques introduced, notably artificial dissipation, must not interfere with the new physics added when going from an Euler to a full Navier-Stokes approximation. In order to appreciate the contributions of Euler solvers to the understanding of transonic aerodynamics, it is useful to review the components of these computational tools. Space discretization, time- or pseudo-time marching and boundary procedures, the essential constituents are discussed. The subject of grid generation and grid adaptation to the solution are touched upon only where relevant. A list of unanswered questions and an outlook for the future are covered.
CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. III. MULTIGROUP RADIATION HYDRODYNAMICS
Zhang, W.; Almgren, A.; Bell, J.; Howell, L.; Burrows, A.; Dolence, J.
2013-01-15
We present a formulation for multigroup radiation hydrodynamics that is correct to order O(v/c) using the comoving-frame approach and the flux-limited diffusion approximation. We describe a numerical algorithm for solving the system, implemented in the compressible astrophysics code, CASTRO. CASTRO uses a Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. In our multigroup radiation solver, the system is split into three parts: one part that couples the radiation and fluid in a hyperbolic subsystem, another part that advects the radiation in frequency space, and a parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem and the frequency space advection are solved explicitly with high-order Godunov schemes, whereas the parabolic part is solved implicitly with a first-order backward Euler method. Our multigroup radiation solver works for both neutrino and photon radiation.
CASTRO: A New Compressible Astrophysical Solver. III. Multigroup Radiation Hydrodynamics
NASA Astrophysics Data System (ADS)
Zhang, W.; Howell, L.; Almgren, A.; Burrows, A.; Dolence, J.; Bell, J.
2013-01-01
We present a formulation for multigroup radiation hydrodynamics that is correct to order O(v/c) using the comoving-frame approach and the flux-limited diffusion approximation. We describe a numerical algorithm for solving the system, implemented in the compressible astrophysics code, CASTRO. CASTRO uses a Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. In our multigroup radiation solver, the system is split into three parts: one part that couples the radiation and fluid in a hyperbolic subsystem, another part that advects the radiation in frequency space, and a parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem and the frequency space advection are solved explicitly with high-order Godunov schemes, whereas the parabolic part is solved implicitly with a first-order backward Euler method. Our multigroup radiation solver works for both neutrino and photon radiation.
An advanced implicit solver for MHD
NASA Astrophysics Data System (ADS)
Udrea, Bogdan
A new implicit algorithm has been developed for the solution of the time-dependent, viscous and resistive single fluid magnetohydrodynamic (MHD) equations. The algorithm is based on an approximate Riemann solver for the hyperbolic fluxes and central differencing applied on a staggered grid for the parabolic fluxes. The algorithm employs a locally aligned coordinate system that allows the solution to the Riemann problems to be solved in a natural direction, normal to cell interfaces. The result is an original scheme that is robust and reduces the complexity of the flux formulas. The evaluation of the parabolic fluxes is also implemented using a locally aligned coordinate system, this time on the staggered grid. The implicit formulation employed by WARP3 is a two level scheme that was applied for the first time to the single fluid MHD model. The flux Jacobians that appear in the implicit scheme are evaluated numerically. The linear system that results from the implicit discretization is solved using a robust symmetric Gauss-Seidel method. The code has an explicit mode capability so that implementation and test of new algorithms or new physics can be performed in this simpler mode. Last but not least the code was designed and written to run on parallel computers so that complex, high resolution runs can be per formed in hours rather than days. The code has been benchmarked against analytical and experimental gas dynamics and MHD results. The benchmarks consisted of one-dimensional Riemann problems and diffusion dominated problems, two-dimensional supersonic flow over a wedge, axisymmetric magnetoplasmadynamic (MPD) thruster simulation and three-dimensional supersonic flow over intersecting wedges and spheromak stability simulation. The code has been proven to be robust and the results of the simulations showed excellent agreement with analytical and experimental results. Parallel performance studies showed that the code performs as expected when run on parallel
Parallelizing alternating direction implicit solver on GPUs
Technology Transfer Automated Retrieval System (TEKTRAN)
We present a parallel Alternating Direction Implicit (ADI) solver on GPUs. Our implementation significantly improves existing implementations in two aspects. First, we address the scalability issue of existing Parallel Cyclic Reduction (PCR) implementations by eliminating their hardware resource con...
Optimization of solver for gas flow modeling
NASA Astrophysics Data System (ADS)
Savichkin, D.; Dodulad, O.; Kloss, Yu
2014-05-01
The main purpose of the work is optimization of the solver for rarefied gas flow modeling based on the Boltzmann equation. Optimization method is based on SIMD extensions for ×86 processors. Computational code is profiled and manually optimized with SSE instructions. Heat flow, shock waves and Knudsen pump are modeled with optimized solver. Dependencies of computational time from mesh sizes and CPU capabilities are provided.
A parallel PCG solver for MODFLOW.
Dong, Yanhui; Li, Guomin
2009-01-01
In order to simulate large-scale ground water flow problems more efficiently with MODFLOW, the OpenMP programming paradigm was used to parallelize the preconditioned conjugate-gradient (PCG) solver with in this study. Incremental parallelization, the significant advantage supported by OpenMP on a shared-memory computer, made the solver transit to a parallel program smoothly one block of code at a time. The parallel PCG solver, suitable for both MODFLOW-2000 and MODFLOW-2005, is verified using an 8-processor computer. Both the impact of compilers and different model domain sizes were considered in the numerical experiments. Based on the timing results, execution times using the parallel PCG solver are typically about 1.40 to 5.31 times faster than those using the serial one. In addition, the simulation results are the exact same as the original PCG solver, because the majority of serial codes were not changed. It is worth noting that this parallelizing approach reduces cost in terms of software maintenance because only a single source PCG solver code needs to be maintained in the MODFLOW source tree. PMID:19563427
Finite Element Interface to Linear Solvers
Energy Science and Technology Software Center (ESTSC)
2005-03-18
Sparse systems of linear equations arise in many engineering applications, including finite elements, finite volumes, and others. The solution of linear systems is often the most computationally intensive portion of the application. Depending on the complexity of problems addressed by the application, there may be no single solver capable of solving all of the linear systems that arise. This motivates the desire to switch an application from one solver librwy to another, depending on themore » problem being solved. The interfaces provided by solver libraries differ greatly, making it difficult to switch an application code from one library to another. The amount of library-specific code in an application Can be greatly reduced by having an abstraction layer between solver libraries and the application, putting a common "face" on various solver libraries. One such abstraction layer is the Finite Element Interface to Linear Solvers (EEl), which has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory.« less
Development and assessment of the CONTAIN hybrid flow solver
Murata, K.K.; Stamps, D.W.
1996-11-01
A new gravitational head formulation for the treatment of stratified conditions has been developed for CONTAIN 1.2, a control volume code used primarily for the analyses of postulated accidents in nuclear power plants. The new CONTAIN formulation of gravitational heads, termed the hybrid formulation, is described. This method of calculating stratified conditions is compared with the old, average-density formulation used in code versions prior to CONTAIN 1.2. Both formulations are assessed in this report with experimental data from three large-scale experiments in which stratified conditions formed by injection of a buoyant gas were observed. In general, the hybrid formulation gives a substantially higher degree of stratification than the old formulation. For stable, fully developed stratifications, the hybrid formulation also gives much better agreement with the measured degree of stratification than the old formulation. In addition, the predicted degree of stratification is robust and not sensitive to nodalization, provided a set of nodalization guidelines are followed. However, for stratification behavior controlled by special physics not modeled in CONTAIN, such as momentum convection, plume entrainment, or bulk molecular diffusion, one should not expect good agreement with experiment unless special measures to accommodate the missing physics are taken.
PSPIKE: A Parallel Hybrid Sparse Linear System Solver
NASA Astrophysics Data System (ADS)
Manguoglu, Murat; Sameh, Ahmed H.; Schenk, Olaf
The availability of large-scale computing platforms comprised of tens of thousands of multicore processors motivates the need for the next generation of highly scalable sparse linear system solvers. These solvers must optimize parallel performance, processor (serial) performance, as well as memory requirements, while being robust across broad classes of applications and systems. In this paper, we present a new parallel solver that combines the desirable characteristics of direct methods (robustness) and effective iterative solvers (low computational cost), while alleviating their drawbacks (memory requirements, lack of robustness). Our proposed hybrid solver is based on the general sparse solver PARDISO, and the “Spike” family of hybrid solvers. The resulting algorithm, called PSPIKE, is as robust as direct solvers, more reliable than classical preconditioned Krylov subspace methods, and much more scalable than direct sparse solvers. We support our performance and parallel scalability claims using detailed experimental studies and comparison with direct solvers, as well as classical preconditioned Krylov methods.
Small renal tumor with lymph nodal enlargement: A histopathological surprise
Thottathil, Mujeeburahiman; Verma, Ashish; D’souza, Nischith; Khan, Altaf
2016-01-01
Renal cancer with lymph nodal mass on the investigation is clinically suggestive of an advanced tumor. Small renal cancers are not commonly associated with lymph nodal metastasis. Association of renal cell carcinoma with renal tuberculosis (TB) in the same kidney is also rare. We report here a case of small renal cancer with multiple hilar and paraaortic lymph nodes who underwent radical nephrectomy, and histopathology report showed renal and lymph nodal TB too. PMID:27453671
Plasticity underlies tumor progression: role of Nodal signaling.
Bodenstine, Thomas M; Chandler, Grace S; Seftor, Richard E B; Seftor, Elisabeth A; Hendrix, Mary J C
2016-03-01
The transforming growth factor beta (TGFβ) superfamily member Nodal is an established regulator of early embryonic development, with primary roles in endoderm induction, left-right asymmetry, and primitive streak formation. Nodal signals through TGFβ family receptors at the plasma membrane and induces signaling cascades leading to diverse transcriptional regulation. While conceptually simple, the regulation of Nodal and its molecular effects are profoundly complex and context dependent. Pioneering work by developmental biologists has characterized the signaling pathways, regulatory components, and provided detailed insight into the mechanisms by which Nodal mediates changes at the cellular and organismal levels. Nodal is also an important factor in maintaining pluripotency of embryonic stem cells through regulation of core transcriptional programs. Collectively, this work has led to an appreciation for Nodal as a powerful morphogen capable of orchestrating multiple cellular phenotypes. Although Nodal is not active in most adult tissues, its reexpression and signaling have been linked to multiple types of human cancer, and Nodal has emerged as a driver of tumor growth and cellular plasticity. In vitro and in vivo experimental evidence has demonstrated that inhibition of Nodal signaling reduces cancer cell aggressive characteristics, while clinical data have established associations with Nodal expression and patient outcomes. As a result, there is great interest in the potential targeting of Nodal activity in a therapeutic setting for cancer patients that may provide new avenues for suppressing tumor growth and metastasis. In this review, we evaluate our current understanding of the complexities of Nodal function in cancer and highlight recent experimental evidence that sheds light on the therapeutic potential of its inhibition. PMID:26951550
Error analysis of the quadratic nodal expansion method in slab geometry
Penland, R.C.; Turinsky, P.J.; Azmy, Y.Y.
1994-10-01
As part of an effort to develop an adaptive mesh refinement strategy for use in state-of-the-art nodal diffusion codes, the authors derive error bounds on the solution variables of the quadratic Nodal Expansion Method (NEM) in slab geometry. Closure of the system is obtained through flux discontinuity relationships and boundary conditions. In order to verify the analysis presented, the authors compare the quadratic NEM to the analytic solution of a test problem. The test problem for this investigation is a one-dimensional slab [0,20cm] with L{sup 2} = 6.495cm{sup 2} and D = 0.1429cm. The slab has a unit neutron source distributed uniformly throughout and zero flux boundary conditions. The analytic solution to this problem is used to compute the node-average fluxes over a variety of meshes, and these are used to compute the NEM maximum error on each mesh.
Phonon analogue of topological nodal semimetals
NASA Astrophysics Data System (ADS)
Po, Hoi Chun; Bahri, Yasaman; Vishwanath, Ashvin
2015-03-01
Recently, Kane and Lubensky proposed a mapping between bosonic phonon problems on isostatic lattices to chiral fermion systems based on factorization of the dynamical matrix [Nat. Phys. 10, 39 (2014)]. The existence of topologically protected zero modes in such mechanical problems is related to their presence in the fermionic system and is dictated by a local index theorem. Here we adopt the proposed mapping to construct a two-dimensional mechanical analogue of a fermionic topological nodal semimetal that hosts a robust bulk node in its linearized phonon spectrum. Such topologically protected soft modes with tunable wavevector may be useful in designing mechanical structures with fault-tolerant properties.
An essential role for maternal control of Nodal signaling
Kumari, Pooja; Gilligan, Patrick C; Lim, Shimin; Tran, Long Duc; Winkler, Sylke; Philp, Robin; Sampath, Karuna
2013-01-01
Growth factor signaling is essential for pattern formation, growth, differentiation, and maintenance of stem cell pluripotency. Nodal-related signaling factors are required for axis formation and germ layer specification from sea urchins to mammals. Maternal transcripts of the zebrafish Nodal factor, Squint (Sqt), are localized to future embryonic dorsal. The mechanisms by which maternal sqt/nodal RNA is localized and regulated have been unclear. Here, we show that maternal control of Nodal signaling via the conserved Y box-binding protein 1 (Ybx1) is essential. We identified Ybx1 via a proteomic screen. Ybx1 recognizes the 3’ untranslated region (UTR) of sqt RNA and prevents premature translation and Sqt/Nodal signaling. Maternal-effect mutations in zebrafish ybx1 lead to deregulated Nodal signaling, gastrulation failure, and embryonic lethality. Implanted Nodal-coated beads phenocopy ybx1 mutant defects. Thus, Ybx1 prevents ectopic Nodal activity, revealing a new paradigm in the regulation of Nodal signaling, which is likely to be conserved. DOI: http://dx.doi.org/10.7554/eLife.00683.001 PMID:24040511
Zero-energy bound states in a nodal topological lattice
NASA Astrophysics Data System (ADS)
Lee, Soo-Yong; Han, Jung Hoon
2015-06-01
A nodal topological lattice is a form of magnetic crystal with topologically nontrivial spin texture, which further exhibits a periodic array of nodes with vanishing magnetization. An electronic structure for conduction electrons strongly Hund coupled to such a nodal topological lattice is examined. Our analysis shows that each node attracts two localized states which form narrow bands through internode hybridization within the mid-gap region. Nodal bands carry a Chern number under suitable perturbations, suggesting their potential role in the topological Hall effect. Enhancement of the density of states near zero energy observable in a tunneling experiment will provide a signature of the formation of a nodal topological lattice.
Code Verification of the HIGRAD Computational Fluid Dynamics Solver
Van Buren, Kendra L.; Canfield, Jesse M.; Hemez, Francois M.; Sauer, Jeremy A.
2012-05-04
The purpose of this report is to outline code and solution verification activities applied to HIGRAD, a Computational Fluid Dynamics (CFD) solver of the compressible Navier-Stokes equations developed at the Los Alamos National Laboratory, and used to simulate various phenomena such as the propagation of wildfires and atmospheric hydrodynamics. Code verification efforts, as described in this report, are an important first step to establish the credibility of numerical simulations. They provide evidence that the mathematical formulation is properly implemented without significant mistakes that would adversely impact the application of interest. Highly accurate analytical solutions are derived for four code verification test problems that exercise different aspects of the code. These test problems are referred to as: (i) the quiet start, (ii) the passive advection, (iii) the passive diffusion, and (iv) the piston-like problem. These problems are simulated using HIGRAD with different levels of mesh discretization and the numerical solutions are compared to their analytical counterparts. In addition, the rates of convergence are estimated to verify the numerical performance of the solver. The first three test problems produce numerical approximations as expected. The fourth test problem (piston-like) indicates the extent to which the code is able to simulate a 'mild' discontinuity, which is a condition that would typically be better handled by a Lagrangian formulation. The current investigation concludes that the numerical implementation of the solver performs as expected. The quality of solutions is sufficient to provide credible simulations of fluid flows around wind turbines. The main caveat associated to these findings is the low coverage provided by these four problems, and somewhat limited verification activities. A more comprehensive evaluation of HIGRAD may be beneficial for future studies.
Bordner, J.; Saied, F.
1996-12-31
GLab3D is an enhancement of an interactive environment (MGLab) for experimenting with iterative solvers and multigrid algorithms. It is implemented in MATLAB. The new version has built-in 3D elliptic pde`s and several iterative methods and preconditioners that were not available in the original version. A sparse direct solver option has also been included. The multigrid solvers have also been extended to 3D. The discretization and pde domains are restricted to standard finite differences on the unit square/cube. The power of this software studies in the fact that no programming is needed to solve, for example, the convection-diffusion equation in 3D with TFQMR and a customized V-cycle preconditioner, for a variety of problem sizes and mesh Reynolds, numbers. In addition to the graphical user interface, some sample drivers are included to show how experiments can be composed using the underlying suite of problems and solvers.
New iterative solvers for the NAG Libraries
Salvini, S.; Shaw, G.
1996-12-31
The purpose of this paper is to introduce the work which has been carried out at NAG Ltd to update the iterative solvers for sparse systems of linear equations, both symmetric and unsymmetric, in the NAG Fortran 77 Library. Our current plans to extend this work and include it in our other numerical libraries in our range are also briefly mentioned. We have added to the Library the new Chapter F11, entirely dedicated to sparse linear algebra. At Mark 17, the F11 Chapter includes sparse iterative solvers, preconditioners, utilities and black-box routines for sparse symmetric (both positive-definite and indefinite) linear systems. Mark 18 will add solvers, preconditioners, utilities and black-boxes for sparse unsymmetric systems: the development of these has already been completed.
Using SPARK as a Solver for Modelica
Wetter, Michael; Wetter, Michael; Haves, Philip; Moshier, Michael A.; Sowell, Edward F.
2008-06-30
Modelica is an object-oriented acausal modeling language that is well positioned to become a de-facto standard for expressing models of complex physical systems. To simulate a model expressed in Modelica, it needs to be translated into executable code. For generating run-time efficient code, such a translation needs to employ algebraic formula manipulations. As the SPARK solver has been shown to be competitive for generating such code but currently cannot be used with the Modelica language, we report in this paper how SPARK's symbolic and numerical algorithms can be implemented in OpenModelica, an open-source implementation of a Modelica modeling and simulation environment. We also report benchmark results that show that for our air flow network simulation benchmark, the SPARK solver is competitive with Dymola, which is believed to provide the best solver for Modelica.
FETI Prime Domain Decomposition base Parallel Iterative Solver Library Ver.1.0
Energy Science and Technology Software Center (ESTSC)
2003-09-15
FETI Prime is a library for the iterative solution of linear equations in solid and structural mechanics. The algorithm employs preconditioned conjugate gradients, with a domain decomposition-based preconditioner. The software is written in C++ and is designed for use with massively parallel computers, using MPI. The algorithm is based on the FETI-DP method, with additional capabilities for handling constraint equations, as well as interfacing with the Salinas structural dynamics code and the Finite Element Interfacemore » (FEI) library. Practical Application: FETI Prime is designed for use with finite element-based simulation codes for solid and structural mechanics. The solver uses element matrices, connectivity information, nodal information, and force vectors computed by the host code and provides back the solution to the linear system of equations, to the user specified level of accuracy, The library is compiled with the host code and becomes an integral part of the host code executable.« less
An Adaptive Flow Solver for Air-Borne Vehicles Undergoing Time-Dependent Motions/Deformations
NASA Technical Reports Server (NTRS)
Singh, Jatinder; Taylor, Stephen
1997-01-01
This report describes a concurrent Euler flow solver for flows around complex 3-D bodies. The solver is based on a cell-centered finite volume methodology on 3-D unstructured tetrahedral grids. In this algorithm, spatial discretization for the inviscid convective term is accomplished using an upwind scheme. A localized reconstruction is done for flow variables which is second order accurate. Evolution in time is accomplished using an explicit three-stage Runge-Kutta method which has second order temporal accuracy. This is adapted for concurrent execution using another proven methodology based on concurrent graph abstraction. This solver operates on heterogeneous network architectures. These architectures may include a broad variety of UNIX workstations and PCs running Windows NT, symmetric multiprocessors and distributed-memory multi-computers. The unstructured grid is generated using commercial grid generation tools. The grid is automatically partitioned using a concurrent algorithm based on heat diffusion. This results in memory requirements that are inversely proportional to the number of processors. The solver uses automatic granularity control and resource management techniques both to balance load and communication requirements, and deal with differing memory constraints. These ideas are again based on heat diffusion. Results are subsequently combined for visualization and analysis using commercial CFD tools. Flow simulation results are demonstrated for a constant section wing at subsonic, transonic, and a supersonic case. These results are compared with experimental data and numerical results of other researchers. Performance results are under way for a variety of network topologies.
Multigrid in energy preconditioner for Krylov solvers
Slaybaugh, R.N.; Evans, T.M.; Davidson, G.G.; Wilson, P.P.H.
2013-06-01
We have added a new multigrid in energy (MGE) preconditioner to the Denovo discrete-ordinates radiation transport code. This preconditioner takes advantage of a new multilevel parallel decomposition. A multigroup Krylov subspace iterative solver that is decomposed in energy as well as space-angle forms the backbone of the transport solves in Denovo. The space-angle-energy decomposition facilitates scaling to hundreds of thousands of cores. The multigrid in energy preconditioner scales well in the energy dimension and significantly reduces the number of Krylov iterations required for convergence. This preconditioner is well-suited for use with advanced eigenvalue solvers such as Rayleigh Quotient Iteration and Arnoldi.
ODE System Solver W. Krylov Iteration & Rootfinding
Hindmarsh, Alan C.
1991-09-09
LSODKR is a new initial value ODE solver for stiff and nonstiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: (a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, (b) Within the corrector iteration, LSODKR does automatic switching between functional (fixpoint) iteration and modified Newton iteration, (c) LSODKR includes the ability to find roots of given functions of the solution during the integration.
ODE System Solver W. Krylov Iteration & Rootfinding
Energy Science and Technology Software Center (ESTSC)
1991-09-09
LSODKR is a new initial value ODE solver for stiff and nonstiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: (a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, (b) Within the corrector iteration,more » LSODKR does automatic switching between functional (fixpoint) iteration and modified Newton iteration, (c) LSODKR includes the ability to find roots of given functions of the solution during the integration.« less
Steady potential solver for unsteady aerodynamic analyses
NASA Technical Reports Server (NTRS)
Hoyniak, Dan
1994-01-01
Development of a steady flow solver for use with LINFLO was the objective of this report. The solver must be compatible with LINFLO, be composed of composite mesh, and have transonic capability. The approaches used were: (1) steady flow potential equations written in nonconservative form; (2) Newton's Method; (3) implicit, least-squares, interpolation method to obtain finite difference equations; and (4) matrix inversion routines from LINFLO. This report was given during the NASA LeRC Workshop on Forced Response in Turbomachinery in August of 1993.
Wave Speeds, Riemann Solvers and Artificial Viscosity
Rider, W.J.
1999-07-18
A common perspective on the numerical solution of the equation Euler equations for shock physics is examined. The common viewpoint is based upon the selection of nonlinear wavespeeds upon which the dissipation (implicit or explicit) is founded. This perspective shows commonality between Riemann solver based method (i.e. Godunov-type) and artificial viscosity (i.e. von Neumann-Richtmyer). As an example we derive an improved nonlinear viscous stabilization of a Richtmyer-Lax-Wendroff method. Additionally, we will define a form of classical artificial viscosity based upon the HLL Riemann solver.
Enthalpy Diffusion in Multicomponent Flows
Cook, A W
2008-11-12
The enthalpy diffusion flux in the multicomponent energy equation is a well known yet frequently neglected term. It accounts for energy changes, associated with compositional changes, resulting from species diffusion. Enthalpy diffusion is important in flows where significant mixing occurs between species of dissimilar molecular weight. The term plays a critical role in preventing local violations of the entropy condition. In simulations of nonpremixed combustion, omission of the enthalpy flux can lead to anomalous temperature gradients, which may cause mixing regions to exceed ignition conditions. The term can also play a role in generating acoustic noise in turbulent mixing layers. Euler solvers that rely on numerical diffusion to mix fluids cannot accurately predict the temperature in mixed regions. On the other hand, Navier-Stokes solvers that incorporate enthalpy diffusion can provide much more accurate results.
Market redesign and technology upgrade: a nodal implementation
Isemonger, Alan G.
2009-10-15
The California ISO and its market participants collectively cut over to a new nodal-based market on April 1, largely without incident and 11 years to the day from the initial startup in 1998. Thus far, the new nodal framework has proven robust, and the inevitable design and implementation issues that have emerged since cutover have been manageable. (author)
Radar response from vegetation with nodal structure
NASA Technical Reports Server (NTRS)
Blanchard, B. J.; Oneill, P. E.
1984-01-01
Radar images from the SEASAT synthetic aperture radar (SAR) produced unusually high returns from corn and sorghum fields, which seem to indicate a correlation between nodal separation in the stalk and the wavelength of the radar. These images also show no difference in return from standing or harvested corn. Further investigation using images from the Shuttle Imaging Radar (SIR-A) substantiated these observations and showed a degradation of the high return with time after harvest. From portions of corn and sweet sorghum stalks that were sampled to measure stalk water content, it was determined that near and after maturity the water becomes more concentrated in the stalk nodes. The stalk then becomes a linear sequence of alternating dielectrics as opposed to a long slender cylinder with uniform dielectric properties.
Nodal aberration theory applied to freeform surfaces
NASA Astrophysics Data System (ADS)
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.
Experience with advanced nodal codes at YAEC
Cacciapouti, R.J.
1990-01-01
Yankee Atomic Electric Company (YAEC) has been performing reload licensing analysis since 1969. The basic pressurized water reactor (PWR) methodology involves the use of LEOPARD for cross-section generation, PDQ for radial power distributions and integral control rod worth, and SIMULATE for axial power distributions and differential control rod worth. In 1980, YAEC began performing reload licensing analysis for the Vermont Yankee boiling water reactor (BWR). The basic BWR methodology involves the use of CASMO for cross-section generation and SIMULATE for three-dimensional power distributions. In 1986, YAEC began investigating the use of CASMO-3 for cross-section generation and the advanced nodal code SIMULATE-3 for power distribution analysis. Based on the evaluation, the CASMO-3/SIMULATE-3 methodology satisfied all requirements. After careful consideration, the cost of implementing the new methodology is expected to be offset by reduced computing costs, improved engineering productivity, and fuel-cycle performance gains.
Loop-Nodal and Point-Nodal Semimetals in Three-Dimensional Honeycomb Lattices
NASA Astrophysics Data System (ADS)
Ezawa, Motohiko
2016-03-01
A honeycomb structure has a natural extension to three dimensions. Simple examples are hyperhoneycomb and stripy-honeycomb lattices, which are realized in β -Li2IrO3 and γ -Li2IrO3 , respectively. We propose a wide class of three-dimensional (3D) honeycomb lattices which are loop-nodal semimetals. Their edge states have intriguing properties similar to the two-dimensional honeycomb lattice in spite of a dimensional difference. Partial flat bands emerge at the zigzag or bearded edge of the 3D honeycomb lattice, whose boundary is given by the Fermi loop in the bulk spectrum. On the other hand, perfect flat bands emerge in the zigzag-bearded edge or when the anisotropy is large. The loop-nodal structure is destroyed once staggered potential or antiferromagnetic order is introduced. All these 3D honeycomb lattices become strong topological insulators with the inclusion of the spin-orbit interaction (SOI). Furthermore, point-nodal semimetals may be realized in the presence of both antiferromagnetic order and the SOI. We construct the effective four-band theory with the SOI to understand the physics near the Fermi level, based upon which the density of states and the dc conductivity are calculated.
Loop-Nodal and Point-Nodal Semimetals in Three-Dimensional Honeycomb Lattices.
Ezawa, Motohiko
2016-03-25
A honeycomb structure has a natural extension to three dimensions. Simple examples are hyperhoneycomb and stripy-honeycomb lattices, which are realized in β-Li_{2}IrO_{3} and γ-Li_{2}IrO_{3}, respectively. We propose a wide class of three-dimensional (3D) honeycomb lattices which are loop-nodal semimetals. Their edge states have intriguing properties similar to the two-dimensional honeycomb lattice in spite of a dimensional difference. Partial flat bands emerge at the zigzag or bearded edge of the 3D honeycomb lattice, whose boundary is given by the Fermi loop in the bulk spectrum. On the other hand, perfect flat bands emerge in the zigzag-bearded edge or when the anisotropy is large. The loop-nodal structure is destroyed once staggered potential or antiferromagnetic order is introduced. All these 3D honeycomb lattices become strong topological insulators with the inclusion of the spin-orbit interaction (SOI). Furthermore, point-nodal semimetals may be realized in the presence of both antiferromagnetic order and the SOI. We construct the effective four-band theory with the SOI to understand the physics near the Fermi level, based upon which the density of states and the dc conductivity are calculated. PMID:27058097
Simulation of turbulent flows using nodal integral method
NASA Astrophysics Data System (ADS)
Singh, Suneet
Nodal methods are the backbone of the production codes for neutron-diffusion and transport equations. Despite their high accuracy, use of these methods for simulation of fluid flow is relatively new. Recently, a modified nodal integral method (MNIM) has been developed for simulation of laminar flows. In view of its high accuracy and efficiency, extension of this method for the simulation of turbulent flows is a logical step forward. In this dissertation, MNIM is extended in two ways to simulate incompressible turbulent flows---a new MNIM is developed for the 2D k-epsilon equations; and 3D, parallel MNIM is developed for direct numerical simulations. Both developments are validated, and test problems are solved. In this dissertation, a new nodal numerical scheme is developed to solve the k-epsilon equations to simulate turbulent flows. The MNIM developed earlier for laminar flow equations is modified to incorporate eddy viscosity approximation and coupled with the above mentioned schemes for the k and epsilon equations, to complete the implementation of the numerical scheme for the k-epsilon model. The scheme developed is validated by comparing the results obtained by the developed method with the results available in the literature obtained using direct numerical simulations (DNS). The results of current simulations match reasonably well with the DNS results. The discrepancies in the results are mainly due to the limitations of the k-epsilon model rather than the deficiency in the developed MNIM. A parallel version of the MNIM is needed to enhance its capability, in order to carry out DNS of the turbulent flows. The parallelization of the scheme, however, presents some unique challenges as dependencies of the discrete variables are different from those that exist in other schemes (for example in finite volume based schemes). Hence, a parallel MNIM (PMNIM) is developed and implemented into a computer code with communication strategies based on the above mentioned
NODAL — The second life of the accelerator control language
NASA Astrophysics Data System (ADS)
Cuisinier, G.; Perriollat, F.; Ribeiro, P.; Kagarmanov, A.; Kovaltsov, V.
1994-12-01
NODAL has been a popular interpreter language for accelerator controls since the beginning of the 1970s. NODAL has been rewritten in the C language to be easily portable to the different computer platforms which are in use in accelerator controls. The paper describes the major features of this new version of NODAL, the major software packages which are available through this implementation, the platforms on which it is currently running, and some relevant performances. The experience gained during the rejuvenation project of the CERN accelerator control systems is presented. The benefit of this is discussed, in particular in a view of the prevailing strong constraints in personnel and money resources.
Optimal Hedge for Nodal Price Risk using FTR
NASA Astrophysics Data System (ADS)
Tanaka, Hiroaki; Makino, Michiko; Ichida, Yoshio; Akiyoshi, Masanori
As the deregulation of electric business proceeds, each company needs to construct a risk hedging system. So far many companies have not been taking much care of this suffciently. In this paper, we address the nodal price hedge issue. Most companies have risks for the nodal prices which tend to be highly volatile. There's almost no doubt that such a company actually needs hedge products to make profits stable. We suggest the usage of FTR for this purpose. First, we briefly note the mechanisms of nodal price in PJM market and FTR, and suggest the mathematical formulations. Then we show some numerical examples and discuss our findings.
Tunable Weyl Points in Periodically Driven Nodal Line Semimetals.
Yan, Zhongbo; Wang, Zhong
2016-08-19
Weyl semimetals and nodal line semimetals are characterized by linear band touching at zero-dimensional points and one-dimensional lines, respectively. We predict that a circularly polarized light drives nodal line semimetals into Weyl semimetals. The Floquet Weyl points thus obtained are tunable by the incident light, which enables investigations of them in a highly controllable manner. The transition from nodal line semimetals to Weyl semimetals is accompanied by the emergence of a large and tunable anomalous Hall conductivity. Our predictions are experimentally testable by transport measurement in film samples or by pump-probe angle-resolved photoemission spectroscopy. PMID:27588882
Veijola, Timo; Råback, Peter
2007-01-01
We present a straightforward method to solve gas damping problems for perforated structures in two dimensions (2D) utilising a Perforation Profile Reynolds (PPR) solver. The PPR equation is an extended Reynolds equation that includes additional terms modelling the leakage flow through the perforations, and variable diffusivity and compressibility profiles. The solution method consists of two phases: 1) determination of the specific admittance profile and relative diffusivity (and relative compressibility) profiles due to the perforation, and 2) solution of the PPR equation with a FEM solver in 2D. Rarefied gas corrections in the slip-flow region are also included. Analytic profiles for circular and square holes with slip conditions are presented in the paper. To verify the method, square perforated dampers with 16–64 holes were simulated with a three-dimensional (3D) Navier-Stokes solver, a homogenised extended Reynolds solver, and a 2D PPR solver. Cases for both translational (in normal to the surfaces) and torsional motion were simulated. The presented method extends the region of accurate simulation of perforated structures to cases where the homogenisation method is inaccurate and the full 3D Navier-Stokes simulation is too time-consuming.
VDJSeq-Solver: In Silico V(D)J Recombination Detection Tool
Paciello, Giulia; Acquaviva, Andrea; Pighi, Chiara; Ferrarini, Alberto; Macii, Enrico; Zamo’, Alberto; Ficarra, Elisa
2015-01-01
In this paper we present VDJSeq-Solver, a methodology and tool to identify clonal lymphocyte populations from paired-end RNA Sequencing reads derived from the sequencing of mRNA neoplastic cells. The tool detects the main clone that characterises the tissue of interest by recognizing the most abundant V(D)J rearrangement among the existing ones in the sample under study. The exact sequence of the clone identified is capable of accounting for the modifications introduced by the enzymatic processes. The proposed tool overcomes limitations of currently available lymphocyte rearrangements recognition methods, working on a single sequence at a time, that are not applicable to high-throughput sequencing data. In this work, VDJSeq-Solver has been applied to correctly detect the main clone and identify its sequence on five Mantle Cell Lymphoma samples; then the tool has been tested on twelve Diffuse Large B-Cell Lymphoma samples. In order to comply with the privacy, ethics and intellectual property policies of the University Hospital and the University of Verona, data is available upon request to supporto.utenti@ateneo.univr.it after signing a mandatory Materials Transfer Agreement. VDJSeq-Solver JAVA/Perl/Bash software implementation is free and available at http://eda.polito.it/VDJSeq-Solver/. PMID:25799103
VDJSeq-Solver: in silico V(D)J recombination detection tool.
Paciello, Giulia; Acquaviva, Andrea; Pighi, Chiara; Ferrarini, Alberto; Macii, Enrico; Zamo', Alberto; Ficarra, Elisa
2015-01-01
In this paper we present VDJSeq-Solver, a methodology and tool to identify clonal lymphocyte populations from paired-end RNA Sequencing reads derived from the sequencing of mRNA neoplastic cells. The tool detects the main clone that characterises the tissue of interest by recognizing the most abundant V(D)J rearrangement among the existing ones in the sample under study. The exact sequence of the clone identified is capable of accounting for the modifications introduced by the enzymatic processes. The proposed tool overcomes limitations of currently available lymphocyte rearrangements recognition methods, working on a single sequence at a time, that are not applicable to high-throughput sequencing data. In this work, VDJSeq-Solver has been applied to correctly detect the main clone and identify its sequence on five Mantle Cell Lymphoma samples; then the tool has been tested on twelve Diffuse Large B-Cell Lymphoma samples. In order to comply with the privacy, ethics and intellectual property policies of the University Hospital and the University of Verona, data is available upon request to supporto.utenti@ateneo.univr.it after signing a mandatory Materials Transfer Agreement. VDJSeq-Solver JAVA/Perl/Bash software implementation is free and available at http://eda.polito.it/VDJSeq-Solver/. PMID:25799103
Aleph Field Solver Challenge Problem Results Summary.
Hooper, Russell; Moore, Stan Gerald
2015-01-01
Aleph models continuum electrostatic and steady and transient thermal fields using a finite-element method. Much work has gone into expanding the core solver capability to support enriched mod- eling consisting of multiple interacting fields, special boundary conditions and two-way interfacial coupling with particles modeled using Aleph's complementary particle-in-cell capability. This report provides quantitative evidence for correct implementation of Aleph's field solver via order- of-convergence assessments on a collection of problems of increasing complexity. It is intended to provide Aleph with a pedigree and to establish a basis for confidence in results for more challeng- ing problems important to Sandia's mission that Aleph was specifically designed to address.
Verifying a Local Generic Solver in Coq
NASA Astrophysics Data System (ADS)
Hofmann, Martin; Karbyshev, Aleksandr; Seidl, Helmut
Fixpoint engines are the core components of program analysis tools and compilers. If these tools are to be trusted, special attention should be paid also to the correctness of such solvers. In this paper we consider the local generic fixpoint solver RLD which can be applied to constraint systems {x}sqsupseteq fx,{x}in V, over some lattice {D} where the right-hand sides f x are given as arbitrary functions implemented in some specification language. The verification of this algorithm is challenging, because it uses higher-order functions and relies on side effects to track variable dependences as they are encountered dynamically during fixpoint iterations. Here, we present a correctness proof of this algorithm which has been formalized by means of the interactive proof assistant Coq.
Present Status of GNF New Nodal Simulator
Iwamoto, T.; Tamitani, M.; Moore, B.
2001-06-17
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.
Domain decomposition for the SPN solver MINOS
Jamelot, Erell; Baudron, Anne-Marie; Lautard, Jean-Jacques
2012-07-01
In this article we present a domain decomposition method for the mixed SPN equations, discretized with Raviart-Thomas-Nedelec finite elements. This domain decomposition is based on the iterative Schwarz algorithm with Robin interface conditions to handle communications. After having described this method, we give details on how to optimize the convergence. Finally, we give some numerical results computed in a realistic 3D domain. The computations are done with the MINOS solver of the APOLLO3 (R) code. (authors)
A perspective on unstructured grid flow solvers
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.
1995-01-01
This survey paper assesses the status of compressible Euler and Navier-Stokes solvers on unstructured grids. Different spatial and temporal discretization options for steady and unsteady flows are discussed. The integration of these components into an overall framework to solve practical problems is addressed. Issues such as grid adaptation, higher order methods, hybrid discretizations and parallel computing are briefly discussed. Finally, some outstanding issues and future research directions are presented.
Josephson, Mark E
2016-01-01
Atrioventricular nodal reentrant tachycardia (AVNRT) should be classified as typical or atypical. The term ‘fast-slow AVNRT’ is rather misleading. Retrograde atrial activation during tachycardia should not be relied upon as a diagnostic criterion. Both typical and atypical atrioventricular nodal reentrant tachycardia are compatible with varying retrograde atrial activation patterns. Attempts at establishing the presence of a ‘lower common pathway’ are probably of no practical significance. When the diagnosis of AVNRT is established, ablation should be only directed towards the anatomic position of the slow pathway. If right septal attempts are unsuccessful, the left septal side should be tried. Ablation targeting earliest atrial activation sites during typical atrioventricular nodal reentrant tachycardia or the fast pathway in general for any kind of typical or atypical atrioventricular nodal reentrant tachycardia, are not justified. In this review we discuss current concepts about the tachycardia circuit, electrophysiologic diagnosis, and ablation of this arrhythmia.
Nodal analysis for reactor kinetics and stability. [PWR; BWR
Park, J.K.; Becker, M.; Park, G.C.
1983-07-01
General space kinetics models have been developed for more accurate stability analysis utilizing nodal analysis, a commonly used technique for analyzing power distributions in large power reactors. Kinetics parameters for use in these kinetics models have been properly derived by utilizing self-consistent nodal data and power distributions. The procedure employed in the nodal code SIMULATE has been utilized for power distribution, since that methodology is general and includes various commonly used nodal methods as special cases. Cross sections are correlated as functions of void fraction and exposure. A computer program investigating thermo-hydrodynamic stability, NUFREQ has been modified to accommodate general spatial kinetics models with an improved thermal-hydraulics model. Stability analyses have been performed for density wave oscillations for a representative operating BWR system. Spatial coupling effects on the stability margins were found to be significant.
BEACON: An application of nodal methods for operational support
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
Tightly Coupled Geodynamic Systems: Software, Implicit Solvers & Applications
NASA Astrophysics Data System (ADS)
May, D.; Le Pourhiet, L.; Brown, J.
2011-12-01
The generic term "multi-physics" is used to define physical processes which are described by a collection of partial differential equations, or "physics". Numerous processes in geodynamics fall into this category. For example, the evolution of viscous fluid flow and heat transport within the mantle (Stokes flow + energy conservation), the dynamics of melt migration (Stokes flow + Darcy flow + porosity evolution) and landscape evolution (Stokes + diffusion/advection over a surface). The development of software to numerically investigate processes that are described through the composition of different physics components are typically (a) designed for one particular set of physics and are never intended to be extended, or coupled to other processes (b) enforce that certain non-linearity's (or coupling) are explicitly removed from the system for reasons of computational efficiency, or due the lack of a robust non-linear solver (e.g. most models in the mantle convection community). We describe a software infrastructure which enables us to easily introduce new physics with minimal code modifications; tightly couple all physics without introducing splitting errors; exploit modern linear/non-linear solvers and permit the re-use of monolithic preconditioners for individual physics blocks (e.g. saddle point preconditioners for Stokes). Here we present a number of examples to illustrate the flexibility and importance of using this software infra-structure. Using the Stokes system as a prototype, we show results illustrating (i) visco-plastic shear banding experiments, (ii) how coupling Stokes flow with the evolution of the material coordinates can yield temporal stability in the free surface evolution and (iii) the discretisation error associated with decoupling Stokes equation from the heat transport equation in models of mantle convection with various rheologies.
Bilinear nodal transport method in weighted diamond difference form
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.
Approximate Riemann solvers for the Godunov SPH (GSPH)
NASA Astrophysics Data System (ADS)
Puri, Kunal; Ramachandran, Prabhu
2014-08-01
The Godunov Smoothed Particle Hydrodynamics (GSPH) method is coupled with non-iterative, approximate Riemann solvers for solutions to the compressible Euler equations. The use of approximate solvers avoids the expensive solution of the non-linear Riemann problem for every interacting particle pair, as required by GSPH. In addition, we establish an equivalence between the dissipative terms of GSPH and the signal based SPH artificial viscosity, under the restriction of a class of approximate Riemann solvers. This equivalence is used to explain the anomalous “wall heating” experienced by GSPH and we provide some suggestions to overcome it. Numerical tests in one and two dimensions are used to validate the proposed Riemann solvers. A general SPH pairing instability is observed for two-dimensional problems when using unequal mass particles. In general, Ducowicz Roe's and HLLC approximate Riemann solvers are found to be suitable replacements for the iterative Riemann solver in the original GSPH scheme.
Unstructured Polyhedral Mesh Thermal Radiation Diffusion
Palmer, T.S.; Zika, M.R.; Madsen, N.K.
2000-07-27
Unstructured mesh particle transport and diffusion methods are gaining wider acceptance as mesh generation, scientific visualization and linear solvers improve. This paper describes an algorithm that is currently being used in the KULL code at Lawrence Livermore National Laboratory to solve the radiative transfer equations. The algorithm employs a point-centered diffusion discretization on arbitrary polyhedral meshes in 3D. We present the results of a few test problems to illustrate the capabilities of the radiation diffusion module.
New Multigrid Solver Advances in TOPS
Falgout, R D; Brannick, J; Brezina, M; Manteuffel, T; McCormick, S
2005-06-27
In this paper, we highlight new multigrid solver advances in the Terascale Optimal PDE Simulations (TOPS) project in the Scientific Discovery Through Advanced Computing (SciDAC) program. We discuss two new algebraic multigrid (AMG) developments in TOPS: the adaptive smoothed aggregation method ({alpha}SA) and a coarse-grid selection algorithm based on compatible relaxation (CR). The {alpha}SA method is showing promising results in initial studies for Quantum Chromodynamics (QCD) applications. The CR method has the potential to greatly improve the applicability of AMG.
DPS--a computerised diagnostic problem solver.
Bartos, P; Gyárfas, F; Popper, M
1982-01-01
The paper contains a short description of the DPS system which is a computerized diagnostic problem solver. The system is under development of the Research Institute of Medical Bionics in Bratislava, Czechoslovakia. Its underlying philosophy yields from viewing the diagnostic process as process of cognitive problem solving. The implementation of the system is based on the methods of Artificial Intelligence and utilisation of production systems and frame theory should be noted in this context. Finally a list of program modules and their characterisation is presented. PMID:6811229
Updates to the NEQAIR Radiation Solver
NASA Technical Reports Server (NTRS)
Cruden, Brett A.; Brandis, Aaron M.
2014-01-01
The NEQAIR code is one of the original heritage solvers for radiative heating prediction in aerothermal environments, and is still used today for mission design purposes. This paper discusses the implementation of the first major revision to the NEQAIR code in the last five years, NEQAIR v14.0. The most notable features of NEQAIR v14.0 are the parallelization of the radiation computation, reducing runtimes by about 30×, and the inclusion of mid-wave CO2 infrared radiation.
Input-output-controlled nonlinear equation solvers
NASA Technical Reports Server (NTRS)
Padovan, Joseph
1988-01-01
To upgrade the efficiency and stability of the successive substitution (SS) and Newton-Raphson (NR) schemes, the concept of input-output-controlled solvers (IOCS) is introduced. By employing the formal properties of the constrained version of the SS and NR schemes, the IOCS algorithm can handle indefiniteness of the system Jacobian, can maintain iterate monotonicity, and provide for separate control of load incrementation and iterate excursions, as well as having other features. To illustrate the algorithmic properties, the results for several benchmark examples are presented. These define the associated numerical efficiency and stability of the IOCS.
Comparison of electromagnetic solvers for antennas mounted on vehicles
NASA Astrophysics Data System (ADS)
Mocker, M. S. L.; Hipp, S.; Spinnler, F.; Tazi, H.; Eibert, T. F.
2015-11-01
An electromagnetic solver comparison for various use cases of antennas mounted on vehicles is presented. For this purpose, several modeling approaches, called transient, frequency and integral solver, including the features fast resonant method and autoregressive filter, offered by CST MWS, are investigated. The solvers and methods are compared for a roof antenna itself, a simplified vehicle, a roof including a panorama window and a combination of antenna and vehicle. With these examples, the influence of different materials, data formats and parameters such as size and complexity are investigated. Also, the necessary configurations for the mesh and the solvers are described.
Nodal signaling promotes a tumorigenic phenotype in human breast cancer.
Kirsammer, Gina; Strizzi, Luigi; Margaryan, Naira V; Gilgur, Alina; Hyser, Matthew; Atkinson, Janis; Kirschmann, Dawn A; Seftor, Elisabeth A; Hendrix, Mary J C
2014-12-01
The Ras-ERK pathway is deregulated in approximately a third of human cancers, particularly those of epithelial origin. In aggressive, triple-negative, basal-like breast cancers, most tumors display increased MEK and ERK phosphorylation and exhibit a gene expression profile characteristic of Kras or EGFR mutant tumors; however, Ras family genetic mutations are uncommon in triple-negative breast cancer and EGFR mutations account for only a subset of these tumors. Therefore, the upstream events that activate MAPK signaling and promote tumor aggression in triple-negative breast cancers remain poorly defined. We have previously shown that a secreted TGF-β family signaling ligand, Nodal, is expressed in breast cancer in correlation with disease progression. Here we highlight key findings demonstrating that Nodal is required in aggressive human breast cancer cells to activate ERK signaling and downstream tumorigenic phenotypes both in vitro and in vivo. Experimental knockdown of Nodal signaling downregulates ERK activity, resulting in loss of c-myc, upregulation of p27, G1 cell cycle arrest, increased apoptosis and decreased tumorigenicity. The data suggest that ERK activation by Nodal signaling regulates c-myc and p27 proteins post-translationally and that this cascade is essential for aggressive breast tumor behavior in vivo. As the MAPK pathway is an important target for treating triple-negative breast cancers, upstream Nodal signaling may represent a promising target for breast cancer diagnosis and combined therapies aimed at blocking ERK pathway activation. PMID:25073112
Nodal signaling promotes a tumorigenic phenotype in human breast cancer
Kirsammer, Gina; Strizzi, Luigi; Margaryan, Naira V.; Gilgur, Alina; Hyser, Matthew; Atkinson, Janis; Kirschmann, Dawn A.; Seftor, Elisabeth A.; Hendrix, Mary J.C.
2014-01-01
The Ras-ERK pathway is deregulated in approximately a third of human cancers, particularly those of epithelial origin. In aggressive, triple-negative, basal-like breast cancers, most tumors display increased MEK and ERK phosphorylation and exhibit a gene expression profile characteristic of Kras or EGFR mutant tumors; however, Ras family genetic mutations are uncommon in triple-negative breast cancer and EGFR mutations account for only a subset of these tumors. Therefore, the upstream events that activate MAPK signaling and promote tumor aggression in triple-negative breast cancers remain poorly defined. We have previously shown that a secreted TGF-β family signaling ligand, Nodal, is expressed in breast cancer in correlation with disease progression. Here we highlight key findings demonstrating that Nodal is required in aggressive human breast cancer cells to activate ERK signaling and downstream tumorigenic phenotypes both in vitro and in vivo. Experimental knockdown of Nodal signaling downregulates ERK activity, resulting in loss of c-myc, upregulation of p27, G1 cell cycle arrest, increased apoptosis and decreased tumorigenicity. The data suggest that ERK activation by Nodal signaling regulates c-myc and p27 proteins post-translationally and that this cascade is essential for aggressive breast tumor behavior in vivo. As the MAPK pathway is an important target for treating triple-negative breast cancers, upstream Nodal signaling may represent a promising target for breast cancer diagnosis and combined therapies aimed at blocking ERK pathway activation. PMID:25073112
Algebraic Multiscale Solver for Elastic Geomechanical Deformation
NASA Astrophysics Data System (ADS)
Castelletto, N.; Hajibeygi, H.; Tchelepi, H.
2015-12-01
Predicting the geomechanical response of geological formations to thermal, pressure, and mechanical loading is important in many engineering applications. The mathematical formulation that describes deformation of a reservoir coupled with flow and transport entails heterogeneous coefficients with a wide range of length scales. Such detailed heterogeneous descriptions of reservoir properties impose severe computational challenges for the study of realistic-scale (km) reservoirs. To deal with these challenges, we developed an Algebraic Multiscale Solver for ELastic geomechanical deformation (EL-AMS). Constructed on finite element fine-scale system, EL-AMS imposes a coarse-scale grid, which is a non-overlapping decomposition of the domain. Then, local (coarse) basis functions for the displacement vector are introduced. These basis functions honor the elastic properties of the local domains subject to the imposed local boundary conditions. The basis form the Restriction and Prolongation operators. These operators allow for the construction of accurate coarse-scale systems for the displacement. While the multiscale system is efficient for resolving low-frequency errors, coupling it with a fine-scale smoother, e.g., ILU(0), leads to an efficient iterative solver. Numerical results for several test cases illustrate that EL-AMS is quite efficient and applicable to simulate elastic deformation of large-scale heterogeneous reservoirs.
Using the scalable nonlinear equations solvers package
Gropp, W.D.; McInnes, L.C.; Smith, B.F.
1995-02-01
SNES (Scalable Nonlinear Equations Solvers) is a software package for the numerical solution of large-scale systems of nonlinear equations on both uniprocessors and parallel architectures. SNES also contains a component for the solution of unconstrained minimization problems, called SUMS (Scalable Unconstrained Minimization Solvers). Newton-like methods, which are known for their efficiency and robustness, constitute the core of the package. As part of the multilevel PETSc library, SNES incorporates many features and options from other parts of PETSc. In keeping with the spirit of the PETSc library, the nonlinear solution routines are data-structure-neutral, making them flexible and easily extensible. This users guide contains a detailed description of uniprocessor usage of SNES, with some added comments regarding multiprocessor usage. At this time the parallel version is undergoing refinement and extension, as we work toward a common interface for the uniprocessor and parallel cases. Thus, forthcoming versions of the software will contain additional features, and changes to parallel interface may result at any time. The new parallel version will employ the MPI (Message Passing Interface) standard for interprocessor communication. Since most of these details will be hidden, users will need to perform only minimal message-passing programming.
A computational study of nodal-based tetrahedral element behavior.
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 transient, quadratic nodal method for triangular-Z geometry
DeLorey, T.F.
1993-06-01
Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is developed for triangular-Z geometry. This development is particularly challenging because the quadratic expansion in each node must be performed between the node faces and the triangular points. As a consequence, in the 2-D plane, the flux and current at the points of the triangles must be treated. Quadratic nodal equations are solved using a non-linear iteration scheme, which utilizes the corrected, mesh-centered finite difference equations, and forces these equations to match the quadratic equations by computing discontinuity factors during the solution. Transient nodal equations are solved using the improved quasi-static method, which has been shown to be a very efficient solution method for transient problems. Several static problems are used to compare the quadratic nodal method to the Coarse Mesh Finite Difference (CMFD) method. The quadratic method is shown to give more accurate node-averaged fluxes. However, it appears that the method has difficulty predicting node leakages near reactor boundaries and severe material interfaces. The consequence is that the eigenvalue may be poorly predicted for certain reactor configurations. The transient methods are tested using a simple analytic test problem, a heterogeneous heavy water reactor benchmark problem, and three thermal hydraulic test problems. Results indicate that the transient methods have been implemented correctly.
Chiral Spin-Orbital Liquids with Nodal Lines
NASA Astrophysics Data System (ADS)
Natori, W. M. H.; Andrade, E. C.; Miranda, E.; Pereira, R. G.
2016-07-01
Strongly correlated materials with strong spin-orbit coupling hold promise for realizing topological phases with fractionalized excitations. Here, we propose a chiral spin-orbital liquid as a stable phase of a realistic model for heavy-element double perovskites. This spin liquid state has Majorana fermion excitations with a gapless spectrum characterized by nodal lines along the edges of the Brillouin zone. We show that the nodal lines are topological defects of a non-Abelian Berry connection and that the system exhibits dispersing surface states. We discuss some experimental signatures of this state and compare them with properties of the spin liquid candidate Ba2YMoO6.
Long period nodal motion of sun synchronous orbits
NASA Technical Reports Server (NTRS)
Duck, K. I.
1975-01-01
An approximative model is formulated for assessing these perturbations that significantly affect long term modal motion of sun synchronous orbits. Computer simulations with several independent computer programs consider zonal and tesseral gravitational harmonics, third body gravitational disturbances induced by the sun and the moon, and atmospheric drag. A pendulum model consisting of evenzonal harmonics through order 4 and solar gravity dominated nodal motion approximation. This pendulum motion results from solar gravity inducing an inclination oscillation which couples into the nodal precession induced by the earth's oblateness. The pendulum model correlated well with simulations observed flight data.
jShyLU Scalable Hybrid Preconditioner and Solver
Energy Science and Technology Software Center (ESTSC)
2012-09-11
ShyLU is numerical software to solve sparse linear systems of equations. ShyLU uses a hybrid direct-iterative Schur complement method, and may be used either as a preconditioner or as a solver. ShyLU is parallel and optimized for a single compute Solver node. ShyLU will be a package in the Trilinos software framework.
Experiences with linear solvers for oil reservoir simulation problems
Joubert, W.; Janardhan, R.; Biswas, D.; Carey, G.
1996-12-31
This talk will focus on practical experiences with iterative linear solver algorithms used in conjunction with Amoco Production Company`s Falcon oil reservoir simulation code. The goal of this study is to determine the best linear solver algorithms for these types of problems. The results of numerical experiments will be presented.
Shatilla, Y.A.M.; Henry, A.F.
1993-12-31
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.
Shape reanalysis and sensitivities utilizing preconditioned iterative boundary solvers
NASA Technical Reports Server (NTRS)
Guru Prasad, K.; Kane, J. H.
1992-01-01
The computational advantages associated with the utilization of preconditined iterative equation solvers are quantified for the reanalysis of perturbed shapes using continuum structural boundary element analysis (BEA). Both single- and multi-zone three-dimensional problems are examined. Significant reductions in computer time are obtained by making use of previously computed solution vectors and preconditioners in subsequent analyses. The effectiveness of this technique is demonstrated for the computation of shape response sensitivities required in shape optimization. Computer times and accuracies achieved using the preconditioned iterative solvers are compared with those obtained via direct solvers and implicit differentiation of the boundary integral equations. It is concluded that this approach employing preconditioned iterative equation solvers in reanalysis and sensitivity analysis can be competitive with if not superior to those involving direct solvers.
A multigrid fluid pressure solver handling separating solid boundary conditions.
Chentanez, Nuttapong; Müller-Fischer, Matthias
2012-08-01
We present a multigrid method for solving the linear complementarity problem (LCP) resulting from discretizing the Poisson equation subject to separating solid boundary conditions in an Eulerian liquid simulation’s pressure projection step. The method requires only a few small changes to a multigrid solver for linear systems. Our generalized solver is fast enough to handle 3D liquid simulations with separating boundary conditions in practical domain sizes. Previous methods could only handle relatively small 2D domains in reasonable time, because they used expensive quadratic programming (QP) solvers. We demonstrate our technique in several practical scenarios, including nonaxis-aligned containers and moving solids in which the omission of separating boundary conditions results in disturbing artifacts of liquid sticking to solids. Our measurements show, that the convergence rate of our LCP solver is close to that of a standard multigrid solver. PMID:22411885
A real-time impurity solver for DMFT
NASA Astrophysics Data System (ADS)
Kim, Hyungwon; Aron, Camille; Han, Jong E.; Kotliar, Gabriel
Dynamical mean-field theory (DMFT) offers a non-perturbative approach to problems with strongly correlated electrons. The method heavily relies on the ability to numerically solve an auxiliary Anderson-type impurity problem. While powerful Matsubara-frequency solvers have been developed over the past two decades to tackle equilibrium situations, the status of real-time impurity solvers that could compete with Matsubara-frequency solvers and be readily generalizable to non-equilibrium situations is still premature. We present a real-time solver which is based on a quantum Master equation description of the dissipative dynamics of the impurity and its exact diagonalization. As a benchmark, we illustrate the strengths of our solver in the context of the equilibrium Mott-insulator transition of the one-band Hubbard model and compare it with iterative perturbation theory (IPT) method. Finally, we discuss its direct application to a nonequilibrium situation.
Linear iterative solvers for implicit ODE methods
NASA Technical Reports Server (NTRS)
Saylor, Paul E.; Skeel, Robert D.
1990-01-01
The numerical solution of stiff initial value problems, which lead to the problem of solving large systems of mildly nonlinear equations are considered. For many problems derived from engineering and science, a solution is possible only with methods derived from iterative linear equation solvers. A common approach to solving the nonlinear equations is to employ an approximate solution obtained from an explicit method. The error is examined to determine how it is distributed among the stiff and non-stiff components, which bears on the choice of an iterative method. The conclusion is that error is (roughly) uniformly distributed, a fact that suggests the Chebyshev method (and the accompanying Manteuffel adaptive parameter algorithm). This method is described, also commenting on Richardson's method and its advantages for large problems. Richardson's method and the Chebyshev method with the Mantueffel algorithm are applied to the solution of the nonlinear equations by Newton's method.
Scalable Adaptive Multilevel Solvers for Multiphysics Problems
Xu, Jinchao
2014-12-01
In this project, we investigated adaptive, parallel, and multilevel methods for numerical modeling of various real-world applications, including Magnetohydrodynamics (MHD), complex fluids, Electromagnetism, Navier-Stokes equations, and reservoir simulation. First, we have designed improved mathematical models and numerical discretizaitons for viscoelastic fluids and MHD. Second, we have derived new a posteriori error estimators and extended the applicability of adaptivity to various problems. Third, we have developed multilevel solvers for solving scalar partial differential equations (PDEs) as well as coupled systems of PDEs, especially on unstructured grids. Moreover, we have integrated the study between adaptive method and multilevel methods, and made significant efforts and advances in adaptive multilevel methods of the multi-physics problems.
Optimising a parallel conjugate gradient solver
Field, M.R.
1996-12-31
This work arises from the introduction of a parallel iterative solver to a large structural analysis finite element code. The code is called FEX and it was developed at Hitachi`s Mechanical Engineering Laboratory. The FEX package can deal with a large range of structural analysis problems using a large number of finite element techniques. FEX can solve either stress or thermal analysis problems of a range of different types from plane stress to a full three-dimensional model. These problems can consist of a number of different materials which can be modelled by a range of material models. The structure being modelled can have the load applied at either a point or a surface, or by a pressure, a centrifugal force or just gravity. Alternatively a thermal load can be applied with a given initial temperature. The displacement of the structure can be constrained by having a fixed boundary or by prescribing the displacement at a boundary.
General purpose nonlinear system solver based on Newton-Krylov method.
Energy Science and Technology Software Center (ESTSC)
2013-12-01
KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].
PoroTomo Subtask 6.3 Nodal Seismometers Metadata
Lesley Parker
2016-03-28
Metadata for the nodal seismometer array deployed at the POROTOMO's Natural Laboratory in Brady Hot Spring, Nevada during the March 2016 testing. Metadata includes location and timing for each instrument as well as file lists of data to be uploaded in a separate submission.
Bud emergence and shoot growth from mature citrus nodal segments
Technology Transfer Automated Retrieval System (TEKTRAN)
Bud emergence and shoot growth from adult phase citrus nodal cultures were studied using Citrus mitis (calamondin), Citrus paradisi (grapefruit), and Citrus sinensis (sweet orange). The effects of 6-benzylaminopurine (BA), indole 3-acetic acid (IAA), and citrus type on shoot quality and growth fro...
Nodal Structure and the Partitioning of Equivalence Classes
ERIC Educational Resources Information Center
Fields, Lanny; Watanabe-Rose, Mari
2008-01-01
By definition, all of the stimuli in an equivalence class have to be functionally interchangeable with each other. The present experiment, however, demonstrated that this was not the case when using post-class-formation dual-option response transfer tests. With college students, two 4-node 6-member equivalence classes with nodal structures of…
47 CFR 101.503 - Digital Electronic Message Service Nodal Stations.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 5 2010-10-01 2010-10-01 false Digital Electronic Message Service Nodal... AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES 24 GHz Service and Digital Electronic Message Service § 101.503 Digital Electronic Message Service Nodal Stations. 10.6 GHz DEMS Nodal Stations may...
47 CFR 101.503 - Digital Electronic Message Service Nodal Stations.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 5 2011-10-01 2011-10-01 false Digital Electronic Message Service Nodal... AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES 24 GHz Service and Digital Electronic Message Service § 101.503 Digital Electronic Message Service Nodal Stations. 10.6 GHz DEMS Nodal Stations may...
Coman, I; Aigrot, M S; Seilhean, D; Reynolds, R; Girault, J A; Zalc, B; Lubetzki, C
2006-12-01
Saltatory conduction in myelinated fibres depends on the specific molecular organization of highly specialized axonal domains at the node of Ranvier, the paranodal and the juxtaparanodal regions. Voltage-gated sodium channels (Na(v)) have been shown to be deployed along the naked demyelinated axon in experimental models of CNS demyelination and in multiple sclerosis lesions. Little is known about aggregation of nodal, paranodal and juxtaparanodal constituents during the repair process. We analysed by immunohistochemistry on free-floating sections from multiple sclerosis brains the expression and distribution of nodal (Na(v) channels), paranodal (paranodin/Caspr) and juxtaparanodal (K(v) channels and Caspr2) molecules in demyelinated and remyelinated lesions. Whereas in demyelinated lesions, paranodal and juxtaparanodal proteins are diffusely distributed on denuded axons, the distribution of Na(v) channels is heterogeneous, with a diffuse immunoreactivity but also few broad Na(v) channel aggregates in all demyelinated lesions. In contrast to the demyelinated plaques, all remyelinated lesions are characterized by the detection of aggregates of Na(v) channels, paranodin/Caspr, K(v) channels and Caspr2. Our data suggest that these aggregates precede remyelination, and that Na(v) channel aggregation is the initial event, followed by aggregation of paranodal and then juxtaparanodal axonal proteins. Remyelination takes place in multiple sclerosis tissue but myelin repair is often incomplete, and the reasons for this remyelination deficit are many. We suggest that a defect of Na(v) channel aggregation might be involved in the remyelination failure in demyelinated lesions with spared axons and oligodendroglial cells. PMID:16766541
NASA Astrophysics Data System (ADS)
Shukla, K.; Wang, Y.; Jaiswal, P.
2014-12-01
In a porous medium the seismic energy not only propagates through matrix but also through pore-fluids. The differential movement between sediment grains of the matrix and interstitial fluid generates a diffusive wave which is commonly referred to as the slow P-wave. A combined system of equation which includes both elastic and diffusive phases is known as the poroelasticity. Analyzing seismic data through poroelastic modeling results in accurate interpretation of amplitude and separation of wave modes, leading to more accurate estimation of geomehanical properties of rocks. Despite its obvious multi-scale application, from sedimentary reservoir characterization to deep-earth fractured crust, poroelasticity remains under-developed primarily due to the complex nature of its constituent equations. We present a detail formulation of poroleastic wave equations for isotropic media by combining the Biot's and Newtonian mechanics. System of poroelastic wave equation constitutes for eight time dependent hyperbolic PDEs in 2D whereas in case of 3D number goes up to thirteen. Eigen decomposition of Jacobian of these systems confirms the presence of an additional slow-P wave phase with velocity lower than shear wave, posing stability issues on numerical scheme. To circumvent the issue, we derived a numerical scheme using nodal discontinuous Galerkin approach by adopting the triangular meshes in 2D which is extended to tetrahedral for 3D problems. In our nodal DG approach the basis function over a triangular element is interpolated using Legendre-Gauss-Lobatto (LGL) function leading to a more accurate local solutions than in the case of simple DG. We have tested the numerical scheme for poroelastic media in 1D and 2D case, and solution obtained for the systems offers high accuracy in results over other methods such as finite difference , finite volume and pseudo-spectral. The nodal nature of our approach makes it easy to convert the application into a multi-threaded algorithm
A New Poisson Solver PIC Simulations on Arbitrary Unstructured Tetrahedral Meshes
NASA Astrophysics Data System (ADS)
Averkin, Sergey; Gatsonis, Nikolaos
2015-11-01
A new node-based algorithm is developed for the solution of Poisson's equation in PIC simulations on arbitrary unstructured tetrahedral meshes. The algorithm is derived by applying the integral form of the Gauss law to the indirect dual mesh constructed by connecting the centroids of edges to the centroids of faces and centroids of faces with the centroids of tetrahedral cells for each tetrahedron. The potential variation is assumed linear inside every cell and allows to estimate the potential gradient in each cell from the nodal values. The obtained sparse linear system is solved with the GMRES solver combined with the ILU(0) preconditioner. The new algorithm is verified with the simulation of the current collection by cylindrical Langmuire probes in the collisionless regime for a wide range of probe to Debye length ratios. The computed electron and ion number density variations as well as electric potential and collected currents compare well with the simulation results of Laframboise. AFOSR-FA9550-14-1-0366 Computational Mathematics Program.
Comparison of open-source linear programming solvers.
Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin D.; Jones, Katherine A.; Martin, Nathaniel; Detry, Richard Joseph
2013-10-01
When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modular In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.
Wind-US Unstructured Flow Solutions for a Transonic Diffuser
NASA Technical Reports Server (NTRS)
Mohler, Stanley R., Jr.
2005-01-01
The Wind-US Computational Fluid Dynamics flow solver computed flow solutions for a transonic diffusing duct. The calculations used an unstructured (hexahedral) grid. The Spalart-Allmaras turbulence model was used. Static pressures along the upper and lower wall agreed well with experiment, as did velocity profiles. The effect of the smoothing input parameters on convergence and solution accuracy was investigated. The meaning and proper use of these parameters are discussed for the benefit of Wind-US users. Finally, the unstructured solver is compared to the structured solver in terms of run times and solution accuracy.
NASA Astrophysics Data System (ADS)
Koldan, Jelena; Puzyrev, Vladimir; de la Puente, Josep; Houzeaux, Guillaume; Cela, José María
2014-06-01
We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element (FE) solvers for 3-D electromagnetic (EM) numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid (AMG) that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation (SSOR) and Gauss-Seidel, as smoothers and the wave front algorithm to create groups, which are used for a coarse-level generation. We have implemented and tested this new preconditioner within our parallel nodal FE solver for 3-D forward problems in EM induction geophysics. We have performed series of experiments for several models with different conductivity structures and characteristics to test the performance of our AMG preconditioning technique when combined with biconjugate gradient stabilized method. The results have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner. Compared to other preconditioning schemes, such as diagonal, SSOR and truncated approximate inverse, the AMG preconditioner greatly improves the convergence of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners succeed to converge to a desired precision, AMG is able to considerably reduce the total execution time of the forward-problem code-up to an order of magnitude. Furthermore, the tests have confirmed that our AMG scheme ensures grid-independent rate of convergence, as well as improvement in convergence regardless of how big local mesh refinements are. In addition, AMG is designed to be a black-box preconditioner, which makes it easy to use and combine with different iterative methods. Finally, it has proved to be very practical and efficient in the
A non-conforming 3D spherical harmonic transport solver
Van Criekingen, S.
2006-07-01
A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)
Multi-GPU kinetic solvers using MPI and CUDA
NASA Astrophysics Data System (ADS)
Zabelok, Sergey; Arslanbekov, Robert; Kolobov, Vladimir
2014-12-01
This paper describes recent progress towards porting a Unified Flow Solver (UFS) to heterogeneous parallel computing. The main challenge of porting UFS to graphics processing units (GPUs) comes from the dynamically adapted mesh, which causes irregular data access. We describe the implementation of CUDA kernels for three modules in UFS: the direct Boltzmann solver using discrete velocity method (DVM), the DSMC module, and the Lattice Boltzmann Method (LBM) solver, all using octree Cartesian mesh with adaptive Mesh Refinement (AMR). Double digit speedup on single GPU and good scaling for multi-GPU has been demonstrated.
Elliptic Solvers for Adaptive Mesh Refinement Grids
Quinlan, D.J.; Dendy, J.E., Jr.; Shapira, Y.
1999-06-03
We are developing multigrid methods that will efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final product will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of other Laboratory groups. The focus of this work is research on serial and parallel elliptic algorithms and the inclusion of our black-box multigrid techniques into this new setting. The approach applies the Los Alamos object-oriented class libraries that greatly simplify the development of serial and parallel adaptive mesh refinement applications. In the final year of this LDRD, we focused on putting the software together; in particular we completed the final AMR++ library, we wrote tutorials and manuals, and we built example applications. We implemented the Fast Adaptive Composite Grid method as the principal elliptic solver. We presented results at the Overset Grid Conference and other more AMR specific conferences. We worked on optimization of serial and parallel performance and published several papers on the details of this work. Performance remains an important issue and is the subject of continuing research work.
Advanced Multigrid Solvers for Fluid Dynamics
NASA Technical Reports Server (NTRS)
Brandt, Achi
1999-01-01
The main objective of this project has been to support the development of multigrid techniques in computational fluid dynamics that can achieve "textbook multigrid efficiency" (TME), which is several orders of magnitude faster than current industrial CFD solvers. Toward that goal we have assembled a detailed table which lists every foreseen kind of computational difficulty for achieving it, together with the possible ways for resolving the difficulty, their current state of development, and references. We have developed several codes to test and demonstrate, in the framework of simple model problems, several approaches for overcoming the most important of the listed difficulties that had not been resolved before. In particular, TME has been demonstrated for incompressible flows on one hand, and for near-sonic flows on the other hand. General approaches were advanced for the relaxation of stagnation points and boundary conditions under various situations. Also, new algebraic multigrid techniques were formed for treating unstructured grid formulations. More details on all these are given below.
Optimization of hydraulic turbine diffuser
NASA Astrophysics Data System (ADS)
Moravec, Prokop; Hliník, Juraj; Rudolf, Pavel
2016-03-01
Hydraulic turbine diffuser recovers pressure energy from residual kinetic energy on turbine runner outlet. Efficiency of this process is especially important for high specific speed turbines, where almost 50% of available head is utilized within diffuser. Magnitude of the coefficient of pressure recovery can be significantly influenced by designing its proper shape. Present paper focuses on mathematical shape optimization method coupled with CFD. First method is based on direct search Nelder-Mead algorithm, while the second method employs adjoint solver and morphing. Results obtained with both methods are discussed and their advantages/disadvantages summarized.
NASA Technical Reports Server (NTRS)
Raju, Manthena S.
1998-01-01
Sprays occur in a wide variety of industrial and power applications and in the processing of materials. A liquid spray is a phase flow with a gas as the continuous phase and a liquid as the dispersed phase (in the form of droplets or ligaments). Interactions between the two phases, which are coupled through exchanges of mass, momentum, and energy, can occur in different ways at different times and locations involving various thermal, mass, and fluid dynamic factors. An understanding of the flow, combustion, and thermal properties of a rapidly vaporizing spray requires careful modeling of the rate-controlling processes associated with the spray's turbulent transport, mixing, chemical kinetics, evaporation, and spreading rates, as well as other phenomena. In an attempt to advance the state-of-the-art in multidimensional numerical methods, we at the NASA Lewis Research Center extended our previous work on sprays to unstructured grids and parallel computing. LSPRAY, which was developed by M.S. Raju of Nyma, Inc., is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo probability density function (PDF) solver. The LSPRAY solver accommodates the use of an unstructured mesh with mixed triangular, quadrilateral, and/or tetrahedral elements in the gas-phase solvers. It is used specifically for fuel sprays within gas turbine combustors, but it has many other uses. The spray model used in LSPRAY provided favorable results when applied to stratified-charge rotary combustion (Wankel) engines and several other confined and unconfined spray flames. The source code will be available with the National Combustion Code (NCC) as a complete package.
Thomas, Jonathan G.; Kashani, Rojano; Balter, James M.; Tatro, Daniel; Kong, F.-M.; Pan, Charlie C.
2009-07-01
The purpose of this study was to determine the intra and interfraction motion of mediastinal lymph node regions. Ten patients with nonsmall-cell lung cancer underwent controlled inhale and exhale computed tomography (CT) scans during two sessions (40 total datasets) and mediastinal nodal stations 1-8 were outlined. Corresponding CT scans from different sessions were registered to remove setup error and, in this reference frame, the centroid of each nodal station was compared for right-left (RL), anterior-posterior (AP), and superior-inferior (SI) displacement. In addition, an anisotropic volume expansion encompassing the change of the nodal region margins in all directions was used. Intrafraction displacement was determined by comparing same session inhale-exhale scans. Interfraction reproducibility of nodal regions was determined by comparing the same respiratory phase scans between two sessions. Intrafraction displacement of centroid varied between nodal stations. All nodal regions moved posteriorly and superiorly with exhalation, and inferior nodal stations showed the most motion. Based on anisotropic expansion, nodal regions expanded mostly in the RL direction from inhale to exhale. The interpatient variations in intrafraction displacement were large compared with the displacements themselves. Moreover, there was substantial interfractional displacement ({approx}5 mm). Mediastinal lymph node regions clearly move during breathing. In addition, deformation of nodal regions between inhale and exhale occurs. The degree of motion and deformation varies by station and by individual. This study indicates the potential advantage of characterizing individualized nodal region motion to safely maximize conformality of mediastinal nodal targets.
Lu, Yujie; Zhu, Banghe; Shen, Haiou; Rasmussen, John C; Wang, Ge; Sevick-Muraca, Eva M
2010-08-21
Fluorescence molecular imaging/tomography may play an important future role in preclinical research and clinical diagnostics. Time- and frequency-domain fluorescence imaging can acquire more measurement information than the continuous wave (CW) counterpart, improving the image quality of fluorescence molecular tomography. Although diffusion approximation (DA) theory has been extensively applied in optical molecular imaging, high-order photon migration models need to be further investigated to match quantitation provided by nuclear imaging. In this paper, a frequency-domain parallel adaptive finite element solver is developed with simplified spherical harmonics (SP(N)) approximations. To fully evaluate the performance of the SP(N) approximations, a fast time-resolved tetrahedron-based Monte Carlo fluorescence simulator suitable for complex heterogeneous geometries is developed using a convolution strategy to realize the simulation of the fluorescence excitation and emission. The validation results show that high-order SP(N) can effectively correct the modeling errors of the diffusion equation, especially when the tissues have high absorption characteristics or when high modulation frequency measurements are used. Furthermore, the parallel adaptive mesh evolution strategy improves the modeling precision and the simulation speed significantly on a realistic digital mouse phantom. This solver is a promising platform for fluorescence molecular tomography using high-order approximations to the radiative transfer equation. PMID:20671350
A Radiation Transfer Solver for Athena Using Short Characteristics
NASA Astrophysics Data System (ADS)
Davis, Shane W.; Stone, James M.; Jiang, Yan-Fei
2012-03-01
We describe the implementation of a module for the Athena magnetohydrodynamics (MHD) code that solves the time-independent, multi-frequency radiative transfer (RT) equation on multidimensional Cartesian simulation domains, including scattering and non-local thermodynamic equilibrium (LTE) effects. The module is based on well known and well tested algorithms developed for modeling stellar atmospheres, including the method of short characteristics to solve the RT equation, accelerated Lambda iteration to handle scattering and non-LTE effects, and parallelization via domain decomposition. The module serves several purposes: it can be used to generate spectra and images, to compute a variable Eddington tensor (VET) for full radiation MHD simulations, and to calculate the heating and cooling source terms in the MHD equations in flows where radiation pressure is small compared with gas pressure. For the latter case, the module is combined with the standard MHD integrators using operator splitting: we describe this approach in detail, including a new constraint on the time step for stability due to radiation diffusion modes. Implementation of the VET method for radiation pressure dominated flows is described in a companion paper. We present results from a suite of test problems for both the RT solver itself and for dynamical problems that include radiative heating and cooling. These tests demonstrate that the radiative transfer solution is accurate and confirm that the operator split method is stable, convergent, and efficient for problems of interest. We demonstrate there is no need to adopt ad hoc assumptions of questionable accuracy to solve RT problems in concert with MHD: the computational cost for our general-purpose module for simple (e.g., LTE gray) problems can be comparable to or less than a single time step of Athena's MHD integrators, and only few times more expensive than that for more general (non-LTE) problems.
A RADIATION TRANSFER SOLVER FOR ATHENA USING SHORT CHARACTERISTICS
Davis, Shane W.; Stone, James M.; Jiang Yanfei
2012-03-01
We describe the implementation of a module for the Athena magnetohydrodynamics (MHD) code that solves the time-independent, multi-frequency radiative transfer (RT) equation on multidimensional Cartesian simulation domains, including scattering and non-local thermodynamic equilibrium (LTE) effects. The module is based on well known and well tested algorithms developed for modeling stellar atmospheres, including the method of short characteristics to solve the RT equation, accelerated Lambda iteration to handle scattering and non-LTE effects, and parallelization via domain decomposition. The module serves several purposes: it can be used to generate spectra and images, to compute a variable Eddington tensor (VET) for full radiation MHD simulations, and to calculate the heating and cooling source terms in the MHD equations in flows where radiation pressure is small compared with gas pressure. For the latter case, the module is combined with the standard MHD integrators using operator splitting: we describe this approach in detail, including a new constraint on the time step for stability due to radiation diffusion modes. Implementation of the VET method for radiation pressure dominated flows is described in a companion paper. We present results from a suite of test problems for both the RT solver itself and for dynamical problems that include radiative heating and cooling. These tests demonstrate that the radiative transfer solution is accurate and confirm that the operator split method is stable, convergent, and efficient for problems of interest. We demonstrate there is no need to adopt ad hoc assumptions of questionable accuracy to solve RT problems in concert with MHD: the computational cost for our general-purpose module for simple (e.g., LTE gray) problems can be comparable to or less than a single time step of Athena's MHD integrators, and only few times more expensive than that for more general (non-LTE) problems.
Parallel iterative solvers and preconditioners using approximate hierarchical methods
Grama, A.; Kumar, V.; Sameh, A.
1996-12-31
In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our solver yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our solver. The combined speedups from approximation and parallelism represent an improvement of several orders in solution time. We also develop fast and paralellizable preconditioners for this problem. We report on the performance of an inner-outer scheme and a preconditioner based on truncated Green`s function. Experimental results on a 256 processor Cray T3D are presented.
Long-range Coulomb interaction in nodal-ring semimetals
NASA Astrophysics Data System (ADS)
Huh, Yejin; Moon, Eun-Gook; Kim, Yong Baek
2016-01-01
Recently there have been several proposals of materials predicted to be nodal-ring semimetals, where zero energy excitations are characterized by a nodal ring in the momentum space. This class of materials falls between the Dirac-like semimetals and the more conventional Fermi-surface systems. As a step towards understanding this unconventional system, we explore the effects of the long-range Coulomb interaction. Due to the vanishing density of states at the Fermi level, Coulomb interaction is only partially screened and remains long-ranged. Through renormalization group and large-Nf computations, we have identified a nontrivial interacting fixed point. The screened Coulomb interaction at the interacting fixed point is an irrelevant perturbation, allowing controlled perturbative evaluations of physical properties of quasiparticles. We discuss unique experimental consequences of such quasiparticles: acoustic wave propagation, anisotropic dc conductivity, and renormalized phonon dispersion as well as energy dependence of quasiparticle lifetime.
Nodal failure index approach to groundwater remediation design
Lee, J.; Reeves, H.W.; Dowding, C.H.
2008-01-01
Computer simulations often are used to design and to optimize groundwater remediation systems. We present a new computationally efficient approach that calculates the reliability of remedial design at every location in a model domain with a single simulation. The estimated reliability and other model information are used to select a best remedial option for given site conditions, conceptual model, and available data. To evaluate design performance, we introduce the nodal failure index (NFI) to determine the number of nodal locations at which the probability of success is below the design requirement. The strength of the NFI approach is that selected areas of interest can be specified for analysis and the best remedial design determined for this target region. An example application of the NFI approach using a hypothetical model shows how the spatial distribution of reliability can be used for a decision support system in groundwater remediation design. ?? 2008 ASCE.
Anomalous contagion and renormalization in networks with nodal mobility
NASA Astrophysics Data System (ADS)
Manrique, Pedro D.; Qi, Hong; Zheng, Minzhang; Xu, Chen; Hui, Pak Ming; Johnson, Neil F.
2016-07-01
A common occurrence in everyday human activity is where people join, leave and possibly rejoin clusters of other individuals —whether this be online (e.g. social media communities) or in real space (e.g. popular meeting places such as cafes). In the steady state, the resulting interaction network would appear static over time if the identities of the nodes are ignored. Here we show that even in this static steady-state limit, a non-zero nodal mobility leads to a diverse set of outbreak profiles that is dramatically different from known forms, and yet matches well with recent real-world social outbreaks. We show how this complication of nodal mobility can be renormalized away for a particular class of networks.
Concomitant nodal involvement by Langerhans cell histiocytosis and Hodgkin's lymphoma.
Geurten, Claire; Thiry, Albert; Jamblin, Paul; Demarche, Martine; Hoyoux, Claire
2015-12-01
A 10-year-old girl with a family history of Hodgkin's lymphoma presented with a 2 month history of cervical lymphadenopathy and weight loss. Biopsy indicated concomitant nodal involvement by Langerhans cell histiocytosis and Hodgkin's lymphoma. Such an association is rare, especially so in children, but is not an isolated phenomenon, thereby prompting the question of whether Langerhans cell histiocytosis is a reactive or a neoplastic process. PMID:26556799
NODAL PATHWAY GENES ARE DOWNREGULATED IN FACIAL ASYMMETRY
Nicot, Romain; Hottenstein, Molly; Raoul, Gwenael; Ferri, Joel; Horton, Michael; Tobias, John W.; Barton, Elisabeth; Gelé, Patrick; Sciote, James J.
2014-01-01
Purpose Facial asymmetry is a common comorbid condition in patients with jaw deformation malocclusion. Heritability of malocclusion is advancing rapidly, but very little is known regarding genetic contributions to asymmetry. This study identifies differences in expression of key asymmetry-producing genes which are down regulated in facial asymmetry patients. Material and Methods Masseter muscle samples were collected during BSSO orthognathic surgery to correct skeletal-based malocclusion. Patients were classified as Class II or III and open or deep bite malocclusion with or without facial asymmetry. Muscle samples were analyzed for gene expression differences on Affymetrix HT2.0 microarray global expression chips. Results Overall gene expression was different for asymmetric patients compared to other malocclusion classifications by principal component analysis (P<0.05). We identified differences in the nodal signaling pathway (NSP) which promotes development of mesoderm and endoderm and left-right patterning during embryogenesis. Nodal and Lefty expression was 1.39–1.84 fold greater (P<3.41×10−5) whereas integral membrane Nodal-modulators Nomo1,2,3 were −5.63 to −5.81 (P<3.05×10−4) less in asymmetry subjects. Fold differences among intracellular pathway members were negative in the range of −7.02 to −2.47 (P<0.003). Finally Pitx2, a upstream effector of Nodal known to influence the size of type II skeletal muscle fibers was also significantly decreased in facial asymmetry (P<0.05). Conclusions When facial asymmetry is part of skeletal malocclusion there are decreases of NSP genes in masseter muscle. This data suggests that the NSP is down regulated to help promote development of asymmetry. Pitx2 expression differences also contributed to both skeletal and muscle development in this condition. PMID:25364968
Nodal Basin Recurrence After Sentinel Lymph Node Biopsy for Melanoma
Kretschmer, Lutz; Bertsch, Hans Peter; Zapf, Antonia; Mitteldorf, Christina; Satzger, Imke; Thoms, Kai-Martin; Völker, Bernward; Schön, Michael Peter; Gutzmer, Ralf; Starz, Hans
2015-01-01
Abstract The objective of this study was to analyze different types of nodal basin recurrence after sentinel lymph node biopsy (SLNB) for melanoma. Patients and Methods: Kaplan–Meier estimates and the Cox proportional hazards model were used to study 2653 patients from 3 German melanoma centers retrospectively. The estimated 5-year negative predictive value of SLNB was 96.4%. The estimated false-negative (FN) rates after 1, 2, 3, 5, and 10 years were 2.5%, 4.6%, 6.4%, 8.7%, and 12.6%, respectively. Independent factors associated with false negativity were older age, fewer SLNs excised, and head or neck location of the primary tumor. Compared with SLN-positive patients, the FNs had a significantly lower survival. In SLN-positive patients undergoing completion lymphadenectomy (CLND), the 5-year nodal basin recurrence rate was 18.3%. The recurrence rates for axilla, groin, and neck were 17.2%, 15.5%, and 44.1%, respectively. Significant factors predicting local relapse after CLND were older age, head, or neck location of the primary tumor, ulceration, deeper penetration of the metastasis into the SLN, tumor-positive CLND, and >2 lymph node metastases. All kinds of nodal relapse were associated with a higher prevalence of in-transit metastases. The FN rate after SLNB steadily increases over the observation period and should, therefore, be estimated by the Kaplan–Meier method. False-negativity is associated with fewer SLNs excised. The beneficial effect of CLND on nodal basin disease control varies considerably across different risk groups. This should be kept in mind about SLN-positive patients when individual decisions on prophylactic CLND are taken. PMID:26356697
LSST Telescope Alignment Plan Based on Nodal Aberration Theory
NASA Astrophysics Data System (ADS)
Sebag, J.; Gressler, W.; Schmid, T.; Rolland, J. P.; Thompson, K. P.
2012-04-01
The optical alignment of the Large Synoptic Survey Telescope (LSST) is potentially challenging, due to its fast three-mirror optical design and its large 3.5° field of view (FOV). It is highly advantageous to align the three-mirror optical system prior to the integration of the complex science camera on the telescope, which corrects the FOV via three refractive elements and includes the operational wavefront sensors. A telescope alignment method based on nodal aberration theory (NAT) is presented here to address this challenge. Without the science camera installed on the telescope, the on-axis imaging performance of the telescope is diffraction-limited, but the field of view is not corrected. The nodal properties of the three-mirror telescope design have been analyzed and an alignment approach has been developed using the intrinsically linear nodal behavior, which is linked via sensitivities to the misalignment parameters. Since mirror figure errors will exist in any real application, a methodology to introduce primary-mirror figure errors into the analysis has been developed and is also presented.
Upper bound shakedown analysis with the nodal natural element method
NASA Astrophysics Data System (ADS)
Zhou, Shutao; Liu, Yinghua; Wang, Dongdong; Wang, Kai; Yu, Suyuan
2014-11-01
In this paper, a novel numerical solution procedure is developed for the upper bound shakedown analysis of elastic-perfectly plastic structures. The nodal natural element method (nodal-NEM) combines the advantages of the NEM and the stabilized conforming nodal integration scheme, and is used to discretize the established mathematical programming formulation of upper bound shakedown analysis based on Koiter's theorem. In this formulation, the displacement field is approximated by using the Sibson interpolation and the difficulty caused by the time integration is solved by König's technique. Meanwhile, the nonlinear and non-differentiable characteristic of objective function is overcome by distinguishing non-plastic areas from plastic areas and modifying associated constraint conditions and goal function at each iteration step. Finally, the objective function subjected to several equality constraints is linearized and the upper bound shakedown load multiplier is obtained. This direct iterative process can ensure the shakedown load to monotonically converge to the upper bound of true solution. Several typical numerical examples confirm the efficiency and accuracy of the proposed method.
Topological Phase Transitions in Line-nodal Superconductors
NASA Astrophysics Data System (ADS)
Cho, Gil Young; Han, Sangeun; Moon, Eun-Gook
Fathoming interplay between symmetry and topology of many-electron wave-functions deepens our understanding in quantum nature of many particle systems. Topology often protects zero-energy excitation, and in a certain class, symmetry is intrinsically tied to the topological protection. Namely, unless symmetry is broken, topological nature is intact. We study one specific case of such class, symmetry-protected line-nodal superconductors in three spatial dimensions (3d). Mismatch between phase spaces of order parameter fluctuation and line-nodal fermion excitation induces an exotic universality class in a drastic contrast to one of the conventional ϕ4 theory in 3d. Hyper-scaling violation and relativistic dynamic scaling with unusually large quantum critical region are main characteristics, and their implication in experiments is discussed. For example, continuous phase transition out of line-nodal superconductors has a linear phase boundary in a temperature-tuning parameter phase-diagram. This work was supported by the Brain Korea 21 PLUS Project of Korea Government and KAIST start-up funding.
A nodal domain theorem for integrable billiards in two dimensions
Samajdar, Rhine; Jain, Sudhir R.
2014-12-15
Eigenfunctions of integrable planar billiards are studied — in particular, the number of nodal domains, ν of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrödinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and non-separable integrable billiards, ν satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of mmodkn, given a particular k, for a set of quantum numbers, m,n. Further, we observe that the patterns in a family are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations. - Highlights: • We find that the number of nodal domains of eigenfunctions of integrable, planar billiards satisfy a class of difference equations. • The eigenfunctions labelled by quantum numbers (m,n) can be classified in terms of mmodkn. • A theorem is presented, realising algebraic representations of geometrical patterns exhibited by the domains. • This work presents a connection between integrable systems and difference equations.
Anomalous scaling of the penetration depth in nodal superconductors
NASA Astrophysics Data System (ADS)
She, Jian-Huang; Lawler, Michael J.; Kim, Eun-Ah
2015-07-01
Recent findings of anomalous superlinear scaling of low-temperature (T ) penetration depth (PD) in several nodal superconductors near putative quantum critical points suggest that the low-temperature PD can be a useful probe of quantum critical fluctuations in a superconductor. On the other hand, cuprates, which are poster child nodal superconductors, have not shown any such anomalous scaling of PD, despite growing evidence of quantum critical points (QCP). Then it is natural to ask when and how can quantum critical fluctuations cause anomalous scaling of PD? Carrying out the renormalization group calculation for the problem of two-dimensional superconductors with point nodes, we show that quantum critical fluctuations associated with a point group symmetry reduction result in nonuniversal logarithmic corrections to the T dependence of the PD. The resulting apparent power law depends on the bare velocity anisotropy ratio. We then compare our results to data sets from two distinct nodal superconductors: YBa2Cu3O6.95 and CeCoIn5. Considering all symmetry-lowering possibilities of the point group of interest, C4 v, we find our results to be remarkably consistent with YBa2Cu3O6.95 being near a vertical nematic QCP and CeCoIn5 being near a diagonal nematic QCP. Our results motivate a search for diagonal nematic fluctuations in CeCoIn5.
A robust multilevel simultaneous eigenvalue solver
NASA Technical Reports Server (NTRS)
Costiner, Sorin; Taasan, Shlomo
1993-01-01
Multilevel (ML) algorithms for eigenvalue problems are often faced with several types of difficulties such as: the mixing of approximated eigenvectors by the solution process, the approximation of incomplete clusters of eigenvectors, the poor representation of solution on coarse levels, and the existence of close or equal eigenvalues. Algorithms that do not treat appropriately these difficulties usually fail, or their performance degrades when facing them. These issues motivated the development of a robust adaptive ML algorithm which treats these difficulties, for the calculation of a few eigenvectors and their corresponding eigenvalues. The main techniques used in the new algorithm include: the adaptive completion and separation of the relevant clusters on different levels, the simultaneous treatment of solutions within each cluster, and the robustness tests which monitor the algorithm's efficiency and convergence. The eigenvectors' separation efficiency is based on a new ML projection technique generalizing the Rayleigh Ritz projection, combined with a technique, the backrotations. These separation techniques, when combined with an FMG formulation, in many cases lead to algorithms of O(qN) complexity, for q eigenvectors of size N on the finest level. Previously developed ML algorithms are less focused on the mentioned difficulties. Moreover, algorithms which employ fine level separation techniques are of O(q(sub 2)N) complexity and usually do not overcome all these difficulties. Computational examples are presented where Schrodinger type eigenvalue problems in 2-D and 3-D, having equal and closely clustered eigenvalues, are solved with the efficiency of the Poisson multigrid solver. A second order approximation is obtained in O(qN) work, where the total computational work is equivalent to only a few fine level relaxations per eigenvector.
A Comparative Study of Randomized Constraint Solvers for Random-Symbolic Testing
NASA Technical Reports Server (NTRS)
Takaki, Mitsuo; Cavalcanti, Diego; Gheyi, Rohit; Iyoda, Juliano; dAmorim, Marcelo; Prudencio, Ricardo
2009-01-01
The complexity of constraints is a major obstacle for constraint-based software verification. Automatic constraint solvers are fundamentally incomplete: input constraints often build on some undecidable theory or some theory the solver does not support. This paper proposes and evaluates several randomized solvers to address this issue. We compare the effectiveness of a symbolic solver (CVC3), a random solver, three hybrid solvers (i.e., mix of random and symbolic), and two heuristic search solvers. We evaluate the solvers on two benchmarks: one consisting of manually generated constraints and another generated with a concolic execution of 8 subjects. In addition to fully decidable constraints, the benchmarks include constraints with non-linear integer arithmetic, integer modulo and division, bitwise arithmetic, and floating-point arithmetic. As expected symbolic solving (in particular, CVC3) subsumes the other solvers for the concolic execution of subjects that only generate decidable constraints. For the remaining subjects the solvers are complementary.
Quantitative analysis of numerical solvers for oscillatory biomolecular system models
Quo, Chang F; Wang, May D
2008-01-01
Background This article provides guidelines for selecting optimal numerical solvers for biomolecular system models. Because various parameters of the same system could have drastically different ranges from 10-15 to 1010, the ODEs can be stiff and ill-conditioned, resulting in non-unique, non-existing, or non-reproducible modeling solutions. Previous studies have not examined in depth how to best select numerical solvers for biomolecular system models, which makes it difficult to experimentally validate the modeling results. To address this problem, we have chosen one of the well-known stiff initial value problems with limit cycle behavior as a test-bed system model. Solving this model, we have illustrated that different answers may result from different numerical solvers. We use MATLAB numerical solvers because they are optimized and widely used by the modeling community. We have also conducted a systematic study of numerical solver performances by using qualitative and quantitative measures such as convergence, accuracy, and computational cost (i.e. in terms of function evaluation, partial derivative, LU decomposition, and "take-off" points). The results show that the modeling solutions can be drastically different using different numerical solvers. Thus, it is important to intelligently select numerical solvers when solving biomolecular system models. Results The classic Belousov-Zhabotinskii (BZ) reaction is described by the Oregonator model and is used as a case study. We report two guidelines in selecting optimal numerical solver(s) for stiff, complex oscillatory systems: (i) for problems with unknown parameters, ode45 is the optimal choice regardless of the relative error tolerance; (ii) for known stiff problems, both ode113 and ode15s are good choices under strict relative tolerance conditions. Conclusions For any given biomolecular model, by building a library of numerical solvers with quantitative performance assessment metric, we show that it is possible
A two-dimensional, semi-analytic expansion method for nodal calculations
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.
Nodal Follicular Lymphomas: A Clinicopathological Study from a Tertiary Care Centre in South India.
Supari, Divya; Ananthamurthy, Anuradha
2016-06-01
The aim of this study was to assess the distribution of nodal follicular lymphomas (FL) among various subtypes of non- Hodgkin lymphoma and to study their clinico-pathological features. Clinical details, histomorphology including grading & patterns and immunoprofile of 44 cases were studied. Majority of the cases were grade 1 (61 %) FL. BCL2 positivity was higher in low grade FLs (97 %). An associated diffuse large B cell lymphoma component was seen in 18 % and was present only in conjunction with grade 3 FL. Majority of our patients (76 %) had a high FLIPI score and belonged to the high risk group. Our study showed that the incidence of FLs is much lower in the Indian population (14.5 %) when compared to western studies and majority were of low grade. Although there was complete initial response to treatment, relapse was common and was much higher in low grade FLs with diffuse areas on histology, Ann Arbor stage III/IV and FLIPI scores of 3-5. PMID:27065580
Euler/Navier-Stokes Solvers Applied to Ducted Fan Configurations
NASA Technical Reports Server (NTRS)
Keith, Theo G., Jr.; Srivastava, Rakesh
1997-01-01
Due to noise considerations, ultra high bypass ducted fans have become a more viable design. These ducted fans typically consist of a rotor stage containing a wide chord fan and a stator stage. One of the concerns for this design is the classical flutter that keeps occurring in various unducted fan blade designs. These flutter are catastrophic and are to be avoided in the flight envelope of the engine. Some numerical investigations by Williams, Cho and Dalton, have suggested that a duct around a propeller makes it more unstable. This needs to be further investigated. In order to design an engine to safely perform a set of desired tasks, accurate information of the stresses on the blade during the entire cycle of blade motion is required. This requirement in turn demands that accurate knowledge of steady and unsteady blade loading be available. Aerodynamic solvers based on unsteady three-dimensional analysis will provide accurate and fast solutions and are best suited for aeroelastic analysis. The Euler solvers capture significant physics of the flowfield and are reasonably fast. An aerodynamic solver Ref. based on Euler equations had been developed under a separate grant from NASA Lewis in the past. Under the current grant, this solver has been modified to calculate the aeroelastic characteristics of unducted and ducted rotors. Even though, the aeroelastic solver based on three-dimensional Euler equations is computationally efficient, it is still very expensive to investigate the effects of multiple stages on the aeroelastic characteristics. In order to investigate the effects of multiple stages, a two-dimensional multi stage aeroelastic solver was also developed under this task, in collaboration with Dr. T. S. R. Reddy of the University of Toledo. Both of these solvers were applied to several test cases and validated against experimental data, where available.
Response of millet and sorghum to a varying water supply around the primary and nodal roots
Rostamza, M.; Richards, R. A.; Watt, M.
2013-01-01
Background and Aims Cereals have two root systems. The primary system originates from the embryo when the seed germinates and can support the plant until it produces grain. The nodal system can emerge from stem nodes throughout the plant's life; its value for yield is unclear and depends on the environment. The aim of this study was to test the role of nodal roots of sorghum and millet in plant growth in response to variation in soil moisture. Sorghum and millet were chosen as both are adapted to dry conditions. Methods Sorghum and millet were grown in a split-pot system that allowed the primary and nodal roots to be watered separately. Key Results When primary and nodal roots were watered (12 % soil water content; SWC), millet nodal roots were seven times longer than those of sorghum and six times longer than millet plants in dry treatments, mainly from an 8-fold increase in branch root length. When soil was allowed to dry in both compartments, millet nodal roots responded and grew 20 % longer branch roots than in the well-watered control. Sorghum nodal roots were unchanged. When only primary roots received water, nodal roots of both species emerged and elongated into extremely dry soil (0·6–1·5 % SWC), possibly with phloem-delivered water from the primary roots in the moist inner pot. Nodal roots were thick, short, branchless and vertical, indicating a tropism that was more pronounced in millet. Total nodal root length increased in both species when the dry soil was covered with plastic, suggesting that stubble retention or leaf mulching could facilitate nodal roots reaching deeper moist layers in dry climates. Greater nodal root length in millet than in sorghum was associated with increased shoot biomass, water uptake and water use efficiency (shoot mass per water). Millet had a more plastic response than sorghum to moisture around the nodal roots due to (1) faster growth and progression through ontogeny for earlier nodal root branch length and (2
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. PMID:21195476
Performance Models for the Spike Banded Linear System Solver
Manguoglu, Murat; Saied, Faisal; Sameh, Ahmed; Grama, Ananth
2011-01-01
With availability of large-scale parallel platforms comprised of tens-of-thousands of processors and beyond, there is significant impetus for the development of scalable parallel sparse linear system solvers and preconditioners. An integral part of this design process is the development of performance models capable of predicting performance and providing accurate cost models for the solvers and preconditioners. There has been some work in the past on characterizing performance of the iterative solvers themselves. In this paper, we investigate the problem of characterizing performance and scalability of banded preconditioners. Recent work has demonstrated the superior convergence properties and robustness of banded preconditioners,more » compared to state-of-the-art ILU family of preconditioners as well as algebraic multigrid preconditioners. Furthermore, when used in conjunction with efficient banded solvers, banded preconditioners are capable of significantly faster time-to-solution. Our banded solver, the Truncated Spike algorithm is specifically designed for parallel performance and tolerance to deep memory hierarchies. Its regular structure is also highly amenable to accurate performance characterization. Using these characteristics, we derive the following results in this paper: (i) we develop parallel formulations of the Truncated Spike solver, (ii) we develop a highly accurate pseudo-analytical parallel performance model for our solver, (iii) we show excellent predication capabilities of our model – based on which we argue the high scalability of our solver. Our pseudo-analytical performance model is based on analytical performance characterization of each phase of our solver. These analytical models are then parameterized using actual runtime information on target platforms. An important consequence of our performance models is that they reveal underlying performance bottlenecks in both serial and parallel formulations. All of our results are validated
Performance of Nonlinear Finite-Difference Poisson-Boltzmann Solvers.
Cai, Qin; Hsieh, Meng-Juei; Wang, Jun; Luo, Ray
2010-01-12
We implemented and optimized seven finite-difference solvers for the full nonlinear Poisson-Boltzmann equation in biomolecular applications, including four relaxation methods, one conjugate gradient method, and two inexact Newton methods. The performance of the seven solvers was extensively evaluated with a large number of nucleic acids and proteins. Worth noting is the inexact Newton method in our analysis. We investigated the role of linear solvers in its performance by incorporating the incomplete Cholesky conjugate gradient and the geometric multigrid into its inner linear loop. We tailored and optimized both linear solvers for faster convergence rate. In addition, we explored strategies to optimize the successive over-relaxation method to reduce its convergence failures without too much sacrifice in its convergence rate. Specifically we attempted to adaptively change the relaxation parameter and to utilize the damping strategy from the inexact Newton method to improve the successive over-relaxation method. Our analysis shows that the nonlinear methods accompanied with a functional-assisted strategy, such as the conjugate gradient method and the inexact Newton method, can guarantee convergence in the tested molecules. Especially the inexact Newton method exhibits impressive performance when it is combined with highly efficient linear solvers that are tailored for its special requirement. PMID:24723843
The novel high-performance 3-D MT inverse solver
NASA Astrophysics Data System (ADS)
Kruglyakov, Mikhail; Geraskin, Alexey; Kuvshinov, Alexey
2016-04-01
We present novel, robust, scalable, and fast 3-D magnetotelluric (MT) inverse solver. The solver is written in multi-language paradigm to make it as efficient, readable and maintainable as possible. Separation of concerns and single responsibility concepts go through implementation of the solver. As a forward modelling engine a modern scalable solver extrEMe, based on contracting integral equation approach, is used. Iterative gradient-type (quasi-Newton) optimization scheme is invoked to search for (regularized) inverse problem solution, and adjoint source approach is used to calculate efficiently the gradient of the misfit. The inverse solver is able to deal with highly detailed and contrasting models, allows for working (separately or jointly) with any type of MT responses, and supports massive parallelization. Moreover, different parallelization strategies implemented in the code allow optimal usage of available computational resources for a given problem statement. To parameterize an inverse domain the so-called mask parameterization is implemented, which means that one can merge any subset of forward modelling cells in order to account for (usually) irregular distribution of observation sites. We report results of 3-D numerical experiments aimed at analysing the robustness, performance and scalability of the code. In particular, our computational experiments carried out at different platforms ranging from modern laptops to HPC Piz Daint (6th supercomputer in the world) demonstrate practically linear scalability of the code up to thousands of nodes.
Adaptive kinetic-fluid solvers for heterogeneous computing architectures
NASA Astrophysics Data System (ADS)
Zabelok, Sergey; Arslanbekov, Robert; Kolobov, Vladimir
2015-12-01
We show feasibility and benefits of porting an adaptive multi-scale kinetic-fluid code to CPU-GPU systems. Challenges are due to the irregular data access for adaptive Cartesian mesh, vast difference of computational cost between kinetic and fluid cells, and desire to evenly load all CPUs and GPUs during grid adaptation and algorithm refinement. Our Unified Flow Solver (UFS) combines Adaptive Mesh Refinement (AMR) with automatic cell-by-cell selection of kinetic or fluid solvers based on continuum breakdown criteria. Using GPUs enables hybrid simulations of mixed rarefied-continuum flows with a million of Boltzmann cells each having a 24 × 24 × 24 velocity mesh. We describe the implementation of CUDA kernels for three modules in UFS: the direct Boltzmann solver using the discrete velocity method (DVM), the Direct Simulation Monte Carlo (DSMC) solver, and a mesoscopic solver based on the Lattice Boltzmann Method (LBM), all using adaptive Cartesian mesh. Double digit speedups on single GPU and good scaling for multi-GPUs have been demonstrated.
Approximate Schur complement preconditioning of the lowest order nodal discretizations
Moulton, J.D.; Ascher, U.M.; Morel, J.E.
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
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 systems with maximal domain of exactness for Gaussian quadrature formulas
NASA Astrophysics Data System (ADS)
Berriochoa, E.; Cachafeiro, A.
2008-03-01
The aim of this work is to study quadrature formulas for measures on the complex plane. The novelty of our contribution is to consider the exactness on subspaces of polynomials on the variables z and . Using this approach we characterize, in a unified way, the classical nodal systems for measures on the real line and the nodal systems for measures on the unit circle, which are based on para-orthogonal polynomials. We also characterize the nodal systems on the unit circle, which are not based on para-orthogonal polynomials (only for the case of nodal systems with 1 or 2 points).
Nodal line optimization and its application to violin top plate design
NASA Astrophysics Data System (ADS)
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.
Translational significance of Nodal, Cripto-1 and Notch4 in adult nevi
Strizzi, Luigi; Margaryan, Naira V.; Gerami, Pedram; Haghighat, Zahra; Harms, Paul W.; Madonna, Gabriele; Botti, Gerardo; Ascierto, Paolo A.; Hendrix, Mary J.C.
2016-01-01
The TGF-β associated growth factor Nodal is highly expressed in aggressive metastatic melanoma. Determining the risk for melanomagenesis from Nodal expression in nevi prior to the development of melanoma may be useful for both the screening and prevention of melanoma. Tissue sections of human adult nevi with or without a history of melanoma were stained by immunohistochemistry (IHC) for Nodal, the Nodal co-receptor Cripto-1, and Notch4, which have previously been shown to be associated with Nodal expression in melanoma. The degree of Nodal, Cripto-1 and Notch4 staining was scored and correlated with available clinical data. Median IHC scores for Nodal, Cripto-1 and Notch4 expression were significantly higher in nevi removed from patients who eventually developed melanoma compared with nevi from patients with no history of melanoma. In addition, the degree of Nodal expression in nevi from patients who eventually developed melanoma correlated significantly with the Breslow depth of the melanoma. Expression of Nodal and components of its signaling pathway in nevi may represent a biomarker for selecting a unique subset of patients requiring increased surveillance for screening and prevention of melanoma.
General Equation Set Solver for Compressible and Incompressible Turbomachinery Flows
NASA Technical Reports Server (NTRS)
Sondak, Douglas L.; Dorney, Daniel J.
2002-01-01
Turbomachines for propulsion applications operate with many different working fluids and flow conditions. The flow may be incompressible, such as in the liquid hydrogen pump in a rocket engine, or supersonic, such as in the turbine which may drive the hydrogen pump. Separate codes have traditionally been used for incompressible and compressible flow solvers. The General Equation Set (GES) method can be used to solve both incompressible and compressible flows, and it is not restricted to perfect gases, as are many compressible-flow turbomachinery solvers. An unsteady GES turbomachinery flow solver has been developed and applied to both air and water flows through turbines. It has been shown to be an excellent alternative to maintaining two separate codes.
A multiple right hand side iterative solver for history matching
Killough, J.E.; Sharma, Y.; Dupuy, A.; Bissell, R.; Wallis, J.
1995-12-31
History matching of oil and gas reservoirs can be accelerated by directly calculating the gradients of observed quantities (e.g., well pressure) with respect to the adjustable reserve parameters (e.g., permeability). This leads to a set of linear equations which add a significant overhead to the full simulation run without gradients. Direct Gauss elimination solvers can be used to address this problem by performing the factorization of the matrix only once and then reusing the factor matrix for the solution of the multiple right hand sides. This is a limited technique, however. Experience has shown that problems with greater than few thousand cells may not be practical for direct solvers because of computation time and memory limitations. This paper discusses the implementation of a multiple right hand side iterative linear equation solver (MRHS) for a system of adjoint equations to significantly enhance the performance of a gradient simulator.
Gpu Implementation of a Viscous Flow Solver on Unstructured Grids
NASA Astrophysics Data System (ADS)
Xu, Tianhao; Chen, Long
2016-06-01
Graphics processing units have gained popularities in scientific computing over past several years due to their outstanding parallel computing capability. Computational fluid dynamics applications involve large amounts of calculations, therefore a latest GPU card is preferable of which the peak computing performance and memory bandwidth are much better than a contemporary high-end CPU. We herein focus on the detailed implementation of our GPU targeting Reynolds-averaged Navier-Stokes equations solver based on finite-volume method. The solver employs a vertex-centered scheme on unstructured grids for the sake of being capable of handling complex topologies. Multiple optimizations are carried out to improve the memory accessing performance and kernel utilization. Both steady and unsteady flow simulation cases are carried out using explicit Runge-Kutta scheme. The solver with GPU acceleration in this paper is demonstrated to have competitive advantages over the CPU targeting one.
Two Solvers for Tractable Temporal Constraints with Preferences
NASA Technical Reports Server (NTRS)
Rossi, F.; Khatib,L.; Morris, P.; Morris, R.; Clancy, Daniel (Technical Monitor)
2002-01-01
A number of reasoning problems involving the manipulation of temporal information can naturally be viewed as implicitly inducing an ordering of potential local decisions involving time on the basis of preferences. Soft temporal constraints problems allow to describe in a natural way scenarios where events happen over time and preferences are associated to event distances and durations. In general, solving soft temporal problems require exponential time in the worst case, but there are interesting subclasses of problems which are polynomially solvable. We describe two solvers based on two different approaches for solving the same tractable subclass. For each solver we present the theoretical results it stands on, a description of the algorithm and some experimental results. The random generator used to build the problems on which tests are performed is also described. Finally, we compare the two solvers highlighting the tradeoff between performance and representational power.