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
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.
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.
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
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
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.
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.
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.
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.
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…
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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
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
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.
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.
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
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.
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.
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.
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.
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.
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
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.
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.
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].
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...
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.
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
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.
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)
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.
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.
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.
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.
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.
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 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
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
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.
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.
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.
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
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
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
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.
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
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.
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.
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.
Generalized methods and solvers for noise removal from piecewise constant signals. II. New methods
Little, Max A.; Jones, Nick S.
2011-01-01
Removing noise from signals which are piecewise constant (PWC) is a challenging signal processing problem that arises in many practical scientific and engineering contexts. In the first paper (part I) of this series of two, we presented background theory building on results from the image processing community to show that the majority of these algorithms, and more proposed in the wider literature, are each associated with a special case of a generalized functional, that, when minimized, solves the PWC denoising problem. It shows how the minimizer can be obtained by a range of computational solver algorithms. In this second paper (part II), using this understanding developed in part I, we introduce several novel PWC denoising methods, which, for example, combine the global behaviour of mean shift clustering with the local smoothing of total variation diffusion, and show example solver algorithms for these new methods. Comparisons between these methods are performed on synthetic and real signals, revealing that our new methods have a useful role to play. Finally, overlaps between the generalized methods of these two papers and others such as wavelet shrinkage, hidden Markov models, and piecewise smooth filtering are touched on. PMID:22003313
Fast Euler solver for transonic airfoils. I - Theory. II - Applications
NASA Technical Reports Server (NTRS)
Dadone, Andrea; Moretti, Gino
1988-01-01
Equations written in terms of generalized Riemann variables are presently integrated by inverting six bidiagonal matrices and two tridiagonal matrices, using an implicit Euler solver that is based on the lambda-formulation. The solution is found on a C-grid whose boundaries are very close to the airfoil. The fast solver is then applied to the computation of several flowfields on a NACA 0012 airfoil at various Mach number and alpha values, yielding results that are primarily concerned with transonic flows. The effects of grid fineness and boundary distances are analyzed; the code is found to be robust and accurate, as well as fast.
Numerical System Solver Developed for the National Cycle Program
NASA Technical Reports Server (NTRS)
Binder, Michael P.
1999-01-01
As part of the National Cycle Program (NCP), a powerful new numerical solver has been developed to support the simulation of aeropropulsion systems. This software uses a hierarchical object-oriented design. It can provide steady-state and time-dependent solutions to nonlinear and even discontinuous problems typically encountered when aircraft and spacecraft propulsion systems are simulated. It also can handle constrained solutions, in which one or more factors may limit the behavior of the engine system. Timedependent simulation capabilities include adaptive time-stepping and synchronization with digital control elements. The NCP solver is playing an important role in making the NCP a flexible, powerful, and reliable simulation package.
Comparison of homogenized and enhanced diffusion solutions of model PWR problems
Lewis, E. E.; Smith, M. A.
2012-07-01
Model problem comparisons in slab geometry are made between two forms of homogenized diffusion theory and enhanced diffusion theory. The pin-cell discontinuity factors for homogenized diffusion calculations are derived from homogenized variational nodal P1 response matrices and from standard finite differencing. Enhanced diffusion theory consists of applying quasi-reflected interface conditions to reduce variational nodal Pn response matrices to one degree of freedom per interface, without homogenization within the cell. As expected both homogenized diffusion methods preserve reaction rates exactly if the discontinuity factors are derived from the P 11 reference solutions. If no reference lattice solution is available, discontinuity factors may be approximated from single cells with reflected boundary conditions; the computational effort is then comparable to calculating the enhanced diffusion response matrices. In this situation enhanced diffusion theory gives the most accurate results and finite difference discontinuity factors the least accurate. (authors)
Symmetry Breaking in a Model for Nodal Cilia
NASA Astrophysics Data System (ADS)
Brokaw, Charles J.
2005-03-01
Nodal cilia are very short cilia found in the embryonic node on the ventral surface of early mammalian embryos. They create a right to left fluid flow that is responsible for determining the normal asymmetry of the internal organs of the mammalian body. To do this, the distal end of the cilium must circle in a counterclockwise sense. Computer simulations with 3-dimensional models of flagella allow examination of 3-dimensional movements such as those of nodal cilia. 3-dimensional circling motions of short cilia can be achieved with velocity controlled models, in which dynein activity is regulated by sliding velocity. If dyneins on one outer doublet are controlled by the sliding velocity experienced by that doublet, the system is symmetric, and the 3-dimensional models can show either clockwise or counterclockwise circling. My computer simulations have examined two possible symmetry breaking mechanisms: 1) dyneins on doublet N are regulated by a mixture of the sliding velocities experienced by doublets N and N+1 (numbered in a clockwise direction, looking from the base). or 2) symmetry is broken by an off-axis force that produces a right-handed twist of the axoneme, consistent with observations that some dyneins can rotate their substrate microtubules in a clockwise direction.
Amyloid precursor protein at node of Ranvier modulates nodal formation.
Xu, De-En; Zhang, Wen-Min; Yang, Zara Zhuyun; Zhu, Hong-Mei; Yan, Ke; Li, Shao; Bagnard, Dominique; Dawe, Gavin S; Ma, Quan-Hong; Xiao, Zhi-Cheng
2014-01-01
Amyloid precursor protein (APP), commonly associated with Alzheimer disease, is upregulated and distributes evenly along the injured axons, and therefore, also known as a marker of demyelinating axonal injury and axonal degeneration. However, the physiological distribution and function of APP along myelinated axons was unknown. We report that APP aggregates at nodes of Ranvier (NOR) in the myelinated central nervous system (CNS) axons but not in the peripheral nervous system (PNS). At CNS NORs, APP expression co-localizes with tenascin-R and is flanked by juxtaparanodal potassium channel expression demonstrating that APP localized to NOR. In APP-knockout (KO) mice, nodal length is significantly increased, while sodium channels are still clustered at NORs. Moreover, APP KO and APP-overexpressing transgenic (APP TG) mice exhibited a decreased and an increased thickness of myelin in spinal cords, respectively, although the changes are limited in comparison to their littermate WT mice. The thickness of myelin in APP KO sciatic nerve also increased in comparison to that in WT mice. Our observations indicate that APP acts as a novel component at CNS NORs, modulating nodal formation and has minor effects in promoting myelination. PMID:25482638
Lin, J; Huang, S; Lai, L; Lin, L; Chen, J; Tseng, Y; Lien, W
2000-01-01
OBJECTIVE—To search for a reliable anatomical landmark within Koch's triangle to predict the risk of atrioventricular (AV) block during radiofrequency slow pathway catheter ablation of AV nodal re-entrant tachycardia (AVNRT). PATIENTS AND METHODS—To test the hypothesis that the distal end of the AV nodal artery represents the anatomical location of the AV node, and thus could be a useful landmark for predicting the risk of AV block, 128 consecutive patients with AVNRT receiving slow pathway catheter ablation were prospectively studied in two phases. In phase I (77 patients), angiographic demonstration of the AV nodal artery and its ending was performed at the end of the ablation procedure, whereas in the subsequent phase II study (51 patients), the angiography was performed immediately before catheter ablation to assess the value of identifying this new landmark in reducing the risk of AV block. Multiple electrophysiologic and anatomical parameters were analysed. The former included the atrial activation sequence between the His bundle recording site (HBE) and the coronary sinus orifice or the catheter ablation site, either during AVNRT or during sinus rhythm. The latter included the spatial distances between the distal end of the AV nodal artery and the HBE and the final catheter ablation site, and the distance between the HBE and the tricuspid border at the coronary sinus orifice floor. RESULTS—In phase I, nine of the 77 patients had complications of transient (seven patients) or permanent (two patients) complete AV block during stepwise, anatomy guided slow pathway catheter ablation. These nine patients had a wider distance between the HBE and the distal end of the AV nodal artery, and a closer approximation of the catheter ablation site to the distal end of the AV nodal artery, which independently predicted the risk of AV block. In contrast, none of the available electrophysiologic parameters were shown to be reliable. When the distance between
NASA Astrophysics Data System (ADS)
Niu, Yang-Yao
2016-03-01
This paper is to continue our previous work in 2008 on solving a two-fluid model for compressible liquid-gas flows. We proposed a pressure-velocity based diffusion term original derived from AUSMD scheme of Wada and Liou in 1997 to enhance its robustness. The proposed AUSMD schemes have been applied to gas and liquid fluids universally to capture fluid discontinuities, such as the fluid interfaces and shock waves, accurately for the Ransom's faucet problem, air-water shock tube problems and 2D shock-water liquid interaction problems. However, the proposed scheme failed at computing liquid-gas interfaces in problems under large ratios of pressure, density and volume of fraction. The numerical instability has been remedied by Chang and Liou in 2007 using the exact Riemann solver to enhance the accuracy and stability of numerical flux across the liquid-gas interface. Here, instead of the exact Riemann solver, we propose a simple AUSMD type primitive variable Riemann solver (PVRS) which can successfully solve 1D stiffened water-air shock tube and 2D shock-gas interaction problems under large ratios of pressure, density and volume of fraction without the expensive cost of tedious computer time. In addition, the proposed approach is shown to deliver a good resolution of the shock-front, rarefaction and cavitation inside the evolution of high-speed droplet impact on the wall.
Assessment of Linear Finite-Difference Poisson-Boltzmann Solvers
Wang, Jun; Luo, Ray
2009-01-01
CPU time and memory usage are two vital issues that any numerical solvers for the Poisson-Boltzmann equation have to face in biomolecular applications. In this study we systematically analyzed the CPU time and memory usage of five commonly used finite-difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson-Boltzmann equation. It turns out that the time-limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson-Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. PMID:20063271
Navier-Stokes Solvers and Generalizations for Reacting Flow Problems
Elman, Howard C
2013-01-27
This is an overview of our accomplishments during the final term of this grant (1 September 2008 -- 30 June 2012). These fall mainly into three categories: fast algorithms for linear eigenvalue problems; solution algorithms and modeling methods for partial differential equations with uncertain coefficients; and preconditioning methods and solvers for models of computational fluid dynamics (CFD).
Assessment of linear finite-difference Poisson-Boltzmann solvers.
Wang, Jun; Luo, Ray
2010-06-01
CPU time and memory usage are two vital issues that any numerical solvers for the Poisson-Boltzmann equation have to face in biomolecular applications. In this study, we systematically analyzed the CPU time and memory usage of five commonly used finite-difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson-Boltzmann equation. It turns out that the time-limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson-Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. PMID:20063271
Advances in computational fluid dynamics solvers for modern computing environments
NASA Astrophysics Data System (ADS)
Hertenstein, Daniel; Humphrey, John R.; Paolini, Aaron L.; Kelmelis, Eric J.
2013-05-01
EM Photonics has been investigating the application of massively multicore processors to a key problem area: Computational Fluid Dynamics (CFD). While the capabilities of CFD solvers have continually increased and improved to support features such as moving bodies and adjoint-based mesh adaptation, the software architecture has often lagged behind. This has led to poor scaling as core counts reach the tens of thousands. In the modern High Performance Computing (HPC) world, clusters with hundreds of thousands of cores are becoming the standard. In addition, accelerator devices such as NVIDIA GPUs and Intel Xeon Phi are being installed in many new systems. It is important for CFD solvers to take advantage of the new hardware as the computations involved are well suited for the massively multicore architecture. In our work, we demonstrate that new features in NVIDIA GPUs are able to empower existing CFD solvers by example using AVUS, a CFD solver developed by the Air Force Research Labratory (AFRL) and the Volcanic Ash Advisory Center (VAAC). The effort has resulted in increased performance and scalability without sacrificing accuracy. There are many well-known codes in the CFD space that can benefit from this work, such as FUN3D, OVERFLOW, and TetrUSS. Such codes are widely used in the commercial, government, and defense sectors.
Coordinate Projection-based Solver for ODE with Invariants
Serban, Radu
2008-04-08
CPODES is a general purpose (serial and parallel) solver for systems of ordinary differential equation (ODE) with invariants. It implements a coordinate projection approach using different types of projection (orthogonal or oblique) and one of several methods for the decompositon of the Jacobian of the invariant equations.
Intellectual Abilities That Discriminate Good and Poor Problem Solvers.
ERIC Educational Resources Information Center
Meyer, Ruth Ann
1981-01-01
This study compared good and poor fourth-grade problem solvers on a battery of 19 "reference" tests for verbal, induction, numerical, word fluency, memory, perceptual speed, and simple visualization abilities. Results suggest verbal, numerical, and especially induction abilities are important to successful mathematical problem solving. (MP)
NASA Astrophysics Data System (ADS)
White, Christopher J.; Stone, James M.; Gammie, Charles F.
2016-08-01
We present a new general relativistic magnetohydrodynamics (GRMHD) code integrated into the Athena++ framework. Improving upon the techniques used in most GRMHD codes, ours allows the use of advanced, less diffusive Riemann solvers, in particular HLLC and HLLD. We also employ a staggered-mesh constrained transport algorithm suited for curvilinear coordinate systems in order to maintain the divergence-free constraint of the magnetic field. Our code is designed to work with arbitrary stationary spacetimes in one, two, or three dimensions, and we demonstrate its reliability through a number of tests. We also report on its promising performance and scalability.
Diffusion in Colocation Contact Networks: The Impact of Nodal Spatiotemporal Dynamics
Thomas, Bryce; Jurdak, Raja; Zhao, Kun; Atkinson, Ian
2016-01-01
Temporal contact networks are studied to understand dynamic spreading phenomena such as communicable diseases or information dissemination. To establish how spatiotemporal dynamics of nodes impact spreading potential in colocation contact networks, we propose “inducement-shuffling” null models which break one or more correlations between times, locations and nodes. By reconfiguring the time and/or location of each node’s presence in the network, these models induce alternative sets of colocation events giving rise to contact networks with varying spreading potential. This enables second-order causal reasoning about how correlations in nodes’ spatiotemporal preferences not only lead to a given contact network but ultimately influence the network’s spreading potential. We find the correlation between nodes and times to be the greatest impediment to spreading, while the correlation between times and locations slightly catalyzes spreading. Under each of the presented null models we measure both the number of contacts and infection prevalence as a function of time, with the surprising finding that the two have no direct causality. PMID:27501240
Nodal versus Total Axonal Strain and the Role of Cholesterol in Traumatic Brain Injury.
Zhu, Feng; Gatti, Domenico L; Yang, King H
2016-05-01
Traumatic brain injury (TBI) is a health threat that affects every year millions of people involved in motor vehicle and sporting accidents, and thousands of soldiers in battlefields. Diffuse axonal injury (DAI) is one of the most frequent types of TBI leading to death. In DAI, the initial traumatic event is followed by a cascade of biochemical changes that take time to develop in full, so that symptoms may not become apparent until days or weeks after the original injury. Hence, DAI is a dynamic process, and the opportunity exists to prevent its progression provided the initial trauma can be predicted at the molecular level. Here, we present preliminary evidence from micro-finite element (FE) simulations that the mechanical response of central nervous system myelinated fibers is dependent on the axonal diameter, the ratio between axon diameter and fiber diameter (g-ratio), the microtubules density, and the cholesterol concentration in the axolemma and myelin. A key outcome of the simulations is that there is a significant difference between the overall level of strain in a given axonal segment and the level of local strain in the Ranvier nodes contained in that segment, with the nodal strain being much larger than the total strain. We suggest that the acquisition of this geometric and biochemical information by means of already available high resolution magnetic resonance imaging techniques, and its incorporation in current FE models of the brain will enhance the models capacity to predict the site and magnitude of primary axonal damage upon TBI. PMID:26393780
Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers
Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em
2015-09-15
Graphical abstract: - Abstract: Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM)
Decision Engines for Software Analysis Using Satisfiability Modulo Theories Solvers
NASA Technical Reports Server (NTRS)
Bjorner, Nikolaj
2010-01-01
The area of software analysis, testing and verification is now undergoing a revolution thanks to the use of automated and scalable support for logical methods. A well-recognized premise is that at the core of software analysis engines is invariably a component using logical formulas for describing states and transformations between system states. The process of using this information for discovering and checking program properties (including such important properties as safety and security) amounts to automatic theorem proving. In particular, theorem provers that directly support common software constructs offer a compelling basis. Such provers are commonly called satisfiability modulo theories (SMT) solvers. Z3 is a state-of-the-art SMT solver. It is developed at Microsoft Research. It can be used to check the satisfiability of logical formulas over one or more theories such as arithmetic, bit-vectors, lists, records and arrays. The talk describes some of the technology behind modern SMT solvers, including the solver Z3. Z3 is currently mainly targeted at solving problems that arise in software analysis and verification. It has been applied to various contexts, such as systems for dynamic symbolic simulation (Pex, SAGE, Vigilante), for program verification and extended static checking (Spec#/Boggie, VCC, HAVOC), for software model checking (Yogi, SLAM), model-based design (FORMULA), security protocol code (F7), program run-time analysis and invariant generation (VS3). We will describe how it integrates support for a variety of theories that arise naturally in the context of the applications. There are several new promising avenues and the talk will touch on some of these and the challenges related to SMT solvers. Proceedings
Migration of vectorized iterative solvers to distributed memory architectures
Pommerell, C.; Ruehl, R.
1994-12-31
Both necessity and opportunity motivate the use of high-performance computers for iterative linear solvers. Necessity results from the size of the problems being solved-smaller problems are often better handled by direct methods. Opportunity arises from the formulation of the iterative methods in terms of simple linear algebra operations, even if this {open_quote}natural{close_quotes} parallelism is not easy to exploit in irregularly structured sparse matrices and with good preconditioners. As a result, high-performance implementations of iterative solvers have attracted a lot of interest in recent years. Most efforts are geared to vectorize or parallelize the dominating operation-structured or unstructured sparse matrix-vector multiplication, or to increase locality and parallelism by reformulating the algorithm-reducing global synchronization in inner products or local data exchange in preconditioners. Target architectures for iterative solvers currently include mostly vector supercomputers and architectures with one or few optimized (e.g., super-scalar and/or super-pipelined RISC) processors and hierarchical memory systems. More recently, parallel computers with physically distributed memory and a better price/performance ratio have been offered by vendors as a very interesting alternative to vector supercomputers. However, programming comfort on such distributed memory parallel processors (DMPPs) still lags behind. Here the authors are concerned with iterative solvers and their changing computing environment. In particular, they are considering migration from traditional vector supercomputers to DMPPs. Application requirements force one to use flexible and portable libraries. They want to extend the portability of iterative solvers rather than reimplementing everything for each new machine, or even for each new architecture.
Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers
NASA Astrophysics Data System (ADS)
Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em
2015-09-01
Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM).
Carl, Matthias; Bianco, Isaac H.; Bajoghli, Baubak; Aghaallaei, Narges; Czerny, Thomas; Wilson, Stephen W.
2007-01-01
Summary Nodal activity in the left lateral plate mesoderm (LPM) is required to activate left-sided Nodal signaling in the epithalamic region of the zebrafish forebrain. Epithalamic Nodal signaling subsequently determines the laterality of neuroanatomical asymmetries. We show that overactivation of Wnt/Axin1/β-catenin signaling during late gastrulation leads to bilateral epithalamic expression of Nodal pathway genes independently of LPM Nodal signaling. This is consistent with a model whereby epithalamic Nodal signaling is normally bilaterally repressed, with Nodal signaling from the LPM unilaterally alleviating repression. We suggest that Wnt signaling regulates the establishment of the bilateral repression. We identify a second role for the Wnt pathway in the left/right regulation of LPM Nodal pathway gene expression, and finally, we show that at later stages Axin1 is required for the elaboration of concordant neuroanatomical asymmetries. PMID:17678853
Less may be more: nodal treatment in neck positive head neck cancer patients.
Studer, Gabriela; Huber, Gerhard F; Holz, Edna; Glanzmann, Christoph
2016-06-01
Ongoing debates about the need and extent of planned neck dissection (PND), and required nodal radiation doses volumes lead to this evaluation. Aim was to assess nodal control after definitive intensity modulated radiation therapy (IMRT ± systemic therapy) followed by PND in our head neck cancer cohort with advanced nodal disease. Between 01/2005 and 12/2013, 99 squamous cell cancer HNC patients with pre-therapeutic nodal metastasis ≥3 cm were treated with definitive IMRT followed by PND. In addition, outcome in 103 patients with nodal relapse after IMRT and observation only (no-PND cohort) were analyzed. Prior to PND, PET-CT, fine needle aspirations, ultrasound and palpation were assessed regarding its predictive value. Patterns of nodal relapse were assessed in patients with isolated neck failure after definitive IMRT alone. 70/99 (70 %) PND specimens showed histopathological complete response (hCR), which translated into statistically significantly superior survival compared with partial response (hPR) with 4-year overall survival, disease specific survival and nodal control rates of 90/83/96 vs 67/60/78 % (p = 0.002/0.001/0.003). 1/99 patient developed isolated subsequent nodal disease. 64/2147 removed nodes contained viable tumor (3 %). Predictive information of the performed diagnostic investigations was not reliable. 17/70 hCR patients showed true negative findings in available three to four investigations (0/29 hPR). 27/103 no-PND patients developed isolated neck disease (26 %) with successful salvage in 21/24 [88 %, or 21/27 (78 %)]. Nearly all failures occurred in the prior nodal gross tumor volume area. A more restrictive approach regarding PND and/or nodal IMRT dose-volumes may be justified. PMID:25920604
Nodal promotes invasive phenotypes via a Mitogen Activated Protein Kinase-dependent pathway
Quail, DF; Zhang, G; Findlay, SD; Hess, DA; Postovit, LM
2016-01-01
The progression of cancer from localized to invasive disease is requisite for metastasis, and is often characterized by epithelial-to-mesenchymal transition (EMT) and alterations in cellular adhesion and migration. Studies have shown that this transition is associated with an up-regulation of embryonic stem cell-associated genes, resulting in a dedifferentiated phenotype and poor patient prognosis. Nodal is an embryonic factor that plays a critical role in promoting early invasive events during development. Nodal is silenced as stem cells differentiate; however, it re-emerges in adult life during placentation and mammary gland development, and is aberrantly expressed in many cancers. Here, we show that Nodal over-expression, in poorly-invasive breast cancer and choriocarcinoma cells, causes increased invasion and migration in vitro. Furthermore, we show that Nodal over-expression in these epithelial cancer types induces an EMT-like event concomitant with the internalization of E-Cadherin. This ability of Nodal to promote cellular invasion and EMT-like phenomena is dependent upon the phosphorylation of ERK1/2. Since Nodal normally signals through SMADs, these findings lend insight into an alternative pathway that is hijacked by this protein in cancer. To evaluate the clinical implications of our results, we show that Nodal inhibition reduces liver tumor burden in a model of spontaneous breast cancer metastasis in vivo, and that Nodal loss-of-function in aggressive breast cancer lines results in a decrease in invasive phenotypes. Our results demonstrate that Nodal is involved in promoting invasion in multiple cellular contexts, and that Nodal inhibition may be useful as a therapeutic target for patients with progressive disease. PMID:23334323
Nodal weighting factor method for ex-core fast neutron fluence evaluation
Chiang, R. T.
2012-07-01
The nodal weighting factor method is developed for evaluating ex-core fast neutron flux in a nuclear reactor by utilizing adjoint neutron flux, a fictitious unit detector cross section for neutron energy above 1 or 0.1 MeV, the unit fission source, and relative assembly nodal powers. The method determines each nodal weighting factor for ex-core neutron fast flux evaluation by solving the steady-state adjoint neutron transport equation with a fictitious unit detector cross section for neutron energy above 1 or 0.1 MeV as the adjoint source, by integrating the unit fission source with a typical fission spectrum to the solved adjoint flux over all energies, all angles and given nodal volume, and by dividing it with the sum of all nodal weighting factors, which is a normalization factor. Then, the fast neutron flux can be obtained by summing the various relative nodal powers times the corresponding nodal weighting factors of the adjacent significantly contributed peripheral assembly nodes and times a proper fast neutron attenuation coefficient over an operating period. A generic set of nodal weighting factors can be used to evaluate neutron fluence at the same location for similar core design and fuel cycles, but the set of nodal weighting factors needs to be re-calibrated for a transition-fuel-cycle. This newly developed nodal weighting factor method should be a useful and simplified tool for evaluating fast neutron fluence at selected locations of interest in ex-core components of contemporary nuclear power reactors. (authors)
2d PDE Linear Symmetric Matrix Solver
Energy Science and Technology Software Center (ESTSC)
1983-10-01
ICCG2 (Incomplete Cholesky factorized Conjugate Gradient algorithm for 2d symmetric problems) was developed to solve a linear symmetric matrix system arising from a 9-point discretization of two-dimensional elliptic and parabolic partial differential equations found in plasma physics applications, such as resistive MHD, spatial diffusive transport, and phase space transport (Fokker-Planck equation) problems. These problems share the common feature of being stiff and requiring implicit solution techniques. When these parabolic or elliptic PDE''s are discretized withmore » finite-difference or finite-element methods,the resulting matrix system is frequently of block-tridiagonal form. To use ICCG2, the discretization of the two-dimensional partial differential equation and its boundary conditions must result in a block-tridiagonal supermatrix composed of elementary tridiagonal matrices. The incomplete Cholesky conjugate gradient algorithm is used to solve the linear symmetric matrix equation. Loops are arranged to vectorize on the Cray1 with the CFT compiler, wherever possible. Recursive loops, which cannot be vectorized, are written for optimum scalar speed. For matrices lacking symmetry, ILUCG2 should be used. Similar methods in three dimensions are available in ICCG3 and ILUCG3. A general source containing extensions and macros, which must be processed by a pre-compiler to obtain the standard FORTRAN source, is provided along with the standard FORTRAN source because it is believed to be more readable. The pre-compiler is not included, but pre-compilation may be performed by a text editor as described in the UCRL-88746 Preprint.« less
2d PDE Linear Asymmetric Matrix Solver
Energy Science and Technology Software Center (ESTSC)
1983-10-01
ILUCG2 (Incomplete LU factorized Conjugate Gradient algorithm for 2d problems) was developed to solve a linear asymmetric matrix system arising from a 9-point discretization of two-dimensional elliptic and parabolic partial differential equations found in plasma physics applications, such as plasma diffusion, equilibria, and phase space transport (Fokker-Planck equation) problems. These equations share the common feature of being stiff and requiring implicit solution techniques. When these parabolic or elliptic PDE''s are discretized with finite-difference or finite-elementmore » methods, the resulting matrix system is frequently of block-tridiagonal form. To use ILUCG2, the discretization of the two-dimensional partial differential equation and its boundary conditions must result in a block-tridiagonal supermatrix composed of elementary tridiagonal matrices. A generalization of the incomplete Cholesky conjugate gradient algorithm is used to solve the matrix equation. Loops are arranged to vectorize on the Cray1 with the CFT compiler, wherever possible. Recursive loops, which cannot be vectorized, are written for optimum scalar speed. For problems having a symmetric matrix ICCG2 should be used since it runs up to four times faster and uses approximately 30% less storage. Similar methods in three dimensions are available in ICCG3 and ILUCG3. A general source, containing extensions and macros, which must be processed by a pre-compiler to obtain the standard FORTRAN source, is provided along with the standard FORTRAN source because it is believed to be more readable. The pre-compiler is not included, but pre-compilation may be performed by a text editor as described in the UCRL-88746 Preprint.« less
Efficient three-dimensional Poisson solvers in open rectangular conducting pipe
NASA Astrophysics Data System (ADS)
Qiang, Ji
2016-06-01
Three-dimensional (3D) Poisson solver plays an important role in the study of space-charge effects on charged particle beam dynamics in particle accelerators. In this paper, we propose three new 3D Poisson solvers for a charged particle beam in an open rectangular conducting pipe. These three solvers include a spectral integrated Green function (IGF) solver, a 3D spectral solver, and a 3D integrated Green function solver. These solvers effectively handle the longitudinal open boundary condition using a finite computational domain that contains the beam itself. This saves the computational cost of using an extra larger longitudinal domain in order to set up an appropriate finite boundary condition. Using an integrated Green function also avoids the need to resolve rapid variation of the Green function inside the beam. The numerical operational cost of the spectral IGF solver and the 3D IGF solver scales as O(N log(N)) , where N is the number of grid points. The cost of the 3D spectral solver scales as O(Nn N) , where Nn is the maximum longitudinal mode number. We compare these three solvers using several numerical examples and discuss the advantageous regime of each solver in the physical application.
Space-angle approximations in the variational nodal method.
Lewis, E. E.; Palmiotti, G.; Taiwo, T.
1999-03-12
The variational nodal method is formulated such that the angular and spatial approximations maybe examined separately. Spherical harmonic, simplified spherical harmonic, and discrete ordinate approximations are coupled to the primal hybrid finite element treatment of the spatial variables. Within this framework, two classes of spatial trial functions are presented: (1) orthogonal polynomials for the treatment of homogeneous nodes and (2) bilinear finite subelement trial functions for the treatment of fuel assembly sized nodes in which fuel-pin cell cross sections are represented explicitly. Polynomial and subelement trial functions are applied to benchmark water-reactor problems containing MOX fuel using spherical harmonic and simplified spherical harmonic approximations. The resulting accuracy and computing costs are compared.
Typical nodal calcifications in the maxillofacial region: a case report
Wu, Guomin; Sun, Xiumei; Ni, Shilei; Zhang, Zhimin
2014-01-01
Multiple nodal calcifications in the maxillofacial region are very rare. This case report described a 49-year-old female patient diagnosed with calcified lymph nodes due to chronic inflammation of the lymphatic nodes, including the parotid lymphatic nodes, the posterior auricular lymphatic nodes and submandibular lymphatic nodes in the right maxillofacial region. In clinical practice, we conducted ultrasonography, three-dimensional reconstruction of CT and sialography make a preliminary diagnosis. Then we took surgery, while removing the calcified blocks within the lymphatic node and cleaning the wound cavity. After surgery, we used anti-inflammatory therapy for one week. Six months follow-up indicated no evidence of other calcified lymph nodes infection. PMID:25356188
CAISO flicks switch on nodal scheme and lights stay on
2009-06-15
In 2000-01, two years after introducing a competitive wholesale power auction in California - with a separate day-ahead zonal market operated by the California Power Exchange and a zonal market for ancillary services and balancing energy operated by the California Independent System Operator (CAISO) - the California market collapsed from exorbitant prices, flagrant gaming, and abuse of market power. Nine years later, CAISO introduced a nodal pricing auction for the wholesale market in April, replacing the zonal scheme, which was among many causes of the original market's demise. With nearly 3,000 nodes on the network, high prices in one region do not affect prices everywhere on the system. After investing some $200 million to upgrade the software, countless delays, and 18 months of market simulation and testing, the new auction was introduced and nothing unusual happened.
Contemporary Management of Recurrent Nodal Disease in Differentiated Thyroid Carcinoma.
Na'ara, Shorook; Amit, Moran; Fridman, Eran; Gil, Ziv
2016-01-01
Differentiated thyroid carcinoma (DTC) comprises over 90% of thyroid tumors and includes papillary and follicular carcinomas. Patients with DTC have an excellent prognosis, with a 10-year survival rate of over 90%. However, the risk of recurrent tumor ranges between 5% and 30% within 10 years of the initial diagnosis. Cervical lymph node disease accounts for the majority of recurrences and in most cases is detected during follow-up by ultrasound or elevated levels of serum thyroglobulin. Recurrent disease is accompanied by increased morbidity. The mainstay of treatment of nodal recurrence is surgical management. We provide an overview of the literature addressing surgical management of recurrent or persistent lymph node disease in patients with DTC. PMID:26886954
Contemporary Management of Recurrent Nodal Disease in Differentiated Thyroid Carcinoma
Na’ara, Shorook; Amit, Moran; Fridman, Eran; Gil, Ziv
2016-01-01
Differentiated thyroid carcinoma (DTC) comprises over 90% of thyroid tumors and includes papillary and follicular carcinomas. Patients with DTC have an excellent prognosis, with a 10-year survival rate of over 90%. However, the risk of recurrent tumor ranges between 5% and 30% within 10 years of the initial diagnosis. Cervical lymph node disease accounts for the majority of recurrences and in most cases is detected during follow-up by ultrasound or elevated levels of serum thyroglobulin. Recurrent disease is accompanied by increased morbidity. The mainstay of treatment of nodal recurrence is surgical management. We provide an overview of the literature addressing surgical management of recurrent or persistent lymph node disease in patients with DTC. PMID:26886954
ProNodal acts via FGFR3 to govern duration of Shh expression in the prechordal mesoderm
Ellis, Pamela S.; Burbridge, Sarah; Soubes, Sandrine; Ohyama, Kyoji; Ben-Haim, Nadav; Chen, Canhe; Dale, Kim; Shen, Michael M.; Constam, Daniel; Placzek, Marysia
2015-01-01
The secreted glycoprotein sonic hedgehog (Shh) is expressed in the prechordal mesoderm, where it plays a crucial role in induction and patterning of the ventral forebrain. Currently little is known about how Shh is regulated in prechordal tissue. Here we show that in the embryonic chick, Shh is expressed transiently in prechordal mesoderm, and is governed by unprocessed Nodal. Exposure of prechordal mesoderm microcultures to Nodal-conditioned medium, the Nodal inhibitor CerS, or to an ALK4/5/7 inhibitor reveals that Nodal is required to maintain both Shh and Gsc expression, but whereas Gsc is largely maintained through canonical signalling, Nodal signals through a non-canonical route to maintain Shh. Further, Shh expression can be maintained by a recombinant Nodal cleavage mutant, proNodal, but not by purified mature Nodal. A number of lines of evidence suggest that proNodal acts via FGFR3. ProNodal and FGFR3 co-immunoprecipitate and proNodal increases FGFR3 tyrosine phosphorylation. In microcultures, soluble FGFR3 abolishes Shh without affecting Gsc expression. Further, prechordal mesoderm cells in which Fgfr3 expression is reduced by Fgfr3 siRNA fail to bind to proNodal. Finally, targeted electroporation of Fgfr3 siRNA to prechordal mesoderm in vivo results in premature Shh downregulation without affecting Gsc. We report an inverse correlation between proNodal-FGFR3 signalling and pSmad1/5/8, and show that proNodal-FGFR3 signalling antagonises BMP-mediated pSmad1/5/8 signalling, which is poised to downregulate Shh. Our studies suggest that proNodal/FGFR3 signalling governs Shh duration by repressing canonical BMP signalling, and that local BMPs rapidly silence Shh once endogenous Nodal-FGFR3 signalling is downregulated. PMID:26417042
ProNodal acts via FGFR3 to govern duration of Shh expression in the prechordal mesoderm.
Ellis, Pamela S; Burbridge, Sarah; Soubes, Sandrine; Ohyama, Kyoji; Ben-Haim, Nadav; Chen, Canhe; Dale, Kim; Shen, Michael M; Constam, Daniel; Placzek, Marysia
2015-11-15
The secreted glycoprotein sonic hedgehog (Shh) is expressed in the prechordal mesoderm, where it plays a crucial role in induction and patterning of the ventral forebrain. Currently little is known about how Shh is regulated in prechordal tissue. Here we show that in the embryonic chick, Shh is expressed transiently in prechordal mesoderm, and is governed by unprocessed Nodal. Exposure of prechordal mesoderm microcultures to Nodal-conditioned medium, the Nodal inhibitor CerS, or to an ALK4/5/7 inhibitor reveals that Nodal is required to maintain both Shh and Gsc expression, but whereas Gsc is largely maintained through canonical signalling, Nodal signals through a non-canonical route to maintain Shh. Further, Shh expression can be maintained by a recombinant Nodal cleavage mutant, proNodal, but not by purified mature Nodal. A number of lines of evidence suggest that proNodal acts via FGFR3. ProNodal and FGFR3 co-immunoprecipitate and proNodal increases FGFR3 tyrosine phosphorylation. In microcultures, soluble FGFR3 abolishes Shh without affecting Gsc expression. Further, prechordal mesoderm cells in which Fgfr3 expression is reduced by Fgfr3 siRNA fail to bind to proNodal. Finally, targeted electroporation of Fgfr3 siRNA to prechordal mesoderm in vivo results in premature Shh downregulation without affecting Gsc. We report an inverse correlation between proNodal-FGFR3 signalling and pSmad1/5/8, and show that proNodal-FGFR3 signalling antagonises BMP-mediated pSmad1/5/8 signalling, which is poised to downregulate Shh. Our studies suggest that proNodal/FGFR3 signalling governs Shh duration by repressing canonical BMP signalling, and that local BMPs rapidly silence Shh once endogenous Nodal-FGFR3 signalling is downregulated. PMID:26417042
Drumhead surface states and topological nodal-line fermions in TlTaSe2
NASA Astrophysics Data System (ADS)
Bian, Guang; Chang, Tay-Rong; Zheng, Hao; Velury, Saavanth; Xu, Su-Yang; Neupert, Titus; Chiu, Ching-Kai; Huang, Shin-Ming; Sanchez, Daniel S.; Belopolski, Ilya; Alidoust, Nasser; Chen, Peng-Jen; Chang, Guoqing; Bansil, Arun; Jeng, Horng-Tay; Lin, Hsin; Hasan, M. Zahid
2016-03-01
A topological nodal-line semimetal is a state of matter with one-dimensional bulk nodal lines and two-dimensional so-called drumhead surface bands. Based on first-principles calculations and an effective k .p model, we theoretically propose the existence of topological nodal-line fermions in the ternary transition-metal chalcogenide TlTaSe2. The noncentrosymmetric structure and strong spin-orbit coupling give rise to spinful nodal-line bulk states which are protected by a mirror reflection symmetry of this compound. This is remarkably distinguished from other proposed nodal-line semimetals such as Cu3NPb (Zn) in which the nodal line exists only in the limit of vanishing spin-orbit coupling and thus is not as robust. In addition, we show that the drumhead surface states in TlTaSe2, which are associated with the topological nodal lines, exhibit an unconventional chiral spin texture and an exotic Lifshitz transition as a consequence of the linkage among multiple drumhead surface-state pockets.
Xantivin suppresses the activity of EGF-CFC genes to regulate nodal signaling.
Tanegashima, Kousuke; Haramoto, Yoshikazu; Yokota, Chika; Takahashi, Shuji; Asashima, Makoto
2004-06-01
Lefty, antivin and related genes act in a feedback inhibition mechanism for nodal signaling at a number of stages of vertebrate embryogenesis. To analyze the function of the feedback inhibitor of nodal signaling, Xantivin in Xenopus embryos, we designed a morpholino antisense oligonucleotide (XatvMO) for this gene. XatvMO caused the expansion of mesodermal tissue and head defects. XatvMO-injected gastrulae showed up-regulated expression of the mesodermal markers Xbra, Xwnt8, Xnot, and Chordin, suggesting expansion of the trunk-tail organizer. As expected, depletion of Xantivin also up-regulated nodal signaling as confirmed by the enhanced ectopic expression of Xantivin mRNA, a known target gene of nodal signaling. Furthermore, we investigated the relationship between Xantivin and the EGF-CFC gene FRL-1, which is a component of the nodal receptor. In animal cap assays, FRL-1 could not induce expression of nodal-responsive genes, but could up-regulate expression of these genes when FRL-1 was coinjected with a low dose of Xnr1; coinjection of Xantivin suppressed this up-regulation by FRL-1. We also found that Xantivin can rescue the caudalized phenotype induced by overexpression of FRL-1. Co-immunoprecipitation assays showed that Xantivin interacted with the EGF-CFC proteins, FRL-1 and cripto. Taken together, these results suggest that Xantivin opposes the activity of EGF-CFC genes and thereby antagonizes nodal signaling. PMID:15300508
Bodenstine, Thomas M; Chandler, Grace S; Reed, David W; Margaryan, Naira V; Gilgur, Alina; Atkinson, Janis; Ahmed, Nida; Hyser, Matthew; Seftor, Elisabeth A; Strizzi, Luigi; Hendrix, Mary J C
2016-05-01
Triple-negative breast cancer (TNBC) represents an aggressive cancer subtype characterized by the lack of expression of estrogen receptor (ER), progesterone receptor (PR) and human epidermal growth factor receptor 2 (HER2). The independence of TNBC from these growth promoting factors eliminates the efficacy of therapies which specifically target them, and limits TNBC patients to traditional systemic neo/adjuvant chemotherapy. To better understand the growth advantage of TNBC - in the absence of ER, PR and HER2, we focused on the embryonic morphogen Nodal (associated with the cancer stem cell phenotype), which is re-expressed in aggressive breast cancers. Most notably, our previous data demonstrated that inhibition of Nodal signaling in breast cancer cells reduces their tumorigenic capacity. Furthermore, inhibiting Nodal in other cancers has resulted in improved effects of chemotherapy, although the mechanisms for this remain unknown. Thus, we hypothesized that targeting Nodal in TNBC cells in combination with conventional chemotherapy may improve efficacy and represent a potential new strategy. Our preliminary data demonstrate that Nodal is highly expressed in TNBC when compared to invasive hormone receptor positive samples. Treatment of Nodal expressing TNBC cell lines with a neutralizing anti-Nodal antibody reduces the viability of cells that had previously survived treatment with the anthracycline doxorubicin. We show that inhibiting Nodal may alter response mechanisms employed by cancer cells undergoing DNA damage. These data suggest that development of therapies which target Nodal in TNBC may lead to additional treatment options in conjunction with chemotherapy regimens - by altering signaling pathways critical to cellular survival. PMID:27007464
Nodal signaling is required for closure of the anterior neural tube in zebrafish
Aquilina-Beck, Allisan; Ilagan, Kristine; Liu, Qin; Liang, Jennifer O
2007-01-01
Background Nodals are secreted signaling proteins with many roles in vertebrate development. Here, we identify a new role for Nodal signaling in regulating closure of the rostral neural tube of zebrafish. Results We find that the neural tube in the presumptive forebrain fails to close in zebrafish Nodal signaling mutants. For instance, the cells that will give rise to the pineal organ fail to move from the lateral edges of the neural plate to the midline of the diencephalon. The open neural tube in Nodal signaling mutants may be due in part to reduced function of N-cadherin, a cell adhesion molecule expressed in the neural tube and required for neural tube closure. N-cadherin expression and localization to the membrane are reduced in fish that lack Nodal signaling. Further, N-cadherin mutants and morphants have a pineal phenotype similar to that of mutants with deficiencies in the Nodal pathway. Overexpression of an activated form of the TGFβ Type I receptor Taram-A (Taram-A*) cell autonomously rescues mesendoderm formation in fish with a severe decrease in Nodal signaling. We find that overexpression of Taram-A* also corrects their open neural tube defect. This suggests that, as in mammals, the mesoderm and endoderm have an important role in regulating closure of the anterior neural tube of zebrafish. Conclusion This work helps establish a role for Nodal signals in neurulation, and suggests that defects in Nodal signaling could underlie human neural tube defects such as exencephaly, a fatal condition characterized by an open neural tube in the anterior brain. PMID:17996054
Birkeland, Andrew C.; Rosko, Andrew J.; Issa, Mohamad R.; Shuman, Andrew G.; Prince, Mark E.; Wolf, Gregory T.; Bradford, Carol R.; McHugh, Jonathan B.; Brenner, J. Chad; Spector, Matthew E.
2016-01-01
Objectives The indications for neck dissection concurrent with salvage laryngectomy in the clinically N0 setting remain unclear. Our goals were to determine the prevalence of occult nodal disease, analyze nodal disease distribution patterns, and identify predictors of occult nodal disease in a salvage laryngectomy cohort. Study Design Case series with planned data collection. Setting Tertiary academic center. Subjects Patients with persistent or recurrent laryngeal squamous cell carcinoma after radiation/chemoradiation failure undergoing salvage laryngectomy with neck dissection. Methods We analyzed a single-institution retrospective case series of patients between 1997–2014 and identified those who had clinically N0 necks (n = 203). Clinical and pathologic data, including nodal prevalence and distribution were collected, and statistical analyses were performed. Results Overall, cN0 necks had histologically positive occult nodes in 17% (n=35) of cases. Univariate predictors of occult nodal positivity included recurrent T4 stage (34% T4 vs. 12% non-T4; p=0.0003), and supraglottic subsite (28% supraglottic vs. 10% non-supraglottic; p=0.0006). Histologically positive nodes associated with supraglottic primaries were most frequently positive in ipsilateral level II and III (17% and 16%). Positive nodes for glottic SCC were most frequently positive in the ipsilateral and contralateral paratracheal nodes (11% and 9%). Conclusion Histologically positive occult nodes are identified in 17% of cN0 patients undergoing salvage laryngectomy with neck dissection. Occult nodal disease varies in frequency and distribution based upon tumor subsite. Predictors of high (>20%) occult nodal positivity include T4 tumors and supraglottic subsite. In glottic SCCs, the most frequent sites of occult nodal disease are the paratracheal nodal basins. PMID:26884365
Elliptic Solvers with Adaptive Mesh Refinement on Complex Geometries
Phillip, B.
2000-07-24
Adaptive Mesh Refinement (AMR) is a numerical technique for locally tailoring the resolution computational grids. Multilevel algorithms for solving elliptic problems on adaptive grids include the Fast Adaptive Composite grid method (FAC) and its parallel variants (AFAC and AFACx). Theory that confirms the independence of the convergence rates of FAC and AFAC on the number of refinement levels exists under certain ellipticity and approximation property conditions. Similar theory needs to be developed for AFACx. The effectiveness of multigrid-based elliptic solvers such as FAC, AFAC, and AFACx on adaptively refined overlapping grids is not clearly understood. Finally, a non-trivial eye model problem will be solved by combining the power of using overlapping grids for complex moving geometries, AMR, and multilevel elliptic solvers.
An Upwind Solver for the National Combustion Code
NASA Technical Reports Server (NTRS)
Sockol, Peter M.
2011-01-01
An upwind solver is presented for the unstructured grid National Combustion Code (NCC). The compressible Navier-Stokes equations with time-derivative preconditioning and preconditioned flux-difference splitting of the inviscid terms are used. First order derivatives are computed on cell faces and used to evaluate the shear stresses and heat fluxes. A new flux limiter uses these same first order derivatives in the evaluation of left and right states used in the flux-difference splitting. The k-epsilon turbulence equations are solved with the same second-order method. The new solver has been installed in a recent version of NCC and the resulting code has been tested successfully in 2D on two laminar cases with known solutions and one turbulent case with experimental data.
Parallel Auxiliary Space AMG Solver for $H(div)$ Problems
Kolev, Tzanio V.; Vassilevski, Panayot S.
2012-12-18
We present a family of scalable preconditioners for matrices arising in the discretization of $H(div)$ problems using the lowest order Raviart--Thomas finite elements. Our approach belongs to the class of “auxiliary space''--based methods and requires only the finite element stiffness matrix plus some minimal additional discretization information about the topology and orientation of mesh entities. Also, we provide a detailed algebraic description of the theory, parallel implementation, and different variants of this parallel auxiliary space divergence solver (ADS) and discuss its relations to the Hiptmair--Xu (HX) auxiliary space decomposition of $H(div)$ [SIAM J. Numer. Anal., 45 (2007), pp. 2483--2509] and to the auxiliary space Maxwell solver AMS [J. Comput. Math., 27 (2009), pp. 604--623]. Finally, an extensive set of numerical experiments demonstrates the robustness and scalability of our implementation on large-scale $H(div)$ problems with large jumps in the material coefficients.
Verification and Validation Studies for the LAVA CFD Solver
NASA Technical Reports Server (NTRS)
Moini-Yekta, Shayan; Barad, Michael F; Sozer, Emre; Brehm, Christoph; Housman, Jeffrey A.; Kiris, Cetin C.
2013-01-01
The verification and validation of the Launch Ascent and Vehicle Aerodynamics (LAVA) computational fluid dynamics (CFD) solver is presented. A modern strategy for verification and validation is described incorporating verification tests, validation benchmarks, continuous integration and version control methods for automated testing in a collaborative development environment. The purpose of the approach is to integrate the verification and validation process into the development of the solver and improve productivity. This paper uses the Method of Manufactured Solutions (MMS) for the verification of 2D Euler equations, 3D Navier-Stokes equations as well as turbulence models. A method for systematic refinement of unstructured grids is also presented. Verification using inviscid vortex propagation and flow over a flat plate is highlighted. Simulation results using laminar and turbulent flow past a NACA 0012 airfoil and ONERA M6 wing are validated against experimental and numerical data.
A spectral Poisson solver for kinetic plasma simulation
NASA Astrophysics Data System (ADS)
Szeremley, Daniel; Obberath, Jens; Brinkmann, Ralf
2011-10-01
Plasma resonance spectroscopy is a well established plasma diagnostic method, realized in several designs. One of these designs is the multipole resonance probe (MRP). In its idealized - geometrically simplified - version it consists of two dielectrically shielded, hemispherical electrodes to which an RF signal is applied. A numerical tool is under development which is capable of simulating the dynamics of the plasma surrounding the MRP in electrostatic approximation. In this contribution we concentrate on the specialized Poisson solver for that tool. The plasma is represented by an ensemble of point charges. By expanding both the charge density and the potential into spherical harmonics, a largely analytical solution of the Poisson problem can be employed. For a practical implementation, the expansion must be appropriately truncated. With this spectral solver we are able to efficiently solve the Poisson equation in a kinetic plasma simulation without the need of introducing a spatial discretization.
Benchmarking ICRF Full-wave Solvers for ITER
R. V. Budny, L. Berry, R. Bilato, P. Bonoli, M. Brambilla, R. J. Dumont, A. Fukuyama, R. Harvey, E. F. Jaeger, K. Indireshkumar, E. Lerche, D. McCune, C. K. Phillips, V. Vdovin, J. Wright, and members of the ITPA-IOS
2011-01-06
Abstract Benchmarking of full-wave solvers for ICRF simulations is performed using plasma profiles and equilibria obtained from integrated self-consistent modeling predictions of four ITER plasmas. One is for a high performance baseline (5.3 T, 15 MA) DT H-mode. The others are for half-field, half-current plasmas of interest for the pre-activation phase with bulk plasma ion species being either hydrogen or He4. The predicted profiles are used by six full-wave solver groups to simulate the ICRF electromagnetic fields and heating, and by three of these groups to simulate the current-drive. Approximate agreement is achieved for the predicted heating power for the DT and He4 cases. Factor of two disagreements are found for the cases with second harmonic He3 heating in bulk H cases. Approximate agreement is achieved simulating the ICRF current drive.
A functional implementation of the Jacobi eigen-solver
Boehm, A.P.W.; Hiromoto, R.E.
1993-02-01
In this paper, we describe the systematic development of two implementations of the Jacobi eigen-solver and give performance results for the MIT/Motorola Monsoon dataflow machine. Our study is carried out using MINT, the MIT Monsoon simulator. The design of these implementations follows from the mathematics of the Jacobi method, and not from a translation of an existing sequential code. The functional semantics with respect to array updates, which cause excessive array copying, has lead us to a new implementation of a parallel ``group-rotations`` algorithm first described by Sameh. Our version of this algorithm requires 0(n{sup 3}) operations, whereas Sameh`s original version requires 0(n{sup 4}) operations. The implementations are programmed in the language Id, and although Id has non-functional features, we have restricted the development of our eigen-solvers to the functional sub-set of the language.
A functional implementation of the Jacobi eigen-solver
Boehm, A.P.W. . Dept. of Computer Science); Hiromoto, R.E. )
1993-01-01
In this paper, we describe the systematic development of two implementations of the Jacobi eigen-solver and give performance results for the MIT/Motorola Monsoon dataflow machine. Our study is carried out using MINT, the MIT Monsoon simulator. The design of these implementations follows from the mathematics of the Jacobi method, and not from a translation of an existing sequential code. The functional semantics with respect to array updates, which cause excessive array copying, has lead us to a new implementation of a parallel group-rotations'' algorithm first described by Sameh. Our version of this algorithm requires 0(n[sup 3]) operations, whereas Sameh's original version requires 0(n[sup 4]) operations. The implementations are programmed in the language Id, and although Id has non-functional features, we have restricted the development of our eigen-solvers to the functional sub-set of the language.
LDRD report : parallel repartitioning for optimal solver performance.
Heaphy, Robert; Devine, Karen Dragon; Preis, Robert; Hendrickson, Bruce Alan; Heroux, Michael Allen; Boman, Erik Gunnar
2004-02-01
We have developed infrastructure, utilities and partitioning methods to improve data partitioning in linear solvers and preconditioners. Our efforts included incorporation of data repartitioning capabilities from the Zoltan toolkit into the Trilinos solver framework, (allowing dynamic repartitioning of Trilinos matrices); implementation of efficient distributed data directories and unstructured communication utilities in Zoltan and Trilinos; development of a new multi-constraint geometric partitioning algorithm (which can generate one decomposition that is good with respect to multiple criteria); and research into hypergraph partitioning algorithms (which provide up to 56% reduction of communication volume compared to graph partitioning for a number of emerging applications). This report includes descriptions of the infrastructure and algorithms developed, along with results demonstrating the effectiveness of our approaches.
On improving linear solver performance: a block variant of GMRES
Baker, A H; Dennis, J M; Jessup, E R
2004-05-10
The increasing gap between processor performance and memory access time warrants the re-examination of data movement in iterative linear solver algorithms. For this reason, we explore and establish the feasibility of modifying a standard iterative linear solver algorithm in a manner that reduces the movement of data through memory. In particular, we present an alternative to the restarted GMRES algorithm for solving a single right-hand side linear system Ax = b based on solving the block linear system AX = B. Algorithm performance, i.e. time to solution, is improved by using the matrix A in operations on groups of vectors. Experimental results demonstrate the importance of implementation choices on data movement as well as the effectiveness of the new method on a variety of problems from different application areas.
A Nonlinear Modal Aeroelastic Solver for FUN3D
NASA Technical Reports Server (NTRS)
Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.
2016-01-01
A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.
Scalable Out-of-Core Solvers on Xeon Phi Cluster
D'Azevedo, Ed F; Chan, Ki Shing; Su, Shiquan; Wong, Kwai
2015-01-01
This paper documents the implementation of a distributive out-of-core (OOC) solver for performing LU and Cholesky factorizations of a large dense matrix on clusters of many-core programmable co-processors. The out-of- core algorithm combines both the left-looking and right-looking schemes aimed to minimize the movement of data between the CPU host and the co-processor, optimizing data locality as well as computing throughput. The OOC solver is built to align with the format of the ScaLAPACK software library, making it readily portable to any existing codes using ScaLAPACK. A runtime analysis conducted on Beacon (an Intel Xeon plus Intel Xeon Phi cluster which composed of 48 nodes of multi-core CPU and MIC) at the Na- tional Institute for Computational Sciences is presented. Comparison of the performance on the Intel Xeon Phi and GPU clusters are also provided.
Brittle Solvers: Lessons and insights into effective solvers for visco-plasticity in geodynamics
NASA Astrophysics Data System (ADS)
Spiegelman, M. W.; May, D.; Wilson, C. R.
2014-12-01
Plasticity/Fracture and rock failure are essential ingredients in geodynamic models as terrestrial rocks do not possess an infinite yield strength. Numerous physical mechanisms have been proposed to limit the strength of rocks, including low temperature plasticity and brittle fracture. While ductile and creep behavior of rocks at depth is largely accepted, the constitutive relations associated with brittle failure, or shear localisation, are more controversial. Nevertheless, there are really only a few macroscopic constitutive laws for visco-plasticity that are regularly used in geodynamics models. Independent of derivation, all of these can be cast as simple effective viscosities which act as stress limiters with different choices for yield surfaces; the most common being a von Mises (constant yield stress) or Drucker-Prager (pressure dependent yield-stress) criterion. The choice of plasticity model, however, can have significant consequences for the degree of non-linearity in a problem and the choice and efficiency of non-linear solvers. Here we describe a series of simplified 2 and 3-D model problems to elucidate several issues associated with obtaining accurate description and solution of visco-plastic problems. We demonstrate that1) Picard/Successive substitution schemes for solution of the non-linear problems can often stall at large values of the non-linear residual, thus producing spurious solutions2) Combined Picard/Newton schemes can be effective for a range of plasticity models, however, they can produce serious convergence problems for strongly pressure dependent plasticity models such as Drucker-Prager.3) Nevertheless, full Drucker-Prager may not be the plasticity model of choice for strong materials as the dynamic pressures produced in these layers can develop pathological behavior with Drucker-Prager, leading to stress strengthening rather than stress weakening behavior.4) In general, for any incompressible Stoke's problem, it is highly advisable to
A chemical reaction network solver for the astrophysics code NIRVANA
NASA Astrophysics Data System (ADS)
Ziegler, U.
2016-02-01
Context. Chemistry often plays an important role in astrophysical gases. It regulates thermal properties by changing species abundances and via ionization processes. This way, time-dependent cooling mechanisms and other chemistry-related energy sources can have a profound influence on the dynamical evolution of an astrophysical system. Modeling those effects with the underlying chemical kinetics in realistic magneto-gasdynamical simulations provide the basis for a better link to observations. Aims: The present work describes the implementation of a chemical reaction network solver into the magneto-gasdynamical code NIRVANA. For this purpose a multispecies structure is installed, and a new module for evolving the rate equations of chemical kinetics is developed and coupled to the dynamical part of the code. A small chemical network for a hydrogen-helium plasma was constructed including associated thermal processes which is used in test problems. Methods: Evolving a chemical network within time-dependent simulations requires the additional solution of a set of coupled advection-reaction equations for species and gas temperature. Second-order Strang-splitting is used to separate the advection part from the reaction part. The ordinary differential equation (ODE) system representing the reaction part is solved with a fourth-order generalized Runge-Kutta method applicable for stiff systems inherent to astrochemistry. Results: A series of tests was performed in order to check the correctness of numerical and technical implementation. Tests include well-known stiff ODE problems from the mathematical literature in order to confirm accuracy properties of the solver used as well as problems combining gasdynamics and chemistry. Overall, very satisfactory results are achieved. Conclusions: The NIRVANA code is now ready to handle astrochemical processes in time-dependent simulations. An easy-to-use interface allows implementation of complex networks including thermal processes
Scaling Algebraic Multigrid Solvers: On the Road to Exascale
Baker, A H; Falgout, R D; Gamblin, T; Kolev, T; Schulz, M; Yang, U M
2010-12-12
Algebraic Multigrid (AMG) solvers are an essential component of many large-scale scientific simulation codes. Their continued numerical scalability and efficient implementation is critical for preparing these codes for exascale. Our experiences on modern multi-core machines show that significant challenges must be addressed for AMG to perform well on such machines. We discuss our experiences and describe the techniques we have used to overcome scalability challenges for AMG on hybrid architectures in preparation for exascale.
Boltzmann Solver with Adaptive Mesh in Velocity Space
Kolobov, Vladimir I.; Arslanbekov, Robert R.; Frolova, Anna A.
2011-05-20
We describe the implementation of direct Boltzmann solver with Adaptive Mesh in Velocity Space (AMVS) using quad/octree data structure. The benefits of the AMVS technique are demonstrated for the charged particle transport in weakly ionized plasmas where the collision integral is linear. We also describe the implementation of AMVS for the nonlinear Boltzmann collision integral. Test computations demonstrate both advantages and deficiencies of the current method for calculations of narrow-kernel distributions.
A contribution to the great Riemann solver debate
NASA Technical Reports Server (NTRS)
Quirk, James J.
1992-01-01
The aims of this paper are threefold: to increase the level of awareness within the shock capturing community to the fact that many Godunov-type methods contain subtle flaws that can cause spurious solutions to be computed; to identify one mechanism that might thwart attempts to produce very high resolution simulations; and to proffer a simple strategy for overcoming the specific failings of individual Riemann solvers.
An automatic ordering method for incomplete factorization iterative solvers
Forsyth, P.A.; Tang, W.P. . Dept. of Computer Science); D'Azevedo, E.F.D. )
1991-01-01
The minimum discarded fill (MDF) ordering strategy for incomplete factorization iterative solvers is developed. MDF ordering is demonstrated for several model son-symmetric problems, as well as a water-flooding simulation which uses an unstructured grid. The model problems show a three to five fold decrease in the number of iterations compared to natural orderings. Greater than twofold improvement was observed for the waterflooding simulation. 26 refs., 7 figs., 3 tabs.
Menu-Driven Solver Of Linear-Programming Problems
NASA Technical Reports Server (NTRS)
Viterna, L. A.; Ferencz, D.
1992-01-01
Program assists inexperienced user in formulating linear-programming problems. A Linear Program Solver (ALPS) computer program is full-featured LP analysis program. Solves plain linear-programming problems as well as more-complicated mixed-integer and pure-integer programs. Also contains efficient technique for solution of purely binary linear-programming problems. Written entirely in IBM's APL2/PC software, Version 1.01. Packed program contains licensed material, property of IBM (copyright 1988, all rights reserved).
Dihge, Looket; Grabau, Dorthe A; Rasmussen, Rogvi W; Bendahl, Pär-Ola; Rydén, Lisa
2016-08-01
Background The outcome of axillary ultrasound (AUS) with fine-needle aspiration biopsy (FNAB) in the diagnostic work-up of primary breast cancer has an impact on therapy decisions. We hypothesize that the accuracy of AUS is modified by nodal metastatic burden and clinico-pathological characteristics. Material and methods The performance of AUS and AUS-guided FNAB for predicting nodal metastases was assessed in a prospective breast cancer cohort subjected for surgery during 2009-2012. Predictors of accuracy were included in multivariate analysis. Results AUS had a sensitivity of 23% and a specificity of 95%, while AUS-guided FNAB obtained 73% and 100%, respectively. AUS-FNAB exclusively detected macro-metastases (median four metastases) and identified patients with more extensive nodal metastatic burden in comparison with sentinel node biopsy. The accuracy of AUS was affected by metastatic size (OR 1.11), obesity (OR 2.46), histological grade (OR 4.43), and HER2-status (OR 3.66); metastatic size and histological grade were significant in the multivariate analysis. Conclusions The clinical utility of AUS in low-risk breast cancer deserves further evaluation as the accuracy decreased with a low nodal metastatic burden. The diagnostic performance is modified by tumor and clinical characteristics. Patients with nodal disease detected by AUS-FNAB represent a group for whom neoadjuvant therapy should be considered. PMID:27050668
Jeong, Won-Ki; Fletcher, P Thomas; Tao, Ran; Whitaker, Ross
2007-01-01
In this paper we present a method to compute and visualize volumetric white matter connectivity in diffusion tensor magnetic resonance imaging (DT-MRI) using a Hamilton-Jacobi (H-J) solver on the GPU (Graphics Processing Unit). Paths through the volume are assigned costs that are lower if they are consistent with the preferred diffusion directions. The proposed method finds a set of voxels in the DTI volume that contain paths between two regions whose costs are within a threshold of the optimal path. The result is a volumetric optimal path analysis, which is driven by clinical and scientific questions relating to the connectivity between various known anatomical regions of the brain. To solve the minimal path problem quickly, we introduce a novel numerical algorithm for solving H-J equations, which we call the Fast Iterative Method (FIM). This algorithm is well-adapted to parallel architectures, and we present a GPU-based implementation, which runs roughly 50-100 times faster than traditional CPU-based solvers for anisotropic H-J equations. The proposed system allows users to freely change the endpoints of interesting pathways and to visualize the optimal volumetric path between them at an interactive rate. We demonstrate the proposed method on some synthetic and real DT-MRI datasets and compare the performance with existing methods. PMID:17968100
Jia, Wei-Dong; Xu, Ge-Liang; Ma, Jin-Liang; Ren, Yun; Chen, Hao; Sun, Si-Nan; Huang, Mei; Li, Jian-Sheng
2014-01-01
Background Nodal, a TGF-β-related embryonic morphogen, is involved in multiple biologic processes. However, the expression of Nodal in hepatocellular carcinoma (HCC) and its correlation with tumor angiogenesis, epithelial-mesenchymal transition, and prognosis is unclear. Methods We used real-time PCR and Western blotting to investigate Nodal expression in 6 HCC cell lines and 1 normal liver cell line, 16 pairs of tumor and corresponding paracarcinomatous tissues from HCC patients. Immunohistochemistry was performed to examine Nodal expression in HCC and corresponding paracarcinomatous tissues from 96 patients. CD34 and Vimentin were only examined in HCC tissues of patients mentioned above. Nodal gene was silenced by shRNA in MHCC97H and HCCLM3 cell lines, and cell migration and invasion were detected. Statistical analyses were applied to evaluate the prognostic value and associations of Nodal expression with clinical parameters. Results Nodal expression was detected in HCC cell lines with high metastatic potential alone. Nodal expression is up-regulated in HCC tissues compared with paracarcinomatous and normal liver tissues. Nodal protein was expressed in 70 of the 96 (72.9%) HCC tumors, and was associated with vascular invasion (P = 0.000), status of metastasis (P = 0.004), AFP (P = 0.049), ICGR15 (indocyanine green retention rate at 15 min) (P = 0.010) and tumor size (P = 0.000). High Nodal expression was positively correlated with high MVD (microvessal density) (P = 0.006), but not with Vimentin expression (P = 0.053). Significantly fewer migrated and invaded cells were seen in shRNA group compared with blank group and negative control group (P<0.05). High Nodal expression was found to be an independent factor for predicting overall survival of HCC. Conclusions Our study demonstrated that Nodal expression is associated with aggressive characteristics of HCC. Its aberrant expression may be a predictive factor of unfavorable prognosis
NITSOL: A Newton iterative solver for nonlinear systems
Pernice, M.; Walker, H.F.
1996-12-31
Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which the linear systems that characterize Newton steps are solved approximately using iterative linear algebra methods. Here, we outline a well-developed Newton iterative algorithm together with a Fortran implementation called NITSOL. The basic algorithm is an inexact Newton method globalized by backtracking, in which each initial trial step is determined by applying an iterative linear solver until an inexact Newton criterion is satisfied. In the implementation, the user can specify inexact Newton criteria in several ways and select an iterative linear solver from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov solver can be either evaluated analytically with a user-supplied routine or approximated using finite differences of function values. A flexible interface permits a wide variety of preconditioning strategies and allows the user to define a preconditioner and optionally update it periodically. We give details of these and other features and demonstrate the performance of the implementation on a representative set of test problems.
Transonic Drag Prediction Using an Unstructured Multigrid Solver
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Levy, David W.
2001-01-01
This paper summarizes the results obtained with the NSU-3D unstructured multigrid solver for the AIAA Drag Prediction Workshop held in Anaheim, CA, June 2001. The test case for the workshop consists of a wing-body configuration at transonic flow conditions. Flow analyses for a complete test matrix of lift coefficient values and Mach numbers at a constant Reynolds number are performed, thus producing a set of drag polars and drag rise curves which are compared with experimental data. Results were obtained independently by both authors using an identical baseline grid and different refined grids. Most cases were run in parallel on commodity cluster-type machines while the largest cases were run on an SGI Origin machine using 128 processors. The objective of this paper is to study the accuracy of the subject unstructured grid solver for predicting drag in the transonic cruise regime, to assess the efficiency of the method in terms of convergence, cpu time, and memory, and to determine the effects of grid resolution on this predictive ability and its computational efficiency. A good predictive ability is demonstrated over a wide range of conditions, although accuracy was found to degrade for cases at higher Mach numbers and lift values where increasing amounts of flow separation occur. The ability to rapidly compute large numbers of cases at varying flow conditions using an unstructured solver on inexpensive clusters of commodity computers is also demonstrated.
A Survey of Solver-Related Geometry and Meshing Issues
NASA Technical Reports Server (NTRS)
Masters, James; Daniel, Derick; Gudenkauf, Jared; Hine, David; Sideroff, Chris
2016-01-01
There is a concern in the computational fluid dynamics community that mesh generation is a significant bottleneck in the CFD workflow. This is one of several papers that will help set the stage for a moderated panel discussion addressing this issue. Although certain general "rules of thumb" and a priori mesh metrics can be used to ensure that some base level of mesh quality is achieved, inadequate consideration is often given to the type of solver or particular flow regime on which the mesh will be utilized. This paper explores how an analyst may want to think differently about a mesh based on considerations such as if a flow is compressible vs. incompressible or hypersonic vs. subsonic or if the solver is node-centered vs. cell-centered. This paper is a high-level investigation intended to provide general insight into how considering the nature of the solver or flow when performing mesh generation has the potential to increase the accuracy and/or robustness of the solution and drive the mesh generation process to a state where it is no longer a hindrance to the analysis process.
Modeling of photon migration in the human lung using a finite volume solver
NASA Astrophysics Data System (ADS)
Sikorski, Zbigniew; Furmanczyk, Michal; Przekwas, Andrzej J.
2006-02-01
The application of the frequency domain and steady-state diffusive optical spectroscopy (DOS) and steady-state near infrared spectroscopy (NIRS) to diagnosis of the human lung injury challenges many elements of these techniques. These include the DOS/NIRS instrument performance and accurate models of light transport in heterogeneous thorax tissue. The thorax tissue not only consists of different media (e.g. chest wall with ribs, lungs) but its optical properties also vary with time due to respiration and changes in thorax geometry with contusion (e.g. pneumothorax or hemothorax). This paper presents a finite volume solver developed to model photon migration in the diffusion approximation in heterogeneous complex 3D tissues. The code applies boundary conditions that account for Fresnel reflections. We propose an effective diffusion coefficient for the void volumes (pneumothorax) based on the assumption of the Lambertian diffusion of photons entering the pleural cavity and accounting for the local pleural cavity thickness. The code has been validated using the MCML Monte Carlo code as a benchmark. The code environment enables a semi-automatic preparation of 3D computational geometry from medical images and its rapid automatic meshing. We present the application of the code to analysis/optimization of the hybrid DOS/NIRS/ultrasound technique in which ultrasound provides data on the localization of thorax tissue boundaries. The code effectiveness (3D complex case computation takes 1 second) enables its use to quantitatively relate detected light signal to absorption and reduced scattering coefficients that are indicators of the pulmonary physiologic state (hemoglobin concentration and oxygenation).
NASA Technical Reports Server (NTRS)
Chang, S. C.; Wang, X. Y.; Chow, C. Y.; Himansu, A.
1995-01-01
The method of space-time conservation element and solution element is a nontraditional numerical method designed from a physicist's perspective, i.e., its development is based more on physics than numerics. It uses only the simplest approximation techniques and yet is capable of generating nearly perfect solutions for a 2-D shock reflection problem used by Helen Yee and others. In addition to providing an overall view of the new method, we introduce a new concept in the design of implicit schemes, and use it to construct a highly accurate solver for a convection-diffusion equation. It is shown that, in the inviscid case, this new scheme becomes explicit and its amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, its principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme.
On the relationship between ODE solvers and iterative solvers for linear equations
Lorber, A.; Joubert, W.; Carey, G.F.
1994-12-31
The connection between the solution of linear systems of equations by both iterative methods and explicit time stepping techniques is investigated. Based on the similarities, a suite of Runge-Kutta time integration schemes with extended stability domains are developed using Chebyshev iteration polynomials. These Runge-Kutta schemes are applied to linear and non-linear systems arising from the numerical solution of PDE`s containing either physical or artificial transient terms. Specifically, the solutions of model linear convection and convection-diffusion equations are presented, as well as the solution of a representative non-linear Navier-Stokes fluid flow problem. Included are results of parallel computations.
Topological nodal Cooper pairing in doped Weyl metals
NASA Astrophysics Data System (ADS)
Li, Yi; Haldane, F. D. M.
We generalize the concept of Berry connection of the single-electron band structure to the two-particle Cooper pair states between two Fermi surfaces with opposite Chern numbers. Because of underlying Fermi surface topology, the pairing Berry phase acquires non-trivial monopole structure. Consequently, pairing gap functions have the topologically-protected nodal structure as vortices in the momentum space with the total vorticity solely determined by the monopole charge qp. The pairing nodes behave as the Weyl-Majorana points of the Bogoliubov-de Gennes pairing Hamiltonian. Their relation with the connection patterns of the surface modes from theWeyl band structure and the Majorana surface modes inside the pairing gap is also discussed. Under the approximation of spherical Fermi surfaces, the pairing symmetry are represented by monopole harmonic functions. The lowest possible pairing channel carries angular momentum number j =|qp|, and the corresponding gap functions are holomorphic or anti-holomorphic functions on Fermi surfaces. F.D.M.H. acknowledges the support from MRSEC NSF-DMR-1420541 and the W. M. Keck Foundation.
Micropropagation of Calophyllum brasiliense (Cambess.) from nodal segments.
Silveira, S S; Cordeiro-Silva, R; Degenhardt-Goldbach, J; Quoirin, M
2016-05-01
Micropropagation of Calophyllum brasiliense Cambess. (Clusiaceae) is a way to overcome difficulties in achieving large-scale plant production, given the recalcitrant nature of the seeds, irregular fructification and absence of natural vegetative propagation of the species. Cultures were established using nodal segments 2 cm in length, obtained from 1-2 year old seedlings, maintained in a greenhouse. Mercury chloride and Plant Preservative Mixture™ were used in the surface sterilizing stage, better results being achieved with Plant Preservative Mixture™ incorporation in culture medium, at any concentration. Polyvinylpyrrolidone, activated charcoal, cysteine, ascorbic acid or citric acid were added to the culture medium to avoid oxidation. After 30 days of culture, polyvinylpirrolidone and ascorbic acid gave better results, eliminating oxidation in most explants. For shoot multiplication, benzylaminopurine was used in concentrations of 4.4 and 8.8 µM in Woody Plant Medium, resulting in an average of 4.43 and 4.68 shoots per explant, respectively, after 90 days. Indole-3-butyric acid and α-naphthalene acetic acid were used to induce root formation, reaching a maximum rooting rate of 24% with 20µM α-naphthalene acetic acid. For acclimatization. the rooted plants were transferred to Plantmax® substrate and cultured in a greenhouse, reaching 79% of survival after 30 days and 60% after one year. PMID:27143061
Jacqmin, R.P.
1991-12-10
The safety and optimal performance of large, commercial, light-water reactors require the knowledge at all time of the neutron-flux distribution in the core. In principle, this information can be obtained by solving the time-dependent neutron diffusion equations. However, this approach is complicated and very expensive. Sufficiently accurate, real-time calculations (time scale of approximately one second) are not yet possible on desktop computers, even with fast-running, nodal kinetics codes. A semi-experimental, nodal synthesis method which avoids the solution of the time-dependent, neutron diffusion equations is described. The essential idea of this method is to approximate instantaneous nodal group-fluxes by a linear combination of K, precomputed, three-dimensional, static expansion-functions. The time-dependent coefficients of the combination are found from the requirement that the reconstructed flux-distribution agree in a least-squares sense with the readings of J ({ge}K) fixed, prompt-responding neutron-detectors. Possible numerical difficulties with the least-squares solution of the ill-conditioned, J-by-K system of equations are brought under complete control by the use of a singular-value-decomposition technique. This procedure amounts to the rearrangement of the original, linear combination of K expansion functions into an equivalent more convenient, linear combination of R ({le}K) orthogonalized modes'' of decreasing magnitude. Exceedingly small modes are zeroed to eliminate any risk of roundoff-error amplification, and to assure consistency with the limited accuracy of the data. Additional modes are zeroed when it is desirable to limit the sensitivity of the results to measurement noise.
Jacqmin, R.P.
1991-12-10
The safety and optimal performance of large, commercial, light-water reactors require the knowledge at all time of the neutron-flux distribution in the core. In principle, this information can be obtained by solving the time-dependent neutron diffusion equations. However, this approach is complicated and very expensive. Sufficiently accurate, real-time calculations (time scale of approximately one second) are not yet possible on desktop computers, even with fast-running, nodal kinetics codes. A semi-experimental, nodal synthesis method which avoids the solution of the time-dependent, neutron diffusion equations is described. The essential idea of this method is to approximate instantaneous nodal group-fluxes by a linear combination of K, precomputed, three-dimensional, static expansion-functions. The time-dependent coefficients of the combination are found from the requirement that the reconstructed flux-distribution agree in a least-squares sense with the readings of J ({ge}K) fixed, prompt-responding neutron-detectors. Possible numerical difficulties with the least-squares solution of the ill-conditioned, J-by-K system of equations are brought under complete control by the use of a singular-value-decomposition technique. This procedure amounts to the rearrangement of the original, linear combination of K expansion functions into an equivalent more convenient, linear combination of R ({le}K) orthogonalized ``modes`` of decreasing magnitude. Exceedingly small modes are zeroed to eliminate any risk of roundoff-error amplification, and to assure consistency with the limited accuracy of the data. Additional modes are zeroed when it is desirable to limit the sensitivity of the results to measurement noise.
Topological Nodal-Line Superfluid in Spin-Orbit Coupled Cold Atomic Systems
NASA Astrophysics Data System (ADS)
He, Wen-Yu; Xu, Dong-Hui; Zhou, Tong; Law, K. T.; Hong Kong University of Science; Technology Collaboration
Topological nodal line superconductivity or superfluidity is a fascinating topological gapless phase which hosts bulk Weyl ring degeneracy in the quasiparticle excitation spectrum and supports Majorana zero bound modes with a large density of states at the edge. In this work, based on the experimental realized 1D spin orbit coupling, we show the emergence of topological nodal line superfluid phase in Fermionic atoms trapped in 3D cubic optical lattice when the s wave pairing field is introduced through Feshbach resonance between the two atomic hyperfine spin states. The nodal line degeneracy is further found to evolve into Weyl nodes once another component of spin orbit coupling field enters to break the chiral symmetry. The momentum resolved radio frequency spectroscopy is suggested to manifest the topological nodal line superfluid phase.
Dose-dependent Nodal/Smad signals pattern the early mouse embryo.
Robertson, Elizabeth J
2014-08-01
Nodal signals in the early post-implantation stage embryo are essential to establish initial proximal-distal (P-D) polarity and generate the final anterior-posterior (A-P) body axis. Nodal signaling in the epiblast results in the phosphorylation of Smad2 in the overlying visceral endoderm necessary to induce the AVE, in part via Smad2-dependent activation of the T-box gene Eomesodermin. Slightly later following mesoderm induction a continuum of dose-dependent Nodal signaling during the process of gastrulation underlies specification of mesodermal and definitive endoderm progenitors. Dynamic Nodal expression during the critical 72 h time window immediately following implantation, accomplished by a series of feed-back and feed-forward mechanisms serves to provide key positional cues required for establishment of the body plan and controls cell fate decisions in the early mammalian embryo. PMID:24704361
Relation between finite element methods and nodal methods in transport theory
Walters, W.F.
1985-01-01
This paper examines the relationship between nodal methods and finite-element methods for solving the discrete-ordinates form of the transport equation in x-y geometry. Specifically, we will examine the relation of three finite-element schemes to the linear-linear (LL) and linear-nodal (LN) nodal schemes. The three finite-element schemes are the linear-continuous-diamond-difference (DD) scheme, the linear-discontinuous (LD) scheme, and the quadratic-discontinuous (QD) scheme. A brief derivation of the (LL) and (LN) nodal schemes is given in the third section of this paper. The approximations that cause the LL scheme to reduce to the DD, LD, and QD schemes are then indicated. An extremely simple method of deriving the finite-element schemes is then introduced.
Nodal signaling in Xenopus gastrulae is cell-autonomous and patterned by beta-catenin.
Hashimoto-Partyka, Minako K; Yuge, Masahiro; Cho, Ken W Y
2003-01-01
The classical three-signal model of amphibian mesoderm induction and more recent modifications together propose that an activin-like signaling activity is uniformly distributed across the vegetal half of the Xenopus blastula and that this activity contributes to mesoderm induction. In support of this, we have previously shown that the activin-response element (DE) of the goosecoid promoter is uniformly activated across the vegetal half of midgastrula-stage embryos. Here, we further examine the nature of this activity by measuring DE activation by endogenous signals over time. We find that the spatiotemporal pattern of DE activation is much more dynamic than was previously appreciated and also conclude that DE(6X)Luc activity reflects endogenous nodal signaling in the embryo. Using both the DE(6X)Luc construct and endogenous Xbra and Xgsc expression as read-outs for nodal activity, and the cleavage-mutant version of Xnr2 (CmXnr2) to regionally suppress endogenous nodal activity, we demonstrate that nodal signals act cell-autonomously in Xenopus gastrulae. Nodal-expressing cells are unable to rescue either reporter gene activation or target gene expression in distant nodal-deficient cells, suggesting that nodals function at short range in this context. Finally, we show that DE activation by endogenous signals occurs in the absence of dorsal beta-catenin-mediated signaling, but that the timing of dorsal initiation is altered. We conclude that nodal signals in Xenopus gastrulae function cell autonomously at short ranges and that the spatiotemporal pattern of this signaling along the dorsoventral axis is regulated by maternal Wnt-like signaling. PMID:12490202
Effects of a novel Nodal-targeting monoclonal antibody in melanoma
Margaryan, Naira V.; Focà, Annalia; Sanguigno, Luca; Bodenstine, Thomas M.; Chandler, Grace S.; Reed, David W.; Gilgur, Alina; Seftor, Elisabeth A.; Seftor, Richard E.B.; Khalkhali-Ellis, Zhila; Leonardi, Antonio; Ruvo, Menotti; Hendrix, Mary J.C.
2015-01-01
Nodal is highly expressed in various human malignancies, thus supporting the rationale for exploring Nodal as a therapeutic target. Here, we describe the effects of a novel monoclonal antibody (mAb), 3D1, raised against human Nodal. In vitro treatment of C8161 human melanoma cells with 3D1 mAb shows reductions in anchorage-independent growth and vasculogenic network formation. 3D1 treated cells also show decreases of Nodal and downstream signaling molecules, P-Smad2 and P-ERK and of P-H3 and CyclinB1, with an increase in p27. Similar effects were previously reported in human breast cancer cells where Nodal expression was generally down-regulated; following 3D1 mAb treatment, both Nodal and P-H3 levels are reduced. Noteworthy is the reduced growth of human melanoma xenografts in Nude mice treated with 3D1 mAb, where immunostaining of representative tumor sections show diminished P-Smad2 expression. Similar effects both in vitro and in vivo were observed in 3D1 treated A375SM melanoma cells harboring the active BRAF(V600E) mutation compared to treatments with IgG control or a BRAF inhibitor, dabrafenib. Finally, we describe a 3D1-based ELISA for the detection of Nodal in serum samples from cancer patients. These data suggest the potential of 3D1 mAb for selecting and targeting Nodal expressing cancers. PMID:26460952
Disrupting Foxh1-Groucho Interaction Reveals Robustness of Nodal-Based Embryonic Patterning
Halstead, Angela M.; Wright, Christopher V. E.
2016-01-01
The winged-helix transcription factor Foxh1 is an essential regulator of Nodal signaling during the key developmental processes of gastrulation, anterior-posterior (A-P) patterning, and the derivation of left-right (L-R) asymmetry. Current models have Foxh1 bound to phospho-Smad2/3 (pSmad2/3) as a central transcriptional activator for genes targeted by Nodal signaling including Nodal itself, the feedback inhibitor Lefty2, and the positive transcriptional effector Pitx2. However, the conserved Engrailed homology-1 (EH1) motif present in Foxh1 suggests that modulated interaction with Groucho (Grg) co-repressors would allow Foxh1 to function as a transcriptional switch, toggling between transcriptional on and off states via pSmad2-Grg protein-switching, to ensure the properly timed initiation and suppression, and/or amplitude, of expression of Nodal and its target genes. We minimally mutated the Foxh1 EH1 motif, creating a novel Foxh1mEH1 allele to test directly the contribution of Foxh1-Grg–mediated repression on the transient, dynamic pattern of Nodal signaling in mice. All aspects of Nodal and its target gene expression in Foxh1mEH1/mEH1 embryos were equivalent to wild type. A-P patterning and organ situs in homozygous embryos and adult mice were also unaffected. The finding that Foxh1-Grg–mediated repression is not essential for Nodal expression during mouse embryogenesis suggests that other regulators compensate for the loss of repressive regulatory input that is mediated by Grg interactions. We suggest that the pervasive inductive properties of Nodal signaling exist within the context of a strongly buffered regulatory system that contributes to resilience and accuracy of its dynamic expression pattern. PMID:25511461
Solution and Study of the Two-Dimensional Nodal Neutron Transport Equation
Panta Pazos, Ruben; Biasotto Hauser, Eliete; Tullio de Vilhena, Marco
2002-07-01
In the last decade Vilhena and coworkers reported an analytical solution to the two-dimensional nodal discrete-ordinates approximations of the neutron transport equation in a convex domain. The key feature of these works was the application of the combined collocation method of the angular variable and nodal approach in the spatial variables. By nodal approach we mean the transverse integration of the SN equations. This procedure leads to a set of one-dimensional S{sub N} equations for the average angular fluxes in the variables x and y. These equations were solved by the old version of the LTS{sub N} method, which consists in the application of the Laplace transform to the set of nodal S{sub N} equations and solution of the resulting linear system by symbolic computation. It is important to recall that this procedure allow us to increase N the order of S{sub N} up to 16. To overcome this drawback we step forward performing a spectral painstaking analysis of the nodal S{sub N} equations for N up to 16 and we begin the convergence of the S{sub N} nodal equations defining an error for the angular flux and estimating the error in terms of the truncation error of the quadrature approximations of the integral term. Furthermore, we compare numerical results of this approach with those of other techniques used to solve the two-dimensional discrete approximations of the neutron transport equation. (authors)
The Apelin receptor enhances Nodal/TGFβ signaling to ensure proper cardiac development
Deshwar, Ashish R; Chng, Serene C; Ho, Lena; Reversade, Bruno; Scott, Ian C
2016-01-01
The Apelin receptor (Aplnr) is essential for heart development, controlling the early migration of cardiac progenitors. Here we demonstrate that in zebrafish Aplnr modulates Nodal/TGFβ signaling, a key pathway essential for mesendoderm induction and migration. Loss of Aplnr function leads to a reduction in Nodal target gene expression whereas activation of Aplnr by a non-peptide agonist increases the expression of these same targets. Furthermore, loss of Aplnr results in a delay in the expression of the cardiogenic transcription factors mespaa/ab. Elevating Nodal levels in aplnra/b morphant and double mutant embryos is sufficient to rescue cardiac differentiation defects. We demonstrate that loss of Aplnr attenuates the activity of a point source of Nodal ligands Squint and Cyclops in a non-cell autonomous manner. Our results favour a model in which Aplnr is required to fine-tune Nodal output, acting as a specific rheostat for the Nodal/TGFβ pathway during the earliest stages of cardiogenesis. DOI: http://dx.doi.org/10.7554/eLife.13758.001 PMID:27077952
NASA Astrophysics Data System (ADS)
Hiorth, A.; Jettestuen, E.; Cathles, L. M.; Madland, M. V.
2013-03-01
Pore water chemistry can dramatically affect the mechanical strength of chalk cores and the recovery of oil from them, but despite a great many core experiments, the mechanisms responsible remain unclear. This is in part because no single model is presently available that can address the changes in surface complexes and potential and mineral dissolution and precipitation that occur when fluids of different chemistry are injected. We report here the construction of a lattice Boltzmann model that includes non-linear dissolution-precipitation kinetics, surface complexation, and ion exchange. A link-based boundary condition which allows mineral boundaries to move and porosity to change is shown to converge to a correct representation of the macroscopic pore surface area. We show the chemical LB model developed predicts mineral dissolution and ion exchange similar to those predicted by PHREEQC for similar parameters, and we show how the methods developed can be applied to chalk core experiments where synthetic seawater is flooded through the core at 130 °C.
TGF-β promotes glioma cell growth via activating Nodal expression through Smad and ERK1/2 pathways
Sun, Jing; Liu, Su-zhi; Lin, Yan; Cao, Xiao-pan; Liu, Jia-ming
2014-01-17
Highlights: •TGF-β promoted Nodal expression in glioma cells. •TGF-β promoted Nodal expression via activating Smad and ERK1/2 pathways. •TGF-β promotes glioma cell growth via activating Nodal expression. -- Abstract: While there were certain studies focusing on the mechanism of TGF-β promoting the growth of glioma cells, the present work revealed another novel mechanism that TGF-β may promote glioma cell growth via enhancing Nodal expression. Our results showed that Nodal expression was significantly upregulated in glioma cells when TGF-β was added, whereas the TGF-β-induced Nodal expression was evidently inhibited by transfection Smad2 or Smad3 siRNAs, and the suppression was especially significant when the Smad3 was downregulated. Another, the attenuation of TGF-β-induced Nodal expression was observed with blockade of the ERK1/2 pathway also. Further detection of the proliferation, apoptosis, and invasion of glioma cells indicated that Nodal overexpression promoted the proliferation and invasion of tumor cells and inhibited their apoptosis, resembling the effect of TGF-β addition. Downregulation of Nodal expression via transfection Nodal-specific siRNA in the presence of TGF-β weakened the promoting effect of the latter on glioma cells growth, and transfecting Nodal siRNA alone in the absence of exogenous TGF-β more profoundly inhibited the growth of glioma cells. These results demonstrated that while both TGF-β and Nodal promoted glioma cells growth, the former might exert such effect by enhancing Nodal expression, which may form a new target for glioma therapy.
NASA Astrophysics Data System (ADS)
Wadle, Stephen; Wuest, Daniel; Cantalupo, John; Lakes, Roderic S.
1994-01-01
Holographic diffusers are prepared using silver halide (Agfa 8E75 and Kodak 649F) and photopolymer (Polaroid DMP 128 and DuPont 600, 705, and 150 series) media. It is possible to control the diffusion angle in three ways: by selection of the properties of the source diffuser, by control of its subtended angle, and by selection of the holographic medium. Several conventional diffusers based on refraction or scattering of light are examined for comparison.
Application of Aeroelastic Solvers Based on Navier Stokes Equations
NASA Technical Reports Server (NTRS)
Keith, Theo G., Jr.; Srivastava, Rakesh
2001-01-01
The propulsion element of the NASA Advanced Subsonic Technology (AST) initiative is directed towards increasing the overall efficiency of current aircraft engines. This effort requires an increase in the efficiency of various components, such as fans, compressors, turbines etc. Improvement in engine efficiency can be accomplished through the use of lighter materials, larger diameter fans and/or higher-pressure ratio compressors. However, each of these has the potential to result in aeroelastic problems such as flutter or forced response. To address the aeroelastic problems, the Structural Dynamics Branch of NASA Glenn has been involved in the development of numerical capabilities for analyzing the aeroelastic stability characteristics and forced response of wide chord fans, multi-stage compressors and turbines. 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 is available. To obtain the steady and unsteady aerodynamic forces for the complex flows around the engine components, for the flow regimes encountered by the rotor, an advanced compressible Navier-Stokes solver is required. A finite volume based Navier-Stokes solver has been developed at Mississippi State University (MSU) for solving the flow field around multistage rotors. The focus of the current research effort, under NASA Cooperative Agreement NCC3- 596 was on developing an aeroelastic analysis code (entitled TURBO-AE) based on the Navier-Stokes solver developed by MSU. The TURBO-AE code has been developed for flutter analysis of turbomachine components and delivered to NASA and its industry partners. The code has been verified. validated and is being applied by NASA Glenn and by aircraft engine manufacturers to analyze the aeroelastic stability characteristics of modem fans, compressors
Mathematical embryology: the fluid mechanics of nodal cilia
NASA Astrophysics Data System (ADS)
Smith, D. J.; Smith, A. A.; Blake, J. R.
2011-07-01
Left-right symmetry breaking is critical to vertebrate embryonic development; in many species this process begins with cilia-driven flow in a structure termed the `node'. Primary `whirling' cilia, tilted towards the posterior, transport morphogen-containing vesicles towards the left, initiating left-right asymmetric development. We review recent theoretical models based on the point-force stokeslet and point-torque rotlet singularities, explaining how rotation and surface-tilt produce directional flow. Analysis of image singularity systems enforcing the no-slip condition shows how tilted rotation produces a far-field `stresslet' directional flow, and how time-dependent point-force and time-independent point-torque models are in this respect equivalent. Associated slender body theory analysis is reviewed; this approach enables efficient and accurate simulation of three-dimensional time-dependent flow, time-dependence being essential in predicting features of the flow such as chaotic advection, which have subsequently been determined experimentally. A new model for the nodal flow utilising the regularized stokeslet method is developed, to model the effect of the overlying Reichert's membrane. Velocity fields and particle paths within the enclosed domain are computed and compared with the flow profiles predicted by previous `membrane-less' models. Computations confirm that the presence of the membrane produces flow-reversal in the upper region, but no continuous region of reverse flow close to the epithelium. The stresslet far-field is no longer evident in the membrane model, due to the depth of the cavity being of similar magnitude to the cilium length. Simulations predict that vesicles released within one cilium length of the epithelium are generally transported to the left via a `loopy drift' motion, sometimes involving highly unpredictable detours around leftward cilia [truncated
Cluster analysis of contaminated sediment data: nodal analysis.
Hartwell, S Ian; Claflin, Larry W
2005-07-01
The objective of the present study was to explore the use of multivariate statistical methods as a means to discern relationships between contaminants and biological and/or toxicological effects in a representative data set from the National Status and Trends (NS&T) Program. Data from the National Oceanic and Atmospheric Administration, NS&T Program's Bioeffects Survey of Delaware Bay, USA, were examined using various univariate and multivariate statistical techniques, including cluster analysis. Each approach identified consistent patterns and relationships between the three types of triad data. The analyses also identified factors that bias the interpretation of the data, primarily the presence of rare and unique species and the dependence of species distributions on physical parameters. Sites and species were clustered with the unweighted pair-group method using arithmetic averages clustering with the Jaccard coefficient that clustered species and sites into mutually consistent groupings. Pearson product moment correlation coefficients, normalized for salinity, also were clustered. The most informative analysis, termed nodal analysis, was the intersection of species cluster analysis with site cluster analysis. This technique produced a visual representation of species association patterns among site clusters. Site characteristics, such as salinity and grain size, not contaminant concentrations, appeared to be the primary factors determining species distributions. This suggests the sediment-quality triad needs to use physical parameters as a distinct leg from chemical concentrations to improve sediment-quality assessments in large bodies of water. Because the Delaware Bay system has confounded gradients of contaminants and physical parameters, analyses were repeated with data from northern Chesapeake Bay, USA, with similar results. PMID:16050601
NASA Astrophysics Data System (ADS)
Fukuyama, Hidenao
Recent advances of magnetic resonance imaging have been described, especially stressed on the diffusion sequences. We have recently applied the diffusion sequence to functional brain imaging, and found the appropriate results. In addition to the neurosciences fields, diffusion weighted images have improved the accuracies of clinical diagnosis depending upon magnetic resonance images in stroke as well as inflammations.
Algorithms for parallel flow solvers on message passing architectures
NASA Technical Reports Server (NTRS)
Vanderwijngaart, Rob F.
1995-01-01
The purpose of this project has been to identify and test suitable technologies for implementation of fluid flow solvers -- possibly coupled with structures and heat equation solvers -- on MIMD parallel computers. In the course of this investigation much attention has been paid to efficient domain decomposition strategies for ADI-type algorithms. Multi-partitioning derives its efficiency from the assignment of several blocks of grid points to each processor in the parallel computer. A coarse-grain parallelism is obtained, and a near-perfect load balance results. In uni-partitioning every processor receives responsibility for exactly one block of grid points instead of several. This necessitates fine-grain pipelined program execution in order to obtain a reasonable load balance. Although fine-grain parallelism is less desirable on many systems, especially high-latency networks of workstations, uni-partition methods are still in wide use in production codes for flow problems. Consequently, it remains important to achieve good efficiency with this technique that has essentially been superseded by multi-partitioning for parallel ADI-type algorithms. Another reason for the concentration on improving the performance of pipeline methods is their applicability in other types of flow solver kernels with stronger implied data dependence. Analytical expressions can be derived for the size of the dynamic load imbalance incurred in traditional pipelines. From these it can be determined what is the optimal first-processor retardation that leads to the shortest total completion time for the pipeline process. Theoretical predictions of pipeline performance with and without optimization match experimental observations on the iPSC/860 very well. Analysis of pipeline performance also highlights the effect of uncareful grid partitioning in flow solvers that employ pipeline algorithms. If grid blocks at boundaries are not at least as large in the wall-normal direction as those
A Simple Quantum Integro-Differential Solver (SQuIDS)
NASA Astrophysics Data System (ADS)
Argüelles Delgado, Carlos A.; Salvado, Jordi; Weaver, Christopher N.
2015-11-01
Simple Quantum Integro-Differential Solver (SQuIDS) is a C++ code designed to solve semi-analytically the evolution of a set of density matrices and scalar functions. This is done efficiently by expressing all operators in an SU(N) basis. SQuIDS provides a base class from which users can derive new classes to include new non-trivial terms from the right hand sides of density matrix equations. The code was designed in the context of solving neutrino oscillation problems, but can be applied to any problem that involves solving the quantum evolution of a collection of particles with Hilbert space of dimension up to six.
Object-Oriented Design for Sparse Direct Solvers
NASA Technical Reports Server (NTRS)
Dobrian, Florin; Kumfert, Gary; Pothen, Alex
1999-01-01
We discuss the object-oriented design of a software package for solving sparse, symmetric systems of equations (positive definite and indefinite) by direct methods. At the highest layers, we decouple data structure classes from algorithmic classes for flexibility. We describe the important structural and algorithmic classes in our design, and discuss the trade-offs we made for high performance. The kernels at the lower layers were optimized by hand. Our results show no performance loss from our object-oriented design, while providing flexibility, case of use, and extensibility over solvers using procedural design.
FDIPS: Finite Difference Iterative Potential-field Solver
NASA Astrophysics Data System (ADS)
Toth, Gabor; van der Holst, Bartholomeus; Huang, Zhenguang
2016-06-01
FDIPS is a finite difference iterative potential-field solver that can generate the 3D potential magnetic field solution based on a magnetogram. It is offered as an alternative to the spherical harmonics approach, as when the number of spherical harmonics is increased, using the raw magnetogram data given on a grid that is uniform in the sine of the latitude coordinate can result in inaccurate and unreliable results, especially in the polar regions close to the Sun. FDIPS is written in Fortran 90 and uses the MPI library for parallel execution.
Hierarchically Parallelized Constrained Nonlinear Solvers with Automated Substructuring
NASA Technical Reports Server (NTRS)
Padovan, Joe; Kwang, Abel
1994-01-01
This paper develops a parallelizable multilevel multiple constrained nonlinear equation solver. The substructuring process is automated to yield appropriately balanced partitioning of each succeeding level. Due to the generality of the procedure,_sequential, as well as partially and fully parallel environments can be handled. This includes both single and multiprocessor assignment per individual partition. Several benchmark examples are presented. These illustrate the robustness of the procedure as well as its capability to yield significant reductions in memory utilization and calculational effort due both to updating and inversion.
Preconditioned CG-solvers and finite element grids
Bauer, R.; Selberherr, S.
1994-12-31
To extract parasitic capacitances in wiring structures of integrated circuits the authors developed the two- and three-dimensional finite element program SCAP (Smart Capacitance Analysis Program). The program computes the task of the electrostatic field from a solution of Poisson`s equation via finite elements and calculates the energies from which the capacitance matrix is extracted. The unknown potential vector, which has for three-dimensional applications 5000-50000 unknowns, is computed by a ICCG solver. Currently three- and six-node triangular, four- and ten-node tetrahedronal elements are supported.
Reformulation of the Fourier-Bessel steady state mode solver
NASA Astrophysics Data System (ADS)
Gauthier, Robert C.
2016-09-01
The Fourier-Bessel resonator state mode solver is reformulated using Maxwell's field coupled curl equations. The matrix generating expressions are greatly simplified as well as a reduction in the number of pre-computed tables making the technique simpler to implement on a desktop computer. The reformulation maintains the theoretical equivalence of the permittivity and permeability and as such structures containing both electric and magnetic properties can be examined. Computation examples are presented for a surface nanoscale axial photonic resonator and hybrid { ε , μ } quasi-crystal resonator.
High Energy Boundary Conditions for a Cartesian Mesh Euler Solver
NASA Technical Reports Server (NTRS)
Pandya, Shishir A.; Murman, Scott M.; Aftosmis, Michael J.
2004-01-01
Inlets and exhaust nozzles are often omitted or fared over in aerodynamic simulations of aircraft due to the complexities involving in the modeling of engine details such as complex geometry and flow physics. However, the assumption is often improper as inlet or plume flows have a substantial effect on vehicle aerodynamics. A tool for specifying inlet and exhaust plume conditions through the use of high-energy boundary conditions in an established inviscid flow solver is presented. The effects of the plume on the flow fields near the inlet and plume are discussed.
A fast solver for the Ornstein-Zernike equations
NASA Astrophysics Data System (ADS)
Kelley, C. T.; Pettitt, B. Montgomery
2004-07-01
In this paper, we report on the design and analysis of a multilevel method for the solution of the Ornstein-Zernike Equations and related systems of integro-algebraic equations. Our approach is based on an extension of the Atkinson-Brakhage method, with Newton-GMRES used as the coarse mesh solver. We report on several numerical experiments to illustrate the effectiveness of the method. The problems chosen are related to simple short ranged fluids with continuous potentials. Speedups over traditional methods for a given accuracy are reported. The new multilevel method is roughly six times faster than Newton-GMRES and 40 times faster than Picard.
Performance issues for iterative solvers in device simulation
NASA Technical Reports Server (NTRS)
Fan, Qing; Forsyth, P. A.; Mcmacken, J. R. F.; Tang, Wei-Pai
1994-01-01
Due to memory limitations, iterative methods have become the method of choice for large scale semiconductor device simulation. However, it is well known that these methods still suffer from reliability problems. The linear systems which appear in numerical simulation of semiconductor devices are notoriously ill-conditioned. In order to produce robust algorithms for practical problems, careful attention must be given to many implementation issues. This paper concentrates on strategies for developing robust preconditioners. In addition, effective data structures and convergence check issues are also discussed. These algorithms are compared with a standard direct sparse matrix solver on a variety of problems.
Evaluating point-based POMDP solvers on multicore machines.
Shani, Guy
2010-08-01
Recent scaling up of partially observable Markov decision process solvers toward realistic applications is largely due to point-based methods which quickly provide approximate solutions for midsized problems. New multicore machines offer an opportunity to scale up to larger domains. These machines support parallel execution and can speed up existing algorithms considerably. In this paper, we evaluate several ways in which point-based algorithms can be adapted to parallel computing. We overview the challenges and opportunities and present experimental results, providing evidence to the usability of our suggestions. PMID:19914897
Dorning, J.J.
1993-05-01
The report is divided into three parts. The main mathematical development of the new systematic simultaneous lattice-cell and fuel-assembly homogenization theory derived from the transport equation is summarized in Part I. Also included in Part I is the validation of this systematic homogenization theory and the resulting calculational procedures for coarse-mesh nodal diffusion methods that follow from it, in the form of their application to a simple one-dimensional test problem. The results of the application of this transport-equation-based systematic homogenization theory are summarized in Part II in which its superior accuracy over traditional flux and volume weighted homogenization procedures and over generalized equivalence theory is demonstrated for small and large practical two-dimensional PWR problems. The mathematical development of a second systematic homogenization theory -- this one derived starting from the diffusion equation -- is summarized in Part III where its application to a practical two-dimensional PWR model also is summarized and its superior accuracy over traditional homogenization methods and generalized equivalence theory is demonstrated for this problem.
A case of primary adrenal diffuse large B-cell lymphoma in HIV.
Malik, Seema; Chapman, Cordelia B-P; Drew, Olivia
2016-07-01
Primary adrenal diffuse large B-cell lymphoma in HIV is a very rare, highly aggressive extra-nodal lymphoma. There is only one previous case reported in the literature. Our patient presented with isolated bilateral adrenal masses with no lymphadenopathy or visceral involvement, which made the diagnosis challenging. PMID:26113518
NASA Astrophysics Data System (ADS)
Wang, Y.; Shu, C.; Yang, L. M.
2016-02-01
A boundary condition-enforced-immersed boundary-lattice Boltzmann flux solver is proposed in this work for effective simulation of thermal flows with Neumann boundary conditions. In this method, two auxiliary layers of Lagrangian points are introduced and respectively placed inside and outside of the solid body, on which the temperature corrections (related to the heat source) are set as unknowns. To effectively consider the fluid-boundary interaction, these unknowns are expressed as algebraic summations of the temperature correction on Eulerian points, which are in turn obtained from biased distributions of unknown temperature corrections on the immersed boundary. By enforcing the temperature gradient at the solid boundary being equal to that approximated by the corrected temperature field, a set of algebraic equations are formed and solved to obtain all the unknowns simultaneously. They are then distributed biasedly to the inner region of the auxiliary layer so that the diffusion from the smooth delta function can be reduced substantially. In addition, the solutions of the flow and temperature fields are obtained by the thermal lattice Boltzmann flux solver with the second order of accuracy. The proposed method is well validated through its applications to simulate several benchmarks of natural, forced and mixed convection problems. It has been demonstrated that the present solver has about 1.724 order of accuracy and the error between the present result and theoretical value for the temperature gradient on the solid surface is in the order of 10-13, which indicates that the proposed method is able to satisfy the Neumann boundary condition accurately.
Multiply scaled constrained nonlinear equation solvers. [for nonlinear heat conduction problems
NASA Technical Reports Server (NTRS)
Padovan, Joe; Krishna, Lala
1986-01-01
To improve the numerical stability of nonlinear equation solvers, a partitioned multiply scaled constraint scheme is developed. This scheme enables hierarchical levels of control for nonlinear equation solvers. To complement the procedure, partitioned convergence checks are established along with self-adaptive partitioning schemes. Overall, such procedures greatly enhance the numerical stability of the original solvers. To demonstrate and motivate the development of the scheme, the problem of nonlinear heat conduction is considered. In this context the main emphasis is given to successive substitution-type schemes. To verify the improved numerical characteristics associated with partitioned multiply scaled solvers, results are presented for several benchmark examples.
A GPU-accelerated flow solver for incompressible two-phase fluid flows
NASA Astrophysics Data System (ADS)
Codyer, Stephen; Raessi, Mehdi; Khanna, Gaurav
2011-11-01
We present a numerical solver for incompressible, immiscible, two-phase fluid flows that is accelerated by using Graphics Processing Units (GPUs). The Navier-Stokes equations are solved by the projection method, which involves solving a pressure Poisson problem at each time step. A second-order discretization of the Poisson problem leads to a sparse matrix with five and seven diagonals for two- and three-dimensional simulations, respectively. Running a serial linear algebra solver on a single CPU can take 50-99.9% of the total simulation time to solve the above system for pressure. To remove this bottleneck, we utilized the large parallelization capabilities of GPUs; we developed a linear algebra solver based on the conjugate gradient iterative method (CGIM) by using CUDA 4.0 libraries and compared its performance with CUSP, an open-source, GPU library for linear algebra. Compared to running the CGIM solver on a single CPU core, for a 2D case, our GPU solver yields speedups of up to 88x in solver time and 81x overall time on a single GPU card. In 3D cases, the speedups are up to 81x (solver) and 15x (overall). Speedup is faster at higher grid resolutions and our GPU solver outperforms CUSP. Current work examines the acceleration versus a parallel CGIM CPU solver.
Seol, Ki Ho
2016-01-01
Purpose To evaluate the patterns of nodal failure after radiotherapy (RT) with the reduced volume approach for elective neck nodal irradiation (ENI) in nasopharyngeal carcinoma (NPC). Materials and Methods Fifty-six NPC patients who underwent definitive chemoradiotherapy with the reduced volume approach for ENI were reviewed. The ENI included retropharyngeal and level II lymph nodes, and only encompassed the echelon inferior to the involved level to eliminate the entire neck irradiation. Patients received either moderate hypofractionated intensity-modulated RT for a total of 72.6 Gy (49.5 Gy to elective nodal areas) or a conventional fractionated three-dimensional conformal RT for a total of 68.4–72 Gy (39.6–45 Gy to elective nodal areas). Patterns of failure, locoregional control, and survival were analyzed. Results The median follow-up was 38 months (range, 3 to 80 months). The out-of-field nodal failure when omitting ENI was none. Three patients developed neck recurrences (one in-field recurrence in the 72.6 Gy irradiated nodal area and two in the elective irradiated region of 39.6 Gy). Overall disease failure at any site developed in 11 patients (19.6%). Among these, there were six local failures (10.7%), three regional failures (5.4%), and five distant metastases (8.9%). The 3-year locoregional control rate was 87.1%, and the distant failure-free rate was 90.4%; disease-free survival and overall survival at 3 years was 80% and 86.8%, respectively. Conclusion No patient developed nodal failure in the omitted ENI site. Our investigation has demonstrated that the reduced volume approach for ENI appears to be a safe treatment approach in NPC. PMID:27104162
Fast solver for systems of axisymmetric ring vortices
NASA Astrophysics Data System (ADS)
Strickland, James H.; Amos, Donald E.
1992-03-01
A method that is capable of efficient calculation of the axisymmetric flowfield produced by a large system of ring vortices is presented in this paper. The system of ring vortices can, in turn, be used to model body surfaces and wakes in incompressible unsteady axisymmetric flowfields. This method takes advantage of source-point and field-point series expansion, which enables one to make calculations for interactions between groups of vortices that are in well-separated spatial domains rather than having to consider interactions between every pair of vortices. A FORTRAN computer code, RSOLV, has been written to execute the fast solution technique. For 100 vortices in the field, there is virtually no CPU time savings with the fast solver. For 10,000 vortices in the flow, the fast solver obtains solutions in about 1-3 percent of the time required for the direct solution technique. Formulas for the self-induced velocity of discretized regions of the flowfield have been developed. Use of these formulas allows correct convection of discretized patches of vorticity in the flowfiled.
An efficient chemical kinetics solver using high dimensional model representation
Shorter, J.A.; Ip, P.C.; Rabitz, H.A.
1999-09-09
A high dimensional model representation (HDMR) technique is introduced to capture the input-output behavior of chemical kinetic models. The HDMR expresses the output chemical species concentrations as a rapidly convergent hierarchical correlated function expansion in the input variables. In this paper, the input variables are taken as the species concentrations at time t{sub i} and the output is the concentrations at time t{sub i} + {delta}, where {delta} can be much larger than conventional integration time steps. A specially designed set of model runs is performed to determine the correlated functions making up the HDMR. The resultant HDMR can be used to (1) identify the key input variables acting independently or cooperatively on the output, and (2) create a high speed fully equivalent operational model (FEOM) serving to replace the original kinetic model and its differential equation solver. A demonstration of the HDMR technique is presented for stratospheric chemical kinetics. The FEOM proved to give accurate and stable chemical concentrations out to long times of many years. In addition, the FEOM was found to be orders of magnitude faster than a conventional stiff equation solver. This computational acceleration should have significance in many chemical kinetic applications.
Using computer algebra and SMT solvers in algebraic biology
NASA Astrophysics Data System (ADS)
Pineda Osorio, Mateo
2014-05-01
Biologic processes are represented as Boolean networks, in a discrete time. The dynamics within these networks are approached with the help of SMT Solvers and the use of computer algebra. Software such as Maple and Z3 was used in this case. The number of stationary states for each network was calculated. The network studied here corresponds to the immune system under the effects of drastic mood changes. Mood is considered as a Boolean variable that affects the entire dynamics of the immune system, changing the Boolean satisfiability and the number of stationary states of the immune network. Results obtained show Z3's great potential as a SMT Solver. Some of these results were verified in Maple, even though it showed not to be as suitable for the problem approach. The solving code was constructed using Z3-Python and Z3-SMT-LiB. Results obtained are important in biology systems and are expected to help in the design of immune therapies. As a future line of research, more complex Boolean network representations of the immune system as well as the whole psychological apparatus are suggested.
Matrix decomposition graphics processing unit solver for Poisson image editing
NASA Astrophysics Data System (ADS)
Lei, Zhao; Wei, Li
2012-10-01
In recent years, gradient-domain methods have been widely discussed in the image processing field, including seamless cloning and image stitching. These algorithms are commonly carried out by solving a large sparse linear system: the Poisson equation. However, solving the Poisson equation is a computational and memory intensive task which makes it not suitable for real-time image editing. A new matrix decomposition graphics processing unit (GPU) solver (MDGS) is proposed to settle the problem. A matrix decomposition method is used to distribute the work among GPU threads, so that MDGS will take full advantage of the computing power of current GPUs. Additionally, MDGS is a hybrid solver (combines both the direct and iterative techniques) and has two-level architecture. These enable MDGS to generate identical solutions with those of the common Poisson methods and achieve high convergence rate in most cases. This approach is advantageous in terms of parallelizability, enabling real-time image processing, low memory-taken and extensive applications.
Agglomeration Multigrid for an Unstructured-Grid Flow Solver
NASA Technical Reports Server (NTRS)
Frink, Neal; Pandya, Mohagna J.
2004-01-01
An agglomeration multigrid scheme has been implemented into the sequential version of the NASA code USM3Dns, tetrahedral cell-centered finite volume Euler/Navier-Stokes flow solver. Efficiency and robustness of the multigrid-enhanced flow solver have been assessed for three configurations assuming an inviscid flow and one configuration assuming a viscous fully turbulent flow. The inviscid studies include a transonic flow over the ONERA M6 wing and a generic business jet with flow-through nacelles and a low subsonic flow over a high-lift trapezoidal wing. The viscous case includes a fully turbulent flow over the RAE 2822 rectangular wing. The multigrid solutions converged with 12%-33% of the Central Processing Unit (CPU) time required by the solutions obtained without multigrid. For all of the inviscid cases, multigrid in conjunction with an explicit time-stepping scheme performed the best with regard to the run time memory and CPU time requirements. However, for the viscous case multigrid had to be used with an implicit backward Euler time-stepping scheme that increased the run time memory requirement by 22% as compared to the run made without multigrid.
Adaptively truncated Hilbert spaces for Hamiltonian-based impurity solvers
NASA Astrophysics Data System (ADS)
Go, Ara; Millis, Andrew
We investigate truncations of the exponentially large Hilbert space in the exact diagonalization (ED) as an impurity solver for the dynamical mean-field theory (DMFT). A key issue is to maintain the high degree of numerical accuracy required in the construction of Greens functions. We test various truncation schemes with similar number of Slater determinants in both Hilbert spaces for the ground state and a particle- or a hole-excited state, and show that the excited states play an important role in accurate computation as well as the ground state. Appropriate truncation for both spaces enables us to compute the accurate self-energy of the impurity Hamiltonian with up to eight correlated orbitals hybridized with a sufficient number of bath orbitals to obtain converged solutions of the self-consistent equation in the DMFT, which is not solvable by the original ED. Application to spin-orbit coupled multi-orbital models and the one-dimensional Hubbard model and comparison to results from exact diagonalization and the configuration interaction based impurity solvers demonstrate the power of the method. This work was supported by the US Department of Energy under Grants No. DE-FG02-04ER46169 and DE-SC0006613.
Assessent of elliptic solvers for the pressure Poisson equation
NASA Astrophysics Data System (ADS)
Strodtbeck, J. P.; Polly, J. B.; McDonough, J. M.
2008-11-01
It is well known that as much as 80% of the total arithmetic needed for a solution of the incompressible Navier--Stokes equations can be expended for solving the pressure Poisson equation, and this has long been one of the prime motivations for study of elliptic solvers. In recent years various Krylov-subspace methods have begun to receive wide use because of their rapid convergence rates and automatic generation of iteration parameters. However, it is actually total floating-point arithmetic operations that must be of concern when selecting a solver for CFD, and not simply required number of iterations. In the present study we recast speed of convergence for typical CFD pressure Poisson problems in terms of CPU time spent on floating-point arithmetic and demonstrate that in many cases simple successive-overrelaxation (SOR) methods are as effective as some of the popular Krylov-subspace techniques such as BiCGStab(l) provided optimal SOR iteration parameters are employed; furthermore, SOR procedures require significantly less memory. We then describe some techniques for automatically predicting optimal SOR parameters.
User documentation for PVODE, an ODE solver for parallel computers
Hindmarsh, A.C., LLNL
1998-05-01
PVODE is a general purpose ordinary differential equation (ODE) solver for stiff and nonstiff ODES It is based on CVODE [5] [6], which is written in ANSI- standard C PVODE uses MPI (Message-Passing Interface) [8] and a revised version of the vector module in CVODE to achieve parallelism and portability PVODE is intended for the SPMD (Single Program Multiple Data) environment with distributed memory, in which all vectors are identically distributed across processors In particular, the vector module is designed to help the user assign a contiguous segment of a given vector to each of the processors for parallel computation The idea is for each processor to solve a certain fixed subset of the ODES To better understand PVODE, we first need to understand CVODE and its historical background The ODE solver CVODE, which was written by Cohen and Hindmarsh, combines features of two earlier Fortran codes, VODE [l] and VODPK [3] Those two codes were written by Brown, Byrne, and Hindmarsh. Both use variable-coefficient multi-step integration methods, and address both stiff and nonstiff systems (Stiffness is defined as the presence of one or more very small damping time constants ) VODE uses direct linear algebraic techniques to solve the underlying banded or dense linear systems of equations in conjunction with a modified Newton method in the stiff ODE case On the other hand, VODPK uses a preconditioned Krylov iterative method [2] to solve the underlying linear system User-supplied preconditioners directly address the dominant source of stiffness Consequently, CVODE implements both the direct and iterative methods Currently, with regard to the nonlinear and linear system solution, PVODE has three method options available. functional iteration, Newton iteration with a diagonal approximate Jacobian, and Newton iteration with the iterative method SPGMR (Scaled Preconditioned Generalized Minimal Residual method) Both CVODE and PVODE are written in such a way that other linear
Heavy fermions: From nodal metals to super-spins
NASA Astrophysics Data System (ADS)
Ramires Neves de Oliveira, Aline
Condensed matter physics is an area of research which lies at a sweet spot between two complementary perspectives: the atomistic point of view which takes into account all the details of the system of interest; and the framework of universality and emergent phenomena, which allows us to make drastic simplifications to the microscopic description of materials while still being able to explain much of the experimentally observed phenomena. This thesis addresses problems from both perspectives, focusing on heavy fermion systems. Heavy fermion systems are prototype materials for the study of strongly correlations and quantum criticality. Theoretical understanding of these systems is important for the design of new materials and for the fundamental understanding of quantum critical phenomena. This thesis is strongly motivated by recent experiments in an intrinsically quantum critical material, beta-YbAlB 4. This system shows anomalous critical exponents in transport and thermodynamics. In Chapter 2 we construct a phenomenological theory for the heavy fermion metal beta-YbAlB4 based on the Anderson model, taking into account the peculiarities of this specific material. We analyze the consequences of a non-trivial, momentum-dependent, hybridization matrix between f-electrons and conduction electrons, which gives rise to a nodal metal with unusual dispersion and singular thermodynamic properties, in accordance with experiments. In Chapter 3 we analyze the Electron Spin Resonance experiments in this same material and propose a theory including spin-orbit coupling, crystal electric fields and hyperfine coupling which can account for many of the features of the experimentally observed signal. Within a broader perspective on heavy fermion systems, the absence of a single unified theoretical description which can account for the plethora of phenomena observed in this class of materials also motivates us to consider new theoretical approaches. In Chapter 4 we generalize the
Recognizing nodal marginal zone lymphoma: recent advances and pitfalls. A systematic review
van den Brand, Michiel; van Krieken, J. Han J.M.
2013-01-01
The diagnosis of nodal marginal zone lymphoma is one of the remaining problem areas in hematopathology. Because no established positive markers exist for this lymphoma, it is frequently a diagnosis of exclusion, making distinction from other low-grade B-cell lymphomas difficult or even impossible. This systematic review summarizes and discusses the current knowledge on nodal marginal zone lymphoma, including clinical features, epidemiology and etiology, histology, and cytogenetic and molecular features. In particular, recent advances in diagnostics and pathogenesis are discussed. New immunohistochemical markers have become available that could be used as positive markers for nodal marginal zone lymphoma. These markers could be used to ensure more homogeneous study groups in future research. Also, recent gene expression studies and studies describing specific gene mutations have provided clues to the pathogenesis of nodal marginal zone lymphoma, suggesting deregulation of the nuclear factor kappa B pathway. Nevertheless, nodal marginal zone lymphoma remains an enigmatic entity, requiring further study to define its pathogenesis to allow an accurate diagnosis and tailored treatment. However, recent data indicate that it is not related to splenic or extranodal lymphoma, and that it is also not related to lymphoplasmacytic lymphoma. Thus, even though the diagnosis is not always easy, it is clearly a separate entity. PMID:23813646
Zeeman Field-Induced Nodal Structures in Rashba-Type Noncentrosymmetric Superconductors
NASA Astrophysics Data System (ADS)
Chen, Chongju; Jin, Biao
2016-02-01
We study theoretically the effect of Zeeman field on the Bogoliubov-de Gennes quasiparticle excitation spectrum of a three-dimensional noncentrosymmetric (s+p)-wave model. The quasiparticle excitation spectrum may possess line nodes due to the mixing of s-wave and p-wave pairing in the absence of Zeeman field. Our calculations show that, depending on the magnitude and the orientation of an applied Zeeman field, a variety of nodal structures including nodal points, nodal lines, and nodal surfaces may be generated in the excitation spectrum. These results are corroborated by numerical computations of the low-temperature electronic specific heat. Specifically, we demonstrate rigorously that the zero-field nodal lines will be robust against a weak z-axis oriented Zeeman field. It is also found that the electronic specific heat calculated for a Zeeman field in the x- y plane may qualitatively account for the novel feature of specific heat observed experimentally in CePt_3Si.
The impact of surgical technique on neck dissection nodal yield: making a difference.
Lörincz, Balazs B; Langwieder, Felix; Möckelmann, Nikolaus; Sehner, Susanne; Knecht, Rainald
2016-05-01
The nodal yield of neck dissections is an independent prognostic factor in several types of head and neck cancer. The authors aimed to determine whether the applied dissection technique has a significant impact on nodal yield. This is a single-institution, prospective study with internal control group (level of evidence: 2A). Data of 150 patients undergoing 223 neck dissections between February 2011 and March 2013 have been collected in a comprehensive cancer centre. Eighty-two patients underwent neck dissection with unwrapping the cervical fascia from lateral to medial, while 68 patients were operated without specifically unwrapping the fascia, in a caudal to cranial fashion. The standardised, horizontal neck dissection technique along the fascial planes resulted in a significantly higher nodal count in Levels I, II, III and IV, as well as in terms of overall nodal yield (mean: n = 22.53) than that of the vertical dissection applied in the control group (mean: n = 15.00). This is the first publication showing a direct correlation between neck dissection nodal yield and surgical technique. Therefore, it is paramount to optimise the applied surgical concept to maximise the oncological benefit. PMID:25784183
Topological nodal-line fermions in spin-orbit metal PbTaSe2
Bian, Guang; Chang, Tay-Rong; Sankar, Raman; Xu, Su-Yang; Zheng, Hao; Neupert, Titus; Chiu, Ching-Kai; Huang, Shin-Ming; Chang, Guoqing; Belopolski, Ilya; et al
2016-02-02
Here we discuss how topological semimetals can support one-dimensional Fermi lines or zero-dimensional Weyl points in momentum space, where the valence and conduction bands touch. While the degeneracy points in Weyl semimetals are robust against any perturbation that preserves translational symmetry, nodal lines require protection by additional crystalline symmetries such as mirror reflection. Here we report, based on a systematic theoretical study and a detailed experimental characterization, the existence of topological nodal-line states in the non-centrosymmetric compound PbTaSe2 with strong spin-orbit coupling. Remarkably, the spin-orbit nodal lines in PbTaSe2 are not only protected by the reflection symmetry but also characterizedmore » by an integer topological invariant. Our detailed angle-resolved photoemission measurements, first-principles simulations and theoretical topological analysis illustrate the physical mechanism underlying the formation of the topological nodal-line states and associated surface states for the first time, thus paving the way towards exploring the exotic properties of the topological nodal-line fermions in condensed matter systems.« less
Tumor microvessel density–associated mast cells in canine nodal lymphoma
Mann, Elizabeth; Whittington, Lisa
2014-01-01
Objective: Mast cells are associated in angiogenesis in various human and animal neoplasms. However, association of mast cells with tumor microvessel density in canine lymphoma was not previously documented. The objective of the study is to determine if mast cells are increased in canine nodal lymphomas and to evaluate their correlation with tumor microvessel density and grading of lymphomas. Methods: Nodal lymphomas from 33 dogs were studied and compared with nonneoplastic lymph nodes from 6 dogs as control. Mast cell count was made on Toluidine blue stained sections. Immunohistochemistry using antibody against Factor VIII was employed to visualize and determine microvessel density. Results: The mast cell count in lymphoma (2.95 ± 2.4) was significantly higher (p < 0.05) than that in the control (0.83 ± 0.3) and was positively correlated with tumor microvessel density (r = 0.44, p = 0.009). Significant difference was not observed in mast cell count and tumor microvessel density among different gradings of lymphomas. Conclusions: Mast cells are associated with tumor microvessel density in canine nodal lymphoma with no significant difference among gradings of lymphomas. Mast cells may play an important role in development of canine nodal lymphomas. Further detailed investigation on the role of mast cells as important part of tumor microenvironment in canine nodal lymphomas is recommended. PMID:26770752
Gonsar, Ngawang; Coughlin, Alicia; Clay-Wright, Jessica A; Borg, Bethanie R; Kindt, Lexy M; Liang, Jennifer O
2016-01-01
Zebrafish with defective Nodal signaling have a phenotype analogous to the fatal human birth defect anencephaly, which is caused by an open anterior neural tube. Previous work in our laboratory found that anterior open neural tube phenotypes in Nodal signaling mutants were caused by lack of mesendodermal/mesodermal tissues. Defects in these mutants are already apparent at neural plate stage, before the neuroepithelium starts to fold into a tube. Consistent with this, we found that the requirement for Nodal signaling maps to mid-late blastula stages. This timing correlates with the timing of prechordal plate mesendoderm and anterior mesoderm induction, suggesting these tissues act to promote neurulation. To further identify tissues important for neurulation, we took advantage of the variable phenotypes in Nodal signaling-deficient sqt mutant and Lefty1-overexpressing embryos. Statistical analysis indicated a strong, positive correlation between a closed neural tube and presence of several mesendoderm/mesoderm-derived tissues (hatching glands, cephalic paraxial mesoderm, notochord, and head muscles). However, the neural tube was closed in a subset of embryos that lacked any one of these tissues. This suggests that several types of Nodal-induced mesendodermal/mesodermal precursors are competent to promote neurulation. PMID:26528772
Topological nodal-line fermions in spin-orbit metal PbTaSe2.
Bian, Guang; Chang, Tay-Rong; Sankar, Raman; Xu, Su-Yang; Zheng, Hao; Neupert, Titus; Chiu, Ching-Kai; Huang, Shin-Ming; Chang, Guoqing; Belopolski, Ilya; Sanchez, Daniel S; Neupane, Madhab; Alidoust, Nasser; Liu, Chang; Wang, BaoKai; Lee, Chi-Cheng; Jeng, Horng-Tay; Zhang, Chenglong; Yuan, Zhujun; Jia, Shuang; Bansil, Arun; Chou, Fangcheng; Lin, Hsin; Hasan, M Zahid
2016-01-01
Topological semimetals can support one-dimensional Fermi lines or zero-dimensional Weyl points in momentum space, where the valence and conduction bands touch. While the degeneracy points in Weyl semimetals are robust against any perturbation that preserves translational symmetry, nodal lines require protection by additional crystalline symmetries such as mirror reflection. Here we report, based on a systematic theoretical study and a detailed experimental characterization, the existence of topological nodal-line states in the non-centrosymmetric compound PbTaSe2 with strong spin-orbit coupling. Remarkably, the spin-orbit nodal lines in PbTaSe2 are not only protected by the reflection symmetry but also characterized by an integer topological invariant. Our detailed angle-resolved photoemission measurements, first-principles simulations and theoretical topological analysis illustrate the physical mechanism underlying the formation of the topological nodal-line states and associated surface states for the first time, thus paving the way towards exploring the exotic properties of the topological nodal-line fermions in condensed matter systems. PMID:26829889
Topological nodal-line fermions in spin-orbit metal PbTaSe2
Bian, Guang; Chang, Tay-Rong; Sankar, Raman; Xu, Su-Yang; Zheng, Hao; Neupert, Titus; Chiu, Ching-Kai; Huang, Shin-Ming; Chang, Guoqing; Belopolski, Ilya; Sanchez, Daniel S.; Neupane, Madhab; Alidoust, Nasser; Liu, Chang; Wang, BaoKai; Lee, Chi-Cheng; Jeng, Horng-Tay; Zhang, Chenglong; Yuan, Zhujun; Jia, Shuang; Bansil, Arun; Chou, Fangcheng; Lin, Hsin; Hasan, M. Zahid
2016-01-01
Topological semimetals can support one-dimensional Fermi lines or zero-dimensional Weyl points in momentum space, where the valence and conduction bands touch. While the degeneracy points in Weyl semimetals are robust against any perturbation that preserves translational symmetry, nodal lines require protection by additional crystalline symmetries such as mirror reflection. Here we report, based on a systematic theoretical study and a detailed experimental characterization, the existence of topological nodal-line states in the non-centrosymmetric compound PbTaSe2 with strong spin-orbit coupling. Remarkably, the spin-orbit nodal lines in PbTaSe2 are not only protected by the reflection symmetry but also characterized by an integer topological invariant. Our detailed angle-resolved photoemission measurements, first-principles simulations and theoretical topological analysis illustrate the physical mechanism underlying the formation of the topological nodal-line states and associated surface states for the first time, thus paving the way towards exploring the exotic properties of the topological nodal-line fermions in condensed matter systems. PMID:26829889
Auxin controls local cytokinin biosynthesis in the nodal stem in apical dominance.
Tanaka, Mina; Takei, Kentaro; Kojima, Mikiko; Sakakibara, Hitoshi; Mori, Hitoshi
2006-03-01
In intact plants, the shoot apex grows predominantly and inhibits outgrowth of axillary buds. After decapitation of the shoot apex, outgrowth of axillary buds begins. This phenomenon is called an apical dominance. Although the involvement of auxin, which represses outgrowth of axillary buds, and cytokinin (CK), which promotes outgrowth of axillary buds, has been proposed, little is known about the underlying molecular mechanisms. In the present study, we demonstrated that auxin negatively regulates local CK biosynthesis in the nodal stem by controlling the expression level of the pea (Pisum sativum L.) gene adenosine phosphate-isopentenyltransferase (PsIPT), which encodes a key enzyme in CK biosynthesis. Before decapitation, PsIPT1 and PsIPT2 transcripts were undetectable; after decapitation, they were markedly induced in the nodal stem along with accumulation of CK. Expression of PsIPT was repressed by the application of indole-3-acetic acid (IAA). In excised nodal stem, PsIPT expression and CK levels also increased under IAA-free conditions. Furthermore, beta-glucuronidase expression, under the control of the PsIPT2 promoter region in transgenic Arabidopsis, was repressed by an IAA. Our results indicate that in apical dominance one role of auxin is to repress local biosynthesis of CK in the nodal stem and that, after decapitation, CKs, which are thought to be derived from the roots, are locally biosynthesized in the nodal stem rather than in the roots. PMID:16507092
Angle Resolved Thermal Conductivity of Superconducting CeCoIn5 along the Nodal Direction
NASA Astrophysics Data System (ADS)
Movshovich, Roman; Kim, Duk Y.; Lin, Shizeng; Weickert, Franziska; Bauer, Eric D.; Ronning, Filip; Thompson, Joe D.
The thermal conductivity measurement in a rotating magnetic field is a powerful probe of the structure of the superconducting energy gap. The four-fold oscillation in thermal conductivity of CeCoIn5, with the heat current in the anti-nodal direction, has revealed the d-wave nature of its order parameter. We have measured the thermal conductivity with the heat current along the [110] (nodal) direction and the magnetic field rotating in the ab-plane. In contrast to the smooth oscillation found with the heat current along the anti-nodal direction, a sharp increase of thermal conductivity was observed when the magnetic field is also in the [110] direction, parallel to the heat current. This suggests that the scattering of the nodal quasiparticle is strongly suppressed along the magnetic field direction. In addition, a smaller increase of the thermal conductivity was observed when the magnetic field is approximately 30 degree away from the nodal direction, perhaps due to a Fermi surface anomaly. Work at Los Alamos was performed under the auspices of the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering.
A phase-field model coupled with lattice kinetics solver for modeling crystal growth in furnaces
Lin, Guang; Bao, Jie; Xu, Zhijie; Tartakovsky, Alexandre M.; Henager, Charles H.
2014-02-02
In this study, we present a new numerical model for crystal growth in a vertical solidification system. This model takes into account the buoyancy induced convective flow and its effect on the crystal growth process. The evolution of the crystal growth interface is simulated using the phase-field method. Two novel phase-field models are developed to model the crystal growth interface in vertical gradient furnaces with two temperature profile setups: 1) fixed wall temperature profile setup and 2) time-dependent temperature profile setup. A semi-implicit lattice kinetics solver based on the Boltzmann equation is employed to model the unsteady incompressible flow. This model is used to investigate the effect of furnace operational conditions on crystal growth interface profiles and growth velocities. For a simple case of macroscopic radial growth, the phase-field model is validated against an analytical solution. Crystal growth in vertical gradient furnaces with two temperature profile setups have been also investigated using the developed model. The numerical simulations reveal that for a certain set of temperature boundary conditions, the heat transport in the melt near the phase interface is diffusion dominant and advection is suppressed.
Haines, D E; Nath, S; DiMarco, J P; Lobban, J H
1997-10-01
The inferoposterior region of the triangle of Koch is hypothesized to be the location of the atrial insertion of the slow atrioventricular (AV) nodal pathway. However, the actual site of conduction slowing in the slow AV nodal pathway is unknown. Entrainment mapping during AV nodal reentry can localize the reentrant pathway as follows: the AH interval measured from the mapping catheter = A'H (where A' is the exit site of the reentrant circuit) minus A'A (the conduction time from A' to the site of mapping); the SH interval during entrainment = SA' (the conduction time from stimulus into the reentry circuit) plus A'H. Thus, in all cases, the SH interval should be greater than or equal to the AH interval, and the deltaAH-SH should increase as distance and conduction time (SA' and A'A) from the reentry circuit increases. Fourteen patients with typical AV nodal reentry (cycle length 346 +/- 62 ms) and 1 with fast-slow (cycle length 430 ms) underwent activation and entrainment mapping from 8 to 12 sites in the triangle of Koch and coronary sinus. Pacing was performed at 2 to 3 mA above threshold, at a cycle length 10 ms shorter than tachycardia. A mapping site was defined as being in close proximity to the circuit if the deltaAH-SH was within 120% of the shortest 20th percentile deltaAH-SH value from all measured sites. In the 14 typical cases, 45 of 83 sites (54%) in the anatomic slow pathway region fulfilled criteria for close proximity to the reentry circuit compared with 13 of 50 sites (26%) outside of this region (p = 0.005). For these patients, the shortest SH interval measured from any entrainment site was 294 +/- 58 ms (89 +/- 10% of tachycardia cycle length, range 70% to 119%), indicating that the site of slow conduction in the slow pathway during AV nodal reentrant tachycardia was distal to all mapped sites. Thus, during typical AV nodal reentry, the "slow" pathway does not conduct slowly, and its insertion is located at or within the inferoposterior or
A block iterative LU solver for weakly coupled linear systems. [in fluid dynamics equations
NASA Technical Reports Server (NTRS)
Cooke, C. H.
1977-01-01
A hybrid technique, called the block iterative LU solver, is proposed for solving the linear equations resulting from a finite element numerical analysis of certain fluid dynamics problems where the equations are weakly coupled between distinct sets of variables. Either the block Jacobi iterative method or the block Gauss-Seidel iterative solver is combined with LU decomposition.
T2CG1, a package of preconditioned conjugate gradient solvers for TOUGH2
Moridis, G.; Pruess, K.; Antunez, E.
1994-03-01
Most of the computational work in the numerical simulation of fluid and heat flows in permeable media arises in the solution of large systems of linear equations. The simplest technique for solving such equations is by direct methods. However, because of large storage requirements and accumulation of roundoff errors, the application of direct solution techniques is limited, depending on matrix bandwidth, to systems of a few hundred to at most a few thousand simultaneous equations. T2CG1, a package of preconditioned conjugate gradient solvers, has been added to TOUGH2 to complement its direct solver and significantly increase the size of problems tractable on PCs. T2CG1 includes three different solvers: a Bi-Conjugate Gradient (BCG) solver, a Bi-Conjugate Gradient Squared (BCGS) solver, and a Generalized Minimum Residual (GMRES) solver. Results from six test problems with up to 30,000 equations show that T2CG1 (1) is significantly (and invariably) faster and requires far less memory than the MA28 direct solver, (2) it makes possible the solution of very large three-dimensional problems on PCs, and (3) that the BCGS solver is the fastest of the three in the tested problems. Sample problems are presented related to heat and fluid flow at Yucca Mountain and WIPP, environmental remediation by the Thermal Enhanced Vapor Extraction System, and geothermal resources.
McGhee, J.M.; Roberts, R.M.; Morel, J.E.
1997-06-01
A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner for scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated.
The role of nodal and internodal responses in gravitropism and autotropism in Galium aparine L
NASA Technical Reports Server (NTRS)
Heathcote, D. G.; Brown, A. H. (Principal Investigator)
1987-01-01
This time course and location of gravitropically induced curvatures in stems of goosegrass (Gallium aparine L.), a member of the Rubiaceae, have been investigated. In the early stages of the response (0-5 h), curvature develops throughout the growing region, and is followed by an autotropic straightening which affects the internodes only, leading to the production of essentially straight internodes some 15 h after the onset of gravistimulation. Curvatures developing in the nodal regions, however, continue to increase over this period, and are not subject to reversal by autotropism. The nodal curvatures are not entirely dependent on the presence of any other part of the plant, since marked curvatures can be induced in isolated nodal segments. This pattern of response leads ultimately to correction of the growth direction of the plant by means of curvature responses confined exclusively to the nodes, despite the initial participation of both nodes and internodes in the gravitropic reaction.
Zebrafish Rab5 proteins and a role for Rab5ab in nodal signalling
Kenyon, Emma J.; Campos, Isabel; Bull, James C.; Williams, P. Huw; Stemple, Derek L.; Clark, Matthew D.
2015-01-01
The RAB5 gene family is the best characterised of all human RAB families and is essential for in vitro homotypic fusion of early endosomes. In recent years, the disruption or activation of Rab5 family proteins has been used as a tool to understand growth factor signal transduction in whole animal systems such as Drosophila melanogaster and zebrafish. In this study we have examined the functions for four rab5 genes in zebrafish. Disruption of rab5ab expression by antisense morpholino oligonucleotide (MO) knockdown abolishes nodal signalling in early zebrafish embryos, whereas overexpression of rab5ab mRNA leads to ectopic expression of markers that are normally downstream of nodal signalling. By contrast MO disruption of other zebrafish rab5 genes shows little or no effect on expression of markers of dorsal organiser development. We conclude that rab5ab is essential for nodal signalling and organizer specification in the developing zebrafish embryo. PMID:25478908
RW Per - Nodal motion changes its amplitude by 1.4 mag
NASA Technical Reports Server (NTRS)
Schaefer, Bradley E.; Fried, Robert E.
1991-01-01
RW Per was found to have large secular changes in its eclipse amplitude. In blue light, for example, the amplitude was 3.2 mag in the early 1900s, 2.2 mag in the late 1960s, and 1.75 mag in 1990. Throughout this time, the brightness at maximum was constant in all colors. It is shown that the only possible explanation is nodal motion, where the inclination varies with a period of roughly 100,000 yr. The nodal motion is caused by a third star, for which the light curve, the colors, and the O - C curve already provide evidence. Thus, RW Per is only the fourth known star with large changes of eclipse amplitude and is only the second example of nodal motion.
Nonequilibrium electron dynamics in a solid with a changing nodal excitation gap
NASA Astrophysics Data System (ADS)
Smallwood, Christopher L.; Miller, Tristan L.; Zhang, Wentao; Kaindl, Robert A.; Lanzara, Alessandra
2016-06-01
We develop a computationally inexpensive model to examine the dynamics of boson-assisted electron relaxation in solids, studying nonequilibrium dynamics in a metal, in a nodal superconductor with a stationary density of states, and in a nodal superconductor where the gap dynamically opens. In the metallic system, the electron population resembles a thermal population at all times, but the presence of even a fixed nodal gap both invalidates a purely thermal treatment and sharply curtails relaxation rates. For a gap that is allowed to open as electron relaxation proceeds, effects are even more pronounced, and gap dynamics become coupled to the dynamics of the electron population. Comparisons to experiments reveal that phase-space restrictions in the presence of a gap are likely to play a significant role in the widespread observation of coexisting femtosecond and picosecond dynamics in the cuprate high-temperature superconductors.
Activin/Nodal signalling before implantation: setting the stage for embryo patterning
Papanayotou, Costis; Collignon, Jérôme
2014-01-01
Activins and Nodal are members of the transforming growth factor beta (TGF-β) family of growth factors. Their Smad2/3-dependent signalling pathway is well known for its implication in the patterning of the embryo after implantation. Although this pathway is active early on at preimplantation stages, embryonic phenotypes for loss-of-function mutations of prominent components of the pathway are not detected before implantation. It is only fairly recently that an understanding of the role of the Activin/Nodal signalling pathway at these stages has started to emerge, notably from studies detailing how it controls the expression of target genes in embryonic stem cells. We review here what is currently known of the TGF-β-related ligands that determine the activity of Activin/Nodal signalling at preimplantation stages, and recent advances in the elucidation of the Smad2/3-dependent mechanisms underlying developmental progression. PMID:25349448
Integration of a Multigrid ODE solver into an open medical simulation framework.
Wu, Xunlei; Yao, Jianhua; Enquobahrie, Andinet; Lee, Huai-Ping; Audette, Michel A
2012-01-01
In this paper, we present the implementation of a Multigrid ODE solver in SOFA framework. By combining the stability advantage of coarse meshes and the transient detail preserving virtue of fine meshes, Multigrid ODE solver computes more efficiently than classic ODE solvers based on a single level discretization. With the ever wider adoption of the SOFA framework in many surgical simulation projects, introducing this Multigrid ODE solver into SOFA's pool of ODE solvers shall benefit the entire community. This contribution potentially has broad ramifications in the surgical simulation research community, given that in a single-resolution system, a constitutively realistic interactive tissue response, which presupposes large elements, is in direct conflict with the need to represent clinically relevant critical tissues in the simulation, which are typically be comprised of small elements. PMID:23366578
High-performance equation solvers and their impact on finite element analysis
NASA Technical Reports Server (NTRS)
Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. Dale, Jr.
1990-01-01
The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number of operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.
A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions
NASA Technical Reports Server (NTRS)
Sun, Xian-He; Zhuang, Yu
1997-01-01
In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.
Accurate derivative evaluation for any Grad-Shafranov solver
NASA Astrophysics Data System (ADS)
Ricketson, L. F.; Cerfon, A. J.; Rachh, M.; Freidberg, J. P.
2016-01-01
We present a numerical scheme that can be combined with any fixed boundary finite element based Poisson or Grad-Shafranov solver to compute the first and second partial derivatives of the solution to these equations with the same order of convergence as the solution itself. At the heart of our scheme is an efficient and accurate computation of the Dirichlet to Neumann map through the evaluation of a singular volume integral and the solution to a Fredholm integral equation of the second kind. Our numerical method is particularly useful for magnetic confinement fusion simulations, since it allows the evaluation of quantities such as the magnetic field, the parallel current density and the magnetic curvature with much higher accuracy than has been previously feasible on the affordable coarse grids that are usually implemented.
Perturbative forward solver software for small localized fluorophores in tissue
Martelli, F.; Bianco, S. Del; Di Ninni, P.
2011-01-01
In this paper a forward solver software for the time domain and the CW domain based on the Born approximation for simulating the effect of small localized fluorophores embedded in a non-fluorescent biological tissue is proposed. The fluorescence emission is treated with a mathematical model that describes the migration of photons from the source to the fluorophore and of emitted fluorescent photons from the fluorophore to the detector for all those geometries for which Green’s functions are available. Subroutines written in FORTRAN that can be used for calculating the fluorescent signal for the infinite medium and for the slab are provided with a linked file. With these subroutines, quantities such as reflectance, transmittance, and fluence rate can be calculated. PMID:22254165
Perturbative forward solver software for small localized fluorophores in tissue.
Martelli, F; Del Bianco, S; Di Ninni, P
2012-01-01
In this paper a forward solver software for the time domain and the CW domain based on the Born approximation for simulating the effect of small localized fluorophores embedded in a non-fluorescent biological tissue is proposed. The fluorescence emission is treated with a mathematical model that describes the migration of photons from the source to the fluorophore and of emitted fluorescent photons from the fluorophore to the detector for all those geometries for which Green's functions are available. Subroutines written in FORTRAN that can be used for calculating the fluorescent signal for the infinite medium and for the slab are provided with a linked file. With these subroutines, quantities such as reflectance, transmittance, and fluence rate can be calculated. PMID:22254165
Periodic Density Functional Theory Solver using Multiresolution Analysis with MADNESS
NASA Astrophysics Data System (ADS)
Harrison, Robert; Thornton, William
2011-03-01
We describe the first implementation of the all-electron Kohn-Sham density functional periodic solver (DFT) using multi-wavelets and fast integral equations using MADNESS (multiresolution adaptive numerical environment for scientific simulation; http://code.google.com/p/m-a-d-n-e-s-s). The multiresolution nature of a multi-wavelet basis allows for fast computation with guaranteed precision. By reformulating the Kohn-Sham eigenvalue equation into the Lippmann-Schwinger equation, we can avoid using the derivative operator which allows better control of overall precision for the all-electron problem. Other highlights include the development of periodic integral operators with low-rank separation, an adaptable model potential for nuclear potential, and an implementation for Hartree Fock exchange. This work was supported by NSF project OCI-0904972 and made use of resources at the Center for Computational Sciences at Oak Ridge National Laboratory under contract DE-AC05-00OR22725.
Progress in developing Poisson-Boltzmann equation solvers
Li, Chuan; Li, Lin; Petukh, Marharyta; Alexov, Emil
2013-01-01
This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects. PMID:24199185
Using parallel banded linear system solvers in generalized eigenvalue problems
NASA Technical Reports Server (NTRS)
Zhang, Hong; Moss, William F.
1993-01-01
Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speed-up is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented.
Progress in developing Poisson-Boltzmann equation solvers.
Li, Chuan; Li, Lin; Petukh, Marharyta; Alexov, Emil
2013-03-01
This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects. PMID:24199185
A fast elliptic solver for simply connected domains
NASA Astrophysics Data System (ADS)
Kamgnia, E.; Sameh, A.
1989-08-01
We present a fast method for solving the Laplace, Poisson, and the Helmholtz equations on two-dimensional simply connected regions with smooth curved boundaries. The region is first mapped onto the unit disk, using a conformal transformation. The transformed equations are then solved on the unit disk, using mainly Rapid Elliptic Solvers (RES). The construction of the mapping itself gives rise to large linear systems of equations in whose solution RES play a major role. Our numerical experiments on the Alliant FX/8 and one CPU of the Cray X-MP/48 indicate that the scheme presented here is suitable for parallel and vector machines, respectively. Our scheme is efficient on any architecture which supports powerful fast Fourier transforms.
AN ADAPTIVE PARTICLE-MESH GRAVITY SOLVER FOR ENZO
Passy, Jean-Claude; Bryan, Greg L.
2014-11-01
We describe and implement an adaptive particle-mesh algorithm to solve the Poisson equation for grid-based hydrodynamics codes with nested grids. The algorithm is implemented and extensively tested within the astrophysical code Enzo against the multigrid solver available by default. We find that while both algorithms show similar accuracy for smooth mass distributions, the adaptive particle-mesh algorithm is more accurate for the case of point masses, and is generally less noisy. We also demonstrate that the two-body problem can be solved accurately in a configuration with nested grids. In addition, we discuss the effect of subcycling, and demonstrate that evolving all the levels with the same timestep yields even greater precision.
Towards a fully automated eclipsing binary solver for Gaia
NASA Astrophysics Data System (ADS)
Tingley, Brandon; Sadowski, Gilles; Siopis, Christos
2009-02-01
Gaia, an ESA cornerstone mission, will obtain of the order of 100 high-precision photometric observations and lower precision radial velocity measurements over five years for around a billion stars several hundred thousand of which will be eclipsing binaries. In order to extract the characteristics of these systems, a fully automated code must be available. During the process of this development, two tools that may be of use to the transit community have emerged: a very fast, simple, detached eclipsing binary simulator/solver based on a new approach and an interacting eclipsing binary simulator with most of the features of the Wilson-Devinney and Nightfall codes, but fully documented and written in easy-to-follow and highly portable Java. Currently undergoing development and testing, this code includes an intuitive graphical interface and an optimizer for the estimation of the physical parameters of the system.
Extending the QUDA Library with the eigCG Solver
Strelchenko, Alexei; Stathopoulos, Andreas
2014-12-12
While the incremental eigCG algorithm [ 1 ] is included in many LQCD software packages, its realization on GPU micro-architectures was still missing. In this session we report our experi- ence of the eigCG implementation in the QUDA library. In particular, we will focus on how to employ the mixed precision technique to accelerate solutions of large sparse linear systems with multiple right-hand sides on GPUs. Although application of mixed precision techniques is a well-known optimization approach for linear solvers, its utilization for the eigenvector com- puting within eigCG requires special consideration. We will discuss implementation aspects of the mixed precision deflation and illustrate its numerical behavior on the example of the Wilson twisted mass fermion matrix inversions
Polyurethanes: versatile materials and sustainable problem solvers for today's challenges.
Engels, Hans-Wilhelm; Pirkl, Hans-Georg; Albers, Reinhard; Albach, Rolf W; Krause, Jens; Hoffmann, Andreas; Casselmann, Holger; Dormish, Jeff
2013-09-01
Polyurethanes are the only class of polymers that display thermoplastic, elastomeric, and thermoset behavior depending on their chemical and morphological makeup. In addition to compact polyurethanes, foamed variations in particular are very widespread, and they achieve their targeted properties at very low weights. The simple production of sandwich structures and material composites in a single processing step is a key advantage of polyurethane technology. The requirement of energy and resource efficiency increasingly demands lightweight structures. Polyurethanes can serve this requirement by acting as matrix materials or as flexible adhesives for composites. Polyurethanes are indispensable when it comes to high-quality decorative coatings or maintaining the value of numerous objects. They are extremely adaptable and sustainable problem solvers for today's challenges facing our society, all of which impose special demands on materials. PMID:23893938
A Navier-Stokes solver for turbomachinery applications
Arnone, A.; Swanson, R.C. )
1993-04-01
A computer code for solving the Reynolds-averaged full Navier-Stokes equations has been developed and applied using H- and C-type grids. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. The integration in time is based on an explicit four-stage Runge-Kutta scheme. Local time stepping, variable coefficient implicit residual smoothing, and a full multigrid method have been implemented to accelerate steady-state calculations. A grid independence analysis is presented for a transonic rotor blade. Comparisons with experimental data show that the code is an accurate viscous solver and can give very good blade-to-blade predictions for engineering applications.
A comparison of solver performance for complex gastric electrophysiology models.
Sathar, Shameer; Cheng, Leo K; Trew, Mark L
2015-08-01
Computational techniques for solving systems of equations arising in gastric electrophysiology have not been studied for efficient solution process. We present a computationally challenging problem of simulating gastric electrophysiology in anatomically realistic stomach geometries with multiple intracellular and extracellular domains. The multiscale nature of the problem and mesh resolution required to capture geometric and functional features necessitates efficient solution methods if the problem is to be tractable. In this study, we investigated and compared several parallel preconditioners for the linear systems arising from tetrahedral discretisation of electrically isotropic and anisotropic problems, with and without stimuli. The results showed that the isotropic problem was computationally less challenging than the anisotropic problem and that the application of extracellular stimuli increased workload considerably. Preconditioning based on block Jacobi and algebraic multigrid solvers were found to have the best overall solution times and least iteration counts, respectively. The algebraic multigrid preconditioner would be expected to perform better on large problems. PMID:26736543
Status Of The UPS Space-Marching Flow Solver
NASA Technical Reports Server (NTRS)
Lawerence, Scott L.; VanDalsem, William (Technical Monitor)
1995-01-01
The status of the three-dimensional parabolized Navier-Stokes solver UPS is described. The UPS code, initiated at NASA Ames Research Center in 1986, continues to develop and evolve through application to supersonic and hypersonic flow fields. Hypersonic applications have motivated enhancement of the physical modeling capabilities of the code, specifically real gas modeling, boundary conditions, and turbulence and transition modeling. The UPS code has also been modified to enhance robustness and efficiency in order to be practically used in concert with an optimization code for supersonic transport design. These developments are briefly described along with some relevant results for generic test problems obtained during verification of the enhancements. Included developments and results have previously been published and widely disseminated domestically.
Workload Characterization of CFD Applications Using Partial Differential Equation Solvers
NASA Technical Reports Server (NTRS)
Waheed, Abdul; Yan, Jerry; Saini, Subhash (Technical Monitor)
1998-01-01
Workload characterization is used for modeling and evaluating of computing systems at different levels of detail. We present workload characterization for a class of Computational Fluid Dynamics (CFD) applications that solve Partial Differential Equations (PDEs). This workload characterization focuses on three high performance computing platforms: SGI Origin2000, EBM SP-2, a cluster of Intel Pentium Pro bases PCs. We execute extensive measurement-based experiments on these platforms to gather statistics of system resource usage, which results in workload characterization. Our workload characterization approach yields a coarse-grain resource utilization behavior that is being applied for performance modeling and evaluation of distributed high performance metacomputing systems. In addition, this study enhances our understanding of interactions between PDE solver workloads and high performance computing platforms and is useful for tuning these applications.
Margaryan, Naira V.; Gilgur, Alina; Seftor, Elisabeth A.; Purnell, Chad; Arva, Nicoleta C.; Gosain, Arun K.; Hendrix, Mary J. C.; Strizzi, Luigi
2016-01-01
Expression of Nodal, a Transforming Growth Factor-beta (TGF-β) related growth factor, is associated with aggressive melanoma. Nodal expression in adult dysplastic nevi may predict the development of aggressive melanoma in some patients. A subset of pediatric patients diagnosed with giant or large congenital melanocytic nevi (LCMN) has shown increased risk for development of melanoma. Here, we investigate whether Nodal expression can help identify the rare cases of LCMN that develop melanoma and shed light on why the majority of these patients do not. Immunohistochemistry (IHC) staining results show varying degree of Nodal expression in pediatric dysplastic nevi and LCMN. Moreover, median scores from Nodal IHC expression analysis were not significantly different between these two groups. Additionally, none of the LCMN patients in this study developed melanoma, regardless of Nodal IHC levels. Co-culture experiments revealed reduced tumor growth and lower levels of Nodal and its signaling molecules P-SMAD2 and P-ERK1/2 when melanoma cells were grown in vivo or in vitro with normal melanocytes. The same was observed in melanoma cells cultured with melanocyte conditioned media containing pigmented melanocyte derived melanosomes (MDM). Since MDM contain molecules capable of inactivating radical oxygen species, to investigate potential anti-oxidant effect of MDM on Nodal expression and signaling in melanoma, melanoma cells were treated with either N-acetyl-l-cysteine (NAC), a component of the anti-oxidant glutathione or synthetic melanin, which in addition to providing pigmentation can also exert free radical scavenging activity. Melanoma cells treated with NAC or synthetic melanin showed reduced levels of Nodal, P-SMAD2 and P-ERK1/2 compared to untreated melanoma cells. Thus, the potential role for Nodal in melanoma development in LCMN is less evident than in adult dysplastic nevi possibly due to melanocyte cross-talk in LCMN capable of offsetting or delaying the pro
Margaryan, Naira V; Gilgur, Alina; Seftor, Elisabeth A; Purnell, Chad; Arva, Nicoleta C; Gosain, Arun K; Hendrix, Mary J C; Strizzi, Luigi
2016-01-01
Expression of Nodal, a Transforming Growth Factor-beta (TGF-β) related growth factor, is associated with aggressive melanoma. Nodal expression in adult dysplastic nevi may predict the development of aggressive melanoma in some patients. A subset of pediatric patients diagnosed with giant or large congenital melanocytic nevi (LCMN) has shown increased risk for development of melanoma. Here, we investigate whether Nodal expression can help identify the rare cases of LCMN that develop melanoma and shed light on why the majority of these patients do not. Immunohistochemistry (IHC) staining results show varying degree of Nodal expression in pediatric dysplastic nevi and LCMN. Moreover, median scores from Nodal IHC expression analysis were not significantly different between these two groups. Additionally, none of the LCMN patients in this study developed melanoma, regardless of Nodal IHC levels. Co-culture experiments revealed reduced tumor growth and lower levels of Nodal and its signaling molecules P-SMAD2 and P-ERK1/2 when melanoma cells were grown in vivo or in vitro with normal melanocytes. The same was observed in melanoma cells cultured with melanocyte conditioned media containing pigmented melanocyte derived melanosomes (MDM). Since MDM contain molecules capable of inactivating radical oxygen species, to investigate potential anti-oxidant effect of MDM on Nodal expression and signaling in melanoma, melanoma cells were treated with either N-acetyl-l-cysteine (NAC), a component of the anti-oxidant glutathione or synthetic melanin, which in addition to providing pigmentation can also exert free radical scavenging activity. Melanoma cells treated with NAC or synthetic melanin showed reduced levels of Nodal, P-SMAD2 and P-ERK1/2 compared to untreated melanoma cells. Thus, the potential role for Nodal in melanoma development in LCMN is less evident than in adult dysplastic nevi possibly due to melanocyte cross-talk in LCMN capable of offsetting or delaying the pro
A fast solver for systems of axisymmetric ring vortices
NASA Astrophysics Data System (ADS)
Strickland, James H.; Amos, Donald E.
1990-09-01
A method which is capable of efficient calculation of the axisymmetric flow field produced by a large system of ring vortices is presented in this report. The system of ring vortices can, in turn, be used to model body surfaces and wakes in incompressible unsteady axisymmetric flow fields. This method takes advantage of source point and field point series expansions which enables one to make calculations for interactions between groups of vortices which are in well separated spatial domains rather than having to consider interactions between every pair of vortices. In this work, series expansions for the stream function of the ring vortex system are obtained. Such expansions explicitly contain the radial and axial velocity components. A FORTRAN computer code RSOLV has been written to execute the fast solution technique to calculate the stream function and the axial and radial velocity components at points in the flow field. Test cases have been run to optimize the code and to benchmark the truncation errors and CPU time savings associated with the method. Non-dimensional truncation errors for the stream function and total velocity field are on the order of 5 times 10(exp -5) and 3 times 10(exp -3) respectively. Single precision accuracy produces errors in these quantities up to about 1 times 10(exp -5). For 100 vortices in the field, there is virtually no CPU time savings with the fast solver. For 10,000 vortices in the flow, the fast solver obtains solutions in about 1 to 3 percent of the time required for the direct solution technique. Simulations of vortices with square and circular cores were run in order to obtain expressions for the self-induced velocities of such vortices.
Accuracy and Efficiency in Fixed-Point Neural ODE Solvers.
Hopkins, Michael; Furber, Steve
2015-10-01
Simulation of neural behavior on digital architectures often requires the solution of ordinary differential equations (ODEs) at each step of the simulation. For some neural models, this is a significant computational burden, so efficiency is important. Accuracy is also relevant because solutions can be sensitive to model parameterization and time step. These issues are emphasized on fixed-point processors like the ARM unit used in the SpiNNaker architecture. Using the Izhikevich neural model as an example, we explore some solution methods, showing how specific techniques can be used to find balanced solutions. We have investigated a number of important and related issues, such as introducing explicit solver reduction (ESR) for merging an explicit ODE solver and autonomous ODE into one algebraic formula, with benefits for both accuracy and speed; a simple, efficient mechanism for cancelling the cumulative lag in state variables caused by threshold crossing between time steps; an exact result for the membrane potential of the Izhikevich model with the other state variable held fixed. Parametric variations of the Izhikevich neuron show both similarities and differences in terms of algorithms and arithmetic types that perform well, making an overall best solution challenging to identify, but we show that particular cases can be improved significantly using the techniques described. Using a 1 ms simulation time step and 32-bit fixed-point arithmetic to promote real-time performance, one of the second-order Runge-Kutta methods looks to be the best compromise; Midpoint for speed or Trapezoid for accuracy. SpiNNaker offers an unusual combination of low energy use and real-time performance, so some compromises on accuracy might be expected. However, with a careful choice of approach, results comparable to those of general-purpose systems should be possible in many realistic cases. PMID:26313605
High Energy Boundary Conditions for a Cartesian Mesh Euler Solver
NASA Technical Reports Server (NTRS)
Pandya, Shishir; Murman, Scott; Aftosmis, Michael
2003-01-01
Inlets and exhaust nozzles are common place in the world of flight. Yet, many aerodynamic simulation packages do not provide a method of modelling such high energy boundaries in the flow field. For the purposes of aerodynamic simulation, inlets and exhausts are often fared over and it is assumed that the flow differences resulting from this assumption are minimal. While this is an adequate assumption for the prediction of lift, the lack of a plume behind the aircraft creates an evacuated base region thus effecting both drag and pitching moment values. In addition, the flow in the base region is often mis-predicted resulting in incorrect base drag. In order to accurately predict these quantities, a method for specifying inlet and exhaust conditions needs to be available in aerodynamic simulation packages. A method for a first approximation of a plume without accounting for chemical reactions is added to the Cartesian mesh based aerodynamic simulation package CART3D. The method consists of 3 steps. In the first step, a components approach where each triangle is assigned a component number is used. Here, a method for marking the inlet or exhaust plane triangles as separate components is discussed. In step two, the flow solver is modified to accept a reference state for the components marked inlet or exhaust. In the third step, the flow solver uses these separated components and the reference state to compute the correct flow condition at that triangle. The present method is implemented in the CART3D package which consists of a set of tools for generating a Cartesian volume mesh from a set of component triangulations. The Euler equations are solved on the resulting unstructured Cartesian mesh. The present methods is implemented in this package and its usefulness is demonstrated with two validation cases. A generic missile body is also presented to show the usefulness of the method on a real world geometry.
Laser engine simulation using pressure based Navier-Stokes solver
NASA Astrophysics Data System (ADS)
Youssef, Hazim Saad
1994-03-01
Analysis of the flow field in a laser engine represents a difficult computational problem involving combinations of complex physical and gas-dynamical processes. Following a brief discussion of these processes a calculation procedure using primitive variables formulation on a nonstaggered grid system is introduced. Based on this procedure, a pressure based Navier-Stokes solver (PBNS) is developed using a generalized curvilinear coordinate system. The solver is first tested in application to a subsonic compressible flow over an insulated flat plate and to a flow in an axisymmetric converging-diverging nozzle. Next, the PBNS code is used to analyze the flowfield and performance of a laser thruster. The physical/numerical model includes the geometric ray tracing for the laser beam, beam power absorption, plasma radiation losses, and plasma thermophysical and optical properties. Equilibrium hydrogen is used as a flowing gas and its properties are calculated using the Hydrogen Properties Calculation (HPC) based on the methods of statistical thermodynamics. Two thrustor configurations, two laser types (CO2 and iodide), various laser power levels, and various injection conditions are tested. The results of these tests include the temperature, pressure, velocity, and Mach number contours, as well as tables of the laser beam power absorbed, radiation losses to the thrustor walls, thrust level, and specific impulse. The maximum specific impulse obtained in these tests is 1537 sec for a CO2 laser thruster and 827 sec for an iodide laser thruster. Up to 100% power absorption can be achieved; however, radiation losses from the hot plasma are quite high disallowing a full conversion of the absorbed power into the thermal energy of the propellant. The PBNS code can be used to study the effects of various design parameters on the performance of a laser thruster and provide guidelines for the preliminary design of a laser engine.
Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers
Pernice, M.
1994-12-31
Domain decomposed preconditioners for nonsymmetric partial differential equations typically require the solution of problems on the subdomains. Most implementations employ exact solvers to obtain these solutions. Consequently work and storage requirements for the subdomain problems grow rapidly with the size of the subdomain problems. Subdomain solves constitute the single largest computational cost of a domain decomposed preconditioner, and improving the efficiency of this phase of the computation will have a significant impact on the performance of the overall method. The small local memory available on the nodes of most message-passing multicomputers motivates consideration of the use of an iterative method for solving subdomain problems. For large-scale systems of equations that are derived from three-dimensional problems, memory considerations alone may dictate the need for using iterative methods for the subdomain problems. In addition to reduced storage requirements, use of an iterative solver on the subdomains allows flexibility in specifying the accuracy of the subdomain solutions. Substantial savings in solution time is possible if the quality of the domain decomposed preconditioner is not degraded too much by relaxing the accuracy of the subdomain solutions. While some work in this direction has been conducted for symmetric problems, similar studies for nonsymmetric problems appear not to have been pursued. This work represents a first step in this direction, and explores the effectiveness of performing subdomain solves using several transpose-free Krylov subspace methods, GMRES, transpose-free QMR, CGS, and a smoothed version of CGS. Depending on the difficulty of the subdomain problem and the convergence tolerance used, a reduction in solution time is possible in addition to the reduced memory requirements. The domain decomposed preconditioner is a Schur complement method in which the interface operators are approximated using interface probing.
A three-dimensional fast solver for arbitrary vorton distributions
Strickland, J.H.; Baty, R.S.
1994-05-01
A method which is capable of an efficient calculation of the three-dimensional flow field produced by a large system of vortons (discretized regions of vorticity) is presented in this report. The system of vortons can, in turn, be used to model body surfaces, container boundaries, free-surfaces, plumes, jets, and wakes in unsteady three-dimensional flow fields. This method takes advantage of multipole and local series expansions which enables one to make calculations for interactions between groups of vortons which are in well-separated spatial domains rather than having to consider interactions between every pair of vortons. In this work, series expansions for the vector potential of the vorton system are obtained. From such expansions, the three components of velocity can be obtained explicitly. A Fortran computer code FAST3D has been written to calculate the vector potential and the velocity components at selected points in the flow field. In this code, the evaluation points do not have to coincide with the location of the vortons themselves. Test cases have been run to benchmark the truncation errors and CPU time savings associated with the method. Non-dimensional truncation errors for the magnitudes of the vector potential and velocity fields are on the order of 10{sup {minus}4}and 10{sup {minus}3} respectively. Single precision accuracy produces errors in these quantities of up to 10{sup {minus}5}. For less than 1,000 to 2,000 vortons in the field, there is virtually no CPU time savings with the fast solver. For 100,000 vortons in the flow, the fast solver obtains solutions in 1 % to 10% of the time required for the direct solution technique depending upon the configuration.
GPU-Accelerated Finite Element Method for Modelling Light Transport in Diffuse Optical Tomography
Schweiger, Martin
2011-01-01
We introduce a GPU-accelerated finite element forward solver for the computation of light transport in scattering media. The forward model is the computationally most expensive component of iterative methods for image reconstruction in diffuse optical tomography, and performance optimisation of the forward solver is therefore crucial for improving the efficiency of the solution of the inverse problem. The GPU forward solver uses a CUDA implementation that evaluates on the graphics hardware the sparse linear system arising in the finite element formulation of the diffusion equation. We present solutions for both time-domain and frequency-domain problems. A comparison with a CPU-based implementation shows significant performance gains of the graphics accelerated solution, with improvements of approximately a factor of 10 for double-precision computations, and factors beyond 20 for single-precision computations. The gains are also shown to be dependent on the mesh complexity, where the largest gains are achieved for high mesh resolutions. PMID:22013431
Wu, Y.; Xie, Z.; Fischer, U.
1999-11-01
A discrete ordinates nodal transport method has been developed for numerical solution of the one-dimensional neutron transport equation in curvilinear geometries. The nodal transport equation is solved by the Green's function method, using the Legendre polynomial expansion for spatial dependence and the discrete ordinates (S{sub N}) approximation for angular dependence. The calculation for various test problems has been performed to verify the method. The numerical results demonstrate that it has very high precision on coarse spatial meshes relative to the standard fine-mesh S{sub N} method with the spatial diamond-differencing scheme.
Adaptive Implicit Non-Equilibrium Radiation Diffusion
Philip, Bobby; Wang, Zhen; Berrill, Mark A; Rodriguez Rodriguez, Manuel; Pernice, Michael
2013-01-01
We describe methods for accurate and efficient long term time integra- tion of non-equilibrium radiation diffusion systems: implicit time integration for effi- cient long term time integration of stiff multiphysics systems, local control theory based step size control to minimize the required global number of time steps while control- ling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton-Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.
Lao, Louis; Hope, Andrew J.; Maganti, Manjula; Brade, Anthony; Bezjak, Andrea; Saibishkumar, Elantholi P.; Giuliani, Meredith; Sun, Alexander; Cho, B. C. John
2014-09-01
Purpose: Reported rates of non-small cell lung cancer (NSCLC) nodal failure following stereotactic body radiation therapy (SBRT) are lower than those reported in the surgical series when matched for stage. We hypothesized that this effect was due to incidental prophylactic nodal irradiation. Methods and Materials: A prospectively collected group of medically inoperable early stage NSCLC patients from 2004 to 2010 was used to identify cases with nodal relapses. Controls were matched to cases, 2:1, controlling for tumor volume (ie, same or greater) and tumor location (ie, same lobe). Reference (normalized to equivalent dose for 2-Gy fractions [EQD2]) point doses at the ipsilateral hilum and carina, demographic data, and clinical outcomes were extracted from the medical records. Univariate conditional logistical regression analyses were performed with variables of interest. Results: Cases and controls were well matched except for size. The controls, as expected, had larger gross tumor volumes (P=.02). The mean ipsilateral hilar doses were 9.6 Gy and 22.4 Gy for cases and controls, respectively (P=.014). The mean carinal doses were 7.0 Gy and 9.2 Gy, respectively (P=.13). Mediastinal nodal relapses, with and without ipsilateral hilar relapse, were associated with mean ipsilateral hilar doses of 3.6 Gy and 19.8 Gy, respectively (P=.01). The conditional density plot appears to demonstrate an inverse dose-effect relationship between ipsilateral hilar normalized total dose and risk of ipsilateral hilar relapse. Conclusions: Incidental hilar dose greater than 20 Gy is significantly associated with fewer ipsilateral hilar relapses in inoperable early stage NSCLC patients treated with SBRT.
Nodal Quasiparticle Meltdown in Ultra-High Resolution Pump-Probe Angle-Resolved Photoemission
Graf, Jeff; Jozwiak, Chris; Smallwood, Chris L.; Eisaki, H.; Kaindl, Robert A.; Lee, Dung-Hai; Lanzara, Alessandra
2011-06-03
High-T{sub c} cuprate superconductors are characterized by a strong momentum-dependent anisotropy between the low energy excitations along the Brillouin zone diagonal (nodal direction) and those along the Brillouin zone face (antinodal direction). Most obvious is the d-wave superconducting gap, with the largest magnitude found in the antinodal direction and no gap in the nodal direction. Additionally, while antin- odal quasiparticle excitations appear only below T{sub c}, superconductivity is thought to be indifferent to nodal excitations as they are regarded robust and insensitive to T{sub c}. Here we reveal an unexpected tie between nodal quasiparticles and superconductivity using high resolution time- and angle-resolved photoemission on optimally doped Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} . We observe a suppression of the nodal quasiparticle spectral weight following pump laser excitation and measure its recovery dynamics. This suppression is dramatically enhanced in the superconducting state. These results reduce the nodal-antinodal dichotomy and challenge the conventional view of nodal excitation neutrality in superconductivity. The electronic structures of high-Tc cuprates are strongly momentum-dependent. This is one reason why the momentum-resolved technique of angle-resolved photoemission spectroscopy (ARPES) has been a central tool in the field of high-temperature superconductivity. For example, coherent low energy excitations with momenta near the Brillouin zone face, or antinodal quasiparticles (QPs), are only observed below T{sub c} and have been linked to superfluid density. They have therefore been the primary focus of ARPES studies. In contrast, nodal QPs, with momenta along the Brillouin zone diagonal, have received less attention and are usually regarded as largely immune to the superconducting transition because they seem insensitive to perturbations such as disorder, doping, isotope exchange, charge ordering, and temperature. Clearly
A Fast Poisson Solver with Periodic Boundary Conditions for GPU Clusters in Various Configurations
NASA Astrophysics Data System (ADS)
Rattermann, Dale Nicholas
Fast Poisson solvers using the Fast Fourier Transform on uniform grids are especially suited for parallel implementation, making them appropriate for portability on graphical processing unit (GPU) devices. The goal of the following work was to implement, test, and evaluate a fast Poisson solver for periodic boundary conditions for use on a variety of GPU configurations. The solver used in this research was FLASH, an immersed-boundary-based method, which is well suited for complex, time-dependent geometries, has robust adaptive mesh refinement/de-refinement capabilities to capture evolving flow structures, and has been successfully implemented on conventional, parallel supercomputers. However, these solvers are still computationally costly to employ, and the total solver time is dominated by the solution of the pressure Poisson equation using state-of-the-art multigrid methods. FLASH improves the performance of its multigrid solvers by integrating a parallel FFT solver on a uniform grid during a coarse level. This hybrid solver could then be theoretically improved by replacing the highly-parallelizable FFT solver with one that utilizes GPUs, and, thus, was the motivation for my research. In the present work, the CPU-utilizing parallel FFT solver (PFFT) used in the base version of FLASH for solving the Poisson equation on uniform grids has been modified to enable parallel execution on CUDA-enabled GPU devices. New algorithms have been implemented to replace the Poisson solver that decompose the computational domain and send each new block to a GPU for parallel computation. One-dimensional (1-D) decomposition of the computational domain minimizes the amount of network traffic involved in this bandwidth-intensive computation by limiting the amount of all-to-all communication required between processes. Advanced techniques have been incorporated and implemented in a GPU-centric code design, while allowing end users the flexibility of parameter control at runtime in
Kimura, Tomoki; Togami, Taro; Nishiyama, Yoshihiro; Ohkawa, Motoomi; Takashima, Hitoshi
2010-06-01
Purpose: To evaluate the incidental irradiation dose to elective nodal regions in the treatment of advanced non-small-cell lung cancer with involved-field radiation therapy (IF-RT) and the pattern of elective nodal failure (ENF). Methods and Materials: Fifty patients with advanced non-small-cell lung cancer, who received IF-RT at Kagawa University were enrolled. To evaluate the dose of incidental irradiation, we delineated nodal regions with a Japanese map and the American Thoracic Society map (levels 1-11) in each patient retrospectively and calculated the dose parameters such as mean dose, D95, and V95 (40 Gy as the prescribed dose of elective nodal irradiation). Results: Using the Japanese map, the median mean dose was more than 40 Gy in most of the nodal regions, except at levels 1, 3, and 7. In particular, each dosimetric parameter of level 1 was significantly lower than those at other levels, and each dosimetric parameter of levels 10 to 11 ipsilateral (11I) was significantly higher than those in other nodal regions. Using the American Thoracic Society map, basically, the results were similar to those of the Japanese map. ENF was observed in 4 patients (8%), five nodal regions, and no mean dose to the nodal region exceeded 40 Gy. On the Japanese map, each parameter of these five nodal region was significantly lower than those of the other nodal regions. Conclusions: These results show that a high dose of incidental irradiation may contribute to the low incidence of ENF in patients who have received IF-RT.
NASA Astrophysics Data System (ADS)
Senoo, Y.
The influence of vaneless diffusers on flow in centrifugal compressors, particularly on surge, is discussed. A vaneless diffuser can demonstrate stable operation in a wide flow range only if it is installed with a backward leaning blade impeller. The circumferential distortion of flow in the impeller disappears quickly in the vaneless diffuser. The axial distortion of flow at the diffuser inlet does not decay easily. In large specific speed compressors, flow out of the impeller is distorted axially. Pressure recovery of diffusers at distorted inlet flow is considerably improved by half guide vanes. The best height of the vanes is a little 1/2 diffuser width. In small specific speed compressors, flow out of the impeller is not much distorted and pressure recovery can be predicted with one-dimensional flow analysis. Wall friction loss is significant in narrow diffusers. The large pressure drop at a small flow rate can cause the positive gradient of the pressure-flow rate characteristic curve, which may cause surging.
Akt Inhibitor MK2206 in Treating Patients With Relapsed or Refractory Diffuse Large B-Cell Lymphoma
2015-07-31
Adult Grade III Lymphomatoid Granulomatosis; Extranodal Marginal Zone Lymphoma of Mucosa-Associated Lymphoid Tissue; Intraocular Lymphoma; Nodal Marginal Zone Lymphoma; Recurrent Adult Diffuse Large Cell Lymphoma; Secondary Central Nervous System Non-Hodgkin Lymphoma; Small Intestinal Lymphoma; Splenic Marginal Zone Lymphoma; Testicular Lymphoma; Waldenstrom Macroglobulinemia
Acceleration of FDTD mode solver by high-performance computing techniques.
Han, Lin; Xi, Yanping; Huang, Wei-Ping
2010-06-21
A two-dimensional (2D) compact finite-difference time-domain (FDTD) mode solver is developed based on wave equation formalism in combination with the matrix pencil method (MPM). The method is validated for calculation of both real guided and complex leaky modes of typical optical waveguides against the bench-mark finite-difference (FD) eigen mode solver. By taking advantage of the inherent parallel nature of the FDTD algorithm, the mode solver is implemented on graphics processing units (GPUs) using the compute unified device architecture (CUDA). It is demonstrated that the high-performance computing technique leads to significant acceleration of the FDTD mode solver with more than 30 times improvement in computational efficiency in comparison with the conventional FDTD mode solver running on CPU of a standard desktop computer. The computational efficiency of the accelerated FDTD method is in the same order of magnitude of the standard finite-difference eigen mode solver and yet require much less memory (e.g., less than 10%). Therefore, the new method may serve as an efficient, accurate and robust tool for mode calculation of optical waveguides even when the conventional eigen value mode solvers are no longer applicable due to memory limitation. PMID:20588502
GORRAM: Introducing accurate operational-speed radiative transfer Monte Carlo solvers
NASA Astrophysics Data System (ADS)
Buras-Schnell, Robert; Schnell, Franziska; Buras, Allan
2016-06-01
We present a new approach for solving the radiative transfer equation in horizontally homogeneous atmospheres. The motivation was to develop a fast yet accurate radiative transfer solver to be used in operational retrieval algorithms for next generation meteorological satellites. The core component is the program GORRAM (Generator Of Really Rapid Accurate Monte-Carlo) which generates solvers individually optimized for the intended task. These solvers consist of a Monte Carlo model capable of path recycling and a representative set of photon paths. Latter is generated using the simulated annealing technique. GORRAM automatically takes advantage of limitations on the variability of the atmosphere. Due to this optimization the number of photon paths necessary for accurate results can be reduced by several orders of magnitude. For the shown example of a forward model intended for an aerosol satellite retrieval, comparison with an exact yet slow solver shows that a precision of better than 1% can be achieved with only 36 photons. The computational time is at least an order of magnitude faster than any other type of radiative transfer solver. Merely the lookup table approach often used in satellite retrieval is faster, but on the other hand suffers from limited accuracy. This makes GORRAM-generated solvers an eligible candidate as forward model in operational-speed retrieval algorithms and data assimilation applications. GORRAM also has the potential to create fast solvers of other integrable equations.
Oasis: A high-level/high-performance open source Navier-Stokes solver
NASA Astrophysics Data System (ADS)
Mortensen, Mikael; Valen-Sendstad, Kristian
2015-03-01
Oasis is a high-level/high-performance finite element Navier-Stokes solver written from scratch in Python using building blocks from the FEniCS project (fenicsproject.org). The solver is unstructured and targets large-scale applications in complex geometries on massively parallel clusters. Oasis utilizes MPI and interfaces, through FEniCS, to the linear algebra backend PETSc. Oasis advocates a high-level, programmable user interface through the creation of highly flexible Python modules for new problems. Through the high-level Python interface the user is placed in complete control of every aspect of the solver. A version of the solver, that is using piecewise linear elements for both velocity and pressure, is shown to reproduce very well the classical, spectral, turbulent channel simulations of Moser et al. (1999). The computational speed is strongly dominated by the iterative solvers provided by the linear algebra backend, which is arguably the best performance any similar implicit solver using PETSc may hope for. Higher order accuracy is also demonstrated and new solvers may be easily added within the same framework.
The impact of improved sparse linear solvers on industrial engineering applications
Heroux, M.; Baddourah, M.; Poole, E.L.; Yang, Chao Wu
1996-12-31
There are usually many factors that ultimately determine the quality of computer simulation for engineering applications. Some of the most important are the quality of the analytical model and approximation scheme, the accuracy of the input data and the capability of the computing resources. However, in many engineering applications the characteristics of the sparse linear solver are the key factors in determining how complex a problem a given application code can solve. Therefore, the advent of a dramatically improved solver often brings with it dramatic improvements in our ability to do accurate and cost effective computer simulations. In this presentation we discuss the current status of sparse iterative and direct solvers in several key industrial CFD and structures codes, and show the impact that recent advances in linear solvers have made on both our ability to perform challenging simulations and the cost of those simulations. We also present some of the current challenges we have and the constraints we face in trying to improve these solvers. Finally, we discuss future requirements for sparse linear solvers on high performance architectures and try to indicate the opportunities that exist if we can develop even more improvements in linear solver capabilities.
The effects of advection solvers on the performance of air quality models
Tanrikulu, S.; Odman, M.T.
1996-12-31
The available numerical solvers for the advection term in the chemical species conservation equation have different properties, and consequently introduce different types of errors. These errors can affect the performance of air quality models and lead to biases in model results. In this study, a large number of advection solvers have been studied and six of them were identified as having potential for use in photochemical models. The identified solvers were evaluated extensively using various numerical tests that are relevant to air quality simulations. Among the solvers evaluated, three of them showed better performance in terms of accuracy and some other characteristics such as conservation of mass and positivity. They are the solvers by Bott, Yuamartino, and Dabdub and Seinfeld. These three solvers were incorporated into the SARMAP Air Quality Model (SAQM) and the August 3-6, 1990 ozone episode in the San Joaquin Valley of California was simulated with each. A model performance analysis was conducted for each simulation using the rich air quality database of the 1990 San Joaquin Valley Air Quality Study. The results of the simulations were compared with each other and the effects of advection solvers on the performance of the model are discussed.
Quantum Transport of Disordered Weyl Semimetals at the Nodal Point
NASA Astrophysics Data System (ADS)
Sbierski, Björn; Pohl, Gregor; Bergholtz, Emil J.; Brouwer, Piet W.
2014-07-01
Weyl semimetals are paradigmatic topological gapless phases in three dimensions. We here address the effect of disorder on charge transport in Weyl semimetals. For a single Weyl node with energy at the degeneracy point and without interactions, theory predicts the existence of a critical disorder strength beyond which the density of states takes on a nonzero value. Predictions for the conductivity are divergent, however. In this work, we present a numerical study of transport properties for a disordered Weyl cone at zero energy. For weak disorder, our results are consistent with a renormalization group flow towards an attractive pseudoballistic fixed point with zero conductivity and a scale-independent conductance; for stronger disorder, diffusive behavior is reached. We identify the Fano factor as a signature that discriminates between these two regimes.
Quantum transport of disordered Weyl semimetals at the nodal point.
Sbierski, Björn; Pohl, Gregor; Bergholtz, Emil J; Brouwer, Piet W
2014-07-11
Weyl semimetals are paradigmatic topological gapless phases in three dimensions. We here address the effect of disorder on charge transport in Weyl semimetals. For a single Weyl node with energy at the degeneracy point and without interactions, theory predicts the existence of a critical disorder strength beyond which the density of states takes on a nonzero value. Predictions for the conductivity are divergent, however. In this work, we present a numerical study of transport properties for a disordered Weyl cone at zero energy. For weak disorder, our results are consistent with a renormalization group flow towards an attractive pseudoballistic fixed point with zero conductivity and a scale-independent conductance; for stronger disorder, diffusive behavior is reached. We identify the Fano factor as a signature that discriminates between these two regimes. PMID:25062216
Nodal signaling regulates endodermal cell motility and actin dynamics via Rac1 and Prex1
Housley, Michael P.; Weiner, Orion D.
2012-01-01
Embryo morphogenesis is driven by dynamic cell behaviors, including migration, that are coordinated with fate specification and differentiation, but how such coordination is achieved remains poorly understood. During zebrafish gastrulation, endodermal cells sequentially exhibit first random, nonpersistent migration followed by oriented, persistent migration and finally collective migration. Using a novel transgenic line that labels the endodermal actin cytoskeleton, we found that these stage-dependent changes in migratory behavior correlated with changes in actin dynamics. The dynamic actin and random motility exhibited during early gastrulation were dependent on both Nodal and Rac1 signaling. We further identified the Rac-specific guanine nucleotide exchange factor Prex1 as a Nodal target and showed that it mediated Nodal-dependent random motility. Reducing Rac1 activity in endodermal cells caused them to bypass the random migration phase and aberrantly contribute to mesodermal tissues. Together, our results reveal a novel role for Nodal signaling in regulating actin dynamics and migration behavior, which are crucial for endodermal morphogenesis and cell fate decisions. PMID:22945937
NASA Astrophysics Data System (ADS)
Grootendorst, Diederik J.; Fratila, Raluca M.; Visscher, Martijn; Ten Haken, Bennie; van Wezel, Richard; Steenbergen, Wiendelt; Manohar, Srirang; Ruers, Theo J. M.
2013-02-01
Detection of tumor metastases in the lymphatic system is essential for accurate staging of various malignancies, however fast, accurate and cost-effective intra-operative evaluation of the nodal status remains difficult to perform with common available medical imaging techniques. In recent years, numerous studies have confirmed the additional value of superparamagnetic iron oxide dispersions (SPIOs) for nodal staging purposes, prompting the clearance of different SPIO dispersions for clinical practice. We evaluate whether a combination of photoacoustic (PA) imaging and a clinically approved SPIO dispersion, could be applied for intra-operative nodal staging. Metastatic adenocarcinoma was inoculated in Copenhagen rats for 5 or 8 days. After SPIO injection, the lymph nodes were photoacoustically imaged both in vivo and ex vivo whereafter imaging results were correlated with MR and histology. Results were compared to a control group without tumor inoculation. In the tumor groups clear irregularities, as small as 1 mm, were observed in the PA contrast pattern of the nodes together with an decrease of PA response. These irregularities could be correlated to the absence of contrast in the MR images and could be linked to metastatic deposits seen in the histological slides. The PA and MR images of the control animals did not show these features. We conclude that the combination of photoacoustic imaging with a clinically approved iron oxide nanoparticle dispersion is able to detect lymph node metastases in an animal model. This approach opens up new possibilities for fast intra-operative nodal staging in a clinical setting.
Sensitivity analysis and optimization of nodal point placement for vibration reduction
NASA Technical Reports Server (NTRS)
Pritchard, J. I.; Adelman, H. M.; Haftka, R. T.
1987-01-01
A method is developed for sensitivity analysis and optimization of nodal point locations in connection with vibration reduction. A straightforward derivation of the expression for the derivative of nodal locations is given, and the role of the derivative in assessing design trends is demonstrated. An optimization process is developed which uses added lumped masses on the structure as design variables to move the node to a preselected location - for example, where low response amplitude is required or to a point which makes the mode shape nearly orthogonal to the force distribution, thereby minimizing the generalized force. The optimization formulation leads to values for added masses that adjust a nodal location while minimizing the total amount of added mass required to do so. As an example, the node of the second mode of a cantilever box beam is relocated to coincide with the centroid of a prescribed force distribution, thereby reducing the generalized force substantially without adding excessive mass. A comparison with an optimization formulation that directly minimizes the generalized force indicates that nodal placement gives essentially a minimum generalized force when the node is appropriately placed.
Sensitivity derivatives and optimization of nodal point locations for vibration reduction
NASA Technical Reports Server (NTRS)
Pritchard, Jocelyn I.; Adelman, Howard M.; Haftka, Raphael T.
1987-01-01
A method is developed for sensitivity analysis and optimization of nodal point locations in connection with vibration reduction. A straightforward derivation of the expression for the derivative of nodal locations is given, and the role of the derivative in assessing design trends is demonstrated. An optimization process is developed which uses added lumped masses on the structure as design variables to move the node to a preselected location; for example, where low response amplitude is required or to a point which makes the mode shape nearly orthogonal to the force distribution, thereby minimizing the generalized force. The optimization formulation leads to values for added masses that adjust a nodal location while minimizing the total amount of added mass required to do so. As an example, the node of the second mode of a cantilever box beam is relocated to coincide with the centroid of a prescribed force distribution, thereby reducing the generalized force substantially without adding excessive mass. A comparison with an optimization formulation that directly minimizes the generalized force indicates that nodal placement gives essentially a minimum generalized force when the node is appropriately placed.
Senstitivty analysis and optimization of nodal point placement for vibration reduction
NASA Technical Reports Server (NTRS)
Pritchard, J. I.; Adelman, H. M.; Haftka, R. T.
1986-01-01
A method is developed for sensitivity analysis and optimization of nodal point locations in connection with vibration reduction. A straightforward derivation of the expression for the derivative of nodal locations is given, and the role of the derivative in assessing design trends is demonstrated. An optimization process is developed which uses added lumped masses on the structure as design variables to move the node to a preselected location - for example, where low response amplitude is required or to a point which makes the mode shape nearly orthogonal to the force distribution, thereby minimizing the generalized force. The optimization formulation leads to values for added masses that adjust a nodal location while minimizing the total amount of added mass required to do so. As an example, the node of the second mode of a cantilever box beam is relocated to coincide with the centroid of a prescribed force distribution, thereby reducing the generalized force substantially without adding excessive mass. A comparison with an optimization formulation that directly minimizes the generalized force indicates that nodal placement gives essentially a minimum generalized force when the node is appropriately placed.
Lin, Pan; Yang, Yong; Jovicich, Jorge; De Pisapia, Nicola; Wang, Xiang; Zuo, Chun S; Levitt, James Jonathan
2016-03-01
Characterization of the default mode network (DMN) as a complex network of functionally interacting dynamic systems has received great interest for the study of DMN neural mechanisms. In particular, understanding the relationship of intrinsic resting-state DMN brain network with cognitive behaviors is an important issue in healthy cognition and mental disorders. However, it is still unclear how DMN functional connectivity links to cognitive behaviors during resting-state. In this study, we hypothesize that static and dynamic DMN nodal topology is associated with upcoming cognitive task performance. We used graph theory analysis in order to understand better the relationship between the DMN functional connectivity and cognitive behavior during resting-state and task performance. Nodal degree of the DMN was calculated as a metric of network topology. We found that the static and dynamic posterior cingulate cortex (PCC) nodal degree within the DMN was associated with task performance (Reaction Time). Our results show that the core node PCC nodal degree within the DMN was significantly correlated with reaction time, which suggests that the PCC plays a key role in supporting cognitive function. PMID:25904156
Sarkar, Prasenjit; Randall, Shan M.; Collier, Timothy S.; Nero, Anthony; Russell, Teal A.; Muddiman, David C.; Rao, Balaji M.
2015-01-01
Human embryonic stem cells (hESCs) have been routinely treated with bone morphogenetic protein and/or inhibitors of activin/nodal signaling to obtain cells that express trophoblast markers. Trophoblasts can terminally differentiate to either extravillous trophoblasts or syncytiotrophoblasts. The signaling pathways that govern the terminal fate of these trophoblasts are not understood. We show that activin/nodal signaling switches the terminal fate of these hESC-derived trophoblasts. Inhibition of activin/nodal signaling leads to formation of extravillous trophoblast, whereas loss of activin/nodal inhibition leads to the formation of syncytiotrophoblasts. Also, the ability of hESCs to form bona fide trophoblasts has been intensely debated. We have examined hESC-derived trophoblasts in the light of stringent criteria that were proposed recently, such as hypomethylation of the ELF5-2b promoter region and down-regulation of HLA class I antigens. We report that trophoblasts that possess these properties can indeed be obtained from hESCs. PMID:25670856
Coordinate Nodal and BMP inhibition directs Baf60c-dependent cardiomyocyte commitment
Cai, Wenqing; Albini, Sonia; Wei, Ke; Willems, Erik; Guzzo, Rosa M.; Tsuda, Masanao; Giordani, Lorenzo; Spiering, Sean; Kurian, Leo; Yeo, Gene W.; Puri, Pier Lorenzo; Mercola, Mark
2013-01-01
A critical but molecularly uncharacterized step in heart formation and regeneration is the process that commits progenitor cells to differentiate into cardiomyocytes. Here, we show that the endoderm-derived dual Nodal/bone morphogenetic protein (BMP) antagonist Cerberus-1 (Cer1) in embryonic stem cell cultures orchestrates two signaling pathways that direct the SWI/SNF chromatin remodeling complex to cardiomyogenic loci in multipotent (KDR/Flk1+) progenitors, activating lineage-specific transcription. Transient inhibition of Nodal by Cer1 induces Brahma-associated factor 60c (Baf60c), one of three Baf60 variants (a, b, and c) that are mutually exclusively assembled into SWI/SNF. Blocking Nodal and BMP also induces lineage-specific transcription factors Gata4 and Tbx5, which interact with Baf60c. siRNA to Cer1, Baf60c, or the catalytic SWI/SNF subunit Brg1 prevented the developmental opening of chromatin surrounding the Nkx2.5 early cardiac enhancer and cardiomyocyte differentiation. Overexpression of Baf60c fully rescued these deficits, positioning Baf60c and SWI/SNF function downstream from Cer1. Thus, antagonism of Nodal and BMP coordinates induction of the myogenic Baf60c variant and interacting transcription factors to program the developmental opening of cardiomyocyte-specific loci in chromatin. This is the first demonstration that cues from the progenitor cell environment direct the subunit variant composition of SWI/SNF to remodel the transcriptional landscape for lineage-specific differentiation. PMID:24186978
ERIC Educational Resources Information Center
Chatzarakis, G. E.
2009-01-01
This paper presents a new pedagogical method for nodal analysis optimization based on the use of virtual current sources, applicable to any linear electric circuit (LEC), regardless of its complexity. The proposed method leads to straightforward solutions, mostly arrived at by inspection. Furthermore, the method is easily adapted to computer…
Topological nodal-line semimetals in alkaline-earth stannides, germanides, and silicides
NASA Astrophysics Data System (ADS)
Huang, Huaqing; Liu, Jianpeng; Vanderbilt, David; Duan, Wenhui
2016-05-01
Based on first-principles calculations and an effective Hamiltonian analysis, we systematically investigate the electronic and topological properties of alkaline-earth compounds A X2 (A =Ca , Sr, Ba; X =Si , Ge, Sn). Taking BaSn2 as an example, we find that when spin-orbit coupling is ignored, these materials are three-dimensional topological nodal-line semimetals characterized by a snakelike nodal loop in three-dimensional momentum space. Drumheadlike surface states emerge either inside or outside the loop circle on the (001) surface depending on surface termination, while complicated double-drumhead-like surface states appear on the (010) surface. When spin-orbit coupling is included, the nodal line is gapped and the system becomes a topological insulator with Z2 topological invariants (1;001). Since spin-orbit coupling effects are weak in light elements, the nodal-line semimetal phase is expected to be achievable in some alkaline-earth germanides and silicides.
Analysis of nodal aberration properties in off-axis freeform system design.
Shi, Haodong; Jiang, Huilin; Zhang, Xin; Wang, Chao; Liu, Tao
2016-08-20
Freeform surfaces have the advantage of balancing off-axis aberration. In this paper, based on the framework of nodal aberration theory (NAT) applied to the coaxial system, the third-order astigmatism and coma wave aberration expressions of an off-axis system with Zernike polynomial surfaces are derived. The relationship between the off-axis and surface shape acting on the nodal distributions is revealed. The nodal aberration properties of the off-axis freeform system are analyzed and validated by using full-field displays (FFDs). It has been demonstrated that adding Zernike terms, up to nine, to the off-axis system modifies the nodal locations, but the field dependence of the third-order aberration does not change. On this basis, an off-axis two-mirror freeform system with 500 mm effective focal length (EFL) and 300 mm entrance pupil diameter (EPD) working in long-wave infrared is designed. The field constant aberrations induced by surface tilting are corrected by selecting specific Zernike terms. The design results show that the nodes of third-order astigmatism and coma move back into the field of view (FOV). The modulation transfer function (MTF) curves are above 0.4 at 20 line pairs per millimeter (lp/mm) which meets the infrared reconnaissance requirement. This work provides essential insight and guidance for aberration correction in off-axis freeform system design. PMID:27557003
Radiation therapy for carcinoma of the hypopharynx with special reference to nodal control
Teshima, T.; Chatani, M.; Inoue, T.; Miyahara, H.; Sato, T.
1988-05-01
From October 1977 through December 1983, 61 patients with carcinoma of the hypopharynx were treated with radiation therapy (RT) and surgery or with RT alone. Five-year survival rates by N-stage, according to the TNM classification by UICC (1978), were 52% for N0 cases, 23% for N1, and 17% for N2-3 (N1 vs. N2-3, not significant). For N1-3 cases, corresponding figures by level of cervical nodal involvement by UICC (1978) were 29% for level 3 cases, 15% for level 2, and 8% for level 4 (level 3 vs. level 4, p less than 0.04). Therefore, the level of cervical nodal involvement was a more useful prognosticator for patients with nodal metastasis than the N-stage. Effective nodal control for patients with clinically positive nodes (N1-3) was obtained with a combination of neck node dissection and RT of 50 Gy or more. For N0 cases, elective RT of 50 Gy or more, encompassing an adequate field, was required.
Bohora, Shomu; Singh, Parvindar; Shah, Kaushal
2016-01-01
A 58 year old gentleman with complaints of palpitations and documented tachycardia was found to have a dilated right atrium, right ventricle and coronary sinus, which were due to partial unroofed coronary sinus without a left superior vena cava. He had upper septal ventricular tachycardia and atrio-ventricular nodal reentrant tachycardia, which was successfully treated by radiofrequency ablation. PMID:25852246
A difference-equation formalism for the nodal domains of separable billiards
NASA Astrophysics Data System (ADS)
Manjunath, Naren; Samajdar, Rhine; Jain, Sudhir R.
2016-09-01
Recently, the nodal domain counts of planar, integrable billiards with Dirichlet boundary conditions were shown to satisfy certain difference equations in Samajdar and Jain (2014). The exact solutions of these equations give the number of domains explicitly. For complete generality, we demonstrate this novel formulation for three additional separable systems and thus extend the statement to all integrable billiards.
Sarkar, Prasenjit; Randall, Shan M; Collier, Timothy S; Nero, Anthony; Russell, Teal A; Muddiman, David C; Rao, Balaji M
2015-04-01
Human embryonic stem cells (hESCs) have been routinely treated with bone morphogenetic protein and/or inhibitors of activin/nodal signaling to obtain cells that express trophoblast markers. Trophoblasts can terminally differentiate to either extravillous trophoblasts or syncytiotrophoblasts. The signaling pathways that govern the terminal fate of these trophoblasts are not understood. We show that activin/nodal signaling switches the terminal fate of these hESC-derived trophoblasts. Inhibition of activin/nodal signaling leads to formation of extravillous trophoblast, whereas loss of activin/nodal inhibition leads to the formation of syncytiotrophoblasts. Also, the ability of hESCs to form bona fide trophoblasts has been intensely debated. We have examined hESC-derived trophoblasts in the light of stringent criteria that were proposed recently, such as hypomethylation of the ELF5-2b promoter region and down-regulation of HLA class I antigens. We report that trophoblasts that possess these properties can indeed be obtained from hESCs. PMID:25670856
Theory of nodal s ± -wave pairing symmetry in the Pu-based 115 superconductor family.
Das, Tanmoy; Zhu, Jian-Xin; Graf, Matthias J
2015-01-01
The spin-fluctuation mechanism of superconductivity usually results in the presence of gapless or nodal quasiparticle states in the excitation spectrum. Nodal quasiparticle states are well established in copper-oxide, and heavy-fermion superconductors, but not in iron-based superconductors. Here, we study the pairing symmetry and mechanism of a new class of plutonium-based high-Tc superconductors and predict the presence of a nodal s(±) wave pairing symmetry in this family. Starting from a density-functional theory (DFT) based electronic structure calculation we predict several three-dimensional (3D) Fermi surfaces in this 115 superconductor family. We identify the dominant Fermi surface "hot-spots" in the inter-band scattering channel, which are aligned along the wavevector Q = (π, π, π), where degeneracy could induce sign-reversal of the pairing symmetry. Our calculation demonstrates that the s(±) wave pairing strength is stronger than the previously thought d-wave pairing; and more importantly, this pairing state allows for the existence of nodal quasiparticles. Finally, we predict the shape of the momentum- and energy-dependent magnetic resonance spectrum for the identification of this pairing symmetry. PMID:25721375
Two novel nodal-related genes initiate early inductive events in Xenopus Nieuwkoop center.
Takahashi, S; Yokota, C; Takano, K; Tanegashima, K; Onuma, Y; Goto, J; Asashima, M
2000-12-01
In vertebrates, Nodal-related protein plays crucial roles in mesoderm and endoderm induction. Here we describe two novel Xenopus nodal-related genes, Xnr5 and Xnr6, which are first zygotically expressed at the mid-blastula transition, in the dorsal-vegetal region including the Nieuwkoop center. Xnr5 and Xnr6 were isolated by expression screening of a library enriched with immediate-early-type transcripts, and are strong inducers of both mesoderm and endoderm. They also induce the other nodal-related genes in the animal cap. In embryos, cerberus-short (nodal-specific inhibitor) can inhibit Xnr1 and Xnr2 express to the same extent goosecoid, but not Xnr5 and Xnr6 transcription. Xnr5 and Xnr6 are regulated completely cell autonomously, differently from other Xnrs in the cell-dissociated embryos. The expression of Xnr5 and Xnr6 is regulated by maternal VegT and (beta)-catenin, but does not require TGF-(beta) signaling. Therefore, expression of Xnr5 and Xnr6 is controlled by different mechanisms from other Xnr family genes. PMID:11076754
Minimizing the caliber of myelinated axons by means of nodal constrictions.
Johnson, Christopher; Holmes, William R; Brown, Anthony; Jung, Peter
2015-09-01
In myelinated axons, most of the voltage-gated ion channels are concentrated at the nodes of Ranvier, which are short gaps in the myelin sheath. This arrangement leads to saltatory conduction and a larger conduction velocity than in nonmyelinated axons. Intriguingly, axons in the peripheral nervous system that exceed about 2 μm in diameter exhibit a characteristic narrowing of the axon at nodes that results in a local reduction of the axonal cross-sectional area. The extent of constriction increases with increasing internodal axonal caliber, reaching a threefold reduction in diameter for the largest axons. In this paper, we use computational modeling to investigate the effect of nodal constrictions on axonal conduction velocity. For a fixed number of ion channels, we find that there is an optimal extent of nodal constriction which minimizes the internodal axon caliber that is required to achieve a given target conduction velocity, and we show that this is sensitive to the precise geometry of the axon and myelin sheath in the flanking paranodal regions. Thus axonal constrictions at nodes of Ranvier appear to be a biological adaptation to minimize axonal volume, thereby maximizing the spatial and metabolic efficiency of these processes, which can be a significant evolutionary constraint. We show that the optimal nodal morphologies are relatively insensitive to changes in the number of nodal sodium channels. PMID:26224772
NASA Technical Reports Server (NTRS)
Nicolet, M. A.
1983-01-01
The choice of the metallic film for the contact to a semiconductor device is discussed. One way to try to stabilize a contact is by interposing a thin film of a material that has low diffusivity for the atoms in question. This thin film application is known as a diffusion barrier. Three types of barriers can be distinguished. The stuffed barrier derives its low atomic diffusivity to impurities that concentrate along the extended defects of a polycrystalline layer. Sacrificial barriers exploit the fact that some (elemental) thin films react in a laterally uniform and reproducible fashion. Sacrificial barriers have the advantage that the point of their failure is predictable. Passive barriers are those most closely approximating an ideal barrier. The most-studied case is that of sputtered TiN films. Stuffed barriers may be viewed as passive barriers whose low diffusivity material extends along the defects of the polycrystalline host.
NASA Technical Reports Server (NTRS)
1981-01-01
A diffuse celestial radiation which is isotropic at least on a course scale were measured from the soft X-ray region to about 150 MeV, at which energy the intensity falls below that of the galactic emission for most galactic latitudes. The spectral shape, the intensity, and the established degree of isotropy of this diffuse radiation already place severe constraints on the possible explanations for this radiation. Among the extragalactic theories, the more promising explanations of the isotropic diffuse emission appear to be radiation from exceptional galaxies from matter antimatter annihilation at the boundaries of superclusters of galaxies of matter and antimatter in baryon symmetric big bang models. Other possible sources for extragalactic diffuse gamma radiation are discussed and include normal galaxies, clusters of galaxies, primordial cosmic rays interacting with intergalactic matter, primordial black holes, and cosmic ray leakage from galaxies.
dftatom: A robust and general Schrödinger and Dirac solver for atomic structure calculations
NASA Astrophysics Data System (ADS)
Čertík, Ondřej; Pask, John E.; Vackář, Jiří
2013-07-01
A robust and general solver for the radial Schrödinger, Dirac, and Kohn-Sham equations is presented. The formulation admits general potentials and meshes: uniform, exponential, or other defined by nodal distribution and derivative functions. For a given mesh type, convergence can be controlled systematically by increasing the number of grid points. Radial integrations are carried out using a combination of asymptotic forms, Runge-Kutta, and implicit Adams methods. Eigenfunctions are determined by a combination of bisection and perturbation methods for robustness and speed. An outward Poisson integration is employed to increase accuracy in the core region, allowing absolute accuracies of 10-8 Hartree to be attained for total energies of heavy atoms such as uranium. Detailed convergence studies are presented and computational parameters are provided to achieve accuracies commonly required in practice. Comparisons to analytic and current-benchmark density-functional results for atomic number Z=1-92 are presented, verifying and providing a refinement to current benchmarks. An efficient, modular Fortran 95 implementation, dftatom, is provided as open source, including examples, tests, and wrappers for interface to other languages; wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines. Program summaryProgram title:dftatom Catalogue identifier: AEPA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: MIT license No. of lines in distributed program, including test data, etc.: 14122 No. of bytes in distributed program, including test data, etc.: 157453 Distribution format: tar.gz Programming language: Fortran 95 with interfaces to Python and C. Computer: Any computer with a Fortran 95 compiler. Operating system: Any OS with a Fortran 95 compiler. RAM: 500 MB
van den Brand, Michiel; van der Velden, Walter J F M; Diets, Illja J; Ector, Geneviève I C G; de Haan, Anton F J; Stevens, Wendy B C; Hebeda, Konnie M; Groenen, Patricia J T A; van Krieken, Han J M
2016-07-01
Nodal marginal zone lymphoma (NMZL) is a rare type of B-cell non-Hodgkin lymphoma. This study assessed the clinical features of 56 patients with NMZL in comparison to 46 patients with follicular lymphoma (FL). Patients with NMZL and FL had a largely similar clinical presentation, but patients with FL had a higher disease stage at presentation, more frequent abdominal lymphadenopathy and bone marrow involvement, and showed more common transformation into diffuse large B-cell lymphoma (DLBCL) during the course of disease. Overall survival and event-free survival were similar for patients with NMZL and FL, but factors associated with worse prognosis differed between the two groups. Transformation into DLBCL was associated with a significantly poorer outcome in both groups, but the phenotypes were different: DLBCL arising in FL was mainly of germinal center B-cell phenotype, whereas DLBCL arising in NMZL was mainly of non-germinal center B-cell phenotype. PMID:26694256
Robust large-scale parallel nonlinear solvers for simulations.
Bader, Brett William; Pawlowski, Roger Patrick; Kolda, Tamara Gibson
2005-11-01
This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based solvers (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their use in important applications at Sandia. Broyden's method replaces the Jacobian with an approximation, allowing codes that cannot evaluate a Jacobian or have an inaccurate Jacobian to converge to a solution. Limited-memory methods, which have been successful in optimization, allow us to extend this approach to large-scale problems. We compare the robustness and efficiency of Newton's method, modified Newton's method, Jacobian-free Newton-Krylov method, and our limited-memory Broyden method. Comparisons are carried out for large-scale applications of fluid flow simulations and electronic circuit simulations. Results show that, in cases where the Jacobian was inaccurate or could not be computed, Broyden's method converged in some cases where Newton's method failed to converge. We identify conditions where Broyden's method can be more efficient than Newton's method. We also present modifications to a large-scale tensor method, originally proposed by Bouaricha, for greater efficiency, better robustness, and wider applicability. Tensor methods are an alternative to Newton-based methods and are based on computing a step based on a local quadratic model rather than a linear model. The advantage of Bouaricha's method is that it can use any existing linear solver, which makes it simple to write
Application of an unstructured grid flow solver to planes, trains and automobiles
NASA Technical Reports Server (NTRS)
Spragle, Gregory S.; Smith, Wayne A.; Yadlin, Yoram
1993-01-01
Rampant, an unstructured flow solver developed at Fluent Inc., is used to compute three-dimensional, viscous, turbulent, compressible flow fields within complex solution domains. Rampant is an explicit, finite-volume flow solver capable of computing flow fields using either triangular (2d) or tetrahedral (3d) unstructured grids. Local time stepping, implicit residual smoothing, and multigrid techniques are used to accelerate the convergence of the explicit scheme. The paper describes the Rampant flow solver and presents flow field solutions about a plane, train, and automobile.
A multigrid solver for semi-implicit global shallow-water models
NASA Technical Reports Server (NTRS)
Barros, Saulo R. M.; Dee, Dick P.; Dickstein, Flavio
1990-01-01
A multigrid solver is developed for the discretized two-dimensional elliptic equation on the sphere that arises from a semiimplicit time discretization of the global shallow-water equations. Different formulations of the semiimplicit scheme result in variable-coefficient Helmholtz-type equations for which no fast direct solvers are available. The efficiency of the multigrid solver is optimal, in the sense that the total operation count is proportional to the number of unknowns. Numerical experiments using initial data derived from actual 300-mb height and wind velocity fields indicate that the present model has very good accuracy and stability properties.
Noh, O Kyu; Lee, Sang-wook; Yoon, Sang Min; Kim, Sung Bae; Kim, Sang Yoon; Kim, Chang Jin; Jo, Kyung Ja; Choi, Eun Kyung; Song, Si Yeol; Kim, Jong Hoon; Ahn, Seung Do
2011-02-01
Purpose: The role of elective nodal irradiation (ENI) in radiotherapy for esthesioneuroblastoma (ENB) has not been clearly defined. We analyzed treatment outcomes of patients with ENB and the frequency of cervical nodal failure in the absence of ENI. Methods and Materials: Between August 1996 and December 2007, we consulted with 19 patients with ENB regarding radiotherapy. Initial treatment consisted of surgery alone in 2 patients; surgery and postoperative radiotherapy in 4; surgery and adjuvant chemotherapy in 1; surgery, postoperative radiotherapy, and chemotherapy in 3; and chemotherapy followed by radiotherapy or concurrent chemoradiotherapy in 5. Five patients did not receive planned radiotherapy because of disease progression. Including 2 patients who received salvage radiotherapy, 14 patients were treated with radiotherapy. Elective nodal irradiation was performed in 4 patients with high-risk factors, including 3 with cervical lymph node metastasis at presentation. Results: Fourteen patients were analyzable, with a median follow-up of 27 months (range, 7-64 months). The overall 3-year survival rate was 73.4%. Local failure occurred in 3 patients (21.4%), regional cervical failure in 3 (21.4%), and distant failure in 2 (14.3%). No cervical nodal failure occurred in patients treated with combined systemic chemotherapy regardless of ENI. Three cervical failures occurred in the 4 patients treated with ENI or neck dissection (75%), none of whom received systemic chemotherapy. Conclusions: ENI during radiotherapy for ENB seems to play a limited role in preventing cervical nodal failure. Omitting ENI may be an option if patients are treated with a combination of radiotherapy and chemotherapy.
A nodal triangle-based spectral element method for the shallow water equations on the sphere
NASA Astrophysics Data System (ADS)
Giraldo, F. X.; Warburton, T.
2005-07-01
A nodal triangle-based spectral element (SE) method for the shallow water equations on the sphere is presented. The original SE method uses quadrilateral elements and high-order nodal Lagrange polynomials, constructed from a tensor-product of the Legendre-Gauss-Lobatto points. In this work, we construct the high-order Lagrange polynomials directly on the triangle using nodal sets obtained from the electrostatics principle [J.S. Hesthaven, From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex, SIAM Journal on Numerical Analysis 35 (1998) 655-676] and Fekete points [M.A. Taylor, B.A. Wingate, R.E. Vincent, An algorithm for computing Fekete points in the triangle, SIAM Journal on Numerical Analysis 38 (2000) 1707-1720]. These points have good approximation properties and far better Lebesgue constants than any other nodal set derived for the triangle. By employing triangular elements as the basic building-blocks of the SE method and the Cartesian coordinate form of the equations, we can use any grid imaginable including adaptive unstructured grids. Results for six test cases are presented to confirm the accuracy and stability of the method. The results show that the triangle-based SE method yields the expected exponential convergence and that it can be more accurate than the quadrilateral-based SE method even while using 30-60% fewer grid points especially when adaptive grids are used to align the grid with the flow direction. However, at the moment, the quadrilateral-based SE method is twice as fast as the triangle-based SE method because the latter does not yield a diagonal mass matrix.
Combined-modality therapy for patients with regional nodal metastases from melanoma
Ballo, Matthew T. . E-mail: mballo@mdanderson.org; Ross, Merrick I.; Cormier, Janice N.; Myers, Jeffrey N.; Lee, Jeffrey E.; Gershenwald, Jeffrey E.; Hwu, Patrick; Zagars, Gunar K.
2006-01-01
Purpose: To evaluate the outcome and patterns of failure for patients with nodal metastases from melanoma treated with combined-modality therapy. Methods and Materials: Between 1983 and 2003, 466 patients with nodal metastases from melanoma were managed with lymphadenectomy and radiation, with or without systemic therapy. Surgery was a therapeutic procedure for clinically apparent nodal disease in 434 patients (regionally advanced nodal disease). Adjuvant radiation was generally delivered with a hypofractionated regimen. Adjuvant systemic therapy was delivered to 154 patients. Results: With a median follow-up of 4.2 years, 252 patients relapsed and 203 patients died of progressive disease. The actuarial 5-year disease-specific, disease-free, and distant metastasis-free survival rates were 49%, 42%, and 44%, respectively. By multivariate analysis, increasing number of involved lymph nodes and primary ulceration were associated with an inferior 5-year actuarial disease-specific and distant metastasis-free survival. Also, the number of involved lymph nodes was associated with the development of brain metastases, whereas thickness was associated with lung metastases, and primary ulceration was associated with liver metastases. The actuarial 5-year regional (in-basin) control rate for all patients was 89%, and on multivariate analysis there were no patient or disease characteristics associated with inferior regional control. The risk of lymphedema was highest for those patients with groin lymph node metastases. Conclusions: Although regional nodal disease can be satisfactorily controlled with lymphadenectomy and radiation, the risk of distant metastases and melanoma death remains high. A management approach to these patients that accounts for the competing risks of distant metastases, regional failure, and long-term toxicity is needed.
Narula, O S; Boveja, B K; Cohen, D M; Narula, J T; Tarjan, P P
1985-02-01
Selective modification of atrioventricular (AV) nodal conduction, that is, induction of varying degrees of AV nodal delays or block (second or third degree), or both, was achieved with a pervenous laser catheter technique. In six adult mongrel dogs anesthetized with pentobarbital (Nembutal), 5F leads were placed through femoral and external jugular veins and placed into the right atrium and His bundle region. Through another femoral vein, a 200 micron optical fiber was inserted by way of a 7F catheter with a preformed curved tip. Guided by fluoroscopy and His bundle electrograms, the fiber's tip was positioned in the AV nodal region. After autonomic blockade was achieved with intravenous propranolol (5 mg) and atropine (1 mg), AV conduction was analyzed. An argon laser delivered 3 to 4 watts into the fiber in bursts of 10 seconds' duration until the desired degree of AV nodal delay or block (second or third degree) was manifested. Monitoring of His bundle electrograms was continued for 2 hours. Four weekly serial electrocardiograms were recorded, after which electrophysiologic studies were repeated. Acute post-lasing studies showed that: in all six dogs, the mean PR interval was prolonged from 116 ms (range 100 to 135) to 153 ms (range 120 to 185), with the prolongation being caused exclusively by AH lengthening from 68 ms (range 50 to 90) to 105 ms (range 65 to 140); the mean effective refractory period of the AV node increased from less than 185 ms (range less than 150 to less than 200) to 215 ms (range 190 to 280); and the mean atrial pacing cycle length, at which second degree AV nodal block was manifested, increased from 210 ms (range 160 to 260) to 261 ms (range 205 to 320).(ABSTRACT TRUNCATED AT 250 WORDS) PMID:3968310
An approach to model reactor core nodalization for deterministic safety analysis
NASA Astrophysics Data System (ADS)
Salim, Mohd Faiz; Samsudin, Mohd Rafie; Mamat @ Ibrahim, Mohd Rizal; Roslan, Ridha; Sadri, Abd Aziz; Farid, Mohd Fairus Abd
2016-01-01
Adopting good nodalization strategy is essential to produce an accurate and high quality input model for Deterministic Safety Analysis (DSA) using System Thermal-Hydraulic (SYS-TH) computer code. The purpose of such analysis is to demonstrate the compliance against regulatory requirements and to verify the behavior of the reactor during normal and accident conditions as it was originally designed. Numerous studies in the past have been devoted to the development of the nodalization strategy for small research reactor (e.g. 250kW) up to the bigger research reactor (e.g. 30MW). As such, this paper aims to discuss the state-of-arts thermal hydraulics channel to be employed in the nodalization for RTP-TRIGA Research Reactor specifically for the reactor core. At present, the required thermal-hydraulic parameters for reactor core, such as core geometrical data (length, coolant flow area, hydraulic diameters, and axial power profile) and material properties (including the UZrH1.6, stainless steel clad, graphite reflector) have been collected, analyzed and consolidated in the Reference Database of RTP using standardized methodology, mainly derived from the available technical documentations. Based on the available information in the database, assumptions made on the nodalization approach and calculations performed will be discussed and presented. The development and identification of the thermal hydraulics channel for the reactor core will be implemented during the SYS-TH calculation using RELAP5-3D® computer code. This activity presented in this paper is part of the development of overall nodalization description for RTP-TRIGA Research Reactor under the IAEA Norwegian Extra-Budgetary Programme (NOKEBP) mentoring project on Expertise Development through the Analysis of Reactor Thermal-Hydraulics for Malaysia, denoted as EARTH-M.
Verification of continuum drift kinetic equation solvers in NIMROD
NASA Astrophysics Data System (ADS)
Held, E. D.; Kruger, S. E.; Ji, J.-Y.; Belli, E. A.; Lyons, B. C.
2015-03-01
Verification of continuum solutions to the electron and ion drift kinetic equations (DKEs) in NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)] is demonstrated through comparison with several neoclassical transport codes, most notably NEO [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)]. The DKE solutions use NIMROD's spatial representation, 2D finite-elements in the poloidal plane and a 1D Fourier expansion in toroidal angle. For 2D velocity space, a novel 1D expansion in finite elements is applied for the pitch angle dependence and a collocation grid is used for the normalized speed coordinate. The full, linearized Coulomb collision operator is kept and shown to be important for obtaining quantitative results. Bootstrap currents, parallel ion flows, and radial particle and heat fluxes show quantitative agreement between NIMROD and NEO for a variety of tokamak equilibria. In addition, velocity space distribution function contours for ions and electrons show nearly identical detailed structure and agree quantitatively. A Θ-centered, implicit time discretization and a block-preconditioned, iterative linear algebra solver provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.
Incremental planning to control a blackboard-based problem solver
NASA Technical Reports Server (NTRS)
Durfee, E. H.; Lesser, V. R.
1987-01-01
To control problem solving activity, a planner must resolve uncertainty about which specific long-term goals (solutions) to pursue and about which sequences of actions will best achieve those goals. A planner is described that abstracts the problem solving state to recognize possible competing and compatible solutions and to roughly predict the importance and expense of developing these solutions. With this information, the planner plans sequences of problem solving activities that most efficiently resolve its uncertainty about which of the possible solutions to work toward. The planner only details actions for the near future because the results of these actions will influence how (and whether) a plan should be pursued. As problem solving proceeds, the planner adds new details to the plan incrementally, and monitors and repairs the plan to insure it achieves its goals whenever possible. Through experiments, researchers illustrate how these new mechanisms significantly improve problem solving decisions and reduce overall computation. They briefly discuss current research directions, including how these mechanisms can improve a problem solver's real-time response and can enhance cooperation in a distributed problem solving network.
Towards Batched Linear Solvers on Accelerated Hardware Platforms
Haidar, Azzam; Dong, Tingzing Tim; Tomov, Stanimire; Dongarra, Jack J
2015-01-01
As hardware evolves, an increasingly effective approach to develop energy efficient, high-performance solvers, is to design them to work on many small and independent problems. Indeed, many applications already need this functionality, especially for GPUs, which are known to be currently about four to five times more energy efficient than multicore CPUs for every floating-point operation. In this paper, we describe the development of the main one-sided factorizations: LU, QR, and Cholesky; that are needed for a set of small dense matrices to work in parallel. We refer to such algorithms as batched factorizations. Our approach is based on representing the algorithms as a sequence of batched BLAS routines for GPU-contained execution. Note that this is similar in functionality to the LAPACK and the hybrid MAGMA algorithms for large-matrix factorizations. But it is different from a straightforward approach, whereby each of GPU's symmetric multiprocessors factorizes a single problem at a time. We illustrate how our performance analysis together with the profiling and tracing tools guided the development of batched factorizations to achieve up to 2-fold speedup and 3-fold better energy efficiency compared to our highly optimized batched CPU implementations based on the MKL library on a two-sockets, Intel Sandy Bridge server. Compared to a batched LU factorization featured in the NVIDIA's CUBLAS library for GPUs, we achieves up to 2.5-fold speedup on the K40 GPU.
Algorithmic Enhancements to the VULCAN Navier-Stokes Solver
NASA Technical Reports Server (NTRS)
Litton, D. K.; Edwards, J. R.; White, J. A.
2003-01-01
VULCAN (Viscous Upwind aLgorithm for Complex flow ANalysis) is a cell centered, finite volume code used to solve high speed flows related to hypersonic vehicles. Two algorithms are presented for expanding the range of applications of the current Navier-Stokes solver implemented in VULCAN. The first addition is a highly implicit approach that uses subiterations to enhance block to block connectivity between adjacent subdomains. The addition of this scheme allows more efficient solution of viscous flows on highly-stretched meshes. The second algorithm addresses the shortcomings associated with density-based schemes by the addition of a time-derivative preconditioning strategy. High speed, compressible flows are typically solved with density based schemes, which show a high level of degradation in accuracy and convergence at low Mach numbers (M less than or equal to 0.1). With the addition of preconditioning and associated modifications to the numerical discretization scheme, the eigenvalues will scale with the local velocity, and the above problems will be eliminated. With these additions, VULCAN now has improved convergence behavior for multi-block, highly-stretched meshes and also can solve the Navier-Stokes equations for very low Mach numbers.
A tearing-based hybrid parallel banded linear system solver
NASA Astrophysics Data System (ADS)
Naumov, Maxim; Sameh, Ahmed H.
2009-04-01
A new parallel algorithm for the solution of banded linear systems is proposed. The scheme tears the coefficient matrix into several overlapped independent blocks in which the size of the overlap is equal to the system's bandwidth. A corresponding splitting of the right-hand side is also provided. The resulting independent, and smaller size, linear systems are solved under the constraint that the solutions corresponding to the overlap regions are identical. This results in a linear system whose size is proportional to the sum of the overlap regions which we refer to as the "balance" system. We propose a solution strategy that does not require obtaining this "balance" system explicitly. Once the balance system is solved, retrieving the rest of the solution can be realized with almost perfect parallelism. Our proposed algorithm is a hybrid scheme that combines direct and iterative methods for solving a single banded system of linear equations on parallel architectures. It has broad applications in finite-element analysis, particularly as a parallel solver of banded preconditioners that can be used in conjunction with outer Krylov iterative schemes.
An optimal iterative solver for the Stokes problem
Wathen, A.; Silvester, D.
1994-12-31
Discretisations of the classical Stokes Problem for slow viscous incompressible flow gives rise to systems of equations in matrix form for the velocity u and the pressure p, where the coefficient matrix is symmetric but necessarily indefinite. The square submatrix A is symmetric and positive definite and represents a discrete (vector) Laplacian and the submatrix C may be the zero matrix or more generally will be symmetric positive semi-definite. For `stabilised` discretisations (C {ne} 0) and descretisations which are inherently `stable` (C = 0) and so do not admit spurious pressure components even as the mesh size, h approaches zero, the Schur compliment of the matrix has spectral condition number independent of h (given also that B is bounded). Here the authors will show how this property together with a multigrid preconditioner only for the Laplacian block A yields an optimal solver for the Stokes problem through use of the Minimum Residual iteration. That is, combining Minimum Residual iteration for the matrix equation with a block preconditioner which comprises a small number of multigrid V-cycles for the Laplacian block A together with a simple diagonal scaling block provides an iterative solution procedure for which the computational work grows only linearly with the problem size.
A generalized Poisson solver for first-principles device simulations
NASA Astrophysics Data System (ADS)
Bani-Hashemian, Mohammad Hossein; Brück, Sascha; Luisier, Mathieu; VandeVondele, Joost
2016-01-01
Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative method in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The solver can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated.
Two-Dimensional Ffowcs Williams/Hawkings Equation Solver
NASA Technical Reports Server (NTRS)
Lockard, David P.
2005-01-01
FWH2D is a Fortran 90 computer program that solves a two-dimensional (2D) version of the equation, derived by J. E. Ffowcs Williams and D. L. Hawkings, for sound generated by turbulent flow. FWH2D was developed especially for estimating noise generated by airflows around such approximately 2D airframe components as slats. The user provides input data on fluctuations of pressure, density, and velocity on some surface. These data are combined with information about the geometry of the surface to calculate histories of thickness and loading terms. These histories are fast-Fourier-transformed into the frequency domain. For each frequency of interest and each observer position specified by the user, kernel functions are integrated over the surface by use of the trapezoidal rule to calculate a pressure signal. The resulting frequency-domain signals are inverse-fast-Fourier-transformed back into the time domain. The output of the code consists of the time- and frequency-domain representations of the pressure signals at the observer positions. Because of its approximate nature, FWH2D overpredicts the noise from a finite-length (3D) component. The advantage of FWH2D is that it requires a fraction of the computation time of a 3D Ffowcs Williams/Hawkings solver.
A generalized Poisson solver for first-principles device simulations.
Bani-Hashemian, Mohammad Hossein; Brück, Sascha; Luisier, Mathieu; VandeVondele, Joost
2016-01-28
Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative method in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The solver can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated. PMID:26827208
A multiblock multigrid three-dimensional Euler equation solver
NASA Technical Reports Server (NTRS)
Cannizzaro, Frank E.; Elmiligui, Alaa; Melson, N. Duane; Vonlavante, E.
1990-01-01
Current aerodynamic designs are often quite complex (geometrically). Flexible computational tools are needed for the analysis of a wide range of configurations with both internal and external flows. In the past, geometrically dissimilar configurations required different analysis codes with different grid topologies in each. The duplicity of codes can be avoided with the use of a general multiblock formulation which can handle any grid topology. Rather than hard wiring the grid topology into the program, it is instead dictated by input to the program. In this work, the compressible Euler equations, written in a body-fitted finite-volume formulation, are solved using a pseudo-time-marching approach. Two upwind methods (van Leer's flux-vector-splitting and Roe's flux-differencing) were investigated. Two types of explicit solvers (a two-step predictor-corrector and a modified multistage Runge-Kutta) were used with multigrid acceleration to enhance convergence. A multiblock strategy is used to allow greater geometric flexibility. A report on simple explicit upwind schemes for solving compressible flows is included.
Parallelizable approximate solvers for recursions arising in preconditioning
Shapira, Y.
1996-12-31
For the recursions used in the Modified Incomplete LU (MILU) preconditioner, namely, the incomplete decomposition, forward elimination and back substitution processes, a parallelizable approximate solver is presented. The present analysis shows that the solutions of the recursions depend only weakly on their initial conditions and may be interpreted to indicate that the inexact solution is close, in some sense, to the exact one. The method is based on a domain decomposition approach, suitable for parallel implementations with message passing architectures. It requires a fixed number of communication steps per preconditioned iteration, independently of the number of subdomains or the size of the problem. The overlapping subdomains are either cubes (suitable for mesh-connected arrays of processors) or constructed by the data-flow rule of the recursions (suitable for line-connected arrays with possibly SIMD or vector processors). Numerical examples show that, in both cases, the overhead in the number of iterations required for convergence of the preconditioned iteration is small relatively to the speed-up gained.
Generation of Minimum-Consistent DFA Using SAT Solver
NASA Astrophysics Data System (ADS)
Inui, Nobuo; Aizawa, Akiko
The purpose of this study is to develop efficient methods for the minimum-consistent DFA (deterministic finite state automaton) problem. The graph-coloring based SAT (satisfiability) approach proposed by Heule is a state of the art method for this problem. It specially achieves high performance computing in dense problems such as in a popular benchmark problem where rich information about labels is included. In contrast, to solve sparse problems is a challenge for the minimum-consistent DFA problem. To solve sparse problems, we propose three approaches to the SAT formulation: a) the binary color representation, b) the dynamic symmetry breaking and c) the hyper-graph coloring constraint. We organized an experiment using the existing benchmark problems and sparse problems made from them. We observed that our symmetry breaking constraints made the speed up the running time of SAT solver. In addition with this, our other proposed methods were showing the possibility to improve the performance. Then we simulated the perfomance of our methods under the condition that we executed the several program set-ups in parallel. Compared with the previous research results, we finally could reduce the average relative time by 66.5% and the total relative time by 7.6% for sparse problems and by 79.7% and 38.5% for dense problems, respectively. These results showed that our proposed methods were effective for difficult problems.
New numerical solver for flows at various Mach numbers
NASA Astrophysics Data System (ADS)
Miczek, F.; Röpke, F. K.; Edelmann, P. V. F.
2015-04-01
Context. Many problems in stellar astrophysics feature flows at low Mach numbers. Conventional compressible hydrodynamics schemes frequently used in the field have been developed for the transonic regime and exhibit excessive numerical dissipation for these flows. Aims: While schemes were proposed that solve hydrodynamics strictly in the low Mach regime and thus restrict their applicability, we aim at developing a scheme that correctly operates in a wide range of Mach numbers. Methods: Based on an analysis of the asymptotic behavior of the Euler equations in the low Mach limit we propose a novel scheme that is able to maintain a low Mach number flow setup while retaining all effects of compressibility. This is achieved by a suitable modification of the well-known Roe solver. Results: Numerical tests demonstrate the capability of this new scheme to reproduce slow flow structures even in moderate numerical resolution. Conclusions: Our scheme provides a promising approach to a consistent multidimensional hydrodynamical treatment of astrophysical low Mach number problems such as convection, instabilities, and mixing in stellar evolution.
Approximate Riemann Solvers for the Cosmic Ray Magnetohydrodynamical Equations
NASA Astrophysics Data System (ADS)
Kudoh, Yuki; Hanawa, Tomoyuki
2016-08-01
We analyze the cosmic-ray magnetohydrodynamic (CR MHD) equations to improve the numerical simulations. We propose to solve them in the fully conservation form, which is equivalent to the conventional CR MHD equations. In the fully conservation form, the CR energy equation is replaced with the CR "number" conservation, where the CR number density is defined as the three fourths power of the CR energy density. The former contains an extra source term, while latter does not. An approximate Riemann solver is derived from the CR MHD equations in the fully conservation form. Based on the analysis, we propose a numerical scheme of which solutions satisfy the Rankine-Hugoniot relation at any shock. We demonstrate that it reproduces the Riemann solution derived by Pfrommer et al. (2006) for a 1D CR hydrodynamic shock tube problem. We compare the solution with those obtained by solving the CR energy equation. The latter solutions deviate from the Riemann solution seriously, when the CR pressure dominates over the gas pressure in the post-shocked gas. The former solutions converge to the Riemann solution and are of the second order accuracy in space and time. Our numerical examples include an expansion of high pressure sphere in an magnetized medium. Fast and slow shocks are sharply resolved in the example. We also discuss possible extension of the CR MHD equations to evaluate the average CR energy.
Cooperative solutions coupling a geometry engine and adaptive solver codes
NASA Technical Reports Server (NTRS)
Dickens, Thomas P.
1995-01-01
Follow-on work has progressed in using Aero Grid and Paneling System (AGPS), a geometry and visualization system, as a dynamic real time geometry monitor, manipulator, and interrogator for other codes. In particular, AGPS has been successfully coupled with adaptive flow solvers which iterate, refining the grid in areas of interest, and continuing on to a solution. With the coupling to the geometry engine, the new grids represent the actual geometry much more accurately since they are derived directly from the geometry and do not use refits to the first-cut grids. Additional work has been done with design runs where the geometric shape is modified to achieve a desired result. Various constraints are used to point the solution in a reasonable direction which also more closely satisfies the desired results. Concepts and techniques are presented, as well as examples of sample case studies. Issues such as distributed operation of the cooperative codes versus running all codes locally and pre-calculation for performance are discussed. Future directions are considered which will build on these techniques in light of changing computer environments.
Shared Memory Parallelism for 3D Cartesian Discrete Ordinates Solver
NASA Astrophysics Data System (ADS)
Moustafa, Salli; Dutka-Malen, Ivan; Plagne, Laurent; Ponçot, Angélique; Ramet, Pierre
2014-06-01
This paper describes the design and the performance of DOMINO, a 3D Cartesian SN solver that implements two nested levels of parallelism (multicore+SIMD) on shared memory computation nodes. DOMINO is written in C++, a multi-paradigm programming language that enables the use of powerful and generic parallel programming tools such as Intel TBB and Eigen. These two libraries allow us to combine multi-thread parallelism with vector operations in an efficient and yet portable way. As a result, DOMINO can exploit the full power of modern multi-core processors and is able to tackle very large simulations, that usually require large HPC clusters, using a single computing node. For example, DOMINO solves a 3D full core PWR eigenvalue problem involving 26 energy groups, 288 angular directions (S16), 46 × 106 spatial cells and 1 × 1012 DoFs within 11 hours on a single 32-core SMP node. This represents a sustained performance of 235 GFlops and 40:74% of the SMP node peak performance for the DOMINO sweep implementation. The very high Flops/Watt ratio of DOMINO makes it a very interesting building block for a future many-nodes nuclear simulation tool.
Verification of continuum drift kinetic equation solvers in NIMROD
Held, E. D.; Ji, J.-Y.; Kruger, S. E.; Belli, E. A.; Lyons, B. C.
2015-03-15
Verification of continuum solutions to the electron and ion drift kinetic equations (DKEs) in NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)] is demonstrated through comparison with several neoclassical transport codes, most notably NEO [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)]. The DKE solutions use NIMROD's spatial representation, 2D finite-elements in the poloidal plane and a 1D Fourier expansion in toroidal angle. For 2D velocity space, a novel 1D expansion in finite elements is applied for the pitch angle dependence and a collocation grid is used for the normalized speed coordinate. The full, linearized Coulomb collision operator is kept and shown to be important for obtaining quantitative results. Bootstrap currents, parallel ion flows, and radial particle and heat fluxes show quantitative agreement between NIMROD and NEO for a variety of tokamak equilibria. In addition, velocity space distribution function contours for ions and electrons show nearly identical detailed structure and agree quantitatively. A Θ-centered, implicit time discretization and a block-preconditioned, iterative linear algebra solver provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.
Extending Diffusion Monte Carlo to Internal Coordinates
NASA Astrophysics Data System (ADS)
Petit, Andrew S.; McCoy, Anne B.
2013-06-01
Diffusion Monte Carlo (DMC) is a powerful technique for studying the properties of molecules and clusters that undergo large-amplitude, zero-point vibrational motions. However, the overall applicability of the method is limited by the need to work in Cartesian coordinates and therefore have available a full-dimensional potential energy surface (PES). As a result, the development of a reduced-dimensional DMC methodology has the potential to significantly extend the range of problems that DMC can address by allowing the calculations to be performed in the subset of coordinates that is physically relevant to the questions being asked, thereby eliminating the need for a full-dimensional PES. As a first step towards this goal, we describe here an internal coordinate extension of DMC that places no constraints on the choice of internal coordinates other than requiring them all to be independent. Using H_3^+ and its isotopologues as model systems, we demonstrate that the methodology is capable of successfully describing the ground state properties of highly fluxional molecules as well as, in conjunction with the fixed-node approximation, the ν=1 vibrationally excited states. The calculations of the fundamentals of H_3^+ and its isotopologues provided general insights into the properties of the nodal surfaces of vibrationally excited states. Specifically, we will demonstrate that analysis of ground state probability distributions can point to the set of coordinates that are less strongly coupled and therefore more suitable for use as nodal coordinates in the fixed-node approximation. In particular, we show that nodal surfaces defined in terms of the curvilinear normal mode coordinates are reasonable for the fundamentals of H_2D^+ and D_2H^+ despite both molecules being highly fluxional.
Update on Advection-Diffusion Purge Flow Model
NASA Technical Reports Server (NTRS)
Brieda, Lubos
2015-01-01
Gaseous purge is commonly used in sensitive spacecraft optical or electronic instruments to prevent infiltration of contaminants and/or water vapor. Typically, purge is sized using simplistic zero-dimensional models that do not take into account instrument geometry, surface effects, and the dependence of diffusive flux on the concentration gradient. For this reason, an axisymmetric computational fluid dynamics (CFD) simulation was recently developed to model contaminant infiltration and removal by purge. The solver uses a combined Navier-Stokes and Advection-Diffusion approach. In this talk, we report on updates in the model, namely inclusion of a particulate transport model.
Second-order Poisson-Nernst-Planck solver for ion transport
NASA Astrophysics Data System (ADS)
Zheng, Qiong; Chen, Duan; Wei, Guo-Wei
2011-06-01
The Poisson-Nernst-Planck (PNP) theory is a simplified continuum model for a wide variety of chemical, physical and biological applications. Its ability of providing quantitative explanation and increasingly qualitative predictions of experimental measurements has earned itself much recognition in the research community. Numerous computational algorithms have been constructed for the solution of the PNP equations. However, in the realistic ion-channel context, no second-order convergent PNP algorithm has ever been reported in the literature, due to many numerical obstacles, including discontinuous coefficients, singular charges, geometric singularities, and nonlinear couplings. The present work introduces a number of numerical algorithms to overcome the abovementioned numerical challenges and constructs the first second-order convergent PNP solver in the ion-channel context. First, a Dirichlet to Neumann mapping (DNM) algorithm is designed to alleviate the charge singularity due to the protein structure. Additionally, the matched interface and boundary (MIB) method is reformulated for solving the PNP equations. The MIB method systematically enforces the interface jump conditions and achieves the second order accuracy in the presence of complex geometry and geometric singularities of molecular surfaces. Moreover, two iterative schemes are utilized to deal with the coupled nonlinear equations. Furthermore, extensive and rigorous numerical validations are carried out over a number of geometries, including a sphere, two proteins and an ion channel, to examine the numerical accuracy and convergence order of the present numerical algorithms. Finally, application is considered to a real transmembrane protein, the Gramicidin A channel protein. The performance of the proposed numerical techniques is tested against a number of factors, including mesh sizes, diffusion coefficient profiles, iterative schemes, ion concentrations, and applied voltages. Numerical predictions are
Second-order Poisson Nernst-Planck solver for ion channel transport.
Zheng, Qiong; Chen, Duan; Wei, Guo-Wei
2011-06-01
The Poisson Nernst-Planck (PNP) theory is a simplified continuum model for a wide variety of chemical, physical and biological applications. Its ability of providing quantitative explanation and increasingly qualitative predictions of experimental measurements has earned itself much recognition in the research community. Numerous computational algorithms have been constructed for the solution of the PNP equations. However, in the realistic ion-channel context, no second order convergent PNP algorithm has ever been reported in the literature, due to many numerical obstacles, including discontinuous coefficients, singular charges, geometric singularities, and nonlinear couplings. The present work introduces a number of numerical algorithms to overcome the abovementioned numerical challenges and constructs the first second-order convergent PNP solver in the ion-channel context. First, a Dirichlet to Neumann mapping (DNM) algorithm is designed to alleviate the charge singularity due to the protein structure. Additionally, the matched interface and boundary (MIB) method is reformulated for solving the PNP equations. The MIB method systematically enforces the interface jump conditions and achieves the second order accuracy in the presence of complex geometry and geometric singularities of molecular surfaces. Moreover, two iterative schemes are utilized to deal with the coupled nonlinear equations. Furthermore, extensive and rigorous numerical validations are carried out over a number of geometries, including a sphere, two proteins and an ion channel, to examine the numerical accuracy and convergence order of the present numerical algorithms. Finally, application is considered to a real transmembrane protein, the Gramicidin A channel protein. The performance of the proposed numerical techniques is tested against a number of factors, including mesh sizes, diffusion coefficient profiles, iterative schemes, ion concentrations, and applied voltages. Numerical predictions are
Second-order Poisson Nernst-Planck solver for ion channel transport
Zheng, Qiong; Chen, Duan; Wei, Guo-Wei
2010-01-01
The Poisson Nernst-Planck (PNP) theory is a simplified continuum model for a wide variety of chemical, physical and biological applications. Its ability of providing quantitative explanation and increasingly qualitative predictions of experimental measurements has earned itself much recognition in the research community. Numerous computational algorithms have been constructed for the solution of the PNP equations. However, in the realistic ion-channel context, no second order convergent PNP algorithm has ever been reported in the literature, due to many numerical obstacles, including discontinuous coefficients, singular charges, geometric singularities, and nonlinear couplings. The present work introduces a number of numerical algorithms to overcome the abovementioned numerical challenges and constructs the first second-order convergent PNP solver in the ion-channel context. First, a Dirichlet to Neumann mapping (DNM) algorithm is designed to alleviate the charge singularity due to the protein structure. Additionally, the matched interface and boundary (MIB) method is reformulated for solving the PNP equations. The MIB method systematically enforces the interface jump conditions and achieves the second order accuracy in the presence of complex geometry and geometric singularities of molecular surfaces. Moreover, two iterative schemes are utilized to deal with the coupled nonlinear equations. Furthermore, extensive and rigorous numerical validations are carried out over a number of geometries, including a sphere, two proteins and an ion channel, to examine the numerical accuracy and convergence order of the present numerical algorithms. Finally, application is considered to a real transmembrane protein, the Gramicidin A channel protein. The performance of the proposed numerical techniques is tested against a number of factors, including mesh sizes, diffusion coefficient profiles, iterative schemes, ion concentrations, and applied voltages. Numerical predictions are
Haramoto, Yoshikazu; Tanegashima, Kousuke; Onuma, Yasuko; Takahashi, Shuji; Sekizaki, Hiroyuki; Asashima, Makoto
2004-01-01
In vertebrates, nodal-related genes are crucial for specifying mesendodermal cell fates. Six nodal-related genes have been identified in Xenopus, but only one, nodal, has been identified in the mouse. The Xenopus nodal-related gene 3 (Xnr3), however, lacks the mesoderm-inducing activity of the other five nodal-related genes in Xenopus, and can directly induce neural tissue in animal caps by antagonizing BMP signals. In this study, we isolated three clones of the Xenopus (Silurana) tropicalis nodal-related gene 3 (Xtnr3) and analyzed their function. The Xtnr3 genes show high homology to Xnr3 and have the same activity. Southern blot and genomic PCR analyses indicate that the X. tropicalis genome has duplications in the Xtnr3 gene sequences and our three clones represent separate gene loci. We also found a partial clone of Xtnr3 that coded for the N-terminal part of its pro-region. Surprisingly, this sequence also induced neural tissue by antagonizing BMP signals, and its coded protein physically associated with BMP4 mature protein. Furthermore, we showed that the pro-region of Xnr5 has the same activity. Together, these findings indicate that the pro-region of nodal-related genes acts antagonistically towards BMP signals, which identifies a novel mechanism for the inhibition of BMP signaling. PMID:14697360
A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems
Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing
2012-01-01
An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849
User's Manual for PCSMS (Parallel Complex Sparse Matrix Solver). Version 1.
NASA Technical Reports Server (NTRS)
Reddy, C. J.
2000-01-01
PCSMS (Parallel Complex Sparse Matrix Solver) is a computer code written to make use of the existing real sparse direct solvers to solve complex, sparse matrix linear equations. PCSMS converts complex matrices into real matrices and use real, sparse direct matrix solvers to factor and solve the real matrices. The solution vector is reconverted to complex numbers. Though, this utility is written for Silicon Graphics (SGI) real sparse matrix solution routines, it is general in nature and can be easily modified to work with any real sparse matrix solver. The User's Manual is written to make the user acquainted with the installation and operation of the code. Driver routines are given to aid the users to integrate PCSMS routines in their own codes.
Li, Xinya; Deng, Z. Daniel; USA, Richland Washington; Sun, Yannan; USA, Richland Washington; Martinez, Jayson J.; USA, Richland Washington; Fu, Tao; USA, Richland Washington; McMichael, Geoffrey A.; et al
2014-11-27
Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood solver was developedmore » using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.« less
Li, Xinya; Deng, Z. Daniel; USA, Richland Washington; Sun, Yannan; USA, Richland Washington; Martinez, Jayson J.; USA, Richland Washington; Fu, Tao; USA, Richland Washington; McMichael, Geoffrey A.; USA, Richland Washington; Carlson, Thomas J.; USA, Richland Washington
2014-11-27
Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood solver was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.
Fault tolerance in an inner-outer solver: A GVR-enabled case study
Zhang, Ziming; Chien, Andrew A.; Teranishi, Keita
2015-04-18
Resilience is a major challenge for large-scale systems. It is particularly important for iterative linear solvers, since they take much of the time of many scientific applications. We show that single bit flip errors in the Flexible GMRES iterative linear solver can lead to high computational overhead or even failure to converge to the right answer. Informed by these results, we design and evaluate several strategies for fault tolerance in both inner and outer solvers appropriate across a range of error rates. We implement them, extending Trilinos’ solver library with the Global View Resilience (GVR) programming model, which provides multi-stream snapshots, multi-version data structures with portable and rich error checking/recovery. Lastly, experimental results validate correct execution with low performance overhead under varied error conditions.
A novel high-order, entropy stable, 3D AMR MHD solver with guaranteed positive pressure
NASA Astrophysics Data System (ADS)
Derigs, Dominik; Winters, Andrew R.; Gassner, Gregor J.; Walch, Stefanie
2016-07-01
We describe a high-order numerical magnetohydrodynamics (MHD) solver built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the solver conserves mass, momentum, and energy and is entropy stable. The method is designed to treat the divergence-free constraint on the magnetic field in a similar fashion to a hyperbolic divergence cleaning technique. The solver described herein is especially well-suited for flows involving strong discontinuities. Furthermore, we present a new formulation to guarantee positivity of the pressure. We present the underlying theory and implementation of the new solver into the multi-physics, multi-scale adaptive mesh refinement (AMR) simulation code FLASH (http://flash.uchicago.edu)
The use of inexact ODE solver in waveform relaxation methods on a massively parallel computer
Luk, W.S.; Wing, O.
1995-12-01
This paper presents the use of inexact ordinary differential equation (ODE) solver in waveform relaxation methods for solving initial value problems: Since the conventional ODE solvers are inherently sequential, the inexact ODE solver is used by taking time points from only previous waveform iteration for time integration. As a result, this method is truly massively parallel, as the equation is completely unfolded both in system and in time. Convergence analysis shows that the spectral radius of the iteration equation resulting from the {open_quotes}inexact{close_quotes} solver is the same as that from the standard method, and hence the new method is robust. The parallel implementation issues on the DECmpp 12000/Sx computer will also be discussed. Numerical results illustrate that though the number of iterations in the inexact method is increased over the exact method, as expected, the computation time is much reduced because of the large-scale parallelism.
Li, Xinya; Deng, Z. Daniel; Sun, Yannan; Martinez, Jayson J.; Fu, Tao; McMichael, Geoffrey A.; Carlson, Thomas J.
2014-01-01
Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood solver was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature. PMID:25427517
i QIST: An open source continuous-time quantum Monte Carlo impurity solver toolkit
NASA Astrophysics Data System (ADS)
Huang, Li; Wang, Yilin; Meng, Zi Yang; Du, Liang; Werner, Philipp; Dai, Xi
2015-10-01
Quantum impurity solvers have a broad range of applications in theoretical studies of strongly correlated electron systems. Especially, they play a key role in dynamical mean-field theory calculations of correlated lattice models and realistic materials. Therefore, the development and implementation of efficient quantum impurity solvers is an important task. In this paper, we present an open source interacting quantum impurity solver toolkit (dubbed i QIST). This package contains several highly optimized quantum impurity solvers which are based on the hybridization expansion continuous-time quantum Monte Carlo algorithm, as well as some essential pre- and post-processing tools. We first introduce the basic principle of continuous-time quantum Monte Carlo algorithm and then discuss the implementation details and optimization strategies. The software framework, major features, and installation procedure for i QIST are also explained. Finally, several simple tutorials are presented in order to demonstrate the usage and power of i QIST.
A novel high-order, entropy stable, 3D AMR MHD solver with guaranteed positive pressure
NASA Astrophysics Data System (ADS)
Derigs, Dominik; Winters, Andrew R.; Gassner, Gregor J.; Walch, Stefanie
2016-07-01
We describe a high-order numerical magnetohydrodynamics (MHD) solver built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the solver conserves mass, momentum, and energy and is entropy stable. The method is designed to treat the divergence-free constraint on the magnetic field in a similar fashion to a hyperbolic divergence cleaning technique. The solver described herein is especially well-suited for flows involving strong discontinuities. Furthermore, we present a new formulation to guarantee positivity of the pressure. We present the underlying theory and implementation of the new solver into the multi-physics, multi-scale adaptive mesh refinement (AMR) simulation code FLASH (http://flash.uchicago.edu).
Li, Xinya; Deng, Z Daniel; Sun, Yannan; Martinez, Jayson J; Fu, Tao; McMichael, Geoffrey A; Carlson, Thomas J
2014-01-01
Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood solver was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature. PMID:25427517
NASA Astrophysics Data System (ADS)
Li, Xinya; Deng, Z. Daniel; Sun, Yannan; Martinez, Jayson J.; Fu, Tao; McMichael, Geoffrey A.; Carlson, Thomas J.
2014-11-01
Better understanding of fish behavior is vital for recovery of many endangered species including salmon. The Juvenile Salmon Acoustic Telemetry System (JSATS) was developed to observe the out-migratory behavior of juvenile salmonids tagged by surgical implantation of acoustic micro-transmitters and to estimate the survival when passing through dams on the Snake and Columbia Rivers. A robust three-dimensional solver was needed to accurately and efficiently estimate the time sequence of locations of fish tagged with JSATS acoustic transmitters, to describe in sufficient detail the information needed to assess the function of dam-passage design alternatives. An approximate maximum likelihood solver was developed using measurements of time difference of arrival from all hydrophones in receiving arrays on which a transmission was detected. Field experiments demonstrated that the developed solver performed significantly better in tracking efficiency and accuracy than other solvers described in the literature.
NASA Astrophysics Data System (ADS)
Guda, A. A.; Guda, S. A.; Soldatov, M. A.; Lomachenko, K. A.; Bugaev, A. L.; Lamberti, C.; Gawelda, W.; Bressler, C.; Smolentsev, G.; Soldatov, A. V.; Joly, Y.
2016-05-01
Finite difference method (FDM) implemented in the FDMNES software [Phys. Rev. B, 2001, 63, 125120] was revised. Thorough analysis shows, that the calculated diagonal in the FDM matrix consists of about 96% zero elements. Thus a sparse solver would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse solvers and the direct one MUMPS solver with METIS ordering turned out to be the best. Compared to the Gaussian solver present method is up to 40 times faster and allows XANES simulations for complex systems already on personal computers. We show applicability of the software for metal-organic [Fe(bpy)3]2+ complex both for low spin and high spin states populated after laser excitation.
Fault tolerance in an inner-outer solver: A GVR-enabled case study
Zhang, Ziming; Chien, Andrew A.; Teranishi, Keita
2015-04-18
Resilience is a major challenge for large-scale systems. It is particularly important for iterative linear solvers, since they take much of the time of many scientific applications. We show that single bit flip errors in the Flexible GMRES iterative linear solver can lead to high computational overhead or even failure to converge to the right answer. Informed by these results, we design and evaluate several strategies for fault tolerance in both inner and outer solvers appropriate across a range of error rates. We implement them, extending Trilinos’ solver library with the Global View Resilience (GVR) programming model, which provides multi-streammore » snapshots, multi-version data structures with portable and rich error checking/recovery. Lastly, experimental results validate correct execution with low performance overhead under varied error conditions.« less
NASA Astrophysics Data System (ADS)
Balsara, Dinshaw S.
2012-09-01
In this paper we present a genuinely two-dimensional HLLC Riemann solver. On logically rectangular meshes, it accepts four input states that come together at an edge and outputs the multi-dimensionally upwinded fluxes in both directions. This work builds on, and improves, our prior work on two-dimensional HLL Riemann solvers. The HLL Riemann solver presented here achieves its stabilization by introducing a constant state in the region of strong interaction, where four one-dimensional Riemann problems interact vigorously with one another. A robust version of the HLL Riemann solver is presented here along with a strategy for introducing sub-structure in the strongly-interacting state. Introducing sub-structure turns the two-dimensional HLL Riemann solver into a two-dimensional HLLC Riemann solver. The sub-structure that we introduce represents a contact discontinuity which can be oriented in any direction relative to the mesh. The Riemann solver presented here is general and can work with any system of conservation laws. We also present a second order accurate Godunov scheme that works in three dimensions and is entirely based on the present multidimensional HLLC Riemann solver technology. The methods presented are cost-competitive with traditional higher order Godunov schemes. The two-dimensional HLLC Riemann solver is shown to work robustly for Euler and Magnetohydrodynamic (MHD) flows. Several stringent test problems are presented to show that the inclusion of genuinely multidimensional effects into higher order Godunov schemes indeed produces some very compelling advantages. For two dimensional problems, we were routinely able to run simulations with CFL numbers of ˜0.7, with some two-dimensional simulations capable of reaching higher CFL numbers. For three dimensional problems, CFL numbers as high as ˜0.6 were found to be stable. We show that on resolution-starved meshes, the scheme presented here outperforms unsplit second order Godunov schemes that are based
Röttinger, Eric; DuBuc, Timothy Q.; Amiel, Aldine R.; Martindale, Mark Q.
2015-01-01
ABSTRACT Nodal signaling plays crucial roles in vertebrate developmental processes such as endoderm and mesoderm formation, and axial patterning events along the anteroposterior, dorsoventral and left-right axes. In echinoderms, Nodal plays an essential role in the establishment of the dorsoventral axis and left-right asymmetry, but not in endoderm or mesoderm induction. In protostomes, Nodal signaling appears to be involved only in establishing left-right asymmetry. Hence, it is hypothesized that Nodal signaling has been co-opted to pattern the dorsoventral axis of deuterostomes and for endoderm, mesoderm formation as well as anteroposterior patterning in chordates. Hemichordata, together with echinoderms, represent the sister taxon to chordates. In this study, we analyze the role of Nodal signaling in the indirect developing hemichordate Ptychodera flava. In particular, we show that during gastrulation nodal transcripts are detected in a ring of cells at the vegetal pole that gives rise to endomesoderm and in the ventral ectoderm at later stages of development. Inhibition of Nodal function disrupts dorsoventral fates and also blocks formation of the larval mesoderm. Interestingly, molecular analysis reveals that only mesodermal, apical and ventral gene expression is affected while the dorsal side appears to be patterned correctly. Taken together, this study suggests that the co-option of Nodal signaling in mesoderm formation and potentially in anteroposterior patterning has occurred prior to the emergence of chordates and that Nodal signaling on the ventral side is uncoupled from BMP signaling on the dorsal side, representing a major difference from the molecular mechanisms of dorsoventral patterning events in echinoderms. PMID:25979707
Röttinger, Eric; DuBuc, Timothy Q; Amiel, Aldine R; Martindale, Mark Q
2015-01-01
Nodal signaling plays crucial roles in vertebrate developmental processes such as endoderm and mesoderm formation, and axial patterning events along the anteroposterior, dorsoventral and left-right axes. In echinoderms, Nodal plays an essential role in the establishment of the dorsoventral axis and left-right asymmetry, but not in endoderm or mesoderm induction. In protostomes, Nodal signaling appears to be involved only in establishing left-right asymmetry. Hence, it is hypothesized that Nodal signaling has been co-opted to pattern the dorsoventral axis of deuterostomes and for endoderm, mesoderm formation as well as anteroposterior patterning in chordates. Hemichordata, together with echinoderms, represent the sister taxon to chordates. In this study, we analyze the role of Nodal signaling in the indirect developing hemichordate Ptychodera flava. In particular, we show that during gastrulation nodal transcripts are detected in a ring of cells at the vegetal pole that gives rise to endomesoderm and in the ventral ectoderm at later stages of development. Inhibition of Nodal function disrupts dorsoventral fates and also blocks formation of the larval mesoderm. Interestingly, molecular analysis reveals that only mesodermal, apical and ventral gene expression is affected while the dorsal side appears to be patterned correctly. Taken together, this study suggests that the co-option of Nodal signaling in mesoderm formation and potentially in anteroposterior patterning has occurred prior to the emergence of chordates and that Nodal signaling on the ventral side is uncoupled from BMP signaling on the dorsal side, representing a major difference from the molecular mechanisms of dorsoventral patterning events in echinoderms. PMID:25979707
Maxwell solvers for the simulations of the laser-matter interaction
NASA Astrophysics Data System (ADS)
Nuter, Rachel; Grech, Mickael; Gonzalez de Alaiza Martinez, Pedro; Bonnaud, Guy; d'Humières, Emmanuel
2014-06-01
With the advent of high intensity laser beams, solving the Maxwell equations with a free-dispersive algorithm is becoming essential. Several Maxwell solvers, implemented in Particle-In-Cell codes, have been proposed. We present here some of them by describing their computational stencil in two-dimensional geometry and defining their stability area as well as their numerical dispersion relation. Numerical simulations of Backward Raman amplification and laser wake-field are presented to compare these different solvers.
The development of an intelligent interface to a computational fluid dynamics flow-solver code
NASA Technical Reports Server (NTRS)
Williams, Anthony D.
1988-01-01
Researchers at NASA Lewis are currently developing an 'intelligent' interface to aid in the development and use of large, computational fluid dynamics flow-solver codes for studying the internal fluid behavior of aerospace propulsion systems. This paper discusses the requirements, design, and implementation of an intelligent interface to Proteus, a general purpose, 3-D, Navier-Stokes flow solver. The interface is called PROTAIS to denote its introduction of artificial intelligence (AI) concepts to the Proteus code.
The development of an intelligent interface to a computational fluid dynamics flow-solver code
NASA Technical Reports Server (NTRS)
Williams, Anthony D.
1988-01-01
Researchers at NASA Lewis are currently developing an 'intelligent' interface to aid in the development and use of large, computational fluid dynamics flow-solver codes for studying the internal fluid behavior of aerospace propulsion systems. This paper discusses the requirements, design, and implementation of an intelligent interface to Proteus, a general purpose, three-dimensional, Navier-Stokes flow solver. The interface is called PROTAIS to denote its introduction of artificial intelligence (AI) concepts to the Proteus code.
Implementation of a parallel unstructured Euler solver on the CM-5
NASA Technical Reports Server (NTRS)
Morano, Eric; Mavriplis, D. J.
1995-01-01
An efficient unstructured 3D Euler solver is parallelized on a Thinking Machine Corporation Connection Machine 5, distributed memory computer with vectoring capability. In this paper, the single instruction multiple data (SIMD) strategy is employed through the use of the CM Fortran language and the CMSSL scientific library. The performance of the CMSSL mesh partitioner is evaluated and the overall efficiency of the parallel flow solver is discussed.