Study of the microbunching instability in single-pass systemsusing a direct 2D Vlasov solver
Venturini, Marco
2007-06-30
We apply a recently developed Vlasov solver to the study ofthemicrobunching instability generated by shot noise in the beamdeliverysystems of x-ray Free Electron Lasers (FELs). We discusstwo latticespresently under consideration for the FEL FERMI project at Elettra andshow that at least one of the two lattices appears capable of deliveringa beam with the desired quality in the longitudinal phasespace.
2d PDE Linear Symmetric Matrix Solver
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
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
Ion acoustic wave collapse via two-ion wave decay: 2D Vlasov simulation and theory
NASA Astrophysics Data System (ADS)
Chapman, Thomas; Berger, Richard; Banks, Jeffrey; Brunner, Stephan
2015-11-01
The decay of ion acoustic waves (IAWs) via two-ion wave decay may transfer energy from the electric field of the IAWs to the particles, resulting in a significant heating of resonant particles. This process has previously been shown in numerical simulations to decrease the plasma reflectivity due to stimulated Brillouin scattering. Two-ion wave decay is a fundamental property of ion acoustic waves that occurs over most if not all of the parameter space of relevance to inertial confinement fusion experiments, and can lead to a sudden collapse of IAWs. The treatment of all species kinetically, and in particular the electrons, is required to describe the decay process correctly. We present fully kinetic 2D+2V Vlasov simulations of IAWs undergoing decay to a highly nonlinear turbulent state using the code LOKI. The scaling of the decay rate with characteristic plasma parameters and wave amplitude is shown. A new theory describing two-ion wave decay in 2D, that incorporates key kinetic properties of the electrons, is presented and used to explain quantitatively for the first time the observed decay of IAWs. Work performed under auspices of U.S. DoE by LLNL, Contract DE-AC52-07NA2734. Funded by LDRD 15-ERD-038 and supported by LLNL Grand Challenge allocation.
Vlasov Fluid stability of a 2-D plasma with a linear magnetic field null
Kim, J.S.
1984-01-01
Vlasov Fluid stability of a 2-dimensional plasma near an O type magnetic null is investigated. Specifically, an elongated Z-pinch is considered, and applied to Field Reversed Configurations at Los Alamos National Laboratory by making a cylindrical approximation of the compact torus. The orbits near an elliptical O type null are found to be very complicated; the orbits are large and some are stochastic. The kinetic corrections to magnetohydrodynamics (MHD) are investigated by evaluating the expectation values of the growth rates of a Vlasov Fluid dispersion functional by using a set of trial functions based on ideal MHD. The dispersion functional involves fluid parts and orbit dependent parts. The latter involves phase integral of two time correlations. The phase integral is replaced by the time integral both for the regular and for the stochastic orbits. Two trial functions are used; one has a large displacement near the null and the other away from the null.
Efficient simulation of pitch angle collisions in a 2+2-D Eulerian Vlasov code
NASA Astrophysics Data System (ADS)
Banks, Jeff; Berger, R.; Brunner, S.; Tran, T.
2014-10-01
Here we discuss pitch angle scattering collisions in the context of the Eulerian-based kinetic code LOKI that evolves the Vlasov-Poisson system in 2+2-dimensional phase space. The collision operator is discretized using 4th order accurate conservative finite-differencing. The treatment of the Vlasov operator in phase-space uses an approach based on a minimally diffuse, fourth-order-accurate discretization (Banks and Hittinger, IEEE T. Plasma Sci. 39, 2198). The overall scheme is therefore discretely conservative and controls unphysical oscillations. Some details of the numerical scheme will be presented, and the implementation on modern highly concurrent parallel computers will be discussed. We will present results of collisional effects on linear and non-linear Landau damping of electron plasma waves (EPWs). In addition we will present initial results showing the effect of collisions on the evolution of EPWs in two space dimensions. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and funded by the LDRD program at LLNL under project tracking code 12-ERD-061.
ColDICE: A parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation
NASA Astrophysics Data System (ADS)
Sousbie, Thierry; Colombi, Stéphane
2016-09-01
Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincaré invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli [65-67] generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a "warm" dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.
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.
Proteus-MOC: A 3D deterministic solver incorporating 2D method of characteristics
Marin-Lafleche, A.; Smith, M. A.; Lee, C.
2013-07-01
A new transport solution methodology was developed by combining the two-dimensional method of characteristics with the discontinuous Galerkin method for the treatment of the axial variable. The method, which can be applied to arbitrary extruded geometries, was implemented in PROTEUS-MOC and includes parallelization in group, angle, plane, and space using a top level GMRES linear algebra solver. Verification tests were performed to show accuracy and stability of the method with the increased number of angular directions and mesh elements. Good scalability with parallelism in angle and axial planes is displayed. (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.
Adaptive Vlasov Simulations of Intense Beams
Sonnendruecker, Eric; Gutnic, Michael; Haefele, Matthieu; Lemaire, Jean-Louis
2005-06-08
Most simulations of intense particle beams are performed nowadays using Particle In Cell (PIC) techniques. Direct grid based Vlasov methods have also been used but mostly for 1D simulations as they become very costly in higher dimensions when using uniform phase space grids. We have recently introduced adaptive mesh refinement techniques that allow us to automatically concentrate the grid points at places where the distribution function is varying most. In this paper we shall introduce this technique and show how it can be used to improve the efficiency of grid based Vlasov solvers.
NASA Astrophysics Data System (ADS)
Bruno, Oscar P.; Cubillos, Max
2016-02-01
This paper introduces alternating-direction implicit (ADI) solvers of higher order of time-accuracy (orders two to six) for the compressible Navier-Stokes equations in two- and three-dimensional curvilinear domains. The higher-order accuracy in time results from 1) An application of the backward differentiation formulae time-stepping algorithm (BDF) in conjunction with 2) A BDF-like extrapolation technique for certain components of the nonlinear terms (which makes use of nonlinear solves unnecessary), as well as 3) A novel application of the Douglas-Gunn splitting (which greatly facilitates handling of boundary conditions while preserving higher-order accuracy in time). As suggested by our theoretical analysis of the algorithms for a variety of special cases, an extensive set of numerical experiments clearly indicate that all of the BDF-based ADI algorithms proposed in this paper are "quasi-unconditionally stable" in the following sense: each algorithm is stable for all couples (h , Δt)of spatial and temporal mesh sizes in a problem-dependent rectangular neighborhood of the form (0 ,Mh) × (0 ,Mt). In other words, for each fixed value of Δt below a certain threshold, the Navier-Stokes solvers presented in this paper are stable for arbitrarily small spatial mesh-sizes. The second-order formulation has further been rigorously shown to be unconditionally stable for linear hyperbolic and parabolic equations in two-dimensional space. Although implicit ADI solvers for the Navier-Stokes equations with nominal second-order of temporal accuracy have been proposed in the past, the algorithms presented in this paper are the first ADI-based Navier-Stokes solvers for which second-order or better accuracy has been verified in practice under non-trivial (non-periodic) boundary conditions.
Vlasov simulation in multiple spatial dimensions
Rose, Harvey A.; Daughton, William
2011-12-15
A long-standing challenge encountered in modeling plasma dynamics is achieving practical Vlasov equation simulation in multiple spatial dimensions over large length and time scales. While direct multi-dimension Vlasov simulation methods using adaptive mesh methods [M. Gutnic et al., Comput. Phys. Commun. 164, 214 (2004)] have recently shown promising results in two dimensions (2D) [J. W. Banks et al., Phys. Plasmas 18, 052102 (2011); B. I. Cohen et al., November 10, 2010, http://meetings.aps.org/link/BAPS.2010.DPP.NP9.142], in this paper, we present an alternative, the Vlasov multi dimensional (VMD) model, that is specifically designed to take advantage of solution properties in regimes when plasma waves are confined to a narrow cone, as may be the case for stimulated Raman scatter in large optic f laser beams. Perpendicular grid spacing large compared to a Debye length is then possible without instability or loss of accuracy, enabling an order 10 decrease in required computational resources compared to standard particle in cell (PIC) methods in 2D, with another reduction of that order in 3D. Further advantage compared to PIC methods accrues in regimes where particle noise is an issue. VMD and PIC results in a 2D model of localized Langmuir waves are in qualitative agreement.
Galler, M. . E-mail: galler@itp.tu-graz.ac.at; Schuerrer, F. . E-mail: schuerrer@itp.tu-graz.ac.at
2005-12-10
The transport of the two-dimensional electron gas formed at an AlGaN/GaN heterostructure in the presence of strain polarization fields is investigated. For this purpose, we develop a deterministic multigroup model to the Boltzmann transport equations. The envelope wave functions for the confined electrons are calculated using a self-consistent Poisson-Schroedinger solver. The electron gas degeneracy and hot phonons are included in our transport equations. Numerical results are given for the dependence of macroscopic quantities on the electric field strength and on time and for the electron and phonon distribution functions. We compare our results to those of Monte Carlo simulations and with experiments.
Comparing the line broadened quasilinear model to Vlasov code
Ghantous, K.; Berk, H. L.; Gorelenkov, N. N.
2014-03-15
The Line Broadened Quasilinear (LBQ) model is revisited to study its predicted saturation level as compared with predictions of a Vlasov solver BOT [Lilley et al., Phys. Rev. Lett. 102, 195003 (2009) and M. Lilley, BOT Manual. The parametric dependencies of the model are modified to achieve more accuracy compared to the results of the Vlasov solver both in regards to a mode amplitude's time evolution to a saturated state and its final steady state amplitude in the parameter space of the model's applicability. However, the regions of stability as predicted by LBQ model and BOT are found to significantly differ from each other. The solutions of the BOT simulations are found to have a larger region of instability than the LBQ simulations.
Comparing the line broadened quasilinear model to Vlasov code
NASA Astrophysics Data System (ADS)
Ghantous, K.; Berk, H. L.; Gorelenkov, N. N.
2014-03-01
The Line Broadened Quasilinear (LBQ) model is revisited to study its predicted saturation level as compared with predictions of a Vlasov solver BOT [Lilley et al., Phys. Rev. Lett. 102, 195003 (2009) and M. Lilley, BOT Manual. The parametric dependencies of the model are modified to achieve more accuracy compared to the results of the Vlasov solver both in regards to a mode amplitude's time evolution to a saturated state and its final steady state amplitude in the parameter space of the model's applicability. However, the regions of stability as predicted by LBQ model and BOT are found to significantly differ from each other. The solutions of the BOT simulations are found to have a larger region of instability than the LBQ simulations.
Ahn, J-W.; Gan, K. F.; Scotti, F.; Lore, J. D.; Maingi, R.; Canik, J. M.; Gray, T. K.; McLean, A. G.; Roquemore, A. L.; Soukhanovskii, V. A.
2013-01-12
Toroidally non-axisymmetric divertor profiles during the 3-D field application and for ELMs are studied with simultaneous observation by a new wide angle visible camera and a high speed IR camera. A newly implemented 3-D heat conduction code, TACO, is used to obtain divertor heat flux. The wide angle camera data confirmed the previously reported result on the validity of vacuum field line tracing on the prediction of split strike point pattern by 3-D fields as well as the phase locking of ELM heat flux to the 3-D fields. TACO calculates the 2- D heat flux distribution allowing assessment of toroidal asymmetry of peak heat flux and heat flux width. Lastly, the degree of asymmetry (ε_{DA}) is defined to quantify the asymmetric heat deposition on the divertor surface and is found to have a strong positive dependence on peak heat flux.
The stability of freely-propagating ion acoustic waves in 2D systems
NASA Astrophysics Data System (ADS)
Chapman, Thomas; Berger, Richard; Banks, Jeffrey; Brunner, Stephan
2014-10-01
The stability of a freely-propagating ion acoustic wave (IAW) is a basic science problem that is made difficult by the need to resolve electron kinetic effects over a timescale that greatly exceeds the IAW period during numerical simulation. Recent results examining IAW stability using a 1D+1V Vlasov-Poisson solver indicate that instability is a fundamental property of IAWs that occurs over most if not all of the parameter space of relevance to ICF experiments. We present here new results addressing the fundamental question of IAW stability across a broad range of plasma conditions in a 2D+2V system using LOKI, ranging from a regime of relatively weak to a regime of relatively strong ion kinetic effects. Work performed under the auspices of the U.S. DOE by LLNL (DE-AC52-07NA27344) and funded by the LDRD Program at LLNL (12-ERD-061).
Vlasov simulations of beams with a moving grid
Sonnendrucker, E.; Filbet, F.; Friedman, A.; Oudet, E.; Vay, J-L.
2003-10-03
Thanks to the rapid increase of computing power in recent years, simulations of plasmas and particle beams based on direct solution of the Vlasov equation on a multi-dimensional phase-space grid are becoming attractive as an alternative to Particle-In-Cell (PIC) simulations. Their strength lies essentially in the fact that they are noiseless and that all parts of phase space, including the tail of the distribution, are equally well resolved. Their major drawback is that, for inhomogeneous systems, many of the grid points (where no particles are present) are wasted. This is especially the case for beam simulations where the beam moves rapidly through the phase space (due to varying alternating-gradient focusing forces, for example). This inefficiency has made such Vlasov simulations unsuitable for those cases. One of the methods which has proven very efficient for the direct resolution of the Vlasov equation is the semi-Lagrangian method [1, 3]. It consists in updating the values of the distribution function at the grid nodes by following the characteristics ending at these nodes backwards and interpolating the value at the bottom of the characteristics from the known values at the previous time step. In general the interpolation grid is fixed, but this is not mandatory. This paper introduces the concept of a moving grid which is mapped at each time step from a logical uniform grid to the beam, so that it contains the whole beam without needing too many points with vanishing values of the distribution function. In order to implement this new method, we introduce a new time stepping algorithm which does not rely on the time splitting procedure traditionally used in Vlasov solvers.
Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
Squire, J.; Tang, W. M.; Qin, H.
2012-08-15
A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of discrete exterior calculus [Desbrun et al., e-print arXiv:math/0508341 (2005)], the field solver, interpolation scheme, and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.
Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
NASA Astrophysics Data System (ADS)
Squire, J.; Qin, H.; Tang, W. M.
2012-08-01
A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of discrete exterior calculus [Desbrun et al., e-print arXiv:math/0508341 (2005)], the field solver, interpolation scheme, and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.
Geometric Integration Of The Vlasov-Maxwell System With A Variational Particle-in-cell Scheme
J. Squire, H. Qin and W.M. Tang
2012-03-27
A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of Discrete Exterior Calculus [1], the field solver, interpolation scheme and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.
Neutral Vlasov kinetic theory of magnetized plasmas
Tronci, Cesare; Camporeale, Enrico
2015-02-15
The low-frequency limit of Maxwell equations is considered in the Maxwell-Vlasov system. This limit produces a neutral Vlasov system that captures essential features of plasma dynamics, while neglecting radiation effects. Euler-Poincaré reduction theory is used to show that the neutral Vlasov kinetic theory possesses a variational formulation in both Lagrangian and Eulerian coordinates. By construction, the new model recovers all collisionless neutral models employed in plasma simulations. Then, comparisons between the neutral Vlasov system and hybrid kinetic-fluid models are presented in the linear regime.
Vlasov multi-dimensional model dispersion relation
Lushnikov, Pavel M.; Rose, Harvey A.; Silantyev, Denis A.; Vladimirova, Natalia
2014-07-15
A hybrid model of the Vlasov equation in multiple spatial dimension D > 1 [H. A. Rose and W. Daughton, Phys. Plasmas 18, 122109 (2011)], the Vlasov multi dimensional model (VMD), consists of standard Vlasov dynamics along a preferred direction, the z direction, and N flows. At each z, these flows are in the plane perpendicular to the z axis. They satisfy Eulerian-type hydrodynamics with coupling by self-consistent electric and magnetic fields. Every solution of the VMD is an exact solution of the original Vlasov equation. We show approximate convergence of the VMD Langmuir wave dispersion relation in thermal plasma to that of Vlasov-Landau as N increases. Departure from strict rotational invariance about the z axis for small perpendicular wavenumber Langmuir fluctuations in 3D goes to zero like θ{sup N}, where θ is the polar angle and flows are arranged uniformly over the azimuthal angle.
NASA Astrophysics Data System (ADS)
Turchetti, G.; Rambaldi, S.; Bazzani, A.; Comunian, M.; Pisent, A.
2003-09-01
We consider a charged plasma of positive ions in a periodic focusing channel of quadrupolar magnets in the presence of RF cavities. The ions are bunched into charged triaxial ellipsoids and their description requires the solution of a fully 3D Poisson-Vlasov equation. We also analyze the trajectories of test particles in the exterior of the ion bunches in order to estimate their diffusion rate. This rate is relevant for a high intensity linac (TRASCO project). A numerical PIC scheme to integrate the Poisson-Vlasov equations in a periodic focusing system in 2 and 3 space dimensions is presented. The scheme consists of a single particle symplectic integrator and a Poisson solver based on FFT plus tri-diagonal matrix inversion. In the 2D version arbitrary boundary conditions can be chosen. Since no analytical self-consistent 3D solution is known, we chose an initial Neuffer-KV distribution in phase space, whose electric field is close to the one generated by a uniformly filled ellipsoid. For a matched (periodic) beam the orbits of test particles moving in the field of an ellipsoidal bunch, whose semi-axis satisfy the envelope equations, is similar to the orbits generated by the self-consistent charge distribition obtained from the PIC simulation, even though it relaxes to a Fermi-Dirac-like distribution. After a transient the RMS radii and emittances have small amplitude oscillations. The PIC simulations for a mismatched (quasiperiodic) beam are no longer comparable with the ellipsoidal bunch model even though the qualitative behavior is the same, namely a stronger diffusion due to the increase of resonances.
Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
NASA Astrophysics Data System (ADS)
Squire, Jonathan; Qin, Hong; Tang, William
2012-10-01
A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of Discrete Exterior Calculus [1], the field solver, interpolation scheme and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law. This work was supported by USDOE Contract DE-AC02-09CH11466.[4pt] [1] M. Desbrun, A. N. Hirani, M. Leok, and J. E. Marsden, (2005), arXiv:math/0508341
Cosmology in one dimension: Vlasov dynamics
NASA Astrophysics Data System (ADS)
Manfredi, Giovanni; Rouet, Jean-Louis; Miller, Bruce; Shiozawa, Yui
2016-04-01
Numerical simulations of self-gravitating systems are generally based on N -body codes, which solve the equations of motion of a large number of interacting particles. This approach suffers from poor statistical sampling in regions of low density. In contrast, Vlasov codes, by meshing the entire phase space, can reach higher accuracy irrespective of the density. Here, we perform one-dimensional Vlasov simulations of a long-standing cosmological problem, namely, the fractal properties of an expanding Einstein-de Sitter universe in Newtonian gravity. The N -body results are confirmed for high-density regions and extended to regions of low matter density, where the N -body approach usually fails.
A wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov Maxwell system
NASA Astrophysics Data System (ADS)
Besse, Nicolas; Latu, Guillaume; Ghizzo, Alain; Sonnendrücker, Eric; Bertrand, Pierre
2008-08-01
In this paper we present a new method for the numerical solution of the relativistic Vlasov-Maxwell system on a phase-space grid using an adaptive semi-Lagrangian method. The adaptivity is performed through a wavelet multiresolution analysis, which gives a powerful and natural refinement criterion based on the local measurement of the approximation error and regularity of the distribution function. Therefore, the multiscale expansion of the distribution function allows to get a sparse representation of the data and thus save memory space and CPU time. We apply this numerical scheme to reduced Vlasov-Maxwell systems arising in laser-plasma physics. Interaction of relativistically strong laser pulses with overdense plasma slabs is investigated. These Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by electromagnetic waves as electron trapping, particle acceleration, and electron plasma wavebreaking. However, the wavelet based adaptive method that we developed here, does not yield significant improvements compared to Vlasov solvers on a uniform mesh due to the substantial overhead that the method introduces. Nonetheless they might be a first step towards more efficient adaptive solvers based on different ideas for the grid refinement or on a more efficient implementation. Here the Vlasov simulations are performed in a two-dimensional phase-space where the development of thin filaments, strongly amplified by relativistic effects requires an important increase of the total number of points of the phase-space grid as they get finer as time goes on. The adaptive method could be more useful in cases where these thin filaments that need to be resolved are a very small fraction of the hyper-volume, which arises in higher dimensions because of the surface-to-volume scaling and the essentially one-dimensional structure of the filaments. Moreover, the main way to improve the efficiency of the adaptive method is to
Documentation for vlasov, version 0.1
Berg, J.S.
1996-03-01
This paper describes how to use the code vlasov, which implements the computation of multibunch frequencies and growth rates when the effects of multibunch mode coupling are included. The theory behind this code is described in [BR95a, BR95b, Ber96]. This paper also describes the algorithm used to compute the modes, and the approximations made.
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.
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
Flow Solver for Incompressible 2-D Drive Cavity
NASA Technical Reports Server (NTRS)
Kalb, Virginia L.
2008-01-01
This software solves the Navier-Stokes equations for the incompressible driven cavity flow problem. The code uses second-order finite differencing on a staggered grid using the Chorin projection method. The resulting intermediate Poisson equation is efficiently solved using the fast Fourier transform. Time stepping is done using fourth-order Runge-Kutta for stability at high Reynolds numbers. Features include check-pointing, periodic field snapshots, ongoing reporting of kinetic energy and changes between time steps, time histories at selected points, and optional streakline generation.
The whistler mode in a Vlasov plasma
NASA Technical Reports Server (NTRS)
Tokar, R. L.; Gary, S. P.
1985-01-01
In this study, properties of small-amplitude parallel and oblique whistler-mode waves are investigated for a wide range of plasma parameters by numerically solving the full electromagnetic Vlasov-dispersion equation. To investigate the cold-plasma and electrostatic approximations for the whistler mode, the results are compared with results obtained using these descriptions. For large wavelengths, the cold-plasma description is often accurate, while for short wavelengths and sufficiently oblique propagation, the electrostatic description is often accurate. The study demonstrates that in a Vlasov plasma the whistler mode near resonance has a group velocity more nearly parallel to the magnetic field than that predicted by cold-plasma theory.
Cosmology in one dimension: Vlasov dynamics.
Manfredi, Giovanni; Rouet, Jean-Louis; Miller, Bruce; Shiozawa, Yui
2016-04-01
Numerical simulations of self-gravitating systems are generally based on N-body codes, which solve the equations of motion of a large number of interacting particles. This approach suffers from poor statistical sampling in regions of low density. In contrast, Vlasov codes, by meshing the entire phase space, can reach higher accuracy irrespective of the density. Here, we perform one-dimensional Vlasov simulations of a long-standing cosmological problem, namely, the fractal properties of an expanding Einstein-de Sitter universe in Newtonian gravity. The N-body results are confirmed for high-density regions and extended to regions of low matter density, where the N-body approach usually fails.
Cosmology in one dimension: Vlasov dynamics.
Manfredi, Giovanni; Rouet, Jean-Louis; Miller, Bruce; Shiozawa, Yui
2016-04-01
Numerical simulations of self-gravitating systems are generally based on N-body codes, which solve the equations of motion of a large number of interacting particles. This approach suffers from poor statistical sampling in regions of low density. In contrast, Vlasov codes, by meshing the entire phase space, can reach higher accuracy irrespective of the density. Here, we perform one-dimensional Vlasov simulations of a long-standing cosmological problem, namely, the fractal properties of an expanding Einstein-de Sitter universe in Newtonian gravity. The N-body results are confirmed for high-density regions and extended to regions of low matter density, where the N-body approach usually fails. PMID:27176297
Kinetic Vlasov simulations of collisionless magnetic reconnection
Schmitz, H.; Grauer, R.
2006-09-15
A fully kinetic Vlasov simulation of the Geospace Environment Modeling Magnetic Reconnection Challenge is presented. Good agreement is found with previous kinetic simulations using particle in cell (PIC) codes, confirming both the PIC and the Vlasov code. In the latter the complete distribution functions f{sub k} (k=i,e) are discretized on a numerical grid in phase space. In contrast to PIC simulations, the Vlasov code does not suffer from numerical noise and allows a more detailed investigation of the distribution functions. The role of the different contributions of Ohm's law are compared by calculating each of the terms from the moments of the f{sub k}. The important role of the off-diagonal elements of the electron pressure tensor could be confirmed. The inductive electric field at the X line is found to be dominated by the nongyrotropic electron pressure, while the bulk electron inertia is of minor importance. Detailed analysis of the electron distribution function within the diffusion region reveals the kinetic origin of the nongyrotropic terms.
Quasi-neutral Vlasov theory of magnetized plasmas
NASA Astrophysics Data System (ADS)
Tronci, Cesare; Camporeale, Enrico
2015-11-01
The low-frequency limit of Maxwell equations is considered in the Maxwell-Vlasov system. This limit produces a quasi-neutral Vlasov system that captures essential features of plasma dynamics, while neglecting radiation effects. Euler-Poincaré reduction theory is used to show that the quasi-neutral Vlasov theory possesses a variational formulation in both Lagrangian and Eulerian coordinates. By construction, the new model recovers all collisionless neutral models employed in plasma simulations. Then, comparisons between the quasi-neutral Vlasov system and hybrid kinetic-fluid models are presented in the linear regime. Financial support by the Leverhulme Trust Research Project Grant 2014-112 is greatly acknowledged.
Noiseless Vlasov-Poisson simulations with linearly transformed particles
Pinto, Martin C.; Sonnendrucker, Eric; Friedman, Alex; Grote, David P.; Lund, Steve M.
2014-06-25
We introduce a deterministic discrete-particle simulation approach, the Linearly-Transformed Particle-In-Cell (LTPIC) method, that employs linear deformations of the particles to reduce the noise traditionally associated with particle schemes. Formally, transforming the particles is justified by local first order expansions of the characteristic flow in phase space. In practice the method amounts of using deformation matrices within the particle shape functions; these matrices are updated via local evaluations of the forward numerical flow. Because it is necessary to periodically remap the particles on a regular grid to avoid excessively deforming their shapes, the method can be seen as a development of Denavit's Forward Semi-Lagrangian (FSL) scheme (Denavit, 1972 [8]). However, it has recently been established (Campos Pinto, 2012 [20]) that the underlying Linearly-Transformed Particle scheme converges for abstract transport problems, with no need to remap the particles; deforming the particles can thus be seen as a way to significantly lower the remapping frequency needed in the FSL schemes, and hence the associated numerical diffusion. To couple the method with electrostatic field solvers, two specific charge deposition schemes are examined, and their performance compared with that of the standard deposition method. Finally, numerical 1d1v simulations involving benchmark test cases and halo formation in an initially mismatched thermal sheet beam demonstrate some advantages of our LTPIC scheme over the classical PIC and FSL methods. Lastly, benchmarked test cases also indicate that, for numerical choices involving similar computational effort, the LTPIC method is capable of accuracy comparable to or exceeding that of state-of-the-art, high-resolution Vlasov schemes.
Noiseless Vlasov-Poisson simulations with linearly transformed particles
Pinto, Martin C.; Sonnendrucker, Eric; Friedman, Alex; Grote, David P.; Lund, Steve M.
2014-06-25
We introduce a deterministic discrete-particle simulation approach, the Linearly-Transformed Particle-In-Cell (LTPIC) method, that employs linear deformations of the particles to reduce the noise traditionally associated with particle schemes. Formally, transforming the particles is justified by local first order expansions of the characteristic flow in phase space. In practice the method amounts of using deformation matrices within the particle shape functions; these matrices are updated via local evaluations of the forward numerical flow. Because it is necessary to periodically remap the particles on a regular grid to avoid excessively deforming their shapes, the method can be seen as a development ofmore » Denavit's Forward Semi-Lagrangian (FSL) scheme (Denavit, 1972 [8]). However, it has recently been established (Campos Pinto, 2012 [20]) that the underlying Linearly-Transformed Particle scheme converges for abstract transport problems, with no need to remap the particles; deforming the particles can thus be seen as a way to significantly lower the remapping frequency needed in the FSL schemes, and hence the associated numerical diffusion. To couple the method with electrostatic field solvers, two specific charge deposition schemes are examined, and their performance compared with that of the standard deposition method. Finally, numerical 1d1v simulations involving benchmark test cases and halo formation in an initially mismatched thermal sheet beam demonstrate some advantages of our LTPIC scheme over the classical PIC and FSL methods. Lastly, benchmarked test cases also indicate that, for numerical choices involving similar computational effort, the LTPIC method is capable of accuracy comparable to or exceeding that of state-of-the-art, high-resolution Vlasov schemes.« less
Noiseless Vlasov-Poisson simulations with linearly transformed particles
NASA Astrophysics Data System (ADS)
Campos Pinto, Martin; Sonnendrücker, Eric; Friedman, Alex; Grote, David P.; Lund, Steve M.
2014-10-01
We introduce a deterministic discrete-particle simulation approach, the Linearly-Transformed Particle-In-Cell (LTPIC) method, that employs linear deformations of the particles to reduce the noise traditionally associated with particle schemes. Formally, transforming the particles is justified by local first order expansions of the characteristic flow in phase space. In practice the method amounts of using deformation matrices within the particle shape functions; these matrices are updated via local evaluations of the forward numerical flow. Because it is necessary to periodically remap the particles on a regular grid to avoid excessively deforming their shapes, the method can be seen as a development of Denavit's Forward Semi-Lagrangian (FSL) scheme (Denavit, 1972 [8]). However, it has recently been established (Campos Pinto, 2012 [20]) that the underlying Linearly-Transformed Particle scheme converges for abstract transport problems, with no need to remap the particles; deforming the particles can thus be seen as a way to significantly lower the remapping frequency needed in the FSL schemes, and hence the associated numerical diffusion. To couple the method with electrostatic field solvers, two specific charge deposition schemes are examined, and their performance compared with that of the standard deposition method. Finally, numerical 1d1v simulations involving benchmark test cases and halo formation in an initially mismatched thermal sheet beam demonstrate some advantages of our LTPIC scheme over the classical PIC and FSL methods. Benchmarked test cases also indicate that, for numerical choices involving similar computational effort, the LTPIC method is capable of accuracy comparable to or exceeding that of state-of-the-art, high-resolution Vlasov schemes.
Chaotic magnetic fields in Vlasov-Maxwell equilibria
Ghosh, Abhijit; Janaki, M. S.; Dasgupta, Brahmananda; Bandyopadhyay, Alak
2014-03-15
Stationary solutions of Vlasov-Maxwell equations are obtained by exploiting the invariants of single particle motion leading to linear or nonlinear functional relations between current and vector potential. For a specific combination of invariants, it is shown that Vlasov-Maxwell equilibria have an associated Hamiltonian that exhibits chaos.
Vlasov-Maxwell and Vlasov-Poisson equations as models of a one-dimensional electron plasma
NASA Technical Reports Server (NTRS)
Klimas, A. J.; Cooper, J.
1983-01-01
The Vlasov-Maxwell and Vlasov-Poisson systems of equations for a one-dimensional electron plasma are defined and discussed. A method for transforming a solution of one system which is periodic over a bounded or unbounded spatial interval to a similar solution of the other is constructed.
A wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov-Maxwell system
Besse, Nicolas Latu, Guillaume Ghizzo, Alain Sonnendruecker, Eric Bertrand, Pierre
2008-08-10
In this paper we present a new method for the numerical solution of the relativistic Vlasov-Maxwell system on a phase-space grid using an adaptive semi-Lagrangian method. The adaptivity is performed through a wavelet multiresolution analysis, which gives a powerful and natural refinement criterion based on the local measurement of the approximation error and regularity of the distribution function. Therefore, the multiscale expansion of the distribution function allows to get a sparse representation of the data and thus save memory space and CPU time. We apply this numerical scheme to reduced Vlasov-Maxwell systems arising in laser-plasma physics. Interaction of relativistically strong laser pulses with overdense plasma slabs is investigated. These Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by electromagnetic waves as electron trapping, particle acceleration, and electron plasma wavebreaking. However, the wavelet based adaptive method that we developed here, does not yield significant improvements compared to Vlasov solvers on a uniform mesh due to the substantial overhead that the method introduces. Nonetheless they might be a first step towards more efficient adaptive solvers based on different ideas for the grid refinement or on a more efficient implementation. Here the Vlasov simulations are performed in a two-dimensional phase-space where the development of thin filaments, strongly amplified by relativistic effects requires an important increase of the total number of points of the phase-space grid as they get finer as time goes on. The adaptive method could be more useful in cases where these thin filaments that need to be resolved are a very small fraction of the hyper-volume, which arises in higher dimensions because of the surface-to-volume scaling and the essentially one-dimensional structure of the filaments. Moreover, the main way to improve the efficiency of the adaptive method is to
Valentini, F. . E-mail: valentin@fis.unical.it; Travnicek, P.; Califano, F.; Hellinger, P.; Mangeney, A.
2007-07-01
We present a numerical scheme for the integration of the Vlasov-Maxwell system of equations for a non-relativistic plasma, in the hybrid approximation, where the Vlasov equation is solved for the ion distribution function and the electrons are treated as a fluid. In the Ohm equation for the electric field, effects of electron inertia have been retained, in order to include the small scale dynamics up to characteristic lengths of the order of the electron skin depth. The low frequency approximation is used by neglecting the time derivative of the electric field, i.e. the displacement current in the Ampere equation. The numerical algorithm consists in coupling the splitting method proposed by Cheng and Knorr in 1976 [C.Z. Cheng, G. Knorr, J. Comput. Phys. 22 (1976) 330-351.] and the current advance method (CAM) introduced by Matthews in 1994 [A.P. Matthews, J. Comput. Phys. 112 (1994) 102-116.] In its present version, the code solves the Vlasov-Maxwell equations in a five-dimensional phase space (2-D in the physical space and 3-D in the velocity space) and it is implemented in a parallel version to exploit the computational power of the modern massively parallel supercomputers. The structure of the algorithm and the coupling between the splitting method and the CAM method (extended to the hybrid case) is discussed in detail. Furthermore, in order to test the hybrid-Vlasov code, the numerical results on propagation and damping of linear ion-acoustic modes and time evolution of linear elliptically polarized Alfven waves (including the so-called whistler regime) are compared to the analytical solutions. Finally, the numerical results of the hybrid-Vlasov code on the parametric instability of Alfven waves are compared with those obtained using a two-fluid approach.
Fermion particle production in semiclassical Boltzmann-Vlasov transport theory
Dawson, John F.; Mihaila, Bogdan; Cooper, Fred
2009-07-01
We present numerical solutions of the semiclassical Boltzmann-Vlasov equation for fermion particle-antiparticle production by strong electric fields in boost-invariant coordinates in (1+1) and (3+1) dimensional QED. We compare the Boltzmann-Vlasov results with those of recent quantum field theory calculations and find good agreement. We conclude that extending the Boltzmann-Vlasov approach to the case of QCD should allow us to do a thorough investigation of how backreaction affects recent results on the dependence of the transverse momentum distribution of quarks and antiquarks on a second Casimir invariant of color SU(3)
Beam-Plasma Instabilities in a 2D Yukawa Lattice
Kyrkos, S.; Kalman, G. J.; Rosenberg, M.
2009-06-05
We consider a 2D Yukawa lattice of grains, with a beam of other charged grains moving in the lattice plane. In contrast to Vlasov plasmas, where the electrostatic instability excited by the beam is only longitudinal, here both longitudinal and transverse instabilities of the lattice phonons can develop. We determine and compare the transverse and longitudinal growth rates. The growth rate spectrum in wave number space exhibits remarkable gaps where no instability can develop. Depending on the system parameters, the transverse instability can be selectively excited.
Parallel Multigrid Equation Solver
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 direct Vlasov simulation of nonlinear plasma waves
NASA Astrophysics Data System (ADS)
Hara, Kentaro; Boyd, Iain; Kaganovich, Igor
2013-10-01
A direct Vlasov simulation, which solves the collisionless Vlasov equation directly on a discretized phase space, achieves good resolution of velocity distribution functions in comparison to particle methods. In this presentation, nonlinear electron plasma waves (EPWs) and ion acoustic waves (IAWs) are investigated with a fully-kinetic one-dimensional Vlasov simulation. A parallelized Vlasov simulation is employed since grid resolution of the discretized phase space is required to be fine enough in order to capture the nonlinear waves with higher harmonic modes. The primary goal is benchmarking our simulation with results obtained from another Vlasov code and verification with the nonlinear theories [R. L. Berger et al., Phys. Plasmas 20, 032107 (2013)]. The frequency shift of nonlinear plasma waves is investigated by applying an initial density perturbation or an external driver potential. It has been observed that the plasma frequency decreases for EPWs and increases for IAWs for Te /Ti = 10 , which agrees with Berger's simulation and theories. A further investigation varying the generation of the nonlinear wave such as driver amplitude and duration time will be performed and discussed. Supported by the U.S. Department of Energy Office of Science, Fusion Energy Sciences Program, Grant # DE-SC0001939, and the Air Force Research Laboratory Grant # F9550-09-1-0695.
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
The parallel implementation of the one-dimensional Fourier transformed Vlasov Poisson system
NASA Astrophysics Data System (ADS)
Eliasson, Bengt
2005-08-01
A parallel implementation of an algorithm for solving the one-dimensional, Fourier transformed Vlasov-Poisson system of equations is documented, together with the code structure, file formats and settings to run the code. The properties of the Fourier transformed Vlasov-Poisson system is discussed in connection with the numerical solution of the system. The Fourier method in velocity space is used to treat numerical problems arising due the filamentation of the solution in velocity space. Outflow boundary conditions in the Fourier transformed velocity space removes the highest oscillations in velocity space. A fourth-order compact Padé scheme is used to calculate derivatives in the Fourier transformed velocity space, and spatial derivatives are calculated with a pseudo-spectral method. The parallel algorithms used are described in more detail, in particular the parallel solver of the tri-diagonal systems occurring in the Padé scheme. Program summaryTitle of program:vlasov Catalogue identifier:ADVQ Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVQ Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Operating system under which the program has been tested: Sun Solaris; HP-UX; Read Hat Linux Programming language used: FORTRAN 90 with Message Passing Interface (MPI) Computers: Sun Ultra Sparc; HP 9000/785; HP IPF (Itanium Processor Family) ia64 Cluster; PCs cluster Number of lines in distributed program, including test data, etc.:3737 Number of bytes in distributed program, including test data, etc.:18 772 Distribution format: tar.gz Nature of physical problem: Kinetic simulations of collisionless electron-ion plasmas. Method of solution: A Fourier method in velocity space, a pseudo-spectral method in space and a fourth-order Runge-Kutta scheme in time. Memory required to execute with typical data: Uses typically of the order 10 5-10 6 double precision numbers. Restriction on the complexity of the problem: The program uses
Vlasov-Poisson in 1D: waterbags
NASA Astrophysics Data System (ADS)
Colombi, Stéphane; Touma, Jihad
2014-07-01
We revisit in one dimension the waterbag method to solve numerically Vlasov-Poisson equations. In this approach, the phase-space distribution function f (x, v) is initially sampled by an ensemble of patches, the waterbags, where f is assumed to be constant. As a consequence of Liouville theorem, it is only needed to follow the evolution of the border of these waterbags, which can be done by employing an orientated, self-adaptive polygon tracing isocontours of f. This method, which is entropy conserving in essence, is very accurate and can trace very well non-linear instabilities as illustrated by specific examples. As an application of the method, we generate an ensemble of single-waterbag simulations with decreasing thickness to perform a convergence study to the cold case. Our measurements show that the system relaxes to a steady state where the gravitational potential profile is a power law of slowly varying index β, with β close to 3/2 as found in the literature. However, detailed analysis of the properties of the gravitational potential shows that at the centre, β > 1.54. Moreover, our measurements are consistent with the value β = 8/5 = 1.6 that can be analytically derived by assuming that the average of the phase-space density per energy level obtained at crossing times is conserved during the mixing phase. These results are incompatible with the logarithmic slope of the projected density profile β - 2 ≃ -0.47 obtained recently by Schulz et al. using an N-body technique. This sheds again strong doubts on the capability of N-body techniques to converge to the correct steady state expected in the continuous limit.
Analysis of cancellation exponents in two-dimensional Vlasov turbulence
De Vita, G.; Valentini, F.; Servidio, S.; Primavera, L.; Carbone, V.; Veltri, P.; Sorriso-Valvo, L.
2014-07-15
Statistical properties of plasma turbulence are investigated by means of two-dimensional Vlasov simulations. In particular, a classical technique called signed measure is used to characterize the scaling behavior and the topology of sign-oscillating structures in simulations of the hybrid Vlasov-Maxwell model. Exploring different turbulence regimes, varying both the plasma β and the level of fluctuations, it is observed that Vlasov turbulence manifests two ranges with different exponents, the transition being observed near the ion skin depth. These results, which may have applications to both laboratory and astrophysical systems, further confirm the singular nature of small scale fluctuations in a plasma, mainly classified as intermittent, narrow, and intense current sheets.
Transient growth in stable linearized Vlasov-Maxwell plasmas
Podesta, J. J.
2010-12-15
Large amplitude transient growth of kinetic scale perturbations in stable collisionless magnetized plasmas has recently been demonstrated using a linearized Landau fluid model. Initial perturbations with lengthscales of the order of the ion gyroradius were shown to have transient timescales that in some cases were long compared to the ion gyroperiod, {Omega}{sub i}t>>1. Moreover, it was suggested that such perturbations are not rare but instead form a large class within the set of all possible initial conditions. For collisionless plasmas, the Vlasov-Maxwell equations provide a more complete description of kinetic physics and the existence of transient growth of solutions for the linearized Vlasov-Maxwell system is an interesting question. The existence of transient growth of solutions is demonstrated here for a special case of the Vlasov-Maxwell equations, namely, the one dimensional Vlasov-Poisson system. The analysis is different from the standard approach of nonmodal analysis since the initial value problem is described by a Volterra integral equation of the second kind, reflecting the fact that the time evolution of the system depends on the memory of the state from time zero through time t. For the case of a thermal equilibrium plasma, it is shown how initial conditions may be constructed to obtain solutions that grow linearly in time; the duration of this growth is the time required for a thermal electron to traverse the wavelength of the initial perturbation, a timescale that can last for many plasma periods 2{pi}/{omega}{sub pe}, thus demonstrating the existence of transient growth of solutions for the linearized Vlasov-Poisson system. The results suggest that the phenomenon of transient growth may be a common feature of the linearized Vlasov-Maxwell system as well as for Landau fluid models.
NASA Astrophysics Data System (ADS)
Chen, Guangye; Chacón, Luis; CoCoMans Team
2014-10-01
For decades, the Vlasov-Darwin model has been recognized to be attractive for PIC simulations (to avoid radiative noise issues) in non-radiative electromagnetic regimes. However, the Darwin model results in elliptic field equations that renders explicit time integration unconditionally unstable. Improving on linearly implicit schemes, fully implicit PIC algorithms for both electrostatic and electromagnetic regimes, with exact discrete energy and charge conservation properties, have been recently developed in 1D. This study builds on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the particle-field equations in multiple dimensions. The algorithm conserves energy, charge, and canonical-momentum exactly, even with grid packing. A simple fluid preconditioner allows efficient use of large timesteps, O (√{mi/me}c/veT) larger than the explicit CFL. We demonstrate the accuracy and efficiency properties of the of the algorithm with various numerical experiments in 2D3V.
On the singularity of the Vlasov-Poisson system
Zheng, Jian; Qin, Hong
2013-09-15
The Vlasov-Poisson system can be viewed as the collisionless limit of the corresponding Fokker-Planck-Poisson system. It is reasonable to expect that the result of Landau damping can also be obtained from the Fokker-Planck-Poisson system when the collision frequency ν approaches zero. However, we show that the collisionless Vlasov-Poisson system is a singular limit of the collisional Fokker-Planck-Poisson system, and Landau's result can be recovered only as the ν approaches zero from the positive side.
Force-free Jacobian equilibria for Vlasov-Maxwell plasmas
Abraham-Shrauner, B.
2013-10-15
New analytic force-free Vlasov-Maxwell equilibria for thin current sheets are presented. The magnetic flux densities are expressed in terms of Jacobian elliptic functions of one Cartesian spatial coordinate. The magnetic flux densities reduce to previously reported hyperbolic functions in one limit and sinusoidal functions in another limit of the modulus k. A much wider class of nonlinear force-free Vlasov-Maxwell equilibria open expanded possibilities for modeling of solar system, astrophysical and laboratory plasmas. Modified Maxwellian distribution functions are determined explicitly in terms of Jacobian elliptic functions. Conditions for double peaked distribution functions that could be unstable are developed.
On the Singularity of the Vlasov-Poisson System
and Hong Qin, Jian Zheng
2013-04-26
The Vlasov-Poisson system can be viewed as the collisionless limit of the corresponding Fokker- Planck-Poisson system. It is reasonable to expect that the result of Landau damping can also be obtained from the Fokker-Planck-Poisson system when the collision frequency v approaches zero. However, we show that the colllisionless Vlasov-Poisson system is a singular limit of the collisional Fokker-Planck-Poisson system, and Landau's result can be recovered only as the approaching zero from the positive side.
Hamiltonian time integrators for Vlasov-Maxwell equations
He, Yang; Xiao, Jianyuan; Zhang, Ruili; Liu, Jian; Qin, Hong; Sun, Yajuan
2015-12-15
Hamiltonian time integrators for the Vlasov-Maxwell equations are developed by a Hamiltonian splitting technique. The Hamiltonian functional is split into five parts, which produces five exactly solvable subsystems. Each subsystem is a Hamiltonian system equipped with the Morrison-Marsden-Weinstein Poisson bracket. Compositions of the exact solutions provide Poisson structure preserving/Hamiltonian methods of arbitrary high order for the Vlasov-Maxwell equations. They are then accurate and conservative over a long time because of the Poisson-preserving nature.
Comparison of 1D and 2D CSR Models with Application to the FERMI@ELETTRA Bunch Compressors
Bassi, G.; Ellison, J.A.; Heinemann, K.
2011-03-28
We compare our 2D mean field (Vlasov-Maxwell) treatment of coherent synchrotron radiation (CSR) effects with 1D approximations of the CSR force which are commonly implemented in CSR codes. In our model we track particles in 4D phase space and calculate 2D forces [1]. The major cost in our calculation is the computation of the 2D force. To speed up the computation and improve 1D models we also investigate approximations to our exact 2D force. As an application, we present numerical results for the Fermi{at}Elettra first bunch compressor with the configuration described in [1].
Chen, Guangye; Chacon, Luis; Knoll, Dana Alan; Barnes, Daniel C
2015-07-31
A multi-rate PIC formulation was developed that employs large timesteps for slow field evolution, and small (adaptive) timesteps for particle orbit integrations. Implementation is based on a JFNK solver with nonlinear elimination and moment preconditioning. The approach is free of numerical instabilities (ω_{pe}Δt >>1, and Δx >> λ_{D}), and requires many fewer dofs (vs. explicit PIC) for comparable accuracy in challenging problems. Significant gains (vs. conventional explicit PIC) may be possible for large scale simulations. The paper is organized as follows: Vlasov-Maxwell Particle-in-cell (PIC) methods for plasmas; Explicit, semi-implicit, and implicit time integrations; Implicit PIC formulation (Jacobian-Free Newton-Krylov (JFNK) with nonlinear elimination allows different treatments of disparate scales, discrete conservation properties (energy, charge, canonical momentum, etc.)); Some numerical examples; and Summary.
Heroux, Michael A.
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 scaled to 100s or 1000s of porcessors, it can be an attractive study code for computer system designers.
Scalable solvers and applications
Ribbens, C J
2000-10-27
The purpose of this report is to summarize research activities carried out under Lawrence Livermore National Laboratory (LLNL) research subcontract B501073. This contract supported the principal investigator (P1), Dr. Calvin Ribbens, during his sabbatical visit to LLNL from August 1999 through June 2000. Results and conclusions from the work are summarized below in two major sections. The first section covers contributions to the Scalable Linear Solvers and hypre projects in the Center for Applied Scientific Computing (CASC). The second section describes results from collaboration with Patrice Turchi of LLNL's Chemistry and Materials Science Directorate (CMS). A list of publications supported by this subcontract appears at the end of the report.
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
A survey of deterministic solvers for rarefied flows (Invited)
NASA Astrophysics Data System (ADS)
Mieussens, Luc
2014-12-01
Numerical simulations of rarefied gas flows are generally made with DSMC methods. Up to a recent period, deterministic numerical methods based on a discretization of the Boltzmann equation were restricted to simple problems (1D, linearized flows, or simple geometries, for instance). In the last decade, several deterministic solvers have been developed in different teams to tackle more complex problems like 2D and 3D flows. Some of them are based on the full Boltzmann equation. Solving this equation numerically is still very challenging, and 3D solvers are still restricted to monoatomic gases, even if recent works have proved it was possible to simulate simple flows for polyatomic gases. Other solvers are based on simpler BGK like models: they allow for much more intensive simulations on 3D flows for realistic geometries, but treating complex gases requires extended BGK models that are still under development. In this paper, we discuss the main features of these existing solvers, and we focus on their strengths and inefficiencies. We will also review some recent results that show how these solvers can be improved: - higher accuracy (higher order finite volume methods, discontinuous Galerkin approaches) - lower memory and CPU costs with special velocity discretization (adaptive grids, spectral methods) - multi-scale simulations by using hybrid and asymptotic preserving schemes - efficient implementation on high performance computers (parallel computing, hybrid parallelization) Finally, we propose some perspectives to make these solvers more efficient and more popular.
Hamiltonian dynamics of spatially-homogeneous Vlasov-Einstein systems
NASA Astrophysics Data System (ADS)
Okabe, Takahide; Morrison, P. J.; Friedrichsen, J. E., III; Shepley, L. C.
2011-07-01
We introduce a new matter action principle, with a wide range of applicability, for the Vlasov equation in terms of a conjugate pair of functions. Here we apply this action principle to the study of matter in Bianchi cosmological models in general relativity. The Bianchi models are spatially-homogeneous solutions to the Einstein field equations, classified by the three-dimensional Lie algebra that describes the symmetry group of the model. The Einstein equations for these models reduce to a set of coupled ordinary differential equations. The class A Bianchi models admit a Hamiltonian formulation in which the components of the metric tensor and their time derivatives yield the canonical coordinates. The evolution of anisotropy in the vacuum Bianchi models is determined by a potential due to the curvature of the model, according to its symmetry. For illustrative purposes, we examine the evolution of anisotropy in models with Vlasov matter. The Vlasov content is further simplified by the assumption of cold, counter-streaming matter, a kind of matter that is far from thermal equilibrium and is not describable by an ordinary fluid model nor other more simplistic matter models. Qualitative differences and similarities are found in the dynamics of certain vacuum class A Bianchi models and Bianchi type I models with cold, counter-streaming Vlasov-matter potentials analogous to the curvature potentials of corresponding vacuum models.
Maxwell-Vlasov equations as a continuous Hamiltonian system
Morrison, P.J.
1980-11-01
The well-known Maxwell-Vlasov equations that describe a collisionless plasma are cast into Hamiltonian form. The dynamical variables are the physical although noncanonical variables E, B, and f. We present a Poisson bracket which acts on these variables and the energy functional to produce the equations of motion.
Global Weak Solutions to the Magnetohydrodynamic and Vlasov Equations
NASA Astrophysics Data System (ADS)
Chen, Robin Ming; Hu, Jilong; Wang, Dehua
2016-06-01
An initial-boundary value problem for the fluid-particle system of the inhomogeneous incompressible magnetohydrodynamic equations coupled with the Vlasov equation is studied in a three-dimensional bounded domain. New ideas are introduced to construct the approximate solutions. The existence of global weak solutions is established by the energy estimates and the weak convergence method.
2005-07-01
Aniso2d is a two-dimensional seismic forward modeling code. The earth is parameterized by an X-Z plane in which the seismic properties Can have monoclinic with x-z plane symmetry. The program uses a user define time-domain wavelet to produce synthetic seismograms anrwhere within the two-dimensional media.
NASA Astrophysics Data System (ADS)
Jang, Hyun-Sook; Yu, Changqian; Hayes, Robert; Granick, Steve
2015-03-01
Polymer vesicles (``polymersomes'') are an intriguing class of soft materials, commonly used to encapsulate small molecules or particles. Here we reveal they can also effectively incorporate nanoparticles inside their polymer membrane, leading to novel ``2D nanocomposites.'' The embedded nanoparticles alter the capacity of the polymersomes to bend and to stretch upon external stimuli.
2011-12-31
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j0) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assignsmore » an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations.« 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
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.
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
Design of the LRP airfoil series using 2D CFD
NASA Astrophysics Data System (ADS)
Zahle, Frederik; Bak, Christian; Sørensen, Niels N.; Vronsky, Tomas; Gaudern, Nicholas
2014-06-01
This paper describes the design and wind tunnel testing of a high-Reynolds number, high lift airfoil series designed for wind turbines. The airfoils were designed using direct gradient- based numerical multi-point optimization based on a Bezier parameterization of the shape, coupled to the 2D Navier-Stokes flow solver EllipSys2D. The resulting airfoils, the LRP2-30 and LRP2-36, achieve both higher operational lift coefficients and higher lift to drag ratios compared to the equivalent FFA-W3 airfoils.
Linear Vlasov Analysis for Stability of a Bunched Beam
Warnock, R
2004-08-12
The authors study the linearized Vlasov equation for a bunched beam subject to an arbitrary wake function. Following Oide and Yokoya, the equation is reduced to an integral equation expressed in angle-action coordinates of the distorted potential well. Numerical solution of the equation as a formal eigenvalue problem leads to difficulties, because of singular eigenmodes from the incoherent spectrum. The authors rephrase the equation so that it becomes non-singular in the sense of operatory theory, and has only regular solutions for coherent modes. They report on a code that finds thresholds of instability by detecting zeros of the determinant of the system as they enter the upper-half frequency plane, upon increase of current. Results are compared with a time-domain integration of the nonlinear Vlasov equation with a realistic wake function for the SLC damping rings. There is close agreement between the two calculations.
Vlasov simulations of beams with a moving grid
Friedman, A; Sonnendrucker, E; Filbet, F; Oudet, E; Vay, J
2003-10-02
Thanks to the rapid increase of computing power in recent years, simulations of plasmas and particle beams based on direct solution of the Vlasov equation on a multi-dimensional phase-space grid are becoming attractive as an alternative to Particle-In-Cell (PIC) simulations. Their strength lies essentially in the fact that they are noiseless and that all parts of phase space, including the tail of the distribution, are equally well resolved. Their major drawback is that, for inhomogeneous systems, many of the grid points (where no particles are present) are wasted. This is especially the case for beam simulations where the beam moves rapidly through the phase space (due to varying alternating-gradient focusing forces, for example). This inefficiency has made such Vlasov simulations unsuitable for those cases.
Critical collapse in the spherically symmetric Einstein-Vlasov model
NASA Astrophysics Data System (ADS)
Akbarian, Arman; Choptuik, Matthew W.
2014-11-01
We solve the coupled Einstein-Vlasov system in spherical symmetry using direct numerical integration of the Vlasov equation in phase space. Focusing on the case of massless particles we study critical phenomena in the model, finding strong evidence for generic type I behavior at the black hole threshold that parallels what has previously been observed in the massive sector. For differing families of initial data we find distinct critical solutions, so there is no universality of the critical configuration itself. However we find indications of at least a weak universality in the lifetime scaling exponent, which is yet to be understood. Additionally, we clarify the role that angular momentum plays in the critical behavior in the massless case.
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.
Variational formulations of guiding-center Vlasov-Maxwell theory
NASA Astrophysics Data System (ADS)
Brizard, Alain J.; Tronci, Cesare
2016-06-01
The variational formulations of guiding-center Vlasov-Maxwell theory based on Lagrange, Euler, and Euler-Poincaré variational principles are presented. Each variational principle yields a different approach to deriving guiding-center polarization and magnetization effects into the guiding-center Maxwell equations. The conservation laws of energy, momentum, and angular momentum are also derived by Noether method, where the guiding-center stress tensor is now shown to be explicitly symmetric.
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.
Vlasov simulations of collisionless magnetic reconnection without background density
NASA Astrophysics Data System (ADS)
Schmitz, H.; Grauer, R.
2008-02-01
A standard starting point for the simulation of collisionless reconnection is the Harris equilibrium which is made up of a current sheet that separates two regions of opposing magnetic field. Magnetohydrodynamic simulations of collisionless reconnection usually include a homogeneous background density for reasons of numerical stability. While, in some cases, this is a realistic assumption, the background density may introduce new effects both due to the more involved structure of the distribution function or due to the fact that the Alfvèn speed remains finite far away from the current sheet. We present a fully kinetic Vlasov simulation of the perturbed Harris equilibrium using a Vlasov code. Parameters are chosen to match the Geospace Environment Modeling (GEM) Magnetic Reconnection Challenge but excluding the background density. This allows to compare with earlier simulations [Schmitz H, Grauer R. Kinetic Vlasov simulations of collisionless magnetic reconnection. Phys Plasmas 2006;13:092309] which include the background density. It is found that the absence of a background density causes the reconnection rate to be higher. On the other hand, the time until the onset of reconnection is hardly affected. Again the off diagonal elements of the pressure tensor are found to be important on the X-line but with modified importance for the individual terms.
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)
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.
NASA Astrophysics Data System (ADS)
Chen, G.; Chacón, L.
2015-12-01
For decades, the Vlasov-Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. Here, we explore a fully implicit PIC algorithm for the Vlasov-Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space-time-centered, employing particle sub-cycling and orbit-averaging. The algorithm conserves total energy, local charge, canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 2D-3V.
Second order guiding-center Vlasov-Maxwell equations
Madsen, Jens
2010-08-15
Second order gyrogauge invariant guiding-center coordinates with strong ExB-flow are derived using the Lie transformation method. The corresponding Poisson bracket structure and equations of motion are obtained. From a variational principle the explicit Vlasov-Maxwell equations are derived including second order terms. The second order contributions contain the lowest order finite-Larmor-radius corrections to the electromagnetic field. Therefore, the model is capable of describing situations where strong ExB-flows and finite-Larmor-radius effects are mutually important.
A splitting algorithm for Vlasov simulation with filamentation filtration
NASA Technical Reports Server (NTRS)
Klimas, A. J.; Farrell, W. M.
1994-01-01
A Fourier-Fourier transformed version of the splitting algorithm for simulating solutions of the Vlasov-Poisson system of equations is introduced. It is shown that with the inclusion of filamentation filtration in this transformed algorithm it is both faster and more stable than the standard splitting algorithm. It is further shown that in a scalar computer environment this new algorithm is approximately equal in speed and far less noisy than its particle-in-cell counterpart. It is conjectured that in a multiprocessor environment the filtered splitting algorithm would be faster while producing more precise results.
Trapping scaling for bifurcations in the Vlasov systems.
Barré, J; Métivier, D; Yamaguchi, Y Y
2016-04-01
We study nonoscillating bifurcations of nonhomogeneous steady states of the Vlasov equation, a situation occurring in galactic models, or for Bernstein-Greene-Kruskal modes in plasma physics. Through an unstable manifold expansion, we show that in one spatial dimension the dynamics is very sensitive to the initial perturbation: the instability may saturate at small amplitude-generalizing the "trapping scaling" of plasma physics-or may grow to produce a large-scale modification of the system. Furthermore, resonances are strongly suppressed, leading to different phenomena with respect to the homogeneous case. These analytical findings are illustrated and extended by direct numerical simulations with a cosine interaction potential.
Vlasov equation and collisionless hydrodynamics adapted to curved spacetime
Dodin, I. Y.; Fisch, N. J.
2010-11-15
The modification of the Vlasov equation, in its standard form describing a charged particle distribution in the six-dimensional phase space, is derived explicitly within a formal Hamiltonian approach for arbitrarily curved spacetime. The equation accounts simultaneously for the Lorentz force and the effects of general relativity, with the latter appearing as the gravity force and an additional force due to the extrinsic curvature of spatial hypersurfaces. For an arbitrary spatial metric, the equations of collisionless hydrodynamics are also obtained in the usual three-vector form.
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.
NASA Astrophysics Data System (ADS)
Wang, Jin; Ma, Jianyong; Zhou, Changhe
2014-11-01
A 3×3 high divergent 2D-grating with period of 3.842μm at wavelength of 850nm under normal incidence is designed and fabricated in this paper. This high divergent 2D-grating is designed by the vector theory. The Rigorous Coupled Wave Analysis (RCWA) in association with the simulated annealing (SA) is adopted to calculate and optimize this 2D-grating.The properties of this grating are also investigated by the RCWA. The diffraction angles are more than 10 degrees in the whole wavelength band, which are bigger than the traditional 2D-grating. In addition, the small period of grating increases the difficulties of fabrication. So we fabricate the 2D-gratings by direct laser writing (DLW) instead of traditional manufacturing method. Then the method of ICP etching is used to obtain the high divergent 2D-grating.
Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Philip, Bobby; Chacón, Luis; Pernice, Michael
2008-10-01
An implicit structured adaptive mesh refinement (SAMR) solver for 2D reduced magnetohydrodynamics (MHD) is described. The time-implicit discretization is able to step over fast normal modes, while the spatial adaptivity resolves thin, dynamically evolving features. A Jacobian-free Newton-Krylov method is used for the nonlinear solver engine. For preconditioning, we have extended the optimal "physics-based" approach developed in [L. Chacón, D.A. Knoll, J.M. Finn, An implicit, nonlinear reduced resistive MHD solver, J. Comput. Phys. 178 (2002) 15-36] (which employed multigrid solver technology in the preconditioner for scalability) to SAMR grids using the well-known Fast Adaptive Composite grid (FAC) method [S. McCormick, Multilevel Adaptive Methods for Partial Differential Equations, SIAM, Philadelphia, PA, 1989]. A grid convergence study demonstrates that the solver performance is independent of the number of grid levels and only depends on the finest resolution considered, and that it scales well with grid refinement. The study of error generation and propagation in our SAMR implementation demonstrates that high-order (cubic) interpolation during regridding, combined with a robustly damping second-order temporal scheme such as BDF2, is required to minimize impact of grid errors at coarse-fine interfaces on the overall error of the computation for this MHD application. We also demonstrate that our implementation features the desired property that the overall numerical error is dependent only on the finest resolution level considered, and not on the base-grid resolution or on the number of refinement levels present during the simulation. We demonstrate the effectiveness of the tool on several challenging problems.
Phase segregation via Vlasov-Boltzmann particle dynamics
Bastea, S
1999-01-19
In order to better understand and model the phase segregation of binary fluids we opted for a mesoscopic description that proves to be simplifying both conceptually and computationally. The system that we studied is a mixture of two kinds of particles. All particles interact with each other through strong short-range interactions modeled by hard spheres with the same mass and diameter. There is also a smooth long-range repulsion between particles of different kinds. At low overall densities and weak enough repulsion the natural dynamical description for this system is given in terms of two coupled, energy and momentum conserving Vlasov- Boltzmann equations, making it what we call a dynamical mean-field model. The computational scheme that we used is a combination of direct sim- ulation Monte Carlo (DSMC) and particle-in-the-cell (PIC) evolution, that inherits the efficiency and robustness of these two algorithms. The DSMC is a stochastic algorithm due to Bird that consistently incorporates the as- sumptions behind the Boltzmann equation into the particle dynamics. The method is essentially the following: the physical space is divided into a net- work of cells containing typically tens of particles and the free flow of the particles over a small time interval {Delta}t is followed by representative collisions among pairs of particles sharing the same cell. The typical linear dimension of a cell is a fraction of the mean free path between collisions. The PIC method for integrating the equations of motion was first used to deal with the l/r potential in plasma physics. It takes advantage of the simple form of the Vlasov potential, which is a product in Fourier space, by calculating the densities on a grid through some weighting, then the potentials and forces on the same grid, and finally interpolating the forces at the position of each particle. These two methods can be naturally brought together by replacing the free flow of the DSMC procedure by motion in the
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.
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.
NASA Astrophysics Data System (ADS)
Vencels, Juris; Delzanno, Gian Luca; Manzini, Gianmarco; Markidis, Stefano; Peng, Ivy Bo; Roytershteyn, Vadim
2016-05-01
We present the design and implementation of a spectral code, called SpectralPlasmaSolver (SPS), for the solution of the multi-dimensional Vlasov-Maxwell equations. The method is based on a Hermite-Fourier decomposition of the particle distribution function. The code is written in Fortran and uses the PETSc library for solving the non-linear equations and preconditioning and the FFTW library for the convolutions. SPS is parallelized for shared- memory machines using OpenMP. As a verification example, we discuss simulations of the two-dimensional Orszag-Tang vortex problem and successfully compare them against a fully kinetic Particle-In-Cell simulation. An assessment of the performance of the code is presented, showing a significant improvement in the code running-time achieved by preconditioning, while strong scaling tests show a factor of 10 speed-up using 16 threads.
Parallelized CCHE2D flow model with CUDA Fortran on Graphics Process Units
Technology Transfer Automated Retrieval System (TEKTRAN)
This paper presents the CCHE2D implicit flow model parallelized using CUDA Fortran programming technique on Graphics Processing Units (GPUs). A parallelized implicit Alternating Direction Implicit (ADI) solver using Parallel Cyclic Reduction (PCR) algorithm on GPU is developed and tested. This solve...
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.
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.
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
Zhang, H.; Wu, S. Z.; Zhou, C. T.; He, X. T.; Zhu, S. P.
2013-09-15
The dispersion relation of one-dimensional longitudinal plasma waves in relativistic homogeneous plasmas is investigated with both linear theory and Vlasov simulation in this paper. From the Vlasov-Poisson equations, the linear dispersion relation is derived for the proper one-dimensional Jüttner distribution. Numerically obtained linear dispersion relation as well as an approximate formula for plasma wave frequency in the long wavelength limit is given. The dispersion of longitudinal wave is also simulated with a relativistic Vlasov code. The real and imaginary parts of dispersion relation are well studied by varying wave number and plasma temperature. Simulation results are in agreement with established linear theory.
Nonlinear instability of the one-dimensional Vlasov-Yukawa system
Ha, Seung-Yeal; Lee, Ho; Ha, Taeyoung; Hwang, Chi-Ok
2011-03-15
We discuss the nonlinear instability of some class of stationary solutions to the one-dimensional Vlasov-Yukawa system with a mass parameter m. The Vlasov-Yukawa system corresponds to the short-range correction of the repulsive Vlasov-Poisson system arising from plasma physics. We show that the stationary solutions satisfying the Penrose condition are nonlinearly unstable in small mass regime. In a large mass regime, the massiveness of force carrier particles acts as stabilizer in a finite time interval. We present several numerical results to confirm our analytical results.
On axisymmetric and stationary solutions of the self-gravitating Vlasov system
NASA Astrophysics Data System (ADS)
Ames, Ellery; Andréasson, Håkan; Logg, Anders
2016-08-01
Axisymmetric and stationary solutions are constructed to the Einstein-Vlasov and Vlasov-Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein-Vlasov system which contain ergoregions.
Vlasov tokamak equilibria with shearad toroidal flow and anisotropic pressure
NASA Astrophysics Data System (ADS)
Throumoulopoulos, George; Kuiroukidis, Apostolos; Tasso, Henri
2015-11-01
By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e. the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis. This work has received funding from (a) the National Programme for the Controlled Thermonuclear Fusion, Hellenic Republic, (b) Euratom research and training programme 2014-2018 under grant agreement No 633053.
Variational Principle and Stability of Nonmonotonic Vlasov-Poisson Equilibria
NASA Astrophysics Data System (ADS)
Morrison, P. J.
1987-10-01
The stability of nonmonotonic equilibria of the Vlasov-Poisson equation is assessed by using nonlinear constants of motion . The constants of motion make up the free energy of the system , which upon variation yields nonmonotonic equilibria. Such equilibria have not previously been obtainable from a variation principle, but here this is accomplished by the inclusion of a passively advected tracer field. Definiteness of the second variation of the free energy gives a sufficient condition for stability in agreement with Gardner's theorem [5], Previously, we have argued that indefiniteness implies either spectral in stability or negative energy modes, which are generically unstable when one adds dissipation or nonlinearity [6]. Such is the case for the nonmonotonic equilibria considered.
A numerical method for solving the Vlasov equation
NASA Technical Reports Server (NTRS)
Satofuka, N.
1982-01-01
A numerical procedure is derived for the solution of the Vlasov-Poisson system of equations in two phase-space variables. Derivatives with respect to the phase-space variables are approximated by a weighted sum of the values of the distribution function at property chosen neighboring points. The resulting set of ordinary differential equations is then solved by using an appropriate time intergration scheme. The accuracy of the proposed method is tested with some simple model problems. The results for the free streaming case, linear Landau damping, and nonlinear Landau damping are investigated and compared with those of the splitting scheme. The proposed method is found to be very accurate and efficient.
Vlasov tokamak equilibria with sheared toroidal flow and anisotropic pressure
Kuiroukidis, Ap; Throumoulopoulos, G. N.; Tasso, H.
2015-08-15
By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e., the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions, these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis.
Vlasov equation for long-range interactions on a lattice.
Bachelard, R; Dauxois, T; De Ninno, G; Ruffo, S; Staniscia, F
2011-06-01
We show that, in the continuum limit, the dynamics of Hamiltonian systems defined on a lattice with long-range couplings is well described by the Vlasov equation. This equation can be linearized around the homogeneous state, and a dispersion relation, which depends explicitly on the Fourier modes of the lattice, can be derived. This allows one to compute the stability thresholds of the homogeneous state, which turns out to depend on the mode number. When this state is unstable, the growth rates are also functions of the mode number. Explicit calculations are performed for the α-Hamiltonian mean field model with 0≤α<1, for which the mean-field mode is always found to dominate the exponential growth. The theoretical predictions are successfully compared with numerical simulations performed on a finite lattice.
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.
Baiz, Carlos R.; Schach, Denise; Tokmakoff, Andrei
2014-01-01
We describe a microscope for measuring two-dimensional infrared (2D IR) spectra of heterogeneous samples with μm-scale spatial resolution, sub-picosecond time resolution, and the molecular structure information of 2D IR, enabling the measurement of vibrational dynamics through correlations in frequency, time, and space. The setup is based on a fully collinear “one beam” geometry in which all pulses propagate along the same optics. Polarization, chopping, and phase cycling are used to isolate the 2D IR signals of interest. In addition, we demonstrate the use of vibrational lifetime as a contrast agent for imaging microscopic variations in molecular environments. PMID:25089490
2004-08-01
AnisWave2D is a 2D finite-difference code for a simulating seismic wave propagation in fully anisotropic materials. The code is implemented to run in parallel over multiple processors and is fully portable. A mesh refinement algorithm has been utilized to allow the grid-spacing to be tailored to the velocity model, avoiding the over-sampling of high-velocity materials that usually occurs in fixed-grid schemes.
A Hilbert-Vlasov code for the study of high-frequency plasma beatwave accelerator
Ghizzo, A.; Bertrand, P.; Begue, M.L.; Johnston, T.W.; Shoucri, M.
1996-04-01
High-frequency beatwave simulations relevant to the University of California at Los Angeles (UCLA) experiment with relativistic eulerian hybrid Vlasov code are presented. These Hilbert-Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by beatwave experiment for a high ratio of driver frequency to plasma frequency {omega}{sub pump}/{omega}{sub pump} {approx} 33. The present model allows one to extend detailed modeling to frequency ratios greater than the current practical maximum of 10 or so, for Vlasov or particle-in-cell (PIC) codes, by replacing the Maxwell equations by mode equations for the electromagnetic Vlasov code. Numerical results, including beat frequency chirping (i.e., pump frequency linearly decreasing with time), show that the amplitude limit due to relativistic detuning can be enhanced with accelerated particles up to the ultrarelativistic energies with a high-acceleration gradient of more than 25 GeV/m.
Multi-moment advection scheme in three dimension for Vlasov simulations of magnetized plasma
Minoshima, Takashi; Matsumoto, Yosuke; Amano, Takanobu
2013-03-01
We present an extension of the multi-moment advection scheme [T. Minoshima, Y. Matsumoto, T. Amano, Multi-moment advection scheme for Vlasov simulations, Journal of Computational Physics 230 (2011) 6800–6823] to the three-dimensional case, for full electromagnetic Vlasov simulations of magnetized plasma. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables, and advances them on the basis of their governing equations. Similar to the two-dimensional scheme, the three-dimensional scheme can accurately solve the solid body rotation problem of a gaussian profile with little numerical dispersion or diffusion. This is a very important property for Vlasov simulations of magnetized plasma. We apply the scheme to electromagnetic Vlasov simulations. Propagation of linear waves and nonlinear evolution of the electron temperature anisotropy instability are successfully simulated with a good accuracy of the energy conservation.
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.
Fast Poisson, Fast Helmholtz and fast linear elastostatic solvers on rectangular parallelepipeds
Wiegmann, A.
1999-06-01
FFT-based fast Poisson and fast Helmholtz solvers on rectangular parallelepipeds for periodic boundary conditions in one-, two and three space dimensions can also be used to solve Dirichlet and Neumann boundary value problems. For non-zero boundary conditions, this is the special, grid-aligned case of jump corrections used in the Explicit Jump Immersed Interface method. Fast elastostatic solvers for periodic boundary conditions in two and three dimensions can also be based on the FFT. From the periodic solvers we derive fast solvers for the new 'normal' boundary conditions and essential boundary conditions on rectangular parallelepipeds. The periodic case allows a simple proof of existence and uniqueness of the solutions to the discretization of normal boundary conditions. Numerical examples demonstrate the efficiency of the fast elastostatic solvers for non-periodic boundary conditions. More importantly, the fast solvers on rectangular parallelepipeds can be used together with the Immersed Interface Method to solve problems on non-rectangular domains with general boundary conditions. Details of this are reported in the preprint The Explicit Jump Immersed Interface Method for 2D Linear Elastostatics by the author.
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.
Vlasov Simulations of Ionospheric Turbulence near the Upper Hybrid Layer
NASA Astrophysics Data System (ADS)
Najmi, Amir; Eliasson, Bengt; Shao, Xi; Milikh, Gennady; Sharma, Surja; Papadopoulos, Konstantinos
2015-11-01
High-frequency, ordinary (O) mode electromagnetic waves incident on a magnetized plasma near the upper hybrid resonance can excite magnetic field aligned density striations, associated with both turbulence and electron heating. We have used Vlasov simulations, which combine low noise and high resolution of all areas of phase space, in one spatial and two velocity dimensions to study the induced turbulence in the presence of striations near the upper hybrid resonance, where the O-mode pump is mode converted to large amplitude upper hybrid oscillations trapped in a striation. By taking moments of the resulting electron and ion distribution functions, we were able to correlate the evolution of stationary electron and ion oscillations with the onset of turbulence, and the heating of electrons in the striation with large amplitude, short wavelength electron Bernstein waves. These Bernstein waves excite stochastic electron heating when the normalized gradients of their electric field exceed the electron gyroradius, breaking the drift approximation, and causing particle orbits in phase space to diverge exponentially, rapidly increasing the electron temperature by several thousand Kelvin. These results are relevant to ongoing high-latitude heating experiments.
Vlasov Simulations of Ionospheric Heating Near Upper Hybrid Resonance
NASA Astrophysics Data System (ADS)
Najmi, A. C.; Eliasson, B. E.; Shao, X.; Milikh, G. M.; Papadopoulos, K.
2014-12-01
It is well-known that high-frequency (HF) heating of the ionosphere can excite field- aligned density striations (FAS) in the ionospheric plasma. Furthermore, in the neighborhood of various resonances, the pump wave can undergo parametric instabilities to produce a variety of electrostatic and electromagnetic waves. We have used a Vlasov simulation with 1-spatial dimension, 2-velocity dimensions, and 2-components of fields, to study the effects of ionospheric heating when the pump frequency is in the vicinity of the upper hybrid resonance, employing parameters currently available at ionospheric heaters such as HAARP. We have found that by seeding theplasma with a FAS of width ~20% of the simulation domain, ~10% depletion, and by applying a spatially uniform HF dipole pump electric field, the pump wave gives rise to a broad spectrum of density fluctuations as well as to upper hybrid and lower hybrid oscillating electric fields. We also observe collisionless bulk-heating of the electrons that varies non-linearly with the amplitude of the pump field.
DYNA2D96. Explicit 2-D Hydrodynamic FEM Program
Whirley, R.G.
1992-04-01
DYNA2D is a vectorized, explicit, two-dimensional, axisymmetric and plane strain finite element program for analyzing the large deformation dynamic and hydrodynamic response of inelastic solids. DYNA2D contains 13 material models and 9 equations of state (EOS) to cover a wide range of material behavior. The material models implemented in all machine versions are: elastic, orthotropic elastic, kinematic/isotropic elastic plasticity, thermoelastoplastic, soil and crushable foam, linear viscoelastic, rubber, high explosive burn, isotropic elastic-plastic, temperature-dependent elastic-plastic. The isotropic and temperature-dependent elastic-plastic models determine only the deviatoric stresses. Pressure is determined by one of 9 equations of state including linear polynomial, JWL high explosive, Sack Tuesday high explosive, Gruneisen, ratio of polynomials, linear polynomial with energy deposition, ignition and growth of reaction in HE, tabulated compaction, and tabulated.
KLU2 Direct Linear Solver Package
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.
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.
NASA Astrophysics Data System (ADS)
Cheng, Yingda; Christlieb, Andrew J.; Zhong, Xinghui
2015-05-01
In this paper, we propose energy-conserving Eulerian solvers for the two-species Vlasov-Ampère (VA) system and apply the methods to simulate current-driven ion-acoustic instability. The two-species VA systems are of practical importance in applications, and they conserve many physical quantities including the particle number of each species and the total energy that is comprised of kinetic energy for both species and the electric energy. The main goal of this paper is to generalize our previous work for the single-species VA system [9] and Vlasov-Maxwell (VM) system [8] to the two-species case. The methodologies proposed involve careful design of temporal discretization and the use of the discontinuous Galerkin (DG) spatial discretizations. We show that the energy-conserving time discretizations for single-species equations [9,8] can also work for the two-species case if extended properly. Compared to other high order schemes, we emphasize that our schemes can preserve the total particle number and total energy on the fully discrete level regardless of mesh size, making them very attractive for long time simulations. We benchmark our algorithms on a test example to check the one-species limit, and the current-driven ion-acoustic instability. To simulate the current-driven ion-acoustic instability, a slight modification for the implicit method is necessary to fully decouple the split equations. This is achieved by a Gauss-Seidel type iteration technique. Numerical results verified the conservation and performance of our methods. Finally, we remark that the schemes in this paper can be readily extended to applications when the models take more general form, such as the multi-species VM equations.
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
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
Solar-wind turbulence at kinetic wavelengths: hybrid-Vlasov simulations
NASA Astrophysics Data System (ADS)
Valentini, F.; Califano, F.; Veltri, P.
2010-12-01
The cooling of the expanding solar wind is less efficient than expected. Scientists pointed out that the reason of this empirical evidence is related to the turbulent character of the solar wind plasma. The identification of the physical mechanism replacing "energy dissipation" in a collisionless magnetized plasma and establishing the link between macroscopic and microscopic scales would open a new scenario of broad importance in the field of turbulence and would have far-reaching implications in the problem of space plasma heating. Turbulent heating consists both in a progressive energy degradation and disorder increasing, going from large to small scales. The increase of disorder results into the production, through nonlinear interaction, of small-scale fluctuations involving not only the kinetic energy, as in the case of heat, but also the potential energy associated with electric and magnetic field fluctuations. To numerically analyze the kinetic effects on the evolution of the turbulent spectra in the solar wind, we make use of a recently developed numerical hybrid-Vlasov code [1], where the Vlasov equation is solved for the proton distribution function, while the electron response is taken into account through a generalized Ohm law that retains Hall effects and electron inertia terms. By performing multi-dimensional phase space simulations (1D or 2D in space and 3D in velocity) [2-5] on the last generation of supercomputers, we show that newly identified electrostatic (acoustic-like) modes, in longitudinal propagation with respect to the average magnetic field and driven by particle distribution functions far from local thermodynamic equilibrium, represent a privileged channel for turbulence to carry the energy towards small disordered scales. The system dynamics is analyzed for different electron to ion temperature ratios. Our numerical results provide a qualitative interpretation of a complex phenomenology ubiquitously recovered in many solar
2001-01-31
This software reduces the data from two-dimensional kSA MOS program, k-Space Associates, Ann Arbor, MI. Initial MOS data is recorded without headers in 38 columns, with one row of data per acquisition per lase beam tracked. The final MOSS 2d data file is reduced, graphed, and saved in a tab-delimited column format with headers that can be plotted in any graphing software.
Galerkin CFD solvers for use in a multi-disciplinary suite for modeling advanced flight vehicles
NASA Astrophysics Data System (ADS)
Moffitt, Nicholas J.
This work extends existing Galerkin CFD solvers for use in a multi-disciplinary suite. The suite is proposed as a means of modeling advanced flight vehicles, which exhibit strong coupling between aerodynamics, structural dynamics, controls, rigid body motion, propulsion, and heat transfer. Such applications include aeroelastics, aeroacoustics, stability and control, and other highly coupled applications. The suite uses NASA STARS for modeling structural dynamics and heat transfer. Aerodynamics, propulsion, and rigid body dynamics are modeled in one of the five CFD solvers below. Euler2D and Euler3D are Galerkin CFD solvers created at OSU by Cowan (2003). These solvers are capable of modeling compressible inviscid aerodynamics with modal elastics and rigid body motion. This work reorganized these solvers to improve efficiency during editing and at run time. Simple and efficient propulsion models were added, including rocket, turbojet, and scramjet engines. Viscous terms were added to the previous solvers to create NS2D and NS3D. The viscous contributions were demonstrated in the inertial and non-inertial frames. Variable viscosity (Sutherland's equation) and heat transfer boundary conditions were added to both solvers but not verified in this work. Two turbulence models were implemented in NS2D and NS3D: Spalart-Allmarus (SA) model of Deck, et al. (2002) and Menter's SST model (1994). A rotation correction term (Shur, et al., 2000) was added to the production of turbulence. Local time stepping and artificial dissipation were adapted to each model. CFDsol is a Taylor-Galerkin solver with an SA turbulence model. This work improved the time accuracy, far field stability, viscous terms, Sutherland?s equation, and SA model with NS3D as a guideline and added the propulsion models from Euler3D to CFDsol. Simple geometries were demonstrated to utilize current meshing and processing capabilities. Air-breathing hypersonic flight vehicles (AHFVs) represent the ultimate
Auroral Electrons Trapped and Lost: A Vlasov Simulation Study
NASA Astrophysics Data System (ADS)
Gunell, H.; Andersson, L.; De Keyser, J. M.; Mann, I.
2014-12-01
In the upward current region of the aurora, about two thirds of the total voltage between the auroral ionosphere and the equatorial magnetosphere can be concentrated in a stationary double layer at an altitude of about one earth radius, as Vlasov simulations of the plasma on a magnetic field line have shown (Gunell, et al., Ann. Geophys., 31, 1227-1240, 2013). We perform numerical experiments, changing the total voltage between the ionosphere and the equatorial magnetosphere during the course of the simulation. In the initial state, the total acceleration voltage is 3 kV and there is a double layer approximately 5000 km above the ionospheric end of the system. When the voltage is increased, electrons are trapped between the double layer and the magnetic mirror in a region of velocity space that initially was empty. When the voltage is decreased to its initial value these trapped electrons are released upwards. If the voltage is lowered first and then raised back to where it started, the newly trapped electrons remain trapped. As a consequence of the difference between the two cases, the electron pitch angle distribution, below the double layer, carries information about the recent history of the acceleration voltage. In both cases, most of the change in voltage, ΔV, is assumed by the double layer, in agreement with a study of Cluster data that could confine most of ΔV to altitudes below the spacecraft (Forsyth et al., JGR, 117, A12203, 2012). Hysteresis effects in the double layer position are seen in connection with the electron trapping. This work was supported by the Belgian Science Policy Office through the Solar-Terrestrial Centre of Excellence and by PRODEX/Cluster contract 13127/98/NL/VJ(IC)-PEA 90316.
A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation
Banks, J W; Hittinger, J A
2009-11-24
Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.
ALPS - A LINEAR PROGRAM SOLVER
NASA Technical Reports Server (NTRS)
Viterna, L. A.
1994-01-01
Linear programming is a widely-used engineering and management tool. Scheduling, resource allocation, and production planning are all well-known applications of linear programs (LP's). Most LP's are too large to be solved by hand, so over the decades many computer codes for solving LP's have been developed. ALPS, A Linear Program Solver, is a full-featured LP analysis program. ALPS can solve plain linear programs as well as more complicated mixed integer and pure integer programs. ALPS also contains an efficient solution technique for pure binary (0-1 integer) programs. One of the many weaknesses of LP solvers is the lack of interaction with the user. ALPS is a menu-driven program with no special commands or keywords to learn. In addition, ALPS contains a full-screen editor to enter and maintain the LP formulation. These formulations can be written to and read from plain ASCII files for portability. For those less experienced in LP formulation, ALPS contains a problem "parser" which checks the formulation for errors. ALPS creates fully formatted, readable reports that can be sent to a printer or output file. ALPS is written entirely in IBM's APL2/PC product, Version 1.01. The APL2 workspace containing all the ALPS code can be run on any APL2/PC system (AT or 386). On a 32-bit system, this configuration can take advantage of all extended memory. The user can also examine and modify the ALPS code. The APL2 workspace has also been "packed" to be run on any DOS system (without APL2) as a stand-alone "EXE" file, but has limited memory capacity on a 640K system. A numeric coprocessor (80X87) is optional but recommended. The standard distribution medium for ALPS is a 5.25 inch 360K MS-DOS format diskette. IBM, IBM PC and IBM APL2 are registered trademarks of International Business Machines Corporation. MS-DOS is a registered trademark of Microsoft Corporation.
GARDNER, P.R.
2006-04-01
Sudoku, also known as Number Place, is a logic-based placement puzzle. The aim of the puzzle is to enter a numerical digit from 1 through 9 in each cell of a 9 x 9 grid made up of 3 x 3 subgrids (called ''regions''), starting with various digits given in some cells (the ''givens''). Each row, column, and region must contain only one instance of each numeral. Completing the puzzle requires patience and logical ability. Although first published in a U.S. puzzle magazine in 1979, Sudoku initially caught on in Japan in 1986 and attained international popularity in 2005. Last fall, after noticing Sudoku puzzles in some newspapers and magazines, I attempted a few just to see how hard they were. Of course, the difficulties varied considerably. ''Obviously'' one could use Trial and Error but all the advice was to ''Use Logic''. Thinking to flex, and strengthen, those powers, I began to tackle the puzzles systematically. That is, when I discovered a new tactical rule, I would write it down, eventually generating a list of ten or so, with some having overlap. They served pretty well except for the more difficult puzzles, but even then I managed to develop an additional three rules that covered all of them until I hit the Oregonian puzzle shown. With all of my rules, I could not seem to solve that puzzle. Initially putting my failure down to rapid mental fatigue (being unable to hold a sufficient quantity of information in my mind at one time), I decided to write a program to implement my rules and see what I had failed to notice earlier. The solver, too, failed. That is, my rules were insufficient to solve that particular puzzle. I happened across a book written by a fellow who constructs such puzzles and who claimed that, sometimes, the only tactic left was trial and error. With a trial and error routine implemented, my solver successfully completed the Oregonian puzzle, and has successfully solved every puzzle submitted to it since.
SIERRA framework version 4 : solver services.
Williams, Alan B.
2005-02-01
Several SIERRA applications make use of third-party libraries to solve systems of linear and nonlinear equations, and to solve eigenproblems. The classes and interfaces in the SIERRA framework that provide linear system assembly services and access to solver libraries are collectively referred to as solver services. This paper provides an overview of SIERRA's solver services including the design goals that drove the development, and relationships and interactions among the various classes. The process of assembling and manipulating linear systems will be described, as well as access to solution methods and other operations.
NASA Astrophysics Data System (ADS)
Joglekar, Archis; Thomas, Alec
2013-10-01
Here, we present 2D numerical modeling of near critical density plasma using a fully implicit Vlasov-Fokker-Planck code, IMPACTA, which includes self-consistent magnetic fields as well as anisotropic electron pressure terms in the expansion of the distribution function, as well as an implementation of the Boris CYLRAD algorithm through a ray tracing add-on package. This allows to model inverse brehmsstrahlung heating as a laser travels through a plasma by solving the ray tracing equations. Generated magnetic fields (eg. the Biermann battery effect) as well as field advection through heat fluxes from the laser heating is shown. Additionally, perturbations in the plasma density profile arise as a result of the high pressures and flows in the plasma. These perturbations in the plasma density affect the path of the laser traveling through the plasma and modify the heating profile accordingly. The interplay between these effects is discussed in this study.
The Vlasov-Poisson System for Stellar Dynamics in Spaces of Constant Curvature
NASA Astrophysics Data System (ADS)
Diacu, Florin; Ibrahim, Slim; Lind, Crystal; Shen, Shengyi
2016-09-01
We obtain a natural extension of the Vlasov-Poisson system for stellar dynamics to spaces of constant Gaussian curvature {κ ≠ 0}: the unit sphere {S^2}, for {κ > 0}, and the unit hyperbolic sphere {H^2}, for {κ < 0}. These equations can be easily generalized to higher dimensions. When the particles move on a geodesic, the system reduces to a 1-dimensional problem that is more singular than the classical analogue of the Vlasov-Poisson system. In the analysis of this reduced model, we study the well-posedness of the problem and derive Penrose-type conditions for linear stability around homogeneous solutions in the sense of Landau damping.
Vlasov equation for Schwinger pair production in a time-dependent electric field
NASA Astrophysics Data System (ADS)
Huet, Adolfo; Kim, Sang Pyo; Schubert, Christian
2014-12-01
Schwinger pair creation in a purely time-dependent electric field can be described through a quantum Vlasov equation describing the time evolution of the single-particle momentum distribution function. This equation exists in two versions, both of which can be derived by a Bogoliubov transformation, but whose equivalence is not obvious. For the spinless case, we show here that the difference between these two evolution equations corresponds to the one between the "in-out" and "in-in" formalisms. We give a simple relation between the asymptotic distribution functions generated by the two Vlasov equations. As examples we discuss the Sauter and single-soliton field cases.
A critical comparison of the numerical solution of the 1D filtered Vlasov-Poisson equation
NASA Astrophysics Data System (ADS)
Viñas, A. F.; Klimas, A. J.
2003-04-01
We present a comparison of the numerical solution of the filtered Vlasov-Poisson system of equations using the Fourier-Fourier and the Flux-Balance-MacCormack methods in the electrostatic, non-relativistic case. We show that the splitting method combined with the Flux-Balance-MacCormack scheme provides an efficient and accurate scheme for integrating the filtered Vlasov-Poisson system in their self-consistent field. Finally we present various typical problems of interest in plasma physics research which can be studied with the scheme presented here.
On axisymmetric and stationary solutions of the self-gravitating Vlasov system
NASA Astrophysics Data System (ADS)
Ames, Ellery; Andréasson, Håkan; Logg, Anders
2016-08-01
Axisymmetric and stationary solutions are constructed to the Einstein–Vlasov and Vlasov–Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein–Vlasov system which contain ergoregions.
Constant residual electrostatic electron plasma mode in Vlasov-Ampere system
Xie, Hua-sheng
2013-11-15
In a collisionless Vlasov-Poisson (V-P) electron plasma system, two types of modes for electric field perturbation exist: the exponentially Landau damped electron plasma waves and the initial-value sensitive ballistic modes. Here, the V-P system is modified slightly to a Vlasov-Ampere (V-A) system. A new constant residual mode is revealed. Mathematically, this mode comes from the Laplace transform of an initial electric field perturbation, and physically represents that an initial perturbation (e.g., external electric field perturbation) would not be damped away. Thus, this residual mode is more difficult to be damped than the ballistic mode.
The Vlasov-Poisson Dynamics as the Mean Field Limit of Extended Charges
NASA Astrophysics Data System (ADS)
Lazarovici, Dustin
2016-10-01
The paper treats the validity problem of the nonrelativistic Vlasov-Poisson equation in {d ≥ 2} dimensions. It is shown that the Vlasov-Poisson dynamics can be derived as a combined mean field and point-particle limit of an N-particle Coulomb system of extended charges. This requires a sufficiently fast convergence of the initial empirical distributions. If the electron radius decreases slower than {N^{-{1/d(d+2)}}}, the corresponding initial configurations are typical. This result entails propagation of molecular chaos for the respective dynamics.
Exact momentum conservation laws for the gyrokinetic Vlasov-Poisson equations
Brizard, Alain J.; Tronko, Natalia
2011-08-15
The exact momentum conservation laws for the nonlinear gyrokinetic Vlasov-Poisson equations are derived by applying the Noether method on the gyrokinetic variational principle [A. J. Brizard, Phys. Plasmas 7, 4816 (2000)]. From the gyrokinetic Noether canonical-momentum equation derived by the Noether method, the gyrokinetic parallel momentum equation and other gyrokinetic Vlasov-moment equations are obtained. In addition, an exact gyrokinetic toroidal angular-momentum conservation law is derived in axisymmetric tokamak geometry, where the transport of parallel-toroidal momentum is related to the radial gyrocenter polarization, which includes contributions from the guiding-center and gyrocenter transformations.
Constant residual electrostatic electron plasma mode in Vlasov-Ampere system
NASA Astrophysics Data System (ADS)
Xie, Hua-sheng
2013-11-01
In a collisionless Vlasov-Poisson (V-P) electron plasma system, two types of modes for electric field perturbation exist: the exponentially Landau damped electron plasma waves and the initial-value sensitive ballistic modes. Here, the V-P system is modified slightly to a Vlasov-Ampere (V-A) system. A new constant residual mode is revealed. Mathematically, this mode comes from the Laplace transform of an initial electric field perturbation, and physically represents that an initial perturbation (e.g., external electric field perturbation) would not be damped away. Thus, this residual mode is more difficult to be damped than the ballistic mode.
NASA Technical Reports Server (NTRS)
Ferencz, Donald C.; Viterna, Larry A.
1991-01-01
ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.
Euler solvers for transonic applications
NASA Technical Reports Server (NTRS)
Vanleer, Bram
1989-01-01
The 1980s may well be called the Euler era of applied aerodynamics. Computer codes based on discrete approximations of the Euler equations are now routinely used to obtain solutions of transonic flow problems in which the effects of entropy and vorticity production are significant. Such codes can even predict separation from a sharp edge, owing to the inclusion of artificial dissipation, intended to lend numerical stability to the calculation but at the same time enforcing the Kutta condition. One effect not correctly predictable by Euler codes is the separation from a smooth surface, and neither is viscous drag; for these some form of the Navier-Stokes equation is needed. It, therefore, comes as no surprise to observe that the Navier-Stokes has already begun before Euler solutions were fully exploited. Moreover, most numerical developments for the Euler equations are now constrained by the requirement that the techniques introduced, notably artificial dissipation, must not interfere with the new physics added when going from an Euler to a full Navier-Stokes approximation. In order to appreciate the contributions of Euler solvers to the understanding of transonic aerodynamics, it is useful to review the components of these computational tools. Space discretization, time- or pseudo-time marching and boundary procedures, the essential constituents are discussed. The subject of grid generation and grid adaptation to the solution are touched upon only where relevant. A list of unanswered questions and an outlook for the future are covered.
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...
Georgi, Howard; Kats, Yevgeny
2008-09-26
We discuss what can be learned about unparticle physics by studying simple quantum field theories in one space and one time dimension. We argue that the exactly soluble 2D theory of a massless fermion coupled to a massive vector boson, the Sommerfield model, is an interesting analog of a Banks-Zaks model, approaching a free theory at high energies and a scale-invariant theory with nontrivial anomalous dimensions at low energies. We construct a toy standard model coupling to the fermions in the Sommerfield model and study how the transition from unparticle behavior at low energies to free particle behavior at high energies manifests itself in interactions with the toy standard model particles.
NASA Astrophysics Data System (ADS)
Frickenhaus, Stephan; Hiller, Wolfgang; Best, Meike
The portable software FoSSI is introduced that—in combination with additional free solver software packages—allows for an efficient and scalable parallel solution of large sparse linear equations systems arising in finite element model codes. FoSSI is intended to support rapid model code development, completely hiding the complexity of the underlying solver packages. In particular, the model developer need not be an expert in parallelization and is yet free to switch between different solver packages by simple modifications of the interface call. FoSSI offers an efficient and easy, yet flexible interface to several parallel solvers, most of them available on the web, such as PETSC, AZTEC, MUMPS, PILUT and HYPRE. FoSSI makes use of the concept of handles for vectors, matrices, preconditioners and solvers, that is frequently used in solver libraries. Hence, FoSSI allows for a flexible treatment of several linear equations systems and associated preconditioners at the same time, even in parallel on separate MPI-communicators. The second special feature in FoSSI is the task specifier, being a combination of keywords, each configuring a certain phase in the solver setup. This enables the user to control a solver over one unique subroutine. Furthermore, FoSSI has rather similar features for all solvers, making a fast solver intercomparison or exchange an easy task. FoSSI is a community software, proven in an adaptive 2D-atmosphere model and a 3D-primitive equation ocean model, both formulated in finite elements. The present paper discusses perspectives of an OpenMP-implementation of parallel iterative solvers based on domain decomposition methods. This approach to OpenMP solvers is rather attractive, as the code for domain-local operations of factorization, preconditioning and matrix-vector product can be readily taken from a sequential implementation that is also suitable to be used in an MPI-variant. Code development in this direction is in an advanced state under
Finite Element Interface to Linear Solvers
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
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
Numerical study of a Vlasov equation for systems with interacting particles
Herrera, Dianela; Curilef, Sergio
2015-03-10
We solve numerically the Vlasov equation for the self-gravitating sheet model. We used the method introduced by Cheng and Knorr [Comput Phys 22, 330-351 (1976)]. We discuss the quasi-stationary state for some thermodynamical observables, specifically the kinetic energy, whose trend is depicted for early evolution.
Poisson-Vlasov in a strong magnetic field: A stochastic solution approach
Vilela Mendes, R.
2010-04-15
Stochastic solutions are obtained for the Maxwell-Vlasov equation in the approximation where magnetic field fluctuations are neglected and the electrostatic potential is used to compute the electric field. This is a reasonable approximation for plasmas in a strong external magnetic field. Both Fourier and configuration space solutions are constructed.
Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations
NASA Astrophysics Data System (ADS)
Han-Kwan, Daniel; Nguyen, Toan T.
2016-09-01
In this paper, we develop an abstract framework to establish ill-posedness, in the sense of Hadamard, for some nonlocal PDEs displaying unbounded unstable spectra. We apply this to prove the ill-posedness for the hydrostatic Euler equations as well as for the kinetic incompressible Euler equations and the Vlasov-Dirac-Benney system.
The Vlasov-Maxwell-Boltzmann system with a uniform ionic background near Maxwellians
NASA Astrophysics Data System (ADS)
Lei, Yuanjie; Zhao, Huijiang
2016-02-01
The two-species Vlasov-Maxwell-Boltzmann system is an important model for plasma physics describing the time evolution of dilute charged particles consisting of electrons and ions under the influence of the self-consistent internally generated Lorentz forces. In physical situations the ion mass is usually much larger than the electron mass so that the electrons move much faster than the ions. Thus, the ions are often described by a fixed ion background and only the electrons move. For such a simple case, the two-species Vlasov-Maxwell-Boltzmann system is reduced to the one-species Vlasov-Maxwell-Boltzmann system. Although the one-species Vlasov-Maxwell-Boltzmann system is a simplified model of the two-species Vlasov-Maxwell-Boltzmann system, its global well-posedness theory near a given global Maxwellian in the perturbative framework is more difficult than the two-species case, which is partially due to the slow-decay of the electromagnetic field and up to now, the problem on the construction of global in time solutions near a given global Maxwellian in the perturbative framework for the Cauchy problem of the one-species Vlasov-Maxwell-Boltzmann system with cutoff non-hard sphere intermolecular collisions remains unsolved. It is shown in this paper that the Cauchy problem of the one-species Vlasov-Maxwell-Boltzmann system with cutoff non-hard sphere intermolecular collisions including the cutoff inverse power law potentials is globally well-posed provided that the perturbative initial data satisfies certain regularity, smallness, and integrability conditions. Our analysis is based on a new time-velocity weighted energy method with two key technical parts: one is to introduce the exponentially weighted estimates into the cutoff Boltzmann operator and the other is to design a delicate temporal energy X (t)-norm to obtain its uniform bound. As a by-product of our analysis, we can also deduce certain temporal decay estimates on the global solutions constructed above
NASA Astrophysics Data System (ADS)
Delzanno, G. L.
2015-11-01
A spectral method for the numerical solution of the multi-dimensional Vlasov-Maxwell equations is presented. The plasma distribution function is expanded in Fourier (for the spatial part) and Hermite (for the velocity part) basis functions, leading to a truncated system of ordinary differential equations for the expansion coefficients (moments) that is discretized with an implicit, second order accurate Crank-Nicolson time discretization. The discrete non-linear system is solved with a preconditioned Jacobian-Free Newton-Krylov method. It is shown analytically that the Fourier-Hermite method features exact conservation laws for total mass, momentum and energy in discrete form. Standard tests involving plasma waves and the whistler instability confirm the validity of the conservation laws numerically. The whistler instability test also shows that we can step over the fastest time scale in the system without incurring in numerical instabilities. Some preconditioning strategies are presented, showing that the number of linear iterations of the Krylov solver can be drastically reduced and a significant gain in performance can be obtained.
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.
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.
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.
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.
Ronald C. Davidson; W. Wei-li Lee; Hong Qin; Edward Startsev
2001-11-08
This paper develops a clear procedure for solving the nonlinear Vlasov-Maxwell equations for a one-component intense charged particle beam or finite-length charge bunch propagating through a cylindrical conducting pipe (radius r = r(subscript)w = const.), and confined by an applied focusing force. In particular, the nonlinear Vlasov-Maxwell equations are Lorentz-transformed to the beam frame ('primed' variables) moving with axial velocity relative to the laboratory. In the beam frame, the particle motions are nonrelativistic for the applications of practical interest, already a major simplification. Then, in the beam frame, we make the electrostatic approximation which fully incorporates beam space-charge effects, but neglects any fast electromagnetic processes with transverse polarization (e.g., light waves). The resulting Vlasov-Maxwell equations are then Lorentz-transformed back to the laboratory frame, and properties of the self-generated fields and resulting nonlinear Vlasov-Maxwell equations in the laboratory frame are discussed.
ODE System Solver W. Krylov Iteration & Rootfinding
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
Two-dimensional flux-corrected transport solver for convectively dominated flows
Baer, M.R.; Gross, R.J.
1986-01-01
A numerical technique designed to solve a wide class of convectively dominated flow problems is presented. An attractive feature of the technique is its ability to resolve the behavior of field quantities possessing large gradients and/or shocks. The method is a finite-difference technique known as flux-corrected transport (FCT) that maintains four important numerical considerations - stability, accuracy, monotonicity, and conservation. The theory and methodology of two-dimensional FCT is presented. The method is applied in demonstrative example calculations of a 2-D Riemann problem with known exact solutions and to the Euler equations in a study of classical Rayleigh-Taylor and Kelvin-Helmholtz instability problems. The FCT solver has been vectorized for execution on the Cray 1S - a typical call with a 50 by 50 mesh requires about 0.00428 cpu seconds of execution time per call to the routine. Additionally, we have maintained a modular structure for the solver that eases its implementation. Fortran listings of two versions of the 2-D FCT solvers are appended with a driver main program illustrating the call sequence for the modules. 59 refs., 49 figs.
Lifting particle coordinate changes of magnetic moment type to Vlasov-Maxwell Hamiltonian dynamics
Morrison, P. J.; Vittot, M.; Guillebon, L. de
2013-03-15
Techniques for coordinate changes that depend on both dependent and independent variables are developed and applied to the Maxwell-Vlasov Hamiltonian theory. Particle coordinate changes with a new velocity variable dependent on the magnetic field, with spatial coordinates unchanged, are lifted to the field theoretic level, by transforming the noncanonical Poisson bracket and Hamiltonian structure of the Vlasov-Maxwell dynamics. Several examples are given including magnetic coordinates, where the velocity is decomposed into components parallel and perpendicular to the local magnetic field, and the case of spherical velocity coordinates. An example of the lifting procedure is performed to obtain a simplified version of gyrokinetics, where the magnetic moment is used as a coordinate and the dynamics is reduced by elimination of the electric field energy in the Hamiltonian.
Study of Bunch Instabilities By the Nonlinear Vlasov-Fokker-Planck Equation
Warnock, Robert L.; /SLAC
2006-07-11
Instabilities of the bunch form in storage rings may be induced through the wake field arising from corrugations in the vacuum chamber, or from the wake and precursor fields due to coherent synchrotron radiation (CSR). For over forty years the linearized Vlasov equation has been applied to calculate the threshold in current for an instability, and the initial growth rate. Increasing interest in nonlinear aspects of the motion has led to numerical solutions of the nonlinear Vlasov equation, augmented with Fokker-Planck terms to describe incoherent synchrotron radiation in the case of electron storage rings. This opens the door to much deeper studies of coherent instabilities, revealing a rich variety of nonlinear phenomena. Recent work on this topic by the author and collaborators is reviewed.
Benisti, Didier; Morice, Olivier; Gremillet, Laurent; Siminos, Evangelos; Strozzi, David J.
2010-10-15
In this paper, we present our nonlinear kinetic modeling of stimulated Raman scattering in a uniform and collisionless plasma using envelope equations. We recall the derivation of these equations, as well as our theoretical predictions for each of the nonlinear kinetic terms, the precision of which having been carefully checked against Vlasov simulations. We particularly focus here on the numerical resolution of these equations, which requires the additional concept of ''self-optimization'' that we explain, and we describe the envelope code BRAMA that we used. As an application of our modeling, we present one-dimensional BRAMA simulations of stimulated Raman scattering which predict threshold intensities, as well as time scales for Raman growth above threshold, in very good agreement with those inferred from Vlasov simulations. Finally, we discuss the differences between our modeling and other published ones.
Adaptive Wavelet Techniques, Wigner Distributions and the Direct Simulation of the Vlasov Equation
NASA Astrophysics Data System (ADS)
Afeyan, Bedros; Douglas, Melissa; Spielman, Rick
2000-10-01
The formal analogy between the quantum Liouville equation satisfied by the Wigner function in Quantum Mechanics, and the Vlasov equation satisfied by the single particle distribution function in plasma physics is exploited in order to study the long term evolution of nonlinear electrostatic wave phenomena dictated by the Vlasov-Poisson equations. Adaptive wavelet techniques are used to tile phase space in an optimal manner so as to minimize computational domain sizes and simultaneously to retain accuracy over disparate scales. Traditional MHD calculations will also be analyzed with our wavelet techniques to show the favorable data compression and feature extraction capabilities of multiresolution analysis. Specifically Z51 and Z179 will be compared to show the nature of the improvements in double wire array (Z179) implosions on Z to those obtained with a single wire array (Z51).
Large-time behavior for the Vlasov/compressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Choi, Young-Pil
2016-07-01
We establish the large-time behavior for the coupled kinetic-fluid equations. More precisely, we consider the Vlasov equation coupled to the compressible isentropic Navier-Stokes equations through a drag forcing term. For this system, the large-time behavior shows the exponential alignment between particles and fluid velocities as time evolves. This improves the previous result by Bae et al. [Discrete Contin. Dyn. Syst. 34, 4419-4458 (2014)] in which they considered the Vlasov/Navier-Stokes equations with nonlocal velocity alignment forces for particles. Employing a new Lyapunov functional measuring the fluctuations of momentum and mass from the averaged quantities, we refine assumptions for the large-time behavior of the solutions to that system.
NASA Astrophysics Data System (ADS)
Bénisti, Didier; Morice, Olivier; Gremillet, Laurent; Siminos, Evangelos; Strozzi, David J.
2010-10-01
In this paper, we present our nonlinear kinetic modeling of stimulated Raman scattering in a uniform and collisionless plasma using envelope equations. We recall the derivation of these equations, as well as our theoretical predictions for each of the nonlinear kinetic terms, the precision of which having been carefully checked against Vlasov simulations. We particularly focus here on the numerical resolution of these equations, which requires the additional concept of "self-optimization" that we explain, and we describe the envelope code BRAMA that we used. As an application of our modeling, we present one-dimensional BRAMA simulations of stimulated Raman scattering which predict threshold intensities, as well as time scales for Raman growth above threshold, in very good agreement with those inferred from Vlasov simulations. Finally, we discuss the differences between our modeling and other published ones.
Efficiency of Pareto joint inversion of 2D geophysical data using global optimization methods
NASA Astrophysics Data System (ADS)
Miernik, Katarzyna; Bogacz, Adrian; Kozubal, Adam; Danek, Tomasz; Wojdyła, Marek
2016-04-01
Pareto joint inversion of two or more sets of data is a promising new tool of modern geophysical exploration. In the first stage of our investigation we created software enabling execution of forward solvers of two geophysical methods (2D magnetotelluric and gravity) as well as inversion with possibility of constraining solution with seismic data. In the algorithm solving MT forward solver Helmholtz's equations, finite element method and Dirichlet's boundary conditions were applied. Gravity forward solver was based on Talwani's algorithm. To limit dimensionality of solution space we decided to describe model as sets of polygons, using Sharp Boundary Interface (SBI) approach. The main inversion engine was created using Particle Swarm Optimization (PSO) algorithm adapted to handle two or more target functions and to prevent acceptance of solutions which are non - realistic or incompatible with Pareto scheme. Each inversion run generates single Pareto solution, which can be added to Pareto Front. The PSO inversion engine was parallelized using OpenMP standard, what enabled execution code for practically unlimited amount of threads at once. Thereby computing time of inversion process was significantly decreased. Furthermore, computing efficiency increases with number of PSO iterations. In this contribution we analyze the efficiency of created software solution taking under consideration details of chosen global optimization engine used as a main joint minimization engine. Additionally we study the scale of possible decrease of computational time caused by different methods of parallelization applied for both forward solvers and inversion algorithm. All tests were done for 2D magnetotelluric and gravity data based on real geological media. Obtained results show that even for relatively simple mid end computational infrastructure proposed solution of inversion problem can be applied in practice and used for real life problems of geophysical inversion and interpretation.
Equation solvers for distributed-memory computers
NASA Technical Reports Server (NTRS)
Storaasli, Olaf O.
1994-01-01
A large number of scientific and engineering problems require the rapid solution of large systems of simultaneous equations. The performance of parallel computers in this area now dwarfs traditional vector computers by nearly an order of magnitude. This talk describes the major issues involved in parallel equation solvers with particular emphasis on the Intel Paragon, IBM SP-1 and SP-2 processors.
Frequency Domain Modelling by a Direct-Iterative Solver: A Space and Wavelet Approach
NASA Astrophysics Data System (ADS)
Hustedt, B.; Operto, S.; Virieux, J.
2002-12-01
Seismic forward modelling of wave propagation phenomena in complex rheologic media using a frequency domain finite-difference (FDFD) technique is of special interest for multisource experiments and waveform inversion schemes, because the complete wavefield solution can be computed in a fast and efficient way. FDFD modelling requires the inversion of an extremely large matrix-equation A x x = b, by either a direct or an iterative solver. The direct solver computes an effective inverse of A, called LU factorization. The main handicap is additional computer memory required for storing matrix fill-in coefficients, that are created during the factorization process. Iterative solvers are not limited by memory constraints (additional coefficients), but the convergence depends on a good initial solution difficult to guess before hand. For both solvers, available computer resources has limited wide-spread FDFD modelling applications to mainly two-dimensional (2D) and rarely three-dimensional (3D) problems. In order to overcome these limits, we propose the combination of a direct solver and an iterative solver, called Direct-Iterative Solver (DIS). The direct solver is used to compute an exact wavefield solution on a coarse discretized grid. We use a multifrontal decomposition technique. The coarse-grid size is determined preliminary by limits of the available computer resources, rather than by the wave simulation problem. We project the exact coarse-grid solution on a fine-grid, and use it as an initial solution for an iterative solver, which convergences to an acceptable approximation of the desired fine-grid solution. Two different DIS schemes have been implemented and tested for numerical accuracy and computational performance. The first approach, called the Direct-Iterative-Space Solver (DISS), projects the coarse-grid solution on the fine-grid by a bilinear interpolation. Though the interpolated solution nicely approximates the desired fine-grid solution, still for
Parallel solvers for reservoir simulation on MIMD computers
Piault, E.; Willien, F.; Roux, F.X.
1995-12-01
We have investigated parallel solvers for reservoir simulation. We compare different solvers and preconditioners using T3D and SP1 parallel computers. We use block diagonal domain decomposition preconditioner with non-overlapping sub-domains.
A Vlasov equilibrium for space charge dominated beam in a misaligned solenoidal channel
Sing Babu, P.; Goswami, A.; Pandit, V. S.
2012-08-15
The effect of displacement and rotational misalignments of solenoid magnets with respect to the ideal beam propagation axis on the dynamics of intense charged particle beams have been studied. The equation of motion of the beam centroid has been obtained and found to be independent of any specific beam distribution. A Vlasov equilibrium distribution for the intense beam propagation through misaligned focussing channel has been obtained. Self-consistent simulation confirms the analytical result.
A Legendre-Fourier spectral method with exact conservation laws for the Vlasov-Poisson system
NASA Astrophysics Data System (ADS)
Manzini, G.; Delzanno, G. L.; Vencels, J.; Markidis, S.
2016-07-01
We present the design and implementation of an L2-stable spectral method for the discretization of the Vlasov-Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank-Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations is iteratively solved at any time cycle by a Jacobian-Free Newton-Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre-Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.
One-dimensional Vlasov simulation of parallel electric fields in two-electron population plasma
Saharia, K.; Goswami, K. S.
2007-09-15
One-dimensional Vlasov simulation in electron current carrying multicomponent plasma seeded with a density depression is presented. Considering two electron populations [one is sufficiently hot ({approx}keV) and the other is cold along with cold background ions], the formation of weak double layers is investigated. Simulation results show that in this numerical setting, formation of such double layers needs the majority of the hot electrons.
Perspectives for spintronics in 2D materials
NASA Astrophysics Data System (ADS)
Han, Wei
2016-03-01
The past decade has been especially creative for spintronics since the (re)discovery of various two dimensional (2D) materials. Due to the unusual physical characteristics, 2D materials have provided new platforms to probe the spin interaction with other degrees of freedom for electrons, as well as to be used for novel spintronics applications. This review briefly presents the most important recent and ongoing research for spintronics in 2D materials.
Vlasov Simulation of the Effects of Collisions on the Damping of Electron Plasma Waves
NASA Astrophysics Data System (ADS)
Banks, Jeff; Berger, Richard; Chapman, Thomas; Brunner, Stephan; Tran, T.
2015-11-01
Kinetic simulation of two dimensional plasma waves through direct discretization of the Vlasov equation may be particularly attractive for situations where minimal numerical fluctuation levels are desired, such as when measuring growth rates of plasma wave instabilities. In many cases collisional effects can be important to the evolution of plasma waves because they both set a minimum damping rate for plasma waves and can scatter particles out of resonance through pitch angle scattering. Here we present Vlasov simulations of evolving electron plasma waves (EPWs) in plasmas of varying collisionality. We consider first the effects of electron-ion pitch angle collisions on the frequency and damping, Landau and collisional, of small-amplitude EPWs for a range of collision rates. In addition, the wave phase velocities are extracted from the simulation results and compared with theory. For this study we use the Eulerian-based kinetic code LOKI that evolves the Vlasov-Poisson system in 2+2-dimensional phase space. We then discuss extensions of the collision operator to include thermalization. Discretization of these collision operators using 4th order accurate conservative finite-differencing will be discussed. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and funded by the LDRD program at LLNL under project tracking code 15-ERD-038.
Shoucri, M.; Matte, J.-P.; Vidal, F.
2015-05-15
We apply an Eulerian Vlasov code to study the amplification by Brillouin scattering of a short seed laser pulse by a long pump laser pulse in an underdense plasma. The stimulated Brillouin backscattering interaction is the coupling of the pump and seed electromagnetic waves propagating in opposite directions, and the ion plasma wave. The code solves the one-dimensional relativistic Vlasov-Maxwell set of equations. Large amplitude ion waves are generated. In the simulations we present, the density plateau of the plasma is n{sub e}=0.3 n{sub c} (n{sub c} is the critical density), which excludes spurious stimulated Raman scattering amplification (which can occur only if n{sub e}
L2-stability of the Vlasov-Maxwell-Boltzmann system near global Maxwellians
NASA Astrophysics Data System (ADS)
Ha, Seung-Yeal; Xiao, Qinghua; Xiong, Linjie; Zhao, Huijiang
2013-12-01
We present a L2-stability theory of the Vlasov-Maxwell-Boltzmann system for the two-species collisional plasma. We show that in a perturbative regime of a global Maxwellian, the L2-distance between two strong solutions can be controlled by that between initial data in a Lipschitz manner. Our stability result extends earlier results [Ha, S.-Y. and Xiao, Q.-H., "A revisiting to the L2-stability theory of the Boltzmann equation near global Maxwellians," (submitted) and Ha, S.-Y., Yang, X.-F., and Yun, S.-B., "L2 stability theory of the Boltzmann equation near a global Maxwellian," Arch. Ration. Mech. Anal. 197, 657-688 (2010)] on the L2-stability of the Boltzmann equation to the Boltzmann equation coupled with self-consistent external forces. As a direct application of our stability result, we show that classical solutions in Duan et al. ["Optimal large-time behavior of the Vlasov-Maxwell-Boltzmann system in the whole space," Commun. Pure Appl. Math. 24, 1497-1546 (2011)] and Guo ["The Vlasov-Maxwell-Boltzmann system near Maxwellians," Invent. Math. 153(3), 593-630 (2003)] satisfy a uniform L2-stability estimate. This is the first result on the L2-stability of the Boltzmann equation coupled with self-consistent field equations in three dimensions.
Collisional effects on the numerical recurrence in Vlasov-Poisson simulations
NASA Astrophysics Data System (ADS)
Pezzi, Oreste; Camporeale, Enrico; Valentini, Francesco
2016-02-01
The initial state recurrence in numerical simulations of the Vlasov-Poisson system is a well-known phenomenon. Here, we study the effect on recurrence of artificial collisions modeled through the Lenard-Bernstein operator [A. Lenard and I. B. Bernstein, Phys. Rev. 112, 1456-1459 (1958)]. By decomposing the linear Vlasov-Poisson system in the Fourier-Hermite space, the recurrence problem is investigated in the linear regime of the damping of a Langmuir wave and of the onset of the bump-on-tail instability. The analysis is then confirmed and extended to the nonlinear regime through an Eulerian collisional Vlasov-Poisson code. It is found that, despite being routinely used, an artificial collisionality is not a viable way of preventing recurrence in numerical simulations without compromising the kinetic nature of the solution. Moreover, it is shown how numerical effects associated to the generation of fine velocity scales can modify the physical features of the system evolution even in nonlinear regime. This means that filamentation-like phenomena, usually associated with low amplitude fluctuations contexts, can play a role even in nonlinear regime.
NASA Technical Reports Server (NTRS)
Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung
1996-01-01
The I-D, quasi I-D and 2-D Euler solvers based on the method of space-time conservation element and solution element are used to simulate various flow phenomena including shock waves, Mach stem, contact surface, expansion waves, and their intersections and reflections. Seven test problems are solved to demonstrate the capability of this method for handling unsteady compressible flows in various configurations. Numerical results so obtained are compared with exact solutions and/or numerical solutions obtained by schemes based on other established computational techniques. Comparisons show that the present Euler solvers can generate highly accurate numerical solutions to complex flow problems in a straightforward manner without using any ad hoc techniques in the scheme.
Courant Number and Mach Number Insensitive CE/SE Euler Solvers
NASA Technical Reports Server (NTRS)
Chang, Sin-Chung
2005-01-01
It has been known that the space-time CE/SE method can be used to obtain ID, 2D, and 3D steady and unsteady flow solutions with Mach numbers ranging from 0.0028 to 10. However, it is also known that a CE/SE solution may become overly dissipative when the Mach number is very small. As an initial attempt to remedy this weakness, new 1D Courant number and Mach number insensitive CE/SE Euler solvers are developed using several key concepts underlying the recent successful development of Courant number insensitive CE/SE schemes. Numerical results indicate that the new solvers are capable of resolving crisply a contact discontinuity embedded in a flow with the maximum Mach number = 0.01.
Quantitative 2D liquid-state NMR.
Giraudeau, Patrick
2014-06-01
Two-dimensional (2D) liquid-state NMR has a very high potential to simultaneously determine the absolute concentration of small molecules in complex mixtures, thanks to its capacity to separate overlapping resonances. However, it suffers from two main drawbacks that probably explain its relatively late development. First, the 2D NMR signal is strongly molecule-dependent and site-dependent; second, the long duration of 2D NMR experiments prevents its general use for high-throughput quantitative applications and affects its quantitative performance. Fortunately, the last 10 years has witnessed an increasing number of contributions where quantitative approaches based on 2D NMR were developed and applied to solve real analytical issues. This review aims at presenting these recent efforts to reach a high trueness and precision in quantitative measurements by 2D NMR. After highlighting the interest of 2D NMR for quantitative analysis, the different strategies to determine the absolute concentrations from 2D NMR spectra are described and illustrated by recent applications. The last part of the manuscript concerns the recent development of fast quantitative 2D NMR approaches, aiming at reducing the experiment duration while preserving - or even increasing - the analytical performance. We hope that this comprehensive review will help readers to apprehend the current landscape of quantitative 2D NMR, as well as the perspectives that may arise from it.
Staring 2-D hadamard transform spectral imager
Gentry, Stephen M.; Wehlburg, Christine M.; Wehlburg, Joseph C.; Smith, Mark W.; Smith, Jody L.
2006-02-07
A staring imaging system inputs a 2D spatial image containing multi-frequency spectral information. This image is encoded in one dimension of the image with a cyclic Hadamarid S-matrix. The resulting image is detecting with a spatial 2D detector; and a computer applies a Hadamard transform to recover the encoded image.
NASA Technical Reports Server (NTRS)
Voigt, Kerstin
1992-01-01
We present MENDER, a knowledge based system that implements software design techniques that are specialized to automatically compile generate-and-patch problem solvers that satisfy global resource assignments problems. We provide empirical evidence of the superior performance of generate-and-patch over generate-and-test: even with constrained generation, for a global constraint in the domain of '2D-floorplanning'. For a second constraint in '2D-floorplanning' we show that even when it is possible to incorporate the constraint into a constrained generator, a generate-and-patch problem solver may satisfy the constraint more rapidly. We also briefly summarize how an extended version of our system applies to a constraint in the domain of 'multiprocessor scheduling'.
Geng, Jinyue; Brieda, Lubos; Rose, Laura; Keidar, Michael
2013-09-14
In Hall thrusters, the potential distribution plays an important role in discharge processes and ion acceleration. This paper presents a 2D potential solver in the Hall thruster instead of the “thermalized potential”, and compares equipotential contours solved by these two methods for different magnetic field conditions. The comparison results reveal that the expected “thermalized potential” works very well when the magnetic field is nearly uniform and electron temperature is constant along the magnetic field lines. However for the case with a highly non-uniform magnetic field or variable electron temperature along the magnetic field lines, the “thermalized potential” is not accurate. In some case with magnetic separatrix inside the thruster channel, the “thermalized potential” model cannot be applied at all. In those cases, a full 2D potential solver must be applied. Overall, this paper shows the limit of applicability of the “thermalized potential” model.
2D accelerator design for SITEX negative ion source
Whealton, J.H.; Raridon, R.J.; McGaffey, R.W.; McCollough, D.H.; Stirling, W.L.; Dagenhart, W.K.
1983-01-01
Solving the Poisson-Vlasov equations where the magnetic field, B, is assumed constant, we optimize the optical system of a SITEX negative ion source in infinite slot geometry. Algorithms designed to solve the above equations were modified to include the curved emitter boundary data appropriate to a negative ion source. Other configurations relevant to negative ion sources are examined.
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.
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.
2D materials for nanophotonic devices
NASA Astrophysics Data System (ADS)
Xu, Renjing; Yang, Jiong; Zhang, Shuang; Pei, Jiajie; Lu, Yuerui
2015-12-01
Two-dimensional (2D) materials have become very important building blocks for electronic, photonic, and phononic devices. The 2D material family has four key members, including the metallic graphene, transition metal dichalcogenide (TMD) layered semiconductors, semiconducting black phosphorous, and the insulating h-BN. Owing to the strong quantum confinements and defect-free surfaces, these atomically thin layers have offered us perfect platforms to investigate the interactions among photons, electrons and phonons. The unique interactions in these 2D materials are very important for both scientific research and application engineering. In this talk, I would like to briefly summarize and highlight the key findings, opportunities and challenges in this field. Next, I will introduce/highlight our recent achievements. We demonstrated atomically thin micro-lens and gratings using 2D MoS2, which is the thinnest optical component around the world. These devices are based on our discovery that the elastic light-matter interactions in highindex 2D materials is very strong. Also, I would like to introduce a new two-dimensional material phosphorene. Phosphorene has strongly anisotropic optical response, which creates 1D excitons in a 2D system. The strong confinement in phosphorene also enables the ultra-high trion (charged exciton) binding energies, which have been successfully measured in our experiments. Finally, I will briefly talk about the potential applications of 2D materials in energy harvesting.
Internal Photoemission Spectroscopy of 2-D Materials
NASA Astrophysics Data System (ADS)
Nguyen, Nhan; Li, Mingda; Vishwanath, Suresh; Yan, Rusen; Xiao, Shudong; Xing, Huili; Cheng, Guangjun; Hight Walker, Angela; Zhang, Qin
Recent research has shown the great benefits of using 2-D materials in the tunnel field-effect transistor (TFET), which is considered a promising candidate for the beyond-CMOS technology. The on-state current of TFET can be enhanced by engineering the band alignment of different 2D-2D or 2D-3D heterostructures. Here we present the internal photoemission spectroscopy (IPE) approach to determine the band alignments of various 2-D materials, in particular SnSe2 and WSe2, which have been proposed for new TFET designs. The metal-oxide-2-D semiconductor test structures are fabricated and characterized by IPE, where the band offsets from the 2-D semiconductor to the oxide conduction band minimum are determined by the threshold of the cube root of IPE yields as a function of photon energy. In particular, we find that SnSe2 has a larger electron affinity than most semiconductors and can be combined with other semiconductors to form near broken-gap heterojunctions with low barrier heights which can produce a higher on-state current. The details of data analysis of IPE and the results from Raman spectroscopy and spectroscopic ellipsometry measurements will also be presented and discussed.
A multigrid solver for the semiconductor equations
NASA Technical Reports Server (NTRS)
Bachmann, Bernhard
1993-01-01
We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.
2D materials: to graphene and beyond.
Mas-Ballesté, Rubén; Gómez-Navarro, Cristina; Gómez-Herrero, Julio; Zamora, Félix
2011-01-01
This review is an attempt to illustrate the different alternatives in the field of 2D materials. Graphene seems to be just the tip of the iceberg and we show how the discovery of alternative 2D materials is starting to show the rest of this iceberg. The review comprises the current state-of-the-art of the vast literature in concepts and methods already known for isolation and characterization of graphene, and rationalizes the quite disperse literature in other 2D materials such as metal oxides, hydroxides and chalcogenides, and metal-organic frameworks.
2-d Finite Element Code Postprocessor
1996-07-15
ORION is an interactive program that serves as a postprocessor for the analysis programs NIKE2D, DYNA2D, TOPAZ2D, and CHEMICAL TOPAZ2D. ORION reads binary plot files generated by the two-dimensional finite element codes currently used by the Methods Development Group at LLNL. Contour and color fringe plots of a large number of quantities may be displayed on meshes consisting of triangular and quadrilateral elements. ORION can compute strain measures, interface pressures along slide lines, reaction forcesmore » along constrained boundaries, and momentum. ORION has been applied to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.« less
Ginsparg, P.
1991-01-01
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
Ginsparg, P.
1991-12-31
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
Brittle damage models in DYNA2D
Faux, D.R.
1997-09-01
DYNA2D is an explicit Lagrangian finite element code used to model dynamic events where stress wave interactions influence the overall response of the system. DYNA2D is often used to model penetration problems involving ductile-to-ductile impacts; however, with the advent of the use of ceramics in the armor-anti-armor community and the need to model damage to laser optics components, good brittle damage models are now needed in DYNA2D. This report will detail the implementation of four brittle damage models in DYNA2D, three scalar damage models and one tensor damage model. These new brittle damage models are then used to predict experimental results from three distinctly different glass damage problems.
Impact of high speed civil transports on stratospheric ozone: A 2-D model investigation
Kinnison, D.E.; Connell, P.S.
1996-12-01
This study investigates the effect on stratospheric ozone from a fleet of proposed High Speed Civil Transports (HSCTs). The new LLNL 2-D operator-split chemical-radiative-transport model of the troposphere and stratosphere is used for this HSCT investigation. This model is integrated in a diurnal manner, using an implicit numerical solver. Therefore, rate coefficients are not modified by any sort of diurnal average factor. This model also does not make any assumptions on lumping of chemical species into families. Comparisons to previous model-derived HSCT assessment of ozone change are made, both to the previous LLNL 2-D model and to other models from the international assessment modeling community. The sensitivity to the NO{sub x} emission index and sulfate surface area density is also explored.
Chemical Approaches to 2D Materials.
Samorì, Paolo; Palermo, Vincenzo; Feng, Xinliang
2016-08-01
Chemistry plays an ever-increasing role in the production, functionalization, processing and applications of graphene and other 2D materials. This special issue highlights a selection of enlightening chemical approaches to 2D materials, which nicely reflect the breadth of the field and convey the excitement of the individuals involved in it, who are trying to translate graphene and related materials from the laboratory into a real, high-impact technology. PMID:27478083
Chemical Approaches to 2D Materials.
Samorì, Paolo; Palermo, Vincenzo; Feng, Xinliang
2016-08-01
Chemistry plays an ever-increasing role in the production, functionalization, processing and applications of graphene and other 2D materials. This special issue highlights a selection of enlightening chemical approaches to 2D materials, which nicely reflect the breadth of the field and convey the excitement of the individuals involved in it, who are trying to translate graphene and related materials from the laboratory into a real, high-impact technology.
Yang, Li-Ming; Dornfeld, Matthew; Frauenheim, Thomas; Ganz, Eric
2015-10-21
We predict a highly stable and robust atomically thin gold monolayer with a hexagonal close packed lattice stabilized by metallic bonding with contributions from strong relativistic effects and aurophilic interactions. We have shown that the framework of the Au monolayer can survive 10 ps MD annealing simulations up to 1400 K. The framework is also able to survive large motions out of the plane. Due to the smaller number of bonds per atom in the 2D layer compared to the 3D bulk we observe significantly enhanced energy per bond (0.94 vs. 0.52 eV per bond). This is similar to the increase in bond strength going from 3D diamond to 2D graphene. It is a non-magnetic metal, and was found to be the global minima in the 2D space. Phonon dispersion calculations demonstrate high kinetic stability with no negative modes. This 2D gold monolayer corresponds to the top monolayer of the bulk Au(111) face-centered cubic lattice. The close-packed lattice maximizes the aurophilic interactions. We find that the electrons are completely delocalized in the plane and behave as 2D nearly free electron gas. We hope that the present work can inspire the experimental fabrication of novel free standing 2D metal systems.
2d index and surface operators
NASA Astrophysics Data System (ADS)
Gadde, Abhijit; Gukov, Sergei
2014-03-01
In this paper we compute the superconformal index of 2d (2, 2) supersymmetric gauge theories. The 2d superconformal index, a.k.a. flavored elliptic genus, is computed by a unitary matrix integral much like the matrix integral that computes the 4d superconformal index. We compute the 2d index explicitly for a number of examples. In the case of abelian gauge theories we see that the index is invariant under flop transition and under CY-LG correspondence. The index also provides a powerful check of the Seiberg-type duality for non-abelian gauge theories discovered by Hori and Tong. In the later half of the paper, we study half-BPS surface operators in = 2 super-conformal gauge theories. They are engineered by coupling the 2d (2, 2) supersymmetric gauge theory living on the support of the surface operator to the 4d = 2 theory, so that different realizations of the same surface operator with a given Levi type are related by a 2d analogue of the Seiberg duality. The index of this coupled system is computed by using the tools developed in the first half of the paper. The superconformal index in the presence of surface defect is expected to be invariant under generalized S-duality. We demonstrate that it is indeed the case. In doing so the Seiberg-type duality of the 2d theory plays an important role.
Wave dispersion in the hybrid-Vlasov model: Verification of Vlasiator
Kempf, Yann; Pokhotelov, Dimitry; Koskinen, Hannu E. J.; Alfthan, Sebastian von; Palmroth, Minna; Vaivads, Andris
2013-11-15
Vlasiator is a new hybrid-Vlasov plasma simulation code aimed at simulating the entire magnetosphere of the Earth. The code treats ions (protons) kinetically through Vlasov's equation in the six-dimensional phase space while electrons are a massless charge-neutralizing fluid [M. Palmroth et al., J. Atmos. Sol.-Terr. Phys. 99, 41 (2013); A. Sandroos et al., Parallel Comput. 39, 306 (2013)]. For first global simulations of the magnetosphere, it is critical to verify and validate the model by established methods. Here, as part of the verification of Vlasiator, we characterize the low-β plasma wave modes described by this model and compare with the solution computed by the Waves in Homogeneous, Anisotropic Multicomponent Plasmas (WHAMP) code [K. Rönnmark, Kiruna Geophysical Institute Reports No. 179, 1982], using dispersion curves and surfaces produced with both programs. The match between the two fundamentally different approaches is excellent in the low-frequency, long wavelength range which is of interest in global magnetospheric simulations. The left-hand and right-hand polarized wave modes as well as the Bernstein modes in the Vlasiator simulations agree well with the WHAMP solutions. Vlasiator allows a direct investigation of the importance of the Hall term by including it in or excluding it from Ohm's law in simulations. This is illustrated showing examples of waves obtained using the ideal Ohm's law and Ohm's law including the Hall term. Our analysis emphasizes the role of the Hall term in Ohm's law in obtaining wave modes departing from ideal magnetohydrodynamics in the hybrid-Vlasov model.
Morrison, P.J.; Pfirsch, D.
1992-04-01
Expressions for the energy content of one-dimensional electrostatic perturbations about homogeneous equilibria are revisited. The well-known dielectric energy, {var_epsilon}{sub D}, is compared with the exact plasma free energy expression, {delta}{sup 2}F, that is conserved by the Vlasov-Poisson system. The former is an expression in terms of the perturbed electric field amplitude, while the latter is determined by a generating function, which describes perturbations of the distribution function that respect the important constraint of dynamical accessibility of the system. Thus the comparison requires solving the Vlasov equation for such a perturbations of the distribution function in terms of the electric field. This is done for neutral modes of oscillation that occur for equilibria with stationary inflection points, and it is seen that for these special modes {delta}{sup 2}F = {var_epsilon}{sub D}. In the case of unstable and corresponding damped modes it is seen that {delta}{sup 2}F {ne} {var_epsilon}{sub D}; in fact {delta}{sup 2}F {equivalent_to} 0. This failure of the dielectric energy expression persists even for arbitrarily small growth and damping rates since {var_epsilon}{sub D} is nonzero in this limit, whereas {delta}{sup 2}F remains zero. The connection between the new exact energy expression and the at-best approximate {var_epsilon}{sub D} is described. The new expression motivates natural definitions of Hamiltonian action variables and signature. A general linear integral transform is introduced that maps the linear version of the noncanonical Hamiltonian structure, which describes the Vlasov equation, to action-angle (diagonal) form.
Morrison, P.J. . Inst. for Fusion Studies); Pfirsch, D. )
1992-04-01
Expressions for the energy content of one-dimensional electrostatic perturbations about homogeneous equilibria are revisited. The well-known dielectric energy, {var epsilon}{sub D}, is compared with the exact plasma free energy expression, {delta}{sup 2}F, that is conserved by the Vlasov-Poisson system. The former is an expression in terms of the perturbed electric field amplitude, while the latter is determined by a generating function, which describes perturbations of the distribution function that respect the important constraint of dynamical accessibility of the system. Thus the comparison requires solving the Vlasov equation for such a perturbations of the distribution function in terms of the electric field. This is done for neutral modes of oscillation that occur for equilibria with stationary inflection points, and it is seen that for these special modes {delta}{sup 2}F = {var epsilon}{sub D}. In the case of unstable and corresponding damped modes it is seen that {delta}{sup 2}F {ne} {var epsilon}{sub D}; in fact {delta}{sup 2}F {equivalent to} 0. This failure of the dielectric energy expression persists even for arbitrarily small growth and damping rates since {var epsilon}{sub D} is nonzero in this limit, whereas {delta}{sup 2}F remains zero. The connection between the new exact energy expression and the at-best approximate {var epsilon}{sub D} is described. The new expression motivates natural definitions of Hamiltonian action variables and signature. A general linear integral transform is introduced that maps the linear version of the noncanonical Hamiltonian structure, which describes the Vlasov equation, to action-angle (diagonal) form.
L{sup 2}-stability of the Vlasov-Maxwell-Boltzmann system near global Maxwellians
Ha, Seung-Yeal Xiao, Qinghua; Xiong, Linjie Zhao, Huijiang
2013-12-15
We present a L{sup 2}-stability theory of the Vlasov-Maxwell-Boltzmann system for the two-species collisional plasma. We show that in a perturbative regime of a global Maxwellian, the L{sup 2}-distance between two strong solutions can be controlled by that between initial data in a Lipschitz manner. Our stability result extends earlier results [Ha, S.-Y. and Xiao, Q.-H., “A revisiting to the L{sup 2}-stability theory of the Boltzmann equation near global Maxwellians,” (submitted) and Ha, S.-Y., Yang, X.-F., and Yun, S.-B., “L{sup 2} stability theory of the Boltzmann equation near a global Maxwellian,” Arch. Ration. Mech. Anal. 197, 657–688 (2010)] on the L{sup 2}-stability of the Boltzmann equation to the Boltzmann equation coupled with self-consistent external forces. As a direct application of our stability result, we show that classical solutions in Duan et al. [“Optimal large-time behavior of the Vlasov-Maxwell-Boltzmann system in the whole space,” Commun. Pure Appl. Math. 24, 1497–1546 (2011)] and Guo [“The Vlasov-Maxwell-Boltzmann system near Maxwellians,” Invent. Math. 153(3), 593–630 (2003)] satisfy a uniform L{sup 2}-stability estimate. This is the first result on the L{sup 2}-stability of the Boltzmann equation coupled with self-consistent field equations in three dimensions.
A Uniqueness Criterion for Unbounded Solutions to the Vlasov-Poisson System
NASA Astrophysics Data System (ADS)
Miot, Evelyne
2016-07-01
We prove uniqueness for the Vlasov-Poisson system in two and three dimensions under the condition that the L p norms of the macroscopic density grow at most linearly with respect to p. This allows for solutions with logarithmic singularities. We provide explicit examples of initial data that fulfill the uniqueness condition and that exhibit a logarithmic blow-up. In the gravitational two-dimensional case, such states are intimately related to radially symmetric steady solutions of the system. Our method relies on the Lagrangian formulation for the solutions, exploiting the second-order structure of the corresponding ODE.
A Spectral Algorithm for Solving the Relativistic Vlasov-Maxwell Equations
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2001-01-01
A spectral method algorithm is developed for the numerical solution of the full six-dimensional Vlasov-Maxwell system of equations. Here, the focus is on the electron distribution function, with positive ions providing a constant background. The algorithm consists of a Jacobi polynomial-spherical harmonic formulation in velocity space and a trigonometric formulation in position space. A transform procedure is used to evaluate nonlinear terms. The algorithm is suitable for performing moderate resolution simulations on currently available supercomputers for both scientific and engineering applications.
Vlasov simulations of Langmuir Electrostatic Decay and consequences for Type III observations
Henri, P.; Califano, F.; Briand, C.; Mangeney, A.
2010-03-25
The electrostatic decay enables energy transfer from a finite amplitude Langmuir to a backscattered daughter Langmuir wave and ion acoustic density fluctuations. This mechanism is thought to be a first step for the generation of type III solar radio emissions at twice the plasma frequency. The electrostatic decay is here investigated through Vlasov-Poisson simulations by considering Langmuir localized wave packets in the case T{sub e} = T{sub p}. Simulation results are found to be in good agreement with recently reported observations from the STEREO mission of the electrostatic decay of beam-driven Langmuir waves during a type III burst.
Self-similar analysis of Vlasov-Einstein equations in spherical symmetry
Munier, A.; Burgan, J.R.; Feix, M.; Fijalkow, E.
1980-03-15
The Vlasov-Einstein system of equations is studied from the point of view of group transformations. Continuous groups are shown to generalize the usual infinitesimal treatment of the metric tensor to the case of a distribution function. Reduced equations are obtained, leading to a time-dependent analytical solution, which yields as a limiting case the Schwarzchild metric. The problem of a purely radial motion of null particles is discussed and leads to an expression for the redshift in a nonstatic, inhomogeneous spacetime.
Simulation study of entropy production in the one-dimensional Vlasov system
NASA Astrophysics Data System (ADS)
Dai, Zongliang; Wang, Shaojie
2016-07-01
The coarse-grain averaged distribution function of the one-dimensional Vlasov system is obtained by numerical simulation. The entropy productions in cases of the random field, the linear Landau damping, and the bump-on-tail instability are computed with the coarse-grain averaged distribution function. The computed entropy production is converged with increasing length of coarse-grain average. When the distribution function differs slightly from a Maxwellian distribution, the converged value agrees with the result computed by using the definition of thermodynamic entropy. The length of the coarse-grain average to compute the coarse-grain averaged distribution function is discussed.
A Uniqueness Criterion for Unbounded Solutions to the Vlasov-Poisson System
NASA Astrophysics Data System (ADS)
Miot, Evelyne
2016-09-01
We prove uniqueness for the Vlasov-Poisson system in two and three dimensions under the condition that the L p norms of the macroscopic density grow at most linearly with respect to p. This allows for solutions with logarithmic singularities. We provide explicit examples of initial data that fulfill the uniqueness condition and that exhibit a logarithmic blow-up. In the gravitational two-dimensional case, such states are intimately related to radially symmetric steady solutions of the system. Our method relies on the Lagrangian formulation for the solutions, exploiting the second-order structure of the corresponding ODE.
Nonlinear canonical gyrokinetic Vlasov equation and computation of the gyrocenter motion in tokamaks
Xu Yingfeng; Wang Shaojie
2013-01-15
The nonlinear canonical gyrokinetic Vlasov equation is obtained from the nonlinear noncanonical gyrokinetic theory using the property of the coordinate transform. In the linear approximation, it exactly recovers the previous linear canonical gyrokinetic equations derived by the Lie-transform perturbation method. The computation of the test particle gyrocenter motion in tokamaks with a large magnetic perturbation is presented and discussed. The numerical results indicate that the second-order gyrocenter Hamiltonian is important for the gyrocenter motion of the trapped electron in tokamaks with a large magnetic perturbation.
Coordinate-Space Hartree-Fock-Bogoliubov Solvers for Superfluid Fermi Systems in Large Boxes
Pei, J. C.; Fann, George I; Harrison, Robert J; Nazarewicz, W.; Hill, Judith C; Galindo, Diego A; Jia, Jun
2012-01-01
The self-consistent Hartree-Fock-Bogoliubov problem in large boxes can be solved accurately in the coordinate space with the recently developed solvers HFB-AX (2D) and MADNESS-HFB (3D). This is essential for the description of superfluid Fermi systems with complicated topologies and significant spatial extend, such as fissioning nuclei, weakly-bound nuclei, nuclear matter in the neutron star rust, and ultracold Fermi atoms in elongated traps. The HFB-AX solver based on B-spline techniques uses a hybrid MPI and OpenMP programming model for parallel computation for distributed parallel computation, within a node multi-threaded LAPACK and BLAS libraries are used to further enable parallel calculations of large eigensystems. The MADNESS-HFB solver uses a novel multi-resolution analysis based adaptive pseudo-spectral techniques to enable fully parallel 3D calculations of very large systems. In this work we present benchmark results for HFB-AX and MADNESS-HFB on ultracold trapped fermions.
Flood simulation using an open source quadtree grid shallow water flow solver
NASA Astrophysics Data System (ADS)
An, H.; Yu, S.
2012-12-01
We carry out performance testing of Gerris for flood simulation. Gerris Flow Solver is open source software and has the capability of adaptive quadtree grid generation. In particular, the shallow water flow solver within Gerris Flow Solver implements second-order accurate Gudunov type numerical schemes, with preserving the balance of source and flux terms on quadtree cut cell grids. The combination of quadtree grids with the cut cell method improves the flexibility of quadtree grids for grid generation. In addition, the model has the capacity of adaptive meshing in an easy and effective way, which can improve computational efficiency in 2D modeling. Pre- and post-processors are already well equipped for users. Finally, an extension such as bed erosion or sediment transport can be added if needed. Two flood events, Malpasset dam break in France and Baeksan levee failure in Korea, are simulated using Gerris, with adaptively refining meshes near water fronts and the river boundary. Simulation results are compared with survey data, experimental data as well as simulation results by other researchers. The simulation results demonstrate that the adaptive quadtree model can save approximately 95% of the computational cost while preserving the accuracy. Gerris is a very attractive alternative for flood managers given the favorable features demonstrated in this paper.
Simultaneous elastic parameter inversion in 2-D/3-D TTI medium combined later arrival times
NASA Astrophysics Data System (ADS)
Bai, Chao-ying; Wang, Tao; Yang, Shang-bei; Li, Xing-wang; Huang, Guo-jiao
2016-04-01
Traditional traveltime inversion for anisotropic medium is, in general, based on a "weak" assumption in the anisotropic property, which simplifies both the forward part (ray tracing is performed once only) and the inversion part (a linear inversion solver is possible). But for some real applications, a general (both "weak" and "strong") anisotropic medium should be considered. In such cases, one has to develop a ray tracing algorithm to handle with the general (including "strong") anisotropic medium and also to design a non-linear inversion solver for later tomography. Meanwhile, it is constructive to investigate how much the tomographic resolution can be improved by introducing the later arrivals. For this motivation, we incorporated our newly developed ray tracing algorithm (multistage irregular shortest-path method) for general anisotropic media with a non-linear inversion solver (a damped minimum norm, constrained least squares problem with a conjugate gradient approach) to formulate a non-linear inversion solver for anisotropic medium. This anisotropic traveltime inversion procedure is able to combine the later (reflected) arrival times. Both 2-D/3-D synthetic inversion experiments and comparison tests show that (1) the proposed anisotropic traveltime inversion scheme is able to recover the high contrast anomalies and (2) it is possible to improve the tomographic resolution by introducing the later (reflected) arrivals, but not as expected in the isotropic medium, because the different velocity (qP, qSV and qSH) sensitivities (or derivatives) respective to the different elastic parameters are not the same but are also dependent on the inclination angle.
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.
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.
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.
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.
Gyrokinetic Vlasov-Poisson simulation in slab geometry using the conservative IDO scheme
NASA Astrophysics Data System (ADS)
Imadera, Kenji; Kishimoto, Yasuaki; Li, Jiquan; Saito, Daisuke; Utsumi, Takayuki
2008-11-01
We have introduced the IDO-CF (Conservative Form of Interpolated Differential Operator) scheme [1], which is one of the multi-moment schemes and has been applied to various CFD problems, in solving a Vlasov-Poisson system. The IDO scheme is found to be efficient in capturing a sharp domain interface like shock propagation, and in introducing dissipations like particle collision and also external source/sink terms. Furthermore, the IDO-CF scheme has exact mass conservation properties, so that we can apply it to the problems that need long time scale simulations. We first apply the scheme in studying the nonlinear Landau damping and two-stream instability. We have investigated the conservation property of the total mass, energy and entropy, and found that the IDO-CF scheme allows stable simulation over many bounce periods keeping higher accuracy than other multi-moment schemes. We have also developed a gyrokinetic full-f Vlasov code with the IDO-CF scheme in studying the slab ITG driven turbulence. [1] Y.Imai et al., J. Comput. Phys. 227, 2263(2008).
A numerical method for solving the Vlasov-Poisson equation based on the conservative IDO scheme
NASA Astrophysics Data System (ADS)
Imadera, Kenji; Kishimoto, Yasuaki; Saito, Daisuke; Li, Jiquan; Utsumi, Takayuki
2009-12-01
We have applied the conservative form of the Interpolated Differential Operator (IDO-CF) scheme in order to solve the Vlasov-Poisson equation, which is one of the multi-moment schemes. Through numerical tests of the nonlinear Landau damping and two-stream instability, we compared the present scheme with other schemes such as the Spline and CIP ones. We mainly investigated the conservation property of the L1-norm, energy, entropy and phase space area for each scheme, and demonstrated that the IDO-CF scheme is capable of performing stable long time scale simulation while maintaining high accuracy. The scheme is based on an Eulerian approach, and it can thus be directly used for Fokker-Planck, high dimensional Vlasov-Poisson and also guiding-center drift simulations, aiming at particular problems of plasma physics. The benchmark tests for such simulations have shown that the IDO-CF scheme is superior in keeping the conservation properties without causing serious phase error.
A conservative semi-Lagrangian HWENO method for the Vlasov equation
NASA Astrophysics Data System (ADS)
Cai, Xiaofeng; Qiu, Jianxian; Qiu, Jing-Mei
2016-10-01
In this paper, we propose a high order conservative semi-Lagrangian (SL) finite difference Hermite weighted essentially non-oscillatory (HWENO) method for the Vlasov equation based on dimensional splitting. HWENO was first proposed for solving nonlinear hyperbolic problems by evolving both function values and its first derivative values (Qiu and Shu (2004) [23]). The major advantage of HWENO, compared with the original WENO, lies in its compactness in reconstruction stencils. There are several new ingredients in this paper. Firstly we propose a mass-conservative SL HWENO scheme for a 1-D equation by working with a flux-difference form, following the work of Qiu and Christlieb (2010) [25]. Secondly, we propose a proper splitting for equations of partial derivatives in HWENO framework to ensure local mass conservation. The proposed fifth order SL HWENO scheme with dimensional splitting has been tested to work well in capturing filamentation structures without oscillations when the time step size is within the Eulerian CFL constraint. However, when the time stepping size becomes larger, numerical oscillations are observed for the 'mass conservative' dimensional splitting HWENO scheme, as there are extra source terms in equations of partial derivatives. In this case, we introduce WENO limiters to control oscillations. Classical numerical examples on linear passive transport problems, as well as the nonlinear Vlasov-Poisson system, have been tested to demonstrate the performance of the proposed scheme.
Numerical study of ion-cyclotron resonant interaction via hybrid-Vlasov simulations
Valentini, Francesco; Iazzolino, Antonio; Veltri, Pierluigi
2010-05-15
Hybrid Vlasov-Maxwell numerical simulations are used to investigate the collisionless resonant interaction of ions with ion-cyclotron waves in parallel propagation with respect to a background magnetic field. In linear regime, analytical results on wave damping, obtained by integrating the linearized Vlasov equation through the well-known characteristics method, are compared with the numerical results. Then, the ion heating process and the consequent generation of temperature anisotropy in the direction perpendicular to the background magnetic field are investigated numerically in detail. In nonlinear regime, the numerical results show that the distribution of particle velocities is strongly distorted due to the resonant ion-cyclotron interaction with the formation of diffusive plateaus in the longitudinal direction (with respect to the ambient field) and significantly departs from the Maxwellian equilibrium. These results are relevant in many plasma physics environments, such as the solar wind, where the process of ion-cyclotron heating and the generation of temperature anisotropy and non-Maxwellian velocity distributions are routinely recovered in many in situ measurements, or the laboratory plasmas, where the resonant interaction of ions with ion-cyclotron waves is the primary source of auxiliary heating in the confining apparatus.
Vlasov Simulations of Multi-ion Plasma Turbulence in the Solar Wind
NASA Astrophysics Data System (ADS)
Perrone, D.; Valentini, F.; Servidio, S.; Dalena, S.; Veltri, P.
2013-01-01
Hybrid Vlasov-Maxwell simulations are employed to investigate the role of kinetic effects in a two-dimensional turbulent multi-ion plasma, composed of protons, alpha particles, and fluid electrons. In the typical conditions of the solar-wind environment, and in situations of decaying turbulence, the numerical results show that the velocity distribution functions of both ion species depart from the typical configuration of thermal equilibrium. These non-Maxwellian features are quantified through the statistical analysis of the temperature anisotropy, for both protons and alpha particles, in the reference frame given by the local magnetic field. Anisotropy is found to be higher in regions of high magnetic stress. Both ion species manifest a preferentially perpendicular heating, although the anisotropy is more pronounced for the alpha particles, according to solar wind observations. The anisotropy of the alpha particle, moreover, is correlated to the proton anisotropy and also depends on the local differential flow between the two species. Evident distortions of the particle distribution functions are present, with the production of bumps along the direction of the local magnetic field. The physical phenomenology recovered in these numerical simulations reproduces very common measurements in the turbulent solar wind, suggesting that the multi-ion Vlasov model constitutes a valid approach to understanding the nature of complex kinetic effects in astrophysical plasmas.
A Fully-Implicit, Ion-Electron, Vlasov-Poisson Algorithm
NASA Astrophysics Data System (ADS)
Taitano, William; Knoll, Dana; Chacon, Luis
2010-11-01
The Jacobian-Free-Newton-Krylov method (JFNK) is an advanced non- linear alogorithm that allows solution to a coupled systems of non-linear equations [1]. We put forth a new JFNK-based implicit plasma simulation algorithm. We have studied this algorithm within the context of a two-species Vlasov-Poisson system where the Vlasov equations are solved in an Eulerian frame [2]. We have investigated the route of non-linear-elimination/kinetic- enslavement to reduce the size of block Jacobian matrix in order to solve the field-kinetic system implicitly. The non-linear- elimination/kinetic-enslavement technique allows reduction in the size of non-linear system but still retains high order temporal accuracy and strong non-linear coupling. Our new algorithm make implicit time-dependent, coupled, field-kinetic systems more attractive. As will be shown, a fully implicit run was able to achieve 22 times speed-up compared to the explicit run for our ion-acoustic-showckwave simulation [2].[4pt] [1] D.A. Knoll and D.E. Keyes, J. Comput. Phys. vol. 193 (2004)[0pt] [2] W.T. Taitano, Masters Thesis, Nuclear Engineering, University of Idaho (2010)
VLASOV SIMULATIONS OF MULTI-ION PLASMA TURBULENCE IN THE SOLAR WIND
Perrone, D.; Valentini, F.; Servidio, S.; Dalena, S.; Veltri, P.
2013-01-10
Hybrid Vlasov-Maxwell simulations are employed to investigate the role of kinetic effects in a two-dimensional turbulent multi-ion plasma, composed of protons, alpha particles, and fluid electrons. In the typical conditions of the solar-wind environment, and in situations of decaying turbulence, the numerical results show that the velocity distribution functions of both ion species depart from the typical configuration of thermal equilibrium. These non-Maxwellian features are quantified through the statistical analysis of the temperature anisotropy, for both protons and alpha particles, in the reference frame given by the local magnetic field. Anisotropy is found to be higher in regions of high magnetic stress. Both ion species manifest a preferentially perpendicular heating, although the anisotropy is more pronounced for the alpha particles, according to solar wind observations. The anisotropy of the alpha particle, moreover, is correlated to the proton anisotropy and also depends on the local differential flow between the two species. Evident distortions of the particle distribution functions are present, with the production of bumps along the direction of the local magnetic field. The physical phenomenology recovered in these numerical simulations reproduces very common measurements in the turbulent solar wind, suggesting that the multi-ion Vlasov model constitutes a valid approach to understanding the nature of complex kinetic effects in astrophysical plasmas.
Orthotropic Piezoelectricity in 2D Nanocellulose
NASA Astrophysics Data System (ADS)
García, Y.; Ruiz-Blanco, Yasser B.; Marrero-Ponce, Yovani; Sotomayor-Torres, C. M.
2016-10-01
The control of electromechanical responses within bonding regions is essential to face frontier challenges in nanotechnologies, such as molecular electronics and biotechnology. Here, we present Iβ-nanocellulose as a potentially new orthotropic 2D piezoelectric crystal. The predicted in-layer piezoelectricity is originated on a sui-generis hydrogen bonds pattern. Upon this fact and by using a combination of ab-initio and ad-hoc models, we introduce a description of electrical profiles along chemical bonds. Such developments lead to obtain a rationale for modelling the extended piezoelectric effect originated within bond scales. The order of magnitude estimated for the 2D Iβ-nanocellulose piezoelectric response, ~pm V‑1, ranks this material at the level of currently used piezoelectric energy generators and new artificial 2D designs. Such finding would be crucial for developing alternative materials to drive emerging nanotechnologies.
Orthotropic Piezoelectricity in 2D Nanocellulose
García, Y.; Ruiz-Blanco, Yasser B.; Marrero-Ponce, Yovani; Sotomayor-Torres, C. M.
2016-01-01
The control of electromechanical responses within bonding regions is essential to face frontier challenges in nanotechnologies, such as molecular electronics and biotechnology. Here, we present Iβ-nanocellulose as a potentially new orthotropic 2D piezoelectric crystal. The predicted in-layer piezoelectricity is originated on a sui-generis hydrogen bonds pattern. Upon this fact and by using a combination of ab-initio and ad-hoc models, we introduce a description of electrical profiles along chemical bonds. Such developments lead to obtain a rationale for modelling the extended piezoelectric effect originated within bond scales. The order of magnitude estimated for the 2D Iβ-nanocellulose piezoelectric response, ~pm V−1, ranks this material at the level of currently used piezoelectric energy generators and new artificial 2D designs. Such finding would be crucial for developing alternative materials to drive emerging nanotechnologies. PMID:27708364
2D microwave imaging reflectometer electronics
Spear, A. G.; Domier, C. W. Hu, X.; Muscatello, C. M.; Ren, X.; Luhmann, N. C.; Tobias, B. J.
2014-11-15
A 2D microwave imaging reflectometer system has been developed to visualize electron density fluctuations on the DIII-D tokamak. Simultaneously illuminated at four probe frequencies, large aperture optics image reflections from four density-dependent cutoff surfaces in the plasma over an extended region of the DIII-D plasma. Localized density fluctuations in the vicinity of the plasma cutoff surfaces modulate the plasma reflections, yielding a 2D image of electron density fluctuations. Details are presented of the receiver down conversion electronics that generate the in-phase (I) and quadrature (Q) reflectometer signals from which 2D density fluctuation data are obtained. Also presented are details on the control system and backplane used to manage the electronics as well as an introduction to the computer based control program.
Optical modulators with 2D layered materials
NASA Astrophysics Data System (ADS)
Sun, Zhipei; Martinez, Amos; Wang, Feng
2016-04-01
Light modulation is an essential operation in photonics and optoelectronics. With existing and emerging technologies increasingly demanding compact, efficient, fast and broadband optical modulators, high-performance light modulation solutions are becoming indispensable. The recent realization that 2D layered materials could modulate light with superior performance has prompted intense research and significant advances, paving the way for realistic applications. In this Review, we cover the state of the art of optical modulators based on 2D materials, including graphene, transition metal dichalcogenides and black phosphorus. We discuss recent advances employing hybrid structures, such as 2D heterostructures, plasmonic structures, and silicon and fibre integrated structures. We also take a look at the future perspectives and discuss the potential of yet relatively unexplored mechanisms, such as magneto-optic and acousto-optic modulation.
NASA Technical Reports Server (NTRS)
Reddy, T. S. R.; Srivastava, R.; Mehmed, Oral
2002-01-01
An aeroelastic analysis system for flutter and forced response analysis of turbomachines based on a two-dimensional linearized unsteady Euler solver has been developed. The ASTROP2 code, an aeroelastic stability analysis program for turbomachinery, was used as a basis for this development. The ASTROP2 code uses strip theory to couple a two dimensional aerodynamic model with a three dimensional structural model. The code was modified to include forced response capability. The formulation was also modified to include aeroelastic analysis with mistuning. A linearized unsteady Euler solver, LINFLX2D is added to model the unsteady aerodynamics in ASTROP2. By calculating the unsteady aerodynamic loads using LINFLX2D, it is possible to include the effects of transonic flow on flutter and forced response in the analysis. The stability is inferred from an eigenvalue analysis. The revised code, ASTROP2-LE for ASTROP2 code using Linearized Euler aerodynamics, is validated by comparing the predictions with those obtained using linear unsteady aerodynamic solutions.
Inkjet printing of 2D layered materials.
Li, Jiantong; Lemme, Max C; Östling, Mikael
2014-11-10
Inkjet printing of 2D layered materials, such as graphene and MoS2, has attracted great interests for emerging electronics. However, incompatible rheology, low concentration, severe aggregation and toxicity of solvents constitute critical challenges which hamper the manufacturing efficiency and product quality. Here, we introduce a simple and general technology concept (distillation-assisted solvent exchange) to efficiently overcome these challenges. By implementing the concept, we have demonstrated excellent jetting performance, ideal printing patterns and a variety of promising applications for inkjet printing of 2D layered materials. PMID:25169938
Inkjet printing of 2D layered materials.
Li, Jiantong; Lemme, Max C; Östling, Mikael
2014-11-10
Inkjet printing of 2D layered materials, such as graphene and MoS2, has attracted great interests for emerging electronics. However, incompatible rheology, low concentration, severe aggregation and toxicity of solvents constitute critical challenges which hamper the manufacturing efficiency and product quality. Here, we introduce a simple and general technology concept (distillation-assisted solvent exchange) to efficiently overcome these challenges. By implementing the concept, we have demonstrated excellent jetting performance, ideal printing patterns and a variety of promising applications for inkjet printing of 2D layered materials.
Extension and application of the Preissmann slot model to 2D transient mixed flows
NASA Astrophysics Data System (ADS)
Maranzoni, Andrea; Dazzi, Susanna; Aureli, Francesca; Mignosa, Paolo
2015-08-01
This paper presents an extension of the Preissmann slot concept for the modeling of highly transient two-dimensional (2D) mixed flows. The classic conservative formulation of the 2D shallow water equations for free surface flows is adapted by assuming that two fictitious vertical slots, aligned along the two Cartesian plane directions and normally intersecting, are added on the ceiling of each integration element. Accordingly, transitions between free surface and pressurized flow can be handled in a natural and straightforward way by using the same set of governing equations. The opportunity of coupling free surface and pressurized flows is actually useful not only in one-dimensional (1D) problems concerning sewer systems but also for modeling 2D flooding phenomena in which the pressurization of bridges, culverts, or other crossing hydraulic structures can be expected. Numerical simulations are performed by using a shock-capturing MUSCL-Hancock finite volume scheme combined with the FORCE (First-Order Centred) solver for the evaluation of the numerical fluxes. The validation of the mathematical model is accomplished on the basis of both exact solutions of 1D discontinuous initial value problems and reference radial solutions of idealized test cases with cylindrical symmetry. Furthermore, the capability of the model to deal with practical field-scale applications is assessed by simulating the transit of a bore under an arch bridge. Numerical results show that the proposed model is suitable for the prediction of highly transient 2D mixed flows.
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.
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.
NASA Astrophysics Data System (ADS)
Berger, Richard
2014-10-01
Vlasov simulations of large amplitude electron plasma waves (EPWs), which play an essential role in laser-fusion relevant plasmas, have been carried out in 1D and 2D and compared with theoretical models. The electrons trapped in the wave troughs are shown to be well described by an ``adiabatic'' distribution with a corresponding frequency shift of the EPW. Trapped particles play an essential role in the mechanisms underlying sideband instabilities that may affect the EPW, in particular longitudinal instabilities of trapped particle instability (TPI) type, as well as transverse instabilities of kinetic filamentation type. A systematic study of the spectrum of linearly unstable modes in 1D and 2D systems, including their growth rates and wavevectors, has been completed by scanning the amplitude and wavenumber of the initial wave. Simulation results for the TPI are successfully compared with Kruer's reduced model and are also analyzed for the development of the ``negative mass instability''. In the non-linear phase, both the TPI and filamentation instabilities are shown to lead to a rapid loss of field energy and an associated increase in electron kinetic energy. Saturation of the instabilities is reached in conjunction with the development of significant regions in phase space where trajectories of particles, resonant with the initial wave, become chaotic. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and funded by the Laboratory Research and Development Program at LLNL under project tracking code 12-ERD.
Pareto joint inversion of 2D magnetotelluric and gravity data
NASA Astrophysics Data System (ADS)
Miernik, Katarzyna; Bogacz, Adrian; Kozubal, Adam; Danek, Tomasz; Wojdyła, Marek
2015-04-01
In this contribution, the first results of the "Innovative technology of petrophysical parameters estimation of geological media using joint inversion algorithms" project were described. At this stage of the development, Pareto joint inversion scheme for 2D MT and gravity data was used. Additionally, seismic data were provided to set some constrains for the inversion. Sharp Boundary Interface(SBI) approach and description model with set of polygons were used to limit the dimensionality of the solution space. The main engine was based on modified Particle Swarm Optimization(PSO). This algorithm was properly adapted to handle two or more target function at once. Additional algorithm was used to eliminate non- realistic solution proposals. Because PSO is a method of stochastic global optimization, it requires a lot of proposals to be evaluated to find a single Pareto solution and then compose a Pareto front. To optimize this stage parallel computing was used for both inversion engine and 2D MT forward solver. There are many advantages of proposed solution of joint inversion problems. First of all, Pareto scheme eliminates cumbersome rescaling of the target functions, that can highly affect the final solution. Secondly, the whole set of solution is created in one optimization run, providing a choice of the final solution. This choice can be based off qualitative data, that are usually very hard to be incorporated into the regular inversion schema. SBI parameterisation not only limits the problem of dimensionality, but also makes constraining of the solution easier. At this stage of work, decision to test the approach using MT and gravity data was made, because this combination is often used in practice. It is important to mention, that the general solution is not limited to this two methods and it is flexible enough to be used with more than two sources of data. Presented results were obtained for synthetic models, imitating real geological conditions, where
Parallel stitching of 2D materials
Ling, Xi; Wu, Lijun; Lin, Yuxuan; Ma, Qiong; Wang, Ziqiang; Song, Yi; Yu, Lili; Huang, Shengxi; Fang, Wenjing; Zhang, Xu; et al
2016-01-27
Diverse parallel stitched 2D heterostructures, including metal–semiconductor, semiconductor–semiconductor, and insulator–semiconductor, are synthesized directly through selective “sowing” of aromatic molecules as the seeds in the chemical vapor deposition (CVD) method. Lastly, the methodology enables the large-scale fabrication of lateral heterostructures, which offers tremendous potential for its application in integrated circuits.
Parallel Stitching of 2D Materials.
Ling, Xi; Lin, Yuxuan; Ma, Qiong; Wang, Ziqiang; Song, Yi; Yu, Lili; Huang, Shengxi; Fang, Wenjing; Zhang, Xu; Hsu, Allen L; Bie, Yaqing; Lee, Yi-Hsien; Zhu, Yimei; Wu, Lijun; Li, Ju; Jarillo-Herrero, Pablo; Dresselhaus, Mildred; Palacios, Tomás; Kong, Jing
2016-03-23
Diverse parallel stitched 2D heterostructures, including metal-semiconductor, semiconductor-semiconductor, and insulator-semiconductor, are synthesized directly through selective "sowing" of aromatic molecules as the seeds in the chemical vapor deposition (CVD) method. The methodology enables the large-scale fabrication of lateral heterostructures, which offers tremendous potential for its application in integrated circuits.
Stability and accuracy of 3D neutron transport simulations using the 2D/1D method in MPACT
Collins, Benjamin; Stimpson, Shane; Kelley, Blake W.; Young, Mitchell T. H.; Kochunas, Brendan; Graham, Aaron; Larsen, Edward W.; Downar, Thomas; Godfrey, Andrew
2016-08-25
We derived a consistent “2D/1D” neutron transport method from the 3D Boltzmann transport equation, to calculate fuel-pin-resolved neutron fluxes for realistic full-core Pressurized Water Reactor (PWR) problems. The 2D/1D method employs the Method of Characteristics to discretize the radial variables and a lower order transport solution to discretize the axial variable. Our paper describes the theory of the 2D/1D method and its implementation in the MPACT code, which has become the whole-core deterministic neutron transport solver for the Consortium for Advanced Simulations of Light Water Reactors (CASL) core simulator VERA-CS. We also performed several applications on both leadership-class and industry-classmore » computing clusters. Results are presented for whole-core solutions of the Watts Bar Nuclear Power Station Unit 1 and compared to both continuous-energy Monte Carlo results and plant data.« less
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.
jShyLU Scalable Hybrid Preconditioner and Solver
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.
Application of 2D Non-Graphene Materials and 2D Oxide Nanostructures for Biosensing Technology
Shavanova, Kateryna; Bakakina, Yulia; Burkova, Inna; Shtepliuk, Ivan; Viter, Roman; Ubelis, Arnolds; Beni, Valerio; Starodub, Nickolaj; Yakimova, Rositsa; Khranovskyy, Volodymyr
2016-01-01
The discovery of graphene and its unique properties has inspired researchers to try to invent other two-dimensional (2D) materials. After considerable research effort, a distinct “beyond graphene” domain has been established, comprising the library of non-graphene 2D materials. It is significant that some 2D non-graphene materials possess solid advantages over their predecessor, such as having a direct band gap, and therefore are highly promising for a number of applications. These applications are not limited to nano- and opto-electronics, but have a strong potential in biosensing technologies, as one example. However, since most of the 2D non-graphene materials have been newly discovered, most of the research efforts are concentrated on material synthesis and the investigation of the properties of the material. Applications of 2D non-graphene materials are still at the embryonic stage, and the integration of 2D non-graphene materials into devices is scarcely reported. However, in recent years, numerous reports have blossomed about 2D material-based biosensors, evidencing the growing potential of 2D non-graphene materials for biosensing applications. This review highlights the recent progress in research on the potential of using 2D non-graphene materials and similar oxide nanostructures for different types of biosensors (optical and electrochemical). A wide range of biological targets, such as glucose, dopamine, cortisol, DNA, IgG, bisphenol, ascorbic acid, cytochrome and estradiol, has been reported to be successfully detected by biosensors with transducers made of 2D non-graphene materials. PMID:26861346
Application of 2D Non-Graphene Materials and 2D Oxide Nanostructures for Biosensing Technology.
Shavanova, Kateryna; Bakakina, Yulia; Burkova, Inna; Shtepliuk, Ivan; Viter, Roman; Ubelis, Arnolds; Beni, Valerio; Starodub, Nickolaj; Yakimova, Rositsa; Khranovskyy, Volodymyr
2016-01-01
The discovery of graphene and its unique properties has inspired researchers to try to invent other two-dimensional (2D) materials. After considerable research effort, a distinct "beyond graphene" domain has been established, comprising the library of non-graphene 2D materials. It is significant that some 2D non-graphene materials possess solid advantages over their predecessor, such as having a direct band gap, and therefore are highly promising for a number of applications. These applications are not limited to nano- and opto-electronics, but have a strong potential in biosensing technologies, as one example. However, since most of the 2D non-graphene materials have been newly discovered, most of the research efforts are concentrated on material synthesis and the investigation of the properties of the material. Applications of 2D non-graphene materials are still at the embryonic stage, and the integration of 2D non-graphene materials into devices is scarcely reported. However, in recent years, numerous reports have blossomed about 2D material-based biosensors, evidencing the growing potential of 2D non-graphene materials for biosensing applications. This review highlights the recent progress in research on the potential of using 2D non-graphene materials and similar oxide nanostructures for different types of biosensors (optical and electrochemical). A wide range of biological targets, such as glucose, dopamine, cortisol, DNA, IgG, bisphenol, ascorbic acid, cytochrome and estradiol, has been reported to be successfully detected by biosensors with transducers made of 2D non-graphene materials.
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 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.
Parallel solver for trajectory optimization search directions
NASA Technical Reports Server (NTRS)
Psiaki, M. L.; Park, K. H.
1992-01-01
A key algorithmic element of a real-time trajectory optimization hardware/software implementation is presented, the search step solver. This is one piece of an algorithm whose overall goal is to make nonlinear trajectory optimization fast enough to provide real-time commands during guidance of a vehicle such as an aeromaneuvering orbiter or the National Aerospace Plane. Many methods of nonlinear programming require the solution of a quadratic program (QP) at each iteration to determine the search step. In the trajectory optimization case, the QP has a special dynamic programming structure. The algorithm exploits this special structure with a divide- and conquer type of parallel implementation. The algorithm solves a (p.N)-stage problem on N processors in O(p + log2 N) operations. The algorithm yields a factor of 8 speed-up over the fastest known serial algorithm when solving a 1024-stage test problem on 32 processors.
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.
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].
Stochastic Inversion of 2D Magnetotelluric Data
Chen, Jinsong
2010-07-01
The algorithm is developed to invert 2D magnetotelluric (MT) data based on sharp boundary parametrization using a Bayesian framework. Within the algorithm, we consider the locations and the resistivity of regions formed by the interfaces are as unknowns. We use a parallel, adaptive finite-element algorithm to forward simulate frequency-domain MT responses of 2D conductivity structure. Those unknown parameters are spatially correlated and are described by a geostatistical model. The joint posterior probability distribution function is explored by Markov Chain Monte Carlo (MCMC) sampling methods. The developed stochastic model is effective for estimating the interface locations and resistivity. Most importantly, it provides details uncertainty information on each unknown parameter. Hardware requirements: PC, Supercomputer, Multi-platform, Workstation; Software requirements C and Fortan; Operation Systems/version is Linux/Unix or Windows
Explicit 2-D Hydrodynamic FEM Program
1996-08-07
DYNA2D* is a vectorized, explicit, two-dimensional, axisymmetric and plane strain finite element program for analyzing the large deformation dynamic and hydrodynamic response of inelastic solids. DYNA2D* contains 13 material models and 9 equations of state (EOS) to cover a wide range of material behavior. The material models implemented in all machine versions are: elastic, orthotropic elastic, kinematic/isotropic elastic plasticity, thermoelastoplastic, soil and crushable foam, linear viscoelastic, rubber, high explosive burn, isotropic elastic-plastic, temperature-dependent elastic-plastic. Themore » isotropic and temperature-dependent elastic-plastic models determine only the deviatoric stresses. Pressure is determined by one of 9 equations of state including linear polynomial, JWL high explosive, Sack Tuesday high explosive, Gruneisen, ratio of polynomials, linear polynomial with energy deposition, ignition and growth of reaction in HE, tabulated compaction, and tabulated.« less
Stochastic Inversion of 2D Magnetotelluric Data
2010-07-01
The algorithm is developed to invert 2D magnetotelluric (MT) data based on sharp boundary parametrization using a Bayesian framework. Within the algorithm, we consider the locations and the resistivity of regions formed by the interfaces are as unknowns. We use a parallel, adaptive finite-element algorithm to forward simulate frequency-domain MT responses of 2D conductivity structure. Those unknown parameters are spatially correlated and are described by a geostatistical model. The joint posterior probability distribution function ismore » explored by Markov Chain Monte Carlo (MCMC) sampling methods. The developed stochastic model is effective for estimating the interface locations and resistivity. Most importantly, it provides details uncertainty information on each unknown parameter. Hardware requirements: PC, Supercomputer, Multi-platform, Workstation; Software requirements C and Fortan; Operation Systems/version is Linux/Unix or Windows« less
Static & Dynamic Response of 2D Solids
1996-07-15
NIKE2D is an implicit finite-element code for analyzing the finite deformation, static and dynamic response of two-dimensional, axisymmetric, plane strain, and plane stress solids. The code is fully vectorized and available on several computing platforms. A number of material models are incorporated to simulate a wide range of material behavior including elasto-placicity, anisotropy, creep, thermal effects, and rate dependence. Slideline algorithms model gaps and sliding along material interfaces, including interface friction, penetration and single surfacemore » contact. Interactive-graphics and rezoning is included for analyses with large mesh distortions. In addition to quasi-Newton and arc-length procedures, adaptive algorithms can be defined to solve the implicit equations using the solution language ISLAND. Each of these capabilities and more make NIKE2D a robust analysis tool.« less
Static & Dynamic Response of 2D Solids
Lin, Jerry
1996-07-15
NIKE2D is an implicit finite-element code for analyzing the finite deformation, static and dynamic response of two-dimensional, axisymmetric, plane strain, and plane stress solids. The code is fully vectorized and available on several computing platforms. A number of material models are incorporated to simulate a wide range of material behavior including elasto-placicity, anisotropy, creep, thermal effects, and rate dependence. Slideline algorithms model gaps and sliding along material interfaces, including interface friction, penetration and single surface contact. Interactive-graphics and rezoning is included for analyses with large mesh distortions. In addition to quasi-Newton and arc-length procedures, adaptive algorithms can be defined to solve the implicit equations using the solution language ISLAND. Each of these capabilities and more make NIKE2D a robust analysis tool.
Explicit 2-D Hydrodynamic FEM Program
Lin, Jerry
1996-08-07
DYNA2D* is a vectorized, explicit, two-dimensional, axisymmetric and plane strain finite element program for analyzing the large deformation dynamic and hydrodynamic response of inelastic solids. DYNA2D* contains 13 material models and 9 equations of state (EOS) to cover a wide range of material behavior. The material models implemented in all machine versions are: elastic, orthotropic elastic, kinematic/isotropic elastic plasticity, thermoelastoplastic, soil and crushable foam, linear viscoelastic, rubber, high explosive burn, isotropic elastic-plastic, temperature-dependent elastic-plastic. The isotropic and temperature-dependent elastic-plastic models determine only the deviatoric stresses. Pressure is determined by one of 9 equations of state including linear polynomial, JWL high explosive, Sack Tuesday high explosive, Gruneisen, ratio of polynomials, linear polynomial with energy deposition, ignition and growth of reaction in HE, tabulated compaction, and tabulated.
2D photonic-crystal optomechanical nanoresonator.
Makles, K; Antoni, T; Kuhn, A G; Deléglise, S; Briant, T; Cohadon, P-F; Braive, R; Beaudoin, G; Pinard, L; Michel, C; Dolique, V; Flaminio, R; Cagnoli, G; Robert-Philip, I; Heidmann, A
2015-01-15
We present the optical optimization of an optomechanical device based on a suspended InP membrane patterned with a 2D near-wavelength grating (NWG) based on a 2D photonic-crystal geometry. We first identify by numerical simulation a set of geometrical parameters providing a reflectivity higher than 99.8% over a 50-nm span. We then study the limitations induced by the finite value of the optical waist and lateral size of the NWG pattern using different numerical approaches. The NWG grating, pierced in a suspended InP 265-nm thick membrane, is used to form a compact microcavity involving the suspended nanomembrane as an end mirror. The resulting cavity has a waist size smaller than 10 μm and a finesse in the 200 range. It is used to probe the Brownian motion of the mechanical modes of the nanomembrane. PMID:25679837
NASA Astrophysics Data System (ADS)
Liu, Yan; Shen, Weidong; Tian, Baolin; Mao, De-kang
2015-03-01
We develop a new and more general formula for the construction of two dimensional nodal Riemann solver for a cell-centered Lagrangian scheme developed by Maire and his co-workers which allows us to use general one dimensional Riemann solvers that have intermediate velocity and pressure in the construction. The old formula for the scheme used in the papers of Maire et al. is only a special case of our new formula. We present an entropy discussion, which indicates that the schemes with nodal solvers constructed following the old formula, which can only use the 1D Riemann solvers satisfying our strong entropy condition, are usually numerically very dissipative. To develop numerically less dissipative schemes we introduce a so-called weak entropy condition, and present a one dimensional Riemann solver that satisfies the weak entropy condition but not the strong entropy condition. Analysis shows that the scheme using this 1D solver is numerically less dissipative than the schemes using solvers satisfying the strong condition. Finally, several numerical examples are presented to show that our new formula works well and the scheme using the one dimensional solver satisfying the weak entropy condition improves the accuracy in smooth region, resolution around rarefaction waves and two dimensional symmetry; however it sometimes produces small velocity oscillations and mesh distortions.
Compact 2-D graphical representation of DNA
NASA Astrophysics Data System (ADS)
Randić, Milan; Vračko, Marjan; Zupan, Jure; Novič, Marjana
2003-05-01
We present a novel 2-D graphical representation for DNA sequences which has an important advantage over the existing graphical representations of DNA in being very compact. It is based on: (1) use of binary labels for the four nucleic acid bases, and (2) use of the 'worm' curve as template on which binary codes are placed. The approach is illustrated on DNA sequences of the first exon of human β-globin and gorilla β-globin.
2D materials: Graphene and others
NASA Astrophysics Data System (ADS)
Bansal, Suneev Anil; Singh, Amrinder Pal; Kumar, Suresh
2016-05-01
Present report reviews the recent advancements in new atomically thick 2D materials. Materials covered in this review are Graphene, Silicene, Germanene, Boron Nitride (BN) and Transition metal chalcogenides (TMC). These materials show extraordinary mechanical, electronic and optical properties which make them suitable candidates for future applications. Apart from unique properties, tune-ability of highly desirable properties of these materials is also an important area to be emphasized on.
Layer Engineering of 2D Semiconductor Junctions.
He, Yongmin; Sobhani, Ali; Lei, Sidong; Zhang, Zhuhua; Gong, Yongji; Jin, Zehua; Zhou, Wu; Yang, Yingchao; Zhang, Yuan; Wang, Xifan; Yakobson, Boris; Vajtai, Robert; Halas, Naomi J; Li, Bo; Xie, Erqing; Ajayan, Pulickel
2016-07-01
A new concept for junction fabrication by connecting multiple regions with varying layer thicknesses, based on the thickness dependence, is demonstrated. This type of junction is only possible in super-thin-layered 2D materials, and exhibits similar characteristics as p-n junctions. Rectification and photovoltaic effects are observed in chemically homogeneous MoSe2 junctions between domains of different thicknesses. PMID:27136275
Realistic and efficient 2D crack simulation
NASA Astrophysics Data System (ADS)
Yadegar, Jacob; Liu, Xiaoqing; Singh, Abhishek
2010-04-01
Although numerical algorithms for 2D crack simulation have been studied in Modeling and Simulation (M&S) and computer graphics for decades, realism and computational efficiency are still major challenges. In this paper, we introduce a high-fidelity, scalable, adaptive and efficient/runtime 2D crack/fracture simulation system by applying the mathematically elegant Peano-Cesaro triangular meshing/remeshing technique to model the generation of shards/fragments. The recursive fractal sweep associated with the Peano-Cesaro triangulation provides efficient local multi-resolution refinement to any level-of-detail. The generated binary decomposition tree also provides efficient neighbor retrieval mechanism used for mesh element splitting and merging with minimal memory requirements essential for realistic 2D fragment formation. Upon load impact/contact/penetration, a number of factors including impact angle, impact energy, and material properties are all taken into account to produce the criteria of crack initialization, propagation, and termination leading to realistic fractal-like rubble/fragments formation. The aforementioned parameters are used as variables of probabilistic models of cracks/shards formation, making the proposed solution highly adaptive by allowing machine learning mechanisms learn the optimal values for the variables/parameters based on prior benchmark data generated by off-line physics based simulation solutions that produce accurate fractures/shards though at highly non-real time paste. Crack/fracture simulation has been conducted on various load impacts with different initial locations at various impulse scales. The simulation results demonstrate that the proposed system has the capability to realistically and efficiently simulate 2D crack phenomena (such as window shattering and shards generation) with diverse potentials in military and civil M&S applications such as training and mission planning.
2D Spinodal Decomposition in Forced Turbulence
NASA Astrophysics Data System (ADS)
Fan, Xiang; Diamond, Patrick; Chacon, Luis; Li, Hui
2015-11-01
Spinodal decomposition is a second order phase transition for binary fluid mixture, from one thermodynamic phase to form two coexisting phases. The governing equation for this coarsening process below critical temperature, Cahn-Hilliard Equation, is very similar to 2D MHD Equation, especially the conserved quantities have a close correspondence between each other, so theories for MHD turbulence are used to study spinodal decomposition in forced turbulence. Domain size is increased with time along with the inverse cascade, and the length scale can be arrested by a forced turbulence with direct cascade. The two competing mechanisms lead to a stabilized domain size length scale, which can be characterized by Hinze Scale. The 2D spinodal decomposition in forced turbulence is studied by both theory and simulation with ``pixie2d.'' This work focuses on the relation between Hinze scale and spectra and cascades. Similarities and differences between spinodal decomposition and MHD are investigated. Also some transport properties are studied following MHD theories. This work is supported by the Department of Energy under Award Number DE-FG02-04ER54738.
MAGNUM-2D computer code: user's guide
England, R.L.; Kline, N.W.; Ekblad, K.J.; Baca, R.G.
1985-01-01
Information relevant to the general use of the MAGNUM-2D computer code is presented. This computer code was developed for the purpose of modeling (i.e., simulating) the thermal and hydraulic conditions in the vicinity of a waste package emplaced in a deep geologic repository. The MAGNUM-2D computer computes (1) the temperature field surrounding the waste package as a function of the heat generation rate of the nuclear waste and thermal properties of the basalt and (2) the hydraulic head distribution and associated groundwater flow fields as a function of the temperature gradients and hydraulic properties of the basalt. MAGNUM-2D is a two-dimensional numerical model for transient or steady-state analysis of coupled heat transfer and groundwater flow in a fractured porous medium. The governing equations consist of a set of coupled, quasi-linear partial differential equations that are solved using a Galerkin finite-element technique. A Newton-Raphson algorithm is embedded in the Galerkin functional to formulate the problem in terms of the incremental changes in the dependent variables. Both triangular and quadrilateral finite elements are used to represent the continuum portions of the spatial domain. Line elements may be used to represent discrete conduits. 18 refs., 4 figs., 1 tab.
Engineering light outcoupling in 2D materials.
Lien, Der-Hsien; Kang, Jeong Seuk; Amani, Matin; Chen, Kevin; Tosun, Mahmut; Wang, Hsin-Ping; Roy, Tania; Eggleston, Michael S; Wu, Ming C; Dubey, Madan; Lee, Si-Chen; He, Jr-Hau; Javey, Ali
2015-02-11
When light is incident on 2D transition metal dichalcogenides (TMDCs), it engages in multiple reflections within underlying substrates, producing interferences that lead to enhancement or attenuation of the incoming and outgoing strength of light. Here, we report a simple method to engineer the light outcoupling in semiconducting TMDCs by modulating their dielectric surroundings. We show that by modulating the thicknesses of underlying substrates and capping layers, the interference caused by substrate can significantly enhance the light absorption and emission of WSe2, resulting in a ∼11 times increase in Raman signal and a ∼30 times increase in the photoluminescence (PL) intensity of WSe2. On the basis of the interference model, we also propose a strategy to control the photonic and optoelectronic properties of thin-layer WSe2. This work demonstrates the utilization of outcoupling engineering in 2D materials and offers a new route toward the realization of novel optoelectronic devices, such as 2D LEDs and solar cells.
The general Lie group and similarity solutions for the one-dimensional Vlasov-Maxwell equations
NASA Technical Reports Server (NTRS)
Roberts, D.
1985-01-01
The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov-Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multispecies case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution for a one-species, one-dimensional plasma is one of the general similarity solutions.
Ghizzo, A.
2013-08-15
The saturation of the Weibel instability in the relativistic regime is investigated within the Hamiltonian reduction technique based on the multistream approach developed in paper I in the linear case and in paper II for the nonlinear saturation. In this work, the study is compared with results obtained by full kinetic 1D2V Vlasov-Maxwell simulations based on a semi-Lagrangian technique. For a temperature anisotropy, qualitatively different regimes are realized depending on the excitation of the longitudinal (plasma) electric field, in contrast with the existing theories of the Weibel instability based on their purely transverse characters. The emphasis here is on gaining a better understanding of the nonlinear aspects of the Weibel instability. The multistream model offers an alternate way to make calculations or numerical experiments more tractable, when only a few moments of the velocity distribution of the plasma are considered.
Behjat, E.; Aminmansoor, F.; Abbasi, H.
2015-08-15
Disintegration of a Gaussian profile into ion-acoustic solitons in the presence of trapped electrons [H. Hakimi Pajouh and H. Abbasi, Phys. Plasmas 15, 082105 (2008)] is revisited. Through a hybrid (Vlasov-Fluid) model, the restrictions associated with the simple modified Korteweg de-Vries (mKdV) model are studied. For instance, the lack of vital information in the phase space associated with the evolution of electron velocity distribution, the perturbative nature of mKdV model which limits it to the weak nonlinear cases, and the special spatio-temporal scaling based on which the mKdV is derived. Remarkable differences between the results of the two models lead us to conclude that the mKdV model can only monitor the general aspects of the dynamics, and the precise picture including the correct spatio-temporal scales and the properties of solitons should be studied within the framework of hybrid model.
The Fractional Kinetic Einstein-Vlasov System and its Implications in Bianchi Spacetimes Geometry
NASA Astrophysics Data System (ADS)
El-Nabulsi, Rami Ahmad
2014-08-01
The main purpose of this work is to introduce the basic concepts and global properties of the fractional Einstein-Vlasov equation based on the fractional calculus of variations, mainly the fractional actionlike variational approach. We believe that kinetic theory in non-curved spacetimes is fundamental to a good understanding of kinetic theory in general relativity. Besides, the fractional calculus of variations has proved recently to be an important mathematical field of research which has been applied successfully to a broad range of physical and mathematical researches. We expect therefore that the merge of both fields will bring some new insights to general relativity and accordingly to its cosmological and astrophysical implications. Based on the new fractional settings, some cosmological applications are discussed in this work mainly within the aspects of Bianchi spacetimes geometry.
Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations
NASA Astrophysics Data System (ADS)
He, Yang; Sun, Yajuan; Qin, Hong; Liu, Jian
2016-09-01
In this paper, we study the Vlasov-Maxwell equations based on the Morrison-Marsden-Weinstein bracket. We develop Hamiltonian particle-in-cell methods for this system by employing finite element methods in space and splitting methods in time. In order to derive the semi-discrete system that possesses a discrete non-canonical Poisson structure, we present a criterion for choosing the appropriate finite element spaces. It is confirmed that some conforming elements, e.g., Nédélec's mixed elements, satisfy this requirement. When the Hamiltonian splitting method is used to discretize this semi-discrete system in time, the resulting algorithm is explicit and preserves the discrete Poisson structure. The structure-preserving nature of the algorithm ensures accuracy and fidelity of the numerical simulations over long time.
Squire, J.; Tang, W. M.; Qin, H.; Chandre, C.
2013-02-15
We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in H. Cendra et al., [J. Math. Phys. 39, 3138 (1998)]. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with a modified Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincare theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models, and Casimir type stability methods.
Vlasov simulations of plasma-wall interactions in a magnetized and weakly collisional plasma
Devaux, S.; Manfredi, G.
2006-08-15
A Vlasov code is used to model the transition region between an equilibrium plasma and an absorbing wall in the presence of a tilted magnetic field, for the case of a weakly collisional plasma ({lambda}{sub mfp}>>{rho}{sub i}, where {lambda}{sub mfp} is the ion-neutral mean-free path and {rho}{sub i} is the ion Larmor radius). The phase space structure of the plasma-wall transition is analyzed in detail and theoretical estimates of the magnetic presheath width are tested numerically. It is shown that the distribution near the wall is far from Maxwellian, so that temperature measurements should be interpreted with care. Particular attention is devoted to the angular distribution of ions impinging on the wall, which is an important parameter to determine the level of wall erosion and sputtering.
NASA Technical Reports Server (NTRS)
Kan, J. R.
1972-01-01
A model of equilibrium configurations of Vlasov plasmas is considered which represents a combination of the models of Harris (1962) and Nicholson (1963). These plasma configurations carry a current component along an external magnetic field. The considered slab model contains a diamagnetic current and a field-aligned current for an arbitrary ratio of particle pressure to magnetic pressure of the applied constant field. For a fixed pressure ratio and field-aligned current, the model admits a family of equilibrium solutions in which the diamagnetic currents range from zero to a maximum value. The amount of diamagnetic current flowing in a machine depends on the width of the machine, the field-aligned current and other plasma parameters.
Vlasov simulations of kinetic Alfvén waves at proton kinetic scales
Vásconez, C. L.; Valentini, F.; Veltri, P.; Camporeale, E.
2014-11-15
Kinetic Alfvén waves represent an important subject in space plasma physics, since they are thought to play a crucial role in the development of the turbulent energy cascade in the solar wind plasma at short wavelengths (of the order of the proton gyro radius ρ{sub p} and/or inertial length d{sub p} and beyond). A full understanding of the physical mechanisms which govern the kinetic plasma dynamics at these scales can provide important clues on the problem of the turbulent dissipation and heating in collisionless systems. In this paper, hybrid Vlasov-Maxwell simulations are employed to analyze in detail the features of the kinetic Alfvén waves at proton kinetic scales, in typical conditions of the solar wind environment (proton plasma beta β{sub p} = 1). In particular, linear and nonlinear regimes of propagation of these fluctuations have been investigated in a single-wave situation, focusing on the physical processes of collisionless Landau damping and wave-particle resonant interaction. Interestingly, since for wavelengths close to d{sub p} and β{sub p} ≃ 1 (for which ρ{sub p} ≃ d{sub p}) the kinetic Alfvén waves have small phase speed compared to the proton thermal velocity, wave-particle interaction processes produce significant deformations in the core of the particle velocity distribution, appearing as phase space vortices and resulting in flat-top velocity profiles. Moreover, as the Eulerian hybrid Vlasov-Maxwell algorithm allows for a clean almost noise-free description of the velocity space, three-dimensional plots of the proton velocity distribution help to emphasize how the plasma departs from the Maxwellian configuration of thermodynamic equilibrium due to nonlinear kinetic effects.
Comparison of open-source linear programming solvers.
Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.; 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.
GBL-2D Version 1.0: a 2D geometry boolean library.
McBride, Cory L. (Elemental Technologies, American Fort, UT); Schmidt, Rodney Cannon; Yarberry, Victor R.; Meyers, Ray J.
2006-11-01
This report describes version 1.0 of GBL-2D, a geometric Boolean library for 2D objects. The library is written in C++ and consists of a set of classes and routines. The classes primarily represent geometric data and relationships. Classes are provided for 2D points, lines, arcs, edge uses, loops, surfaces and mask sets. The routines contain algorithms for geometric Boolean operations and utility functions. Routines are provided that incorporate the Boolean operations: Union(OR), XOR, Intersection and Difference. A variety of additional analytical geometry routines and routines for importing and exporting the data in various file formats are also provided. The GBL-2D library was originally developed as a geometric modeling engine for use with a separate software tool, called SummitView [1], that manipulates the 2D mask sets created by designers of Micro-Electro-Mechanical Systems (MEMS). However, many other practical applications for this type of software can be envisioned because the need to perform 2D Boolean operations can arise in many contexts.
A non-conforming 3D spherical harmonic transport solver
Van Criekingen, S.
2006-07-01
A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)
Multi-GPU kinetic solvers using MPI and CUDA
NASA Astrophysics Data System (ADS)
Zabelok, Sergey; Arslanbekov, Robert; Kolobov, Vladimir
2014-12-01
This paper describes recent progress towards porting a Unified Flow Solver (UFS) to heterogeneous parallel computing. The main challenge of porting UFS to graphics processing units (GPUs) comes from the dynamically adapted mesh, which causes irregular data access. We describe the implementation of CUDA kernels for three modules in UFS: the direct Boltzmann solver using discrete velocity method (DVM), the DSMC module, and the Lattice Boltzmann Method (LBM) solver, all using octree Cartesian mesh with adaptive Mesh Refinement (AMR). Double digit speedup on single GPU and good scaling for multi-GPU has been demonstrated.
Tezaur, I. K.; Perego, M.; Salinger, A. G.; Tuminaro, R. S.; Price, S. F.
2015-04-27
This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, alongmore » with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.« less
NASA Astrophysics Data System (ADS)
Tezaur, I. K.; Perego, M.; Salinger, A. G.; Tuminaro, R. S.; Price, S. F.
2015-04-01
This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, along with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.
Tezaur, I. K.; Perego, M.; Salinger, A. G.; Tuminaro, R. S.; Price, S. F.
2015-04-27
This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, along with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.
Periodically sheared 2D Yukawa systems
Kovács, Anikó Zsuzsa; Hartmann, Peter; Donkó, Zoltán
2015-10-15
We present non-equilibrium molecular dynamics simulation studies on the dynamic (complex) shear viscosity of a 2D Yukawa system. We have identified a non-monotonic frequency dependence of the viscosity at high frequencies and shear rates, an energy absorption maximum (local resonance) at the Einstein frequency of the system at medium shear rates, an enhanced collective wave activity, when the excitation is near the plateau frequency of the longitudinal wave dispersion, and the emergence of significant configurational anisotropy at small frequencies and high shear rates.
ENERGY LANDSCAPE OF 2D FLUID FORMS
Y. JIANG; ET AL
2000-04-01
The equilibrium states of 2D non-coarsening fluid foams, which consist of bubbles with fixed areas, correspond to local minima of the total perimeter. (1) The authors find an approximate value of the global minimum, and determine directly from an image how far a foam is from its ground state. (2) For (small) area disorder, small bubbles tend to sort inwards and large bubbles outwards. (3) Topological charges of the same sign repel while charges of opposite sign attract. (4) They discuss boundary conditions and the uniqueness of the pattern for fixed topology.
Quasi-simultaneous interaction method for solving 2D boundary layer flows over plates and airfoils
NASA Astrophysics Data System (ADS)
Bijleveld, H. A.; Veldman, A. E. P.
2012-11-01
This paper studies unsteady 2D boundary layer flows over dented plates and a NACA 0012 airfoil. An inviscid flow is assumed to exist outside the boundary layer and is solved iteratively with the boundary layer flow together with the interaction method until a matching solution is achieved. Hereto a quasi-simultaneous interaction method is applied, in which the integral boundary layer equations are solved together with an interaction-law equation. The interaction-law equation is an approximation of the external flow and based on thin-airfoil theory. It is an algebraic relation between the velocity and displacement thickness. The interaction-law equation ensures that the eigenvalues of the system of equations do not have a sign change and that no singularities occur. Three numerical schemes are used to solve the boundary layer flow with the interaction method. These are: a standard scheme, a splitting method and a characteristics solver. All schemes use a finite difference discretization. The three schemes yield comparable results for the simulations carried out. The standard scheme is deviating most from the splitting and characteristics solvers. The results show that the eigenvalues remain positive, even in separation. As expected, the addition of the interaction-law equation prevents a sign change of the eigenvalues. The quasi-simultaneous interaction scheme is applicable to the three numerical schemes tested.
NASA Astrophysics Data System (ADS)
Li, Jinghe; Song, Linping; Liu, Qing Huo
2016-02-01
A simultaneous multiple frequency contrast source inversion (CSI) method is applied to reconstructing hydrocarbon reservoir targets in a complex multilayered medium in two dimensions. It simulates the effects of a salt dome sedimentary formation in the context of reservoir monitoring. In this method, the stabilized biconjugate-gradient fast Fourier transform (BCGS-FFT) algorithm is applied as a fast solver for the 2D volume integral equation for the forward computation. The inversion technique with CSI combines the efficient FFT algorithm to speed up the matrix-vector multiplication and the stable convergence of the simultaneous multiple frequency CSI in the iteration process. As a result, this method is capable of making quantitative conductivity image reconstruction effectively for large-scale electromagnetic oil exploration problems, including the vertical electromagnetic profiling (VEP) survey investigated here. A number of numerical examples have been demonstrated to validate the effectiveness and capacity of the simultaneous multiple frequency CSI method for a limited array view in VEP.
Toward an Efficient Icing CFD Process Using an Interactive Software Toolkit: Smagglce 2D
NASA Technical Reports Server (NTRS)
Vickerman, Mary B.; Choo, Yung K.; Schilling, Herbert W.; Baez, Marivell; Braun, Donald C.; Cotton, Barbara J.
2001-01-01
Two-dimensional CID analysis for iced airfoils can be a labor-intensive task. The software toolkit SmaggIce 2D is being developed to help streamline the CID process and provide the unique features needed for icing. When complete, it will include a combination of partially automated and fully interactive tools for all aspects of the tasks leading up to the flow analysis: geometry preparation, domain decomposition. block boundary demoralization. gridding, and linking with a flow solver. It also includes tools to perform ice shape characterization, an important aid in determining the relationship between ice characteristics and their effects on aerodynamic performance. Completed tools, work-in-progress, and planned features of the software toolkit are presented here.
A fast and accurate method to predict 2D and 3D aerodynamic boundary layer flows
NASA Astrophysics Data System (ADS)
Bijleveld, H. A.; Veldman, A. E. P.
2014-12-01
A quasi-simultaneous interaction method is applied to predict 2D and 3D aerodynamic flows. This method is suitable for offshore wind turbine design software as it is a very accurate and computationally reasonably cheap method. This study shows the results for a NACA 0012 airfoil. The two applied solvers converge to the experimental values when the grid is refined. We also show that in separation the eigenvalues remain positive thus avoiding the Goldstein singularity at separation. In 3D we show a flow over a dent in which separation occurs. A rotating flat plat is used to show the applicability of the method for rotating flows. The shown capabilities of the method indicate that the quasi-simultaneous interaction method is suitable for design methods for offshore wind turbine blades.
An investigation of DTNS2D for use as an incompressible turbulence modelling test-bed
NASA Technical Reports Server (NTRS)
Steffen, Christopher J., Jr.
1992-01-01
This paper documents an investigation of a two dimensional, incompressible Navier-Stokes solver for use as a test-bed for turbulence modelling. DTNS2D is the code under consideration for use at the Center for Modelling of Turbulence and Transition (CMOTT). This code was created by Gorski at the David Taylor Research Center and incorporates the pseudo compressibility method. Two laminar benchmark flows are used to measure the performance and implementation of the method. The classical solution of the Blasius boundary layer is used for validating the flat plate flow, while experimental data is incorporated in the validation of backward facing step flow. Velocity profiles, convergence histories, and reattachment lengths are used to quantify these calculations. The organization and adaptability of the code are also examined in light of the role as a numerical test-bed.
WFR-2D: an analytical model for PWAS-generated 2D ultrasonic guided wave propagation
NASA Astrophysics Data System (ADS)
Shen, Yanfeng; Giurgiutiu, Victor
2014-03-01
This paper presents WaveFormRevealer 2-D (WFR-2D), an analytical predictive tool for the simulation of 2-D ultrasonic guided wave propagation and interaction with damage. The design of structural health monitoring (SHM) systems and self-aware smart structures requires the exploration of a wide range of parameters to achieve best detection and quantification of certain types of damage. Such need for parameter exploration on sensor dimension, location, guided wave characteristics (mode type, frequency, wavelength, etc.) can be best satisfied with analytical models which are fast and efficient. The analytical model was constructed based on the exact 2-D Lamb wave solution using Bessel and Hankel functions. Damage effects were inserted in the model by considering the damage as a secondary wave source with complex-valued directivity scattering coefficients containing both amplitude and phase information from wave-damage interaction. The analytical procedure was coded with MATLAB, and a predictive simulation tool called WaveFormRevealer 2-D was developed. The wave-damage interaction coefficients (WDICs) were extracted from harmonic analysis of local finite element model (FEM) with artificial non-reflective boundaries (NRB). The WFR-2D analytical simulation results were compared and verified with full scale multiphysics finite element models and experiments with scanning laser vibrometer. First, Lamb wave propagation in a pristine aluminum plate was simulated with WFR-2D, compared with finite element results, and verified by experiments. Then, an inhomogeneity was machined into the plate to represent damage. Analytical modeling was carried out, and verified by finite element simulation and experiments. This paper finishes with conclusions and suggestions for future work.
Generic task problem solvers in Soar
NASA Technical Reports Server (NTRS)
Johnson, Todd R.; Smith, Jack W., Jr.; Chandrasekaran, B.
1989-01-01
Two trends can be discerned in research in problem solving architectures in the last few years. On one hand, interest in task-specific architectures has grown, wherein types of problems of general utility are identified, and special architectures that support the development of problem solving systems for those types of problems are proposed. These architectures help in the acquisition and specification of knowledge by providing inference methods that are appropriate for the type of problem. However, knowledge based systems which use only one type of problem solving method are very brittle, and adding more types of methods requires a principled approach to integrating them in a flexible way. Contrasting with this trend is the proposal for a flexible, general architecture contained in the work on Soar. Soar has features which make it attractive for flexible use of all potentially relevant knowledge or methods. But as the theory Soar does not make commitments to specific types of problem solvers or provide guidance for their construction. It was investigated how task-specific architectures can be constructed in Soar to retain as many of the advantages as possible of both approaches. Examples were used from the Generic Task approach for building knowledge based systems. Though this approach was developed and applied for a number of problems, the ideas are applicable to other task-specific approaches as well.
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.
NASA Astrophysics Data System (ADS)
Barlakas, Vasileios; Macke, Andreas; Wendisch, Manfred
2016-07-01
Non-spherical particles in the atmosphere absorb and scatter solar radiation. They change the polarization state of solar radiation depending on their shape, size, chemical composition and orientation. To quantify polarization effects, a new three-dimensional (3D) vector radiative transfer model, SPARTA (Solver for Polarized Atmospheric Radiative Transfer Applications) is introduced and validated against benchmark results. SPARTA employs the statistical forward Monte Carlo technique for efficient column-response pixel-based radiance calculations including polarization for 3D inhomogeneous cloudless and cloudy atmospheres. A sensitivity study has been carried out and exemplarily results are presented for two lidar-based mineral dust fields. The scattering and absorption properties of the dust particles have been computed for spheroids and irregular shaped particles. Polarized radiance fields in two-dimensional (2D) and one-dimensional (1D) inhomogeneous Saharan dust fields have been calculated at 532 nm wavelength. The domain-averaged results of the normalized reflected radiance are almost identical for the 1D and 2D modes. In the areas with large spatial gradient in optical thickness with expected significant horizontal photon transport, the radiance fields of the 2D mode differ by about ±12% for the first Stokes component (radiance, I) and ±8% for the second Stokes component (linear polarization, Q) from the fields of the 1D mode.
Microwave Assisted 2D Materials Exfoliation
NASA Astrophysics Data System (ADS)
Wang, Yanbin
Two-dimensional materials have emerged as extremely important materials with applications ranging from energy and environmental science to electronics and biology. Here we report our discovery of a universal, ultrafast, green, solvo-thermal technology for producing excellent-quality, few-layered nanosheets in liquid phase from well-known 2D materials such as such hexagonal boron nitride (h-BN), graphite, and MoS2. We start by mixing the uniform bulk-layered material with a common organic solvent that matches its surface energy to reduce the van der Waals attractive interactions between the layers; next, the solutions are heated in a commercial microwave oven to overcome the energy barrier between bulk and few-layers states. We discovered the minutes-long rapid exfoliation process is highly temperature dependent, which requires precise thermal management to obtain high-quality inks. We hypothesize a possible mechanism of this proposed solvo-thermal process; our theory confirms the basis of this novel technique for exfoliation of high-quality, layered 2D materials by using an as yet unknown role of the solvent.
Multienzyme Inkjet Printed 2D Arrays.
Gdor, Efrat; Shemesh, Shay; Magdassi, Shlomo; Mandler, Daniel
2015-08-19
The use of printing to produce 2D arrays is well established, and should be relatively facile to adapt for the purpose of printing biomaterials; however, very few studies have been published using enzyme solutions as inks. Among the printing technologies, inkjet printing is highly suitable for printing biomaterials and specifically enzymes, as it offers many advantages. Formulation of the inkjet inks is relatively simple and can be adjusted to a variety of biomaterials, while providing nonharmful environment to the enzymes. Here we demonstrate the applicability of inkjet printing for patterning multiple enzymes in a predefined array in a very straightforward, noncontact method. Specifically, various arrays of the enzymes glucose oxidase (GOx), invertase (INV) and horseradish peroxidase (HP) were printed on aminated glass surfaces, followed by immobilization using glutardialdehyde after printing. Scanning electrochemical microscopy (SECM) was used for imaging the printed patterns and to ascertain the enzyme activity. The successful formation of 2D arrays consisting of enzymes was explored as a means of developing the first surface confined enzyme based logic gates. Principally, XOR and AND gates, each consisting of two enzymes as the Boolean operators, were assembled, and their operation was studied by SECM. PMID:26214072
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.
Future non-linear stability for solutions of the Einstein-Vlasov system of Bianchi types II and VI0
NASA Astrophysics Data System (ADS)
Nungesser, Ernesto
2012-10-01
In a recent paper [E. Nungesser, "Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI0," Annales Henri Poincare (2012), 10.1007/s00023-012-0201-0], we have treated the future nonlinear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI0. We have been able now to remove the reflection symmetry assumption, thus treating the non-diagonal case. Apart from the increasing complexity, the methods have been essentially the same as in the diagonal case, showing that they are thus quite powerful. Here, the challenge was to put the equations in a form that permits the use of the previous results. We are able to conclude that after a possible basis change, the future of the non-diagonal spacetimes in consideration is asymptotically diagonal.
NASA Astrophysics Data System (ADS)
Zhu, Shao-ping; He, X. T.; Zheng, C. Y.
2001-01-01
Slow-time-scale magnetic fields driven by fast-time-scale electromagnetic waves or plasma waves are examined from the perspective of the Vlasov-Maxwell equations for a relativistic Vlasov plasma. An equation for slow-time-scale magnetic field is obtained. The field proposed in the present paper is a result of wave-wave beating which drives a solenoidal current. The magnitude of the slow-time-scale magnetic field proposed here can be as high as 20 MG at the critical surface for a laser intensity I=1018W/cm2 at wavelength λ0=1.05 μm. The predicted magnetic field is observed in two-dimensional particle simulations presented here.
2-D or not 2-D, that is the question: A Northern California test
Mayeda, K; Malagnini, L; Phillips, W S; Walter, W R; Dreger, D
2005-06-06
Reliable estimates of the seismic source spectrum are necessary for accurate magnitude, yield, and energy estimation. In particular, how seismic radiated energy scales with increasing earthquake size has been the focus of recent debate within the community and has direct implications on earthquake source physics studies as well as hazard mitigation. The 1-D coda methodology of Mayeda et al. has provided the lowest variance estimate of the source spectrum when compared against traditional approaches that use direct S-waves, thus making it ideal for networks that have sparse station distribution. The 1-D coda methodology has been mostly confined to regions of approximately uniform complexity. For larger, more geophysically complicated regions, 2-D path corrections may be required. The complicated tectonics of the northern California region coupled with high quality broadband seismic data provides for an ideal ''apples-to-apples'' test of 1-D and 2-D path assumptions on direct waves and their coda. Using the same station and event distribution, we compared 1-D and 2-D path corrections and observed the following results: (1) 1-D coda results reduced the amplitude variance relative to direct S-waves by roughly a factor of 8 (800%); (2) Applying a 2-D correction to the coda resulted in up to 40% variance reduction from the 1-D coda results; (3) 2-D direct S-wave results, though better than 1-D direct waves, were significantly worse than the 1-D coda. We found that coda-based moment-rate source spectra derived from the 2-D approach were essentially identical to those from the 1-D approach for frequencies less than {approx}0.7-Hz, however for the high frequencies (0.7{le} f {le} 8.0-Hz), the 2-D approach resulted in inter-station scatter that was generally 10-30% smaller. For complex regions where data are plentiful, a 2-D approach can significantly improve upon the simple 1-D assumption. In regions where only 1-D coda correction is available it is still preferable over 2
Performance of NASA Equation Solvers on Computational Mechanics Applications
NASA Technical Reports Server (NTRS)
Storaasli, Olaf O.
1996-01-01
This paper describes the performance of a new family of NASA-developed equation solvers used for large-scale (i.e. 551,705 equations) structural analysis. To minimize computer time and memory, the solvers are divided by application and matrix characteristics (sparse/dense, real/complex, symmetric/nonsymmetric, size: in-core/out of core) and exploit the hardware features of current and future computers. In this paper, the equation solvers, which are written in FORTRAN, and are therefore easily transportable, are shown to be faster than specialized computer library routines utilizing assembly code. Twenty NASA structural benchmark models with NASA solver timings reside on World Wide Web with a challenge to beat them.
Two-dimensional time dependent Riemann solvers for neutron transport
Brunner, Thomas A. . E-mail: tabrunn@sandia.gov; Holloway, James Paul
2005-11-20
A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P{sub 1} equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem.
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.
NASA Astrophysics Data System (ADS)
Prihantoro, Rudy; Sutarno, Doddy; Nurhasan
2016-08-01
In this work, we seek numerical solution of 3-D Magnetotelluric (MT) using edge- based finite element method. This approach is a variant of standard finite element method and commonly referred as vector finite-element (VFE) method. Nonphysical solutions usually occurred when the solution is sought using standard finite element which is a node based element. Vector finite element attempt to overcome those nonphysical solutions by using the edges of the element as vector basis. The proposed approach on solving second order Maxwell differential equation of 3-D MT is using direct solver rather than iterative method. Therefore, divergence correction to accelerate the rate of convergence for its iterative solution is no longer needed. The utilization of direct solver has been verified previously for correctness by comparing the resulting solution to those given by analytical solution, as well as the solution come from the other numerical methods, for earth layered model, 2-D models and COMMEMI 3D-2 model. In this work, further verification resulted from recent comparison model of Dublin Test Model 1 (DTM1) is presented.
Verification and Validation of a Chemical Reaction Solver Coupled to the Piecewise Parabolic Method
NASA Astrophysics Data System (ADS)
Attal, Nitesh; Ramaprabhu, Praveen; Hossain, Jahed; Karkhanis, Varad; Roy, Sukesh; Gord, James; Uddin, Mesbah
2012-11-01
We present a detailed chemical kinetics reaction solver coupled to the Piecewise Parabolic Method (PPM) embedded in the widely used astrophysical FLASH code. The FLASH code solves the compressible Euler equations with a directionally split, PPM with Adaptive Mesh Refinement (AMR). The reaction network is solved using a library of coupled ODE solvers, specialized for handling stiff systems of equations. Finally, the diffusion of heat, mass, and momentum is handled either through an update of the fluxes of each quantity, or by directly solving a diffusion equation for each. The resulting product is capable of handling a variety of physics such as gas-phase chemical kinetics, diffusive transport of mass, momentum, and heat, shocks, sharp interfaces, multi-species mixtures, and thermal radiation. We will present results from verification and validation of the above capabilities through comparison with analytical solutions, and published numerical and experimental data. Our validation cases include advection of reacting fronts in 1-D and 2D, laminar premixed flames in a Bunsen burner configuration, and shock-driven combustion. We acknowledge funding from Spectral Energies LLC.
An efficient implicit unstructured finite volume solver for generalised Newtonian fluids
NASA Astrophysics Data System (ADS)
Jalali, Alireza; Sharbatdar, Mahkame; Ollivier-Gooch, Carl
2016-03-01
An implicit finite volume solver is developed for the steady-state solution of generalised Newtonian fluids on unstructured meshes in 2D. The pseudo-compressibility technique is employed to couple the continuity and momentum equations by transforming the governing equations into a hyperbolic system. A second-order accurate spatial discretisation is provided by performing a least-squares gradient reconstruction within each control volume of unstructured meshes. A central flux function is used for the convective terms and a solution jump term is added to the averaged component for the viscous terms. Global implicit time-stepping using successive evolution-relaxation is utilised to accelerate the convergence to steady-state solutions. The performance of our flow solver is examined for power-law and Carreau-Yasuda non-Newtonian fluids in different geometries. The effects of model parameters and Reynolds number are studied on the convergence rate and flow features. Our results verify second-order accuracy of the discretisation and also fast and efficient convergence to the steady-state solution for a wide range of flow variables.
NASA Astrophysics Data System (ADS)
Hammer, Manfred
2015-03-01
The incidence of thin-film-guided, in-plane unguided waves at oblique angles on straight discontinuities of dielectric slab waveguides, an early problem of integrated optics, is being re-considered. The 3-D frequency domain Maxwell equations reduce to a parametrized inhomogeneous vectorial problem on a 2-D computational domain, with transparent-influx boundary conditions. We propose a rigorous vectorial solver based on simultaneous expansions into polarized local slab eigenmodes along the two orthogonal cross section coordinates (quadridirectional eigenmode propagation QUEP). The quasi-analytical scheme is applicable to configurations with - in principle - arbitrary cross section geometries. Examples for a high-contrast facet of an asymmetric slab waveguide, for the lateral excitation of a channel waveguide, and for a step discontinuity between slab waveguides of different thicknesses are discussed.
An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems
Oosterlee, C.W.; Washio, T.
1996-12-31
In this paper we try to achieve h-independent convergence with preconditioned GMRES and BiCGSTAB for 2D singular perturbed equations. Three recently developed multigrid methods are adopted as a preconditioner. They are also used as solution methods in order to compare the performance of the methods as solvers and as preconditioners. Two of the multigrid methods differ only in the transfer operators. One uses standard matrix- dependent prolongation operators from. The second uses {open_quotes}upwind{close_quotes} prolongation operators, developed. Both employ the Galerkin coarse grid approximation and an alternating zebra line Gauss-Seidel smoother. The third method is based on the block LU decomposition of a matrix and on an approximate Schur complement. This multigrid variant is presented in. All three multigrid algorithms are algebraic methods.
Canard configured aircraft with 2-D nozzle
NASA Technical Reports Server (NTRS)
Child, R. D.; Henderson, W. P.
1978-01-01
A closely-coupled canard fighter with vectorable two-dimensional nozzle was designed for enhanced transonic maneuvering. The HiMAT maneuver goal of a sustained 8g turn at a free-stream Mach number of 0.9 and 30,000 feet was the primary design consideration. The aerodynamic design process was initiated with a linear theory optimization minimizing the zero percent suction drag including jet effects and refined with three-dimensional nonlinear potential flow techniques. Allowances were made for mutual interference and viscous effects. The design process to arrive at the resultant configuration is described, and the design of a powered 2-D nozzle model to be tested in the LRC 16-foot Propulsion Wind Tunnel is shown.
2D Electrostatic Actuation of Microshutter Arrays
NASA Technical Reports Server (NTRS)
Burns, Devin E.; Oh, Lance H.; Li, Mary J.; Kelly, Daniel P.; Kutyrev, Alexander S.; Moseley, Samuel H.
2015-01-01
Electrostatically actuated microshutter arrays consisting of rotational microshutters (shutters that rotate about a torsion bar) were designed and fabricated through the use of models and experiments. Design iterations focused on minimizing the torsional stiffness of the microshutters, while maintaining their structural integrity. Mechanical and electromechanical test systems were constructed to measure the static and dynamic behavior of the microshutters. The torsional stiffness was reduced by a factor of four over initial designs without sacrificing durability. Analysis of the resonant behavior of the microshutters demonstrates that the first resonant mode is a torsional mode occurring around 3000 Hz. At low vacuum pressures, this resonant mode can be used to significantly reduce the drive voltage necessary for actuation requiring as little as 25V. 2D electrostatic latching and addressing was demonstrated using both a resonant and pulsed addressing scheme.
2D Electrostatic Actuation of Microshutter Arrays
NASA Technical Reports Server (NTRS)
Burns, Devin E.; Oh, Lance H.; Li, Mary J.; Jones, Justin S.; Kelly, Daniel P.; Zheng, Yun; Kutyrev, Alexander S.; Moseley, Samuel H.
2015-01-01
An electrostatically actuated microshutter array consisting of rotational microshutters (shutters that rotate about a torsion bar) were designed and fabricated through the use of models and experiments. Design iterations focused on minimizing the torsional stiffness of the microshutters, while maintaining their structural integrity. Mechanical and electromechanical test systems were constructed to measure the static and dynamic behavior of the microshutters. The torsional stiffness was reduced by a factor of four over initial designs without sacrificing durability. Analysis of the resonant behavior of the microshutter arrays demonstrates that the first resonant mode is a torsional mode occurring around 3000 Hz. At low vacuum pressures, this resonant mode can be used to significantly reduce the drive voltage necessary for actuation requiring as little as 25V. 2D electrostatic latching and addressing was demonstrated using both a resonant and pulsed addressing scheme.
2D quantum gravity from quantum entanglement.
Gliozzi, F
2011-01-21
In quantum systems with many degrees of freedom the replica method is a useful tool to study the entanglement of arbitrary spatial regions. We apply it in a way that allows them to backreact. As a consequence, they become dynamical subsystems whose position, form, and extension are determined by their interaction with the whole system. We analyze, in particular, quantum spin chains described at criticality by a conformal field theory. Its coupling to the Gibbs' ensemble of all possible subsystems is relevant and drives the system into a new fixed point which is argued to be that of the 2D quantum gravity coupled to this system. Numerical experiments on the critical Ising model show that the new critical exponents agree with those predicted by the formula of Knizhnik, Polyakov, and Zamolodchikov.
Graphene suspensions for 2D printing
NASA Astrophysics Data System (ADS)
Soots, R. A.; Yakimchuk, E. A.; Nebogatikova, N. A.; Kotin, I. A.; Antonova, I. V.
2016-04-01
It is shown that, by processing a graphite suspension in ethanol or water by ultrasound and centrifuging, it is possible to obtain particles with thicknesses within 1-6 nm and, in the most interesting cases, 1-1.5 nm. Analogous treatment of a graphite suspension in organic solvent yields eventually thicker particles (up to 6-10 nm thick) even upon long-term treatment. Using the proposed ink based on graphene and aqueous ethanol with ethylcellulose and terpineol additives for 2D printing, thin (~5 nm thick) films with sheet resistance upon annealing ~30 MΩ/□ were obtained. With the ink based on aqueous graphene suspension, the sheet resistance was ~5-12 kΩ/□ for 6- to 15-nm-thick layers with a carrier mobility of ~30-50 cm2/(V s).
NASA Astrophysics Data System (ADS)
Schaa, R.; Gross, L.; du Plessis, J.
2016-04-01
We present a general finite-element solver, escript, tailored to solve geophysical forward and inverse modeling problems in terms of partial differential equations (PDEs) with suitable boundary conditions. Escript’s abstract interface allows geoscientists to focus on solving the actual problem without being experts in numerical modeling. General-purpose finite element solvers have found wide use especially in engineering fields and find increasing application in the geophysical disciplines as these offer a single interface to tackle different geophysical problems. These solvers are useful for data interpretation and for research, but can also be a useful tool in educational settings. This paper serves as an introduction into PDE-based modeling with escript where we demonstrate in detail how escript is used to solve two different forward modeling problems from applied geophysics (3D DC resistivity and 2D magnetotellurics). Based on these two different cases, other geophysical modeling work can easily be realized. The escript package is implemented as a Python library and allows the solution of coupled, linear or non-linear, time-dependent PDEs. Parallel execution for both shared and distributed memory architectures is supported and can be used without modifications to the scripts.
Metrology for graphene and 2D materials
NASA Astrophysics Data System (ADS)
Pollard, Andrew J.
2016-09-01
The application of graphene, a one atom-thick honeycomb lattice of carbon atoms with superlative properties, such as electrical conductivity, thermal conductivity and strength, has already shown that it can be used to benefit metrology itself as a new quantum standard for resistance. However, there are many application areas where graphene and other 2D materials, such as molybdenum disulphide (MoS2) and hexagonal boron nitride (h-BN), may be disruptive, areas such as flexible electronics, nanocomposites, sensing and energy storage. Applying metrology to the area of graphene is now critical to enable the new, emerging global graphene commercial world and bridge the gap between academia and industry. Measurement capabilities and expertise in a wide range of scientific areas are required to address this challenge. The combined and complementary approach of varied characterisation methods for structural, chemical, electrical and other properties, will allow the real-world issues of commercialising graphene and other 2D materials to be addressed. Here, examples of metrology challenges that have been overcome through a multi-technique or new approach are discussed. Firstly, the structural characterisation of defects in both graphene and MoS2 via Raman spectroscopy is described, and how nanoscale mapping of vacancy defects in graphene is also possible using tip-enhanced Raman spectroscopy (TERS). Furthermore, the chemical characterisation and removal of polymer residue on chemical vapour deposition (CVD) grown graphene via secondary ion mass spectrometry (SIMS) is detailed, as well as the chemical characterisation of iron films used to grow large domain single-layer h-BN through CVD growth, revealing how contamination of the substrate itself plays a role in the resulting h-BN layer. In addition, the role of international standardisation in this area is described, outlining the current work ongoing in both the International Organization of Standardization (ISO) and the
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.
Gaedigk, Andrea; Bradford, L Dianne; Alander, Sarah W; Leeder, J Steven
2006-04-01
Unexplained cases of CYP2D6 genotype/phenotype discordance continue to be discovered. In previous studies, several African Americans with a poor metabolizer phenotype carried the reduced function CYP2D6*10 allele in combination with a nonfunctional allele. We pursued the possibility that these alleles harbor either a known sequence variation (i.e., CYP2D6*36 carrying a gene conversion in exon 9 along the CYP2D6*10-defining 100C>T single-nucleotide polymorphism) or novel sequences variation(s). Discordant cases were evaluated by long-range polymerase chain reaction (PCR) to test for gene rearrangement events, and a 6.6-kilobase pair PCR product encompassing the CYP2D6 gene was cloned and entirely sequenced. Thereafter, allele frequencies were determined in different study populations comprising whites, African Americans, and Asians. Analyses covering the CYP2D7 to 2D6 gene region established that CYP2D6*36 did not only exist as a gene duplication (CYP2D6*36x2) or in tandem with *10 (CYP2D6*36+*10), as previously reported, but also by itself. This "single" CYP2D6*36 allele was found in nine African Americans and one Asian, but was absent in the whites tested. Ultimately, the presence of CYP2D6*36 resolved genotype/phenotype discordance in three cases. We also discovered an exon 9 conversion-positive CYP2D6*4 gene in a duplication arrangement (CYP2D6*4Nx2) and a CYP2D6*4 allele lacking 100C>T (CYP2D6*4M) in two white subjects. The discovery of an allele that carries only one CYP2D6*36 gene copy provides unequivocal evidence that both CYP2D6*36 and *36x2 are associated with a poor metabolizer phenotype. Given a combined frequency of between 0.5 and 3% in African Americans and Asians, genotyping for CYP2D6*36 should improve the accuracy of genotype-based phenotype prediction in these populations.
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 new inversion method for (T2, D) 2D NMR logging and fluid typing
NASA Astrophysics Data System (ADS)
Tan, Maojin; Zou, Youlong; Zhou, Cancan
2013-02-01
One-dimensional nuclear magnetic resonance (1D NMR) logging technology has some significant limitations in fluid typing. However, not only can two-dimensional nuclear magnetic resonance (2D NMR) provide some accurate porosity parameters, but it can also identify fluids more accurately than 1D NMR. In this paper, based on the relaxation mechanism of (T2, D) 2D NMR in a gradient magnetic field, a hybrid inversion method that combines least-squares-based QR decomposition (LSQR) and truncated singular value decomposition (TSVD) is examined in the 2D NMR inversion of various fluid models. The forward modeling and inversion tests are performed in detail with different acquisition parameters, such as magnetic field gradients (G) and echo spacing (TE) groups. The simulated results are discussed and described in detail, the influence of the above-mentioned observation parameters on the inversion accuracy is investigated and analyzed, and the observation parameters in multi-TE activation are optimized. Furthermore, the hybrid inversion can be applied to quantitatively determine the fluid saturation. To study the effects of noise level on the hybrid method and inversion results, the numerical simulation experiments are performed using different signal-to-noise-ratios (SNRs), and the effect of different SNRs on fluid typing using three fluid models are discussed and analyzed in detail.
Continuum kinetic plasma modeling by the Vlasov-Maxwell system in multiple dimensions
NASA Astrophysics Data System (ADS)
Reddell, Noah; Shumlak, Uri
2014-10-01
A kinetic plasma model for multiple particle species described by the Vlasov equation and coupled to fully dynamic electromagnetic forces is presented. The model is implemented as evolving continuous PDFs (probability density functions) in particle phase space (position-velocity) as opposed to particle-in-cell (PIC) methods which discretely sample the PDF. The hyperbolic model is evolved using a high-order finite element method (discontinuous Galerkin), with excellent conservation of system mass, momentum, and energy - an advantage compared to PIC. Simulations of two- to six-dimensional phase space while resolving the plasma frequency and cyclotron frequency are computationally expensive. To maximize performance and scaling to large simulations, a new framework, WARPM, has been developed for many-core (e.g. GPU) computing architectures. WARPM supports both multi-fluid and continuum kinetic plasma models as coupled hyperbolic systems with nearest neighbor predictable communication. Simulation results are compared to existing benchmark problems and newly achievable studies of wave-particle interactions are presented. This research was supported by a grant from the United States Air Force Office of Scientific Research and Dept. of Energy Computational Science Graduate Fellowship.
Vlasov Simulations of Ionospheric Turbulence near the Upper Hybrid Resonance and Fourth Gyroharmonic
NASA Astrophysics Data System (ADS)
Najmi, A. C.; Eliasson, B. E.; Shao, X.; Milikh, G. M.; Sharma, S.; Papadopoulos, D.
2015-12-01
High-frequency, ordinary (O) mode electromagnetic waves incident on a magnetized plasma near the upper hybrid resonance can excite magnetic field aligned density striations associated with both turbulence and electron heating. We have used Vlasov simulations, which combine low noise and high resolution of all areas of phase space, in one spatial and two velocity dimensions to study the induced turbulence in the presence of striations near the upper hybrid resonance, where the O-mode pump is mode converted to large amplitude upper hybrid oscillations trapped in a striation. We were able to correlate the evolution of stationary electron and ion oscillations with the onset of turbulence, and the heating of electrons in the striation with large amplitude, short wavelength electron Bernstein waves. These Bernstein waves excite stochastic electron heating when the normalized gradients of their electric field exceed the electron gyroradius, breaking the drift approximation, and causing particle orbits in phase space to diverge exponentially, rapidly increasing the electron temperature by several thousand Kelvin. Our most recent results include simulations where the frequency of the pump wave is close to the double resonance, both the upper hybrid and the fourth gyroharmonic. These results are relevant to ongoing high-latitude heating experiments and specifically, to the theory of the formation of descending artificial ionized layers.
Optimal ?-Control for the Global Cauchy Problem of The Relativistic Vlasov-Poisson System
NASA Astrophysics Data System (ADS)
Young, Brent
2011-12-01
Recently, M.K.-H. Kiessling and A.S. Tahvildar-Zadeh proved that a unique global classical solution to the relativistic Vlasov-Poisson system exists whenever the positive, integrable initial datum is spherically symmetric, compactly supported in momentum space, vanishes on characteristics with vanishing angular momentum, and for β⩾3/2 has ?-norm strictly below a positive, critical value ?. Everything else being equal, data leading to finite time blow-up can be found with ?-norm surpassing ? for any β>1, with ? if and only if β⩾3/2. In their paper, the critical value for β=3/2 is calculated explicitly while the value for all other β is merely characterized as the infimum of a functional over an appropriate function space. In this work, the existence of minimizers is established, and the exact expression of ? is calculated in terms of the famous Lane-Emden functions. Numerical computations of the ? are presented along with some elementary asymptotics near the critical exponent 3/2.
High-order continuum kinetic Vlasov-Poisson simulations of magnetized plasmas
NASA Astrophysics Data System (ADS)
Vogman, G. V.; Colella, P.; Shumlak, U.
2014-10-01
Continuum methods offer a high-fidelity means of simulating plasma kinetics as modeled by the Boltzmann-Maxwell equation system. These methods are advantageous because they can be cast in conservation law form, are not susceptible to noise, and can be implemented using high-order numerical methods. Thereby the methods can conserve mass, momentum, and energy to a high degree. A fourth-order accurate finite volume method has been developed to solve the continuum kinetic Vlasov-Poisson equation system in one spatial and two velocity dimensions. The method is validated in cartesian coordinates using the Dory-Guest-Harris instability, which is a special case of a perpendicularly-propagating kinetic electrostatic wave in a warm uniformly magnetized plasma. The instability dispersion relation, and its generalization to arbitrary distribution functions, are demonstrated to be well-suited benchmarks for continuum algorithms in higher-dimensional phase space. The numerical method has also been extended to two spatial dimensions, and has been implemented in cylindrical coordinates to simulate axisymmetric configurations such as a Z-pinch. This work was supported by the DOE SCGF fellowship, and grants from DOE ASCR and AFOSR.
NASA Astrophysics Data System (ADS)
Reddell, Noah
Advances are reported in the three pillars of computational science achieving a new capability for understanding dynamic plasma phenomena outside of local thermodynamic equilibrium. A continuum kinetic model for plasma based on the Vlasov-Maxwell system for multiple particle species is developed. Consideration is added for boundary conditions in a truncated velocity domain and supporting wall interactions. A scheme to scale the velocity domain for multiple particle species with different temperatures and particle mass while sharing one computational mesh is described. A method for assessing the degree to which the kinetic solution differs from a Maxwell-Boltzmann distribution is introduced and tested on a thoroughly studied test case. The discontinuous Galerkin numerical method is extended for efficient solution of hyperbolic conservation laws in five or more particle phase-space dimensions using tensor-product hypercube elements with arbitrary polynomial order. A scheme for velocity moment integration is integrated as required for coupling between the plasma species and electromagnetic waves. A new high performance simulation code WARPM is developed to efficiently implement the model and numerical method on emerging many-core supercomputing architectures. WARPM uses the OpenCL programming model for computational kernels and task parallelism to overlap computation with communication. WARPM single-node performance and parallel scaling efficiency are analyzed with bottlenecks identified guiding future directions for the implementation. The plasma modeling capability is validated against physical problems with analytic solutions and well established benchmark problems.
Nocera, L.; Palumbo, L. J.
2013-01-15
We present new elementary, exact weak singular solutions of the steady state, two species, electrostatic, one dimensional Vlasov-Poisson equations. The distribution of the hot, finite mass, mobile ions is assumed to be log singular at the position of the electric potential's minimum. We show that the electron energy distributions on opposite sides of this minimum are not equal. This leads to a jump discontinuity of the electron distribution across its separatrix. A simple relation exists between the difference of these two electron distributions and that of the ions. The velocity Fourier transform of the electron singular distribution is smooth and appears as a simple Neumann series. Elementary, finite amplitude profiles of the electric potential result from Poisson equation, which are smoothly, but nonmonotonically and asymmetrically distributed in space. Two such profiles are given explicitly as appropriate for a nonmonotonic double layer and for a plasma bounded by a surface. The distributions of both electrons and ions supporting such potential meet smooth and kinetically stable boundary conditions at one plasma boundary. For sufficiently small potential to electron temperature ratios, the nonthermal, discontinuous electron distribution resulting at the other plasma boundary is also stable against Landau damped perturbations of the electron distribution.
From one-dimensional fields to Vlasov equilibria: Theory and application of Hermite polynomials
NASA Astrophysics Data System (ADS)
Allanson, Oliver; Neukirch, Thomas; Troscheit, Sascha; Wilson, Fiona
2016-06-01
We consider the theory and application of a solution method for the inverse problem in collisionless equilibria, namely that of calculating a Vlasov-Maxwell equilibrium for a given macroscopic (fluid) equilibrium. Using Jeans' theorem, the equilibrium distribution functions are expressed as functions of the constants of motion, in the form of a Maxwellian multiplied by an unknown function of the canonical momenta. In this case it is possible to reduce the inverse problem to inverting Weierstrass transforms, which we achieve by using expansions over Hermite polynomials. A sufficient condition on the pressure tensor is found which guarantees the convergence and the boundedness of the candidate solution, when satisfied. This condition is obtained by elementary means, and it is clear how to put it into practice. We also argue that for a given pressure tensor for which our method applies, there always exists a positive distribution function solution for a sufficiently magnetised plasma. Illustrative examples of the use of this method with both force-free and non-force-free macroscopic equilibria are presented, including the full verification of a recently derived distribution function for the force-free Harris sheet (Allanson et al., Phys. Plasmas, vol. 22 (10), 2015, 102116). In the effort to model equilibria with lower values of the plasma β, solutions for the same macroscopic equilibrium in a new gauge are calculated, with numerical results presented for β_{pl}=0.05.
Vlasov Simulation of Electrostatic Solitary Structures in Multi-Component Plasmas
NASA Technical Reports Server (NTRS)
Umeda, Takayuki; Ashour-Abdalla, Maha; Pickett, Jolene S.; Goldstein, Melvyn L.
2012-01-01
Electrostatic solitary structures have been observed in the Earth's magnetosheath by the Cluster spacecraft. Recent theoretical work has suggested that these solitary structures are modeled by electron acoustic solitary waves existing in a four-component plasma system consisting of core electrons, two counter-streaming electron beams, and one species of background ions. In this paper, the excitation of electron acoustic waves and the formation of solitary structures are studied by means of a one-dimensional electrostatic Vlasov simulation. The present result first shows that either electron acoustic solitary waves with negative potential or electron phase-space holes with positive potential are excited in four-component plasma systems. However, these electrostatic solitary structures have longer duration times and higher wave amplitudes than the solitary structures observed in the magnetosheath. The result indicates that a high-speed and small free energy source may be needed as a fifth component. An additional simulation of a five-component plasma consisting of a stable four-component plasma and a weak electron beam shows the generation of small and fast electron phase-space holes by the bump-on-tail instability. The physical properties of the small and fast electron phase-space holes are very similar to those obtained by the previous theoretical analysis. The amplitude and duration time of solitary structures in the simulation are also in agreement with the Cluster observation.
Numerical study of plasma-wall transition using an Eulerian Vlasov code
NASA Astrophysics Data System (ADS)
Shoucri, M.; Cardinali, A.; Matte, J. P.; Spigler, R.
2004-07-01
A one-dimensional Eulerian Vlasov code is used to study the self-consistent solution of a plasma facing a floating collector, in the absence of an external magnetic field. Both electrons and ions are treated with a kinetic equation. A Bhatnagar-Gross-Krook (BGK) collision term is used to describe the collisions. Acceleration of the ion flow at the Debye sheath entrance is observed together with the formation of a stable steep negative electric field in front of the floating collector. This negative electric field acts to accelerate the positive ions towards the plate, pushing back the negative electrons, such that at steady state the total current collected at the plate is zero. The codes are run for a sufficiently long time on the ions time scale to ensure the ions (argon) distribution function is reaching a steady state. For the different parameters used, the solution shows the existence of persistent regular oscillations of constant amplitude when the electron collisions are very small or negligible. These oscillations will be studied. The increase in the electron collisions damps these oscillations and helps the system reach an equilibrium.
Equations of motion of test particles for solving the spin-dependent Boltzmann-Vlasov equation
NASA Astrophysics Data System (ADS)
Xia, Yin; Xu, Jun; Li, Bao-An; Shen, Wen-Qing
2016-08-01
A consistent derivation of the equations of motion (EOMs) of test particles for solving the spin-dependent Boltzmann-Vlasov equation is presented. The resulting EOMs in phase space are similar to the canonical equations in Hamiltonian dynamics, and the EOM of spin is the same as that in the Heisenburg picture of quantum mechanics. Considering further the quantum nature of spin and choosing the direction of total angular momentum in heavy-ion reactions as a reference of measuring nucleon spin, the EOMs of spin-up and spin-down nucleons are given separately. The key elements affecting the spin dynamics in heavy-ion collisions are identified. The resulting EOMs provide a solid foundation for using the test-particle approach in studying spin dynamics in heavy-ion collisions at intermediate energies. Future comparisons of model simulations with experimental data will help to constrain the poorly known in-medium nucleon spin-orbit coupling relevant for understanding properties of rare isotopes and their astrophysical impacts.
Heinemann, Tobias; Quataert, Eliot E-mail: eliot@berkeley.edu
2014-09-01
We derive the conductivity tensor for axisymmetric perturbations of a hot, collisionless, and charge-neutral plasma in the shearing sheet approximation. Our results generalize the well-known linear Vlasov theory for uniform plasmas to differentially rotating plasmas and can be used for wide range of kinetic stability calculations. We apply these results to the linear theory of the magneto-rotational instability (MRI) in collisionless plasmas. We show analytically and numerically how the general kinetic theory results derived here reduce in appropriate limits to previous results in the literature, including the low-frequency guiding center (or 'kinetic MHD') approximation, Hall magnetohydrodynamics (MHD), and the gyro-viscous approximation. We revisit the cold plasma model of the MRI and show that, contrary to previous results, an initially unmagnetized collisionless plasma is linearly stable to axisymmetric perturbations in the cold plasma approximation. In addition to their application to astrophysical plasmas, our results provide a useful framework for assessing the linear stability of differentially rotating plasmas in laboratory experiments.
Direct Vlasov simulations of electron-attracting cylindrical Langmuir probes in flowing plasmas
Sánchez-Arriaga, G.; Pastor-Moreno, D.
2014-07-15
Current collection by positively polarized cylindrical Langmuir probes immersed in flowing plasmas is analyzed using a non-stationary direct Vlasov-Poisson code. A detailed description of plasma density spatial structure as a function of the probe-to-plasma relative velocity U is presented. Within the considered parametric domain, the well-known electron density maximum close to the probe is weakly affected by U. However, in the probe wake side, the electron density minimum becomes deeper as U increases and a rarified plasma region appears. Sheath radius is larger at the wake than at the front side. Electron and ion distribution functions show specific features that are the signature of probe motion. In particular, the ion distribution function at the probe front side exhibits a filament with positive radial velocity. It corresponds to a population of rammed ions that were reflected by the electric field close to the positively biased probe. Numerical simulations reveal that two populations of trapped electrons exist: one orbiting around the probe and the other with trajectories confined at the probe front side. The latter helps to neutralize the reflected ions, thus explaining a paradox in past probe theory.
Hybrid Vlasov-Maxwell simulations of two-dimensional turbulence in plasmas
Valentini, F.; Servidio, S.; Veltri, P.; Perrone, D.; Califano, F.; Matthaeus, W. H.
2014-08-15
Turbulence in plasmas is a very challenging problem since it involves wave-particle interactions, which are responsible for phenomena such as plasma dissipation, acceleration mechanisms, heating, temperature anisotropy, and so on. In this work, a hybrid Vlasov-Maxwell numerical code is employed to study local kinetic processes in a two-dimensional turbulent regime. In the present model, ions are treated as a kinetic species, while electrons are considered as a fluid. As recently reported in [S. Servidio, Phys. Rev. Lett. 108, 045001 (2012)], nearby regions of strong magnetic activity, kinetic effects manifest through a deformation of the ion velocity distribution function that consequently departs from the equilibrium Maxwellian configuration. Here, the structure of turbulence is investigated in detail in phase space, by evaluating the high-order moments of the particle velocity distribution, i.e., temperature, skewness, and kurtosis. This analysis provides quantitative information about the non-Maxwellian character of the system dynamics. This departure from local thermodynamic equilibrium triggers several processes commonly observed in many astrophysical and laboratory plasmas.
Direct Vlasov simulations of electron-attracting cylindrical Langmuir probes in flowing plasmas
NASA Astrophysics Data System (ADS)
Sánchez-Arriaga, G.; Pastor-Moreno, D.
2014-07-01
Current collection by positively polarized cylindrical Langmuir probes immersed in flowing plasmas is analyzed using a non-stationary direct Vlasov-Poisson code. A detailed description of plasma density spatial structure as a function of the probe-to-plasma relative velocity U is presented. Within the considered parametric domain, the well-known electron density maximum close to the probe is weakly affected by U. However, in the probe wake side, the electron density minimum becomes deeper as U increases and a rarified plasma region appears. Sheath radius is larger at the wake than at the front side. Electron and ion distribution functions show specific features that are the signature of probe motion. In particular, the ion distribution function at the probe front side exhibits a filament with positive radial velocity. It corresponds to a population of rammed ions that were reflected by the electric field close to the positively biased probe. Numerical simulations reveal that two populations of trapped electrons exist: one orbiting around the probe and the other with trajectories confined at the probe front side. The latter helps to neutralize the reflected ions, thus explaining a paradox in past probe theory.
NASA Astrophysics Data System (ADS)
Anastasiou, K.; Chan, C. T.
1997-06-01
A 2D, depth-integrated, free surface flow solver for the shallow water equations is developed and tested. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov-type second-order upwind finite volume formulation, whereby the inviscid fluxes of the system of equations are obtained using Roes flux function. The eigensystem of the 2D shallow water equations is derived and is used for the construction of Roes matrix on an unstructured mesh. The viscous terms of the shallow water equations are computed using a finite volume formulation which is second-order-accurate. Verification of the solution technique for the inviscid form of the governing equations as well as for the full system of equations is carried out by comparing the model output with documented published results and very good agreement is obtained. A numerical experiment is also conducted in order to evaluate the performance of the solution technique as applied to linear convection problems. The presented results show that the solution technique is robust.
NASA Astrophysics Data System (ADS)
Cheng, Chingyun; Kangara, Jayampathi; Arakelyan, Ilya; Thomas, John
2016-05-01
We tune the dimensionality of a strongly interacting degenerate 6 Li Fermi gas from 2D to quasi-2D, by adjusting the radial confinement of pancake-shaped clouds to control the radial chemical potential. In the 2D regime with weak radial confinement, the measured pair binding energies are in agreement with 2D-BCS mean field theory, which predicts dimer pairing energies in the many-body regime. In the qausi-2D regime obtained with increased radial confinement, the measured pairing energy deviates significantly from 2D-BCS theory. In contrast to the pairing energy, the measured radii of the cloud profiles are not fit by 2D-BCS theory in either the 2D or quasi-2D regimes, but are fit in both regimes by a beyond mean field polaron-model of the free energy. Supported by DOE, ARO, NSF, and AFOSR.
Competing coexisting phases in 2D water
Zanotti, Jean-Marc; Judeinstein, Patrick; Dalla-Bernardina, Simona; Creff, Gaëlle; Brubach, Jean-Blaise; Roy, Pascale; Bonetti, Marco; Ollivier, Jacques; Sakellariou, Dimitrios; Bellissent-Funel, Marie-Claire
2016-01-01
The properties of bulk water come from a delicate balance of interactions on length scales encompassing several orders of magnitudes: i) the Hydrogen Bond (HBond) at the molecular scale and ii) the extension of this HBond network up to the macroscopic level. Here, we address the physics of water when the three dimensional extension of the HBond network is frustrated, so that the water molecules are forced to organize in only two dimensions. We account for the large scale fluctuating HBond network by an analytical mean-field percolation model. This approach provides a coherent interpretation of the different events experimentally (calorimetry, neutron, NMR, near and far infra-red spectroscopies) detected in interfacial water at 160, 220 and 250 K. Starting from an amorphous state of water at low temperature, these transitions are respectively interpreted as the onset of creation of transient low density patches of 4-HBonded molecules at 160 K, the percolation of these domains at 220 K and finally the total invasion of the surface by them at 250 K. The source of this surprising behaviour in 2D is the frustration of the natural bulk tetrahedral local geometry and the underlying very significant increase in entropy of the interfacial water molecules. PMID:27185018
Phase Engineering of 2D Tin Sulfides.
Mutlu, Zafer; Wu, Ryan J; Wickramaratne, Darshana; Shahrezaei, Sina; Liu, Chueh; Temiz, Selcuk; Patalano, Andrew; Ozkan, Mihrimah; Lake, Roger K; Mkhoyan, K A; Ozkan, Cengiz S
2016-06-01
Tin sulfides can exist in a variety of phases and polytypes due to the different oxidation states of Sn. A subset of these phases and polytypes take the form of layered 2D structures that give rise to a wide host of electronic and optical properties. Hence, achieving control over the phase, polytype, and thickness of tin sulfides is necessary to utilize this wide range of properties exhibited by the compound. This study reports on phase-selective growth of both hexagonal tin (IV) sulfide SnS2 and orthorhombic tin (II) sulfide SnS crystals with diameters of over tens of microns on SiO2 substrates through atmospheric pressure vapor-phase method in a conventional horizontal quartz tube furnace with SnO2 and S powders as the source materials. Detailed characterization of each phase of tin sulfide crystals is performed using various microscopy and spectroscopy methods, and the results are corroborated by ab initio density functional theory calculations. PMID:27099950
Phase Engineering of 2D Tin Sulfides.
Mutlu, Zafer; Wu, Ryan J; Wickramaratne, Darshana; Shahrezaei, Sina; Liu, Chueh; Temiz, Selcuk; Patalano, Andrew; Ozkan, Mihrimah; Lake, Roger K; Mkhoyan, K A; Ozkan, Cengiz S
2016-06-01
Tin sulfides can exist in a variety of phases and polytypes due to the different oxidation states of Sn. A subset of these phases and polytypes take the form of layered 2D structures that give rise to a wide host of electronic and optical properties. Hence, achieving control over the phase, polytype, and thickness of tin sulfides is necessary to utilize this wide range of properties exhibited by the compound. This study reports on phase-selective growth of both hexagonal tin (IV) sulfide SnS2 and orthorhombic tin (II) sulfide SnS crystals with diameters of over tens of microns on SiO2 substrates through atmospheric pressure vapor-phase method in a conventional horizontal quartz tube furnace with SnO2 and S powders as the source materials. Detailed characterization of each phase of tin sulfide crystals is performed using various microscopy and spectroscopy methods, and the results are corroborated by ab initio density functional theory calculations.
Competing coexisting phases in 2D water
NASA Astrophysics Data System (ADS)
Zanotti, Jean-Marc; Judeinstein, Patrick; Dalla-Bernardina, Simona; Creff, Gaëlle; Brubach, Jean-Blaise; Roy, Pascale; Bonetti, Marco; Ollivier, Jacques; Sakellariou, Dimitrios; Bellissent-Funel, Marie-Claire
2016-05-01
The properties of bulk water come from a delicate balance of interactions on length scales encompassing several orders of magnitudes: i) the Hydrogen Bond (HBond) at the molecular scale and ii) the extension of this HBond network up to the macroscopic level. Here, we address the physics of water when the three dimensional extension of the HBond network is frustrated, so that the water molecules are forced to organize in only two dimensions. We account for the large scale fluctuating HBond network by an analytical mean-field percolation model. This approach provides a coherent interpretation of the different events experimentally (calorimetry, neutron, NMR, near and far infra-red spectroscopies) detected in interfacial water at 160, 220 and 250 K. Starting from an amorphous state of water at low temperature, these transitions are respectively interpreted as the onset of creation of transient low density patches of 4-HBonded molecules at 160 K, the percolation of these domains at 220 K and finally the total invasion of the surface by them at 250 K. The source of this surprising behaviour in 2D is the frustration of the natural bulk tetrahedral local geometry and the underlying very significant increase in entropy of the interfacial water molecules.
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
2-D Animation's Not Just for Mickey Mouse.
ERIC Educational Resources Information Center
Weinman, Lynda
1995-01-01
Discusses characteristics of two-dimensional (2-D) animation; highlights include character animation, painting issues, and motion graphics. Sidebars present Silicon Graphics animations tools and 2-D animation programs for the desktop computer. (DGM)
The novel high-performance 3-D MT inverse solver
NASA Astrophysics Data System (ADS)
Kruglyakov, Mikhail; Geraskin, Alexey; Kuvshinov, Alexey
2016-04-01
We present novel, robust, scalable, and fast 3-D magnetotelluric (MT) inverse solver. The solver is written in multi-language paradigm to make it as efficient, readable and maintainable as possible. Separation of concerns and single responsibility concepts go through implementation of the solver. As a forward modelling engine a modern scalable solver extrEMe, based on contracting integral equation approach, is used. Iterative gradient-type (quasi-Newton) optimization scheme is invoked to search for (regularized) inverse problem solution, and adjoint source approach is used to calculate efficiently the gradient of the misfit. The inverse solver is able to deal with highly detailed and contrasting models, allows for working (separately or jointly) with any type of MT responses, and supports massive parallelization. Moreover, different parallelization strategies implemented in the code allow optimal usage of available computational resources for a given problem statement. To parameterize an inverse domain the so-called mask parameterization is implemented, which means that one can merge any subset of forward modelling cells in order to account for (usually) irregular distribution of observation sites. We report results of 3-D numerical experiments aimed at analysing the robustness, performance and scalability of the code. In particular, our computational experiments carried out at different platforms ranging from modern laptops to HPC Piz Daint (6th supercomputer in the world) demonstrate practically linear scalability of the code up to thousands of nodes.
Adaptive kinetic-fluid solvers for heterogeneous computing architectures
NASA Astrophysics Data System (ADS)
Zabelok, Sergey; Arslanbekov, Robert; Kolobov, Vladimir
2015-12-01
We show feasibility and benefits of porting an adaptive multi-scale kinetic-fluid code to CPU-GPU systems. Challenges are due to the irregular data access for adaptive Cartesian mesh, vast difference of computational cost between kinetic and fluid cells, and desire to evenly load all CPUs and GPUs during grid adaptation and algorithm refinement. Our Unified Flow Solver (UFS) combines Adaptive Mesh Refinement (AMR) with automatic cell-by-cell selection of kinetic or fluid solvers based on continuum breakdown criteria. Using GPUs enables hybrid simulations of mixed rarefied-continuum flows with a million of Boltzmann cells each having a 24 × 24 × 24 velocity mesh. We describe the implementation of CUDA kernels for three modules in UFS: the direct Boltzmann solver using the discrete velocity method (DVM), the Direct Simulation Monte Carlo (DSMC) solver, and a mesoscopic solver based on the Lattice Boltzmann Method (LBM), all using adaptive Cartesian mesh. Double digit speedups on single GPU and good scaling for multi-GPUs have been demonstrated.
Generates 2D Input for DYNA NIKE & TOPAZ
Hallquist, J. O.; Sanford, Larry
1996-07-15
MAZE is an interactive program that serves as an input and two-dimensional mesh generator for DYNA2D, NIKE2D, TOPAZ2D, and CHEMICAL TOPAZ2D. MAZE also generates a basic template for ISLAND input. MAZE has been applied to the generation of input data to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.
MAZE96. Generates 2D Input for DYNA NIKE & TOPAZ
Sanford, L.; Hallquist, J.O.
1992-02-24
MAZE is an interactive program that serves as an input and two-dimensional mesh generator for DYNA2D, NIKE2D, TOPAZ2D, and CHEMICAL TOPAZ2D. MAZE also generates a basic template for ISLAND input. MAZE has been applied to the generation of input data to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.
Position control using 2D-to-2D feature correspondences in vision guided cell micromanipulation.
Zhang, Yanliang; Han, Mingli; Shee, Cheng Yap; Ang, Wei Tech
2007-01-01
Conventional camera calibration that utilizes the extrinsic and intrinsic parameters of the camera and the objects has certain limitations for micro-level cell operations due to the presence of hardware deviations and external disturbances during the experimental process, thereby invalidating the extrinsic parameters. This invalidation is often neglected in macro-world visual servoing and affects the visual image processing quality, causing deviation from the desired position in micro-level cell operations. To increase the success rate of vision guided biological micromanipulations, a novel algorithm monitoring the changing image pattern of the manipulators including the injection micropipette and cell holder is designed and implemented based on 2 dimensional (2D)-to 2D feature correspondences and can adjust the manipulator and perform position control simultaneously. When any deviation is found, the manipulator is retracted to the initial focusing plane before continuing the operation.
A Planar Quantum Transistor Based on 2D-2D Tunneling in Double Quantum Well Heterostructures
Baca, W.E.; Blount, M.A.; Hafich, M.J.; Lyo, S.K.; Moon, J.S.; Reno, J.L.; Simmons, J.A.; Wendt, J.R.
1998-12-14
We report on our work on the double electron layer tunneling transistor (DELTT), based on the gate-control of two-dimensional -- two-dimensional (2D-2D) tunneling in a double quantum well heterostructure. While previous quantum transistors have typically required tiny laterally-defined features, by contrast the DELTT is entirely planar and can be reliably fabricated in large numbers. We use a novel epoxy-bond-and-stop-etch (EBASE) flip-chip process, whereby submicron gating on opposite sides of semiconductor epitaxial layers as thin as 0.24 microns can be achieved. Because both electron layers in the DELTT are 2D, the resonant tunneling features are unusually sharp, and can be easily modulated with one or more surface gates. We demonstrate DELTTs with peak-to-valley ratios in the source-drain I-V curve of order 20:1 below 1 K. Both the height and position of the resonant current peak can be controlled by gate voltage over a wide range. DELTTs with larger subband energy offsets ({approximately} 21 meV) exhibit characteristics that are nearly as good at 77 K, in good agreement with our theoretical calculations. Using these devices, we also demonstrate bistable memories operating at 77 K. Finally, we briefly discuss the prospects for room temperature operation, increases in gain, and high-speed.
'Brukin2D': a 2D visualization and comparison tool for LC-MS data
Tsagkrasoulis, Dimosthenis; Zerefos, Panagiotis; Loudos, George; Vlahou, Antonia; Baumann, Marc; Kossida, Sophia
2009-01-01
Background Liquid Chromatography-Mass Spectrometry (LC-MS) is a commonly used technique to resolve complex protein mixtures. Visualization of large data sets produced from LC-MS, namely the chromatogram and the mass spectra that correspond to its compounds is the focus of this work. Results The in-house developed 'Brukin2D' software, built in Matlab 7.4, which is presented here, uses the compound data that are exported from the Bruker 'DataAnalysis' program, and depicts the mean mass spectra of all the chromatogram compounds from one LC-MS run, in one 2D contour/density plot. Two contour plots from different chromatograph runs can then be viewed in the same window and automatically compared, in order to find their similarities and differences. The results of the comparison can be examined through detailed mass quantification tables, while chromatogram compound statistics are also calculated during the procedure. Conclusion 'Brukin2D' provides a user-friendly platform for quick, easy and integrated view of complex LC-MS data. The software is available at . PMID:19534737
Inhibition of human cytochrome P450 2D6 (CYP2D6) by methadone.
Wu, D; Otton, S V; Sproule, B A; Busto, U; Inaba, T; Kalow, W; Sellers, E M
1993-01-01
1. In microsomes prepared from three human livers, methadone competitively inhibited the O-demethylation of dextromethorphan, a marker substrate for CYP2D6. The apparent Ki value of methadone ranged from 2.5 to 5 microM. 2. Two hundred and fifty-two (252) white Caucasians, including 210 unrelated healthy volunteers and 42 opiate abusers undergoing treatment with methadone were phenotyped using dextromethorphan as the marker drug. Although the frequency of poor metabolizers was similar in both groups, the extensive metabolizers among the opiate abusers tended to have higher O-demethylation metabolic ratios and to excrete less of the dose as dextromethorphan metabolites than control extensive metabolizer subjects. These data suggest inhibition of CYP2D6 by methadone in vivo as well. 3. Because methadone is widely used in the treatment of opiate abuse, inhibition of CYP2D6 activity in these patients might contribute to exaggerated response or unexpected toxicity from drugs that are substrates of this enzyme. PMID:8448065
A multiple right hand side iterative solver for history matching
Killough, J.E.; Sharma, Y.; Dupuy, A.; Bissell, R.; Wallis, J.
1995-12-31
History matching of oil and gas reservoirs can be accelerated by directly calculating the gradients of observed quantities (e.g., well pressure) with respect to the adjustable reserve parameters (e.g., permeability). This leads to a set of linear equations which add a significant overhead to the full simulation run without gradients. Direct Gauss elimination solvers can be used to address this problem by performing the factorization of the matrix only once and then reusing the factor matrix for the solution of the multiple right hand sides. This is a limited technique, however. Experience has shown that problems with greater than few thousand cells may not be practical for direct solvers because of computation time and memory limitations. This paper discusses the implementation of a multiple right hand side iterative linear equation solver (MRHS) for a system of adjoint equations to significantly enhance the performance of a gradient simulator.
Gpu Implementation of a Viscous Flow Solver on Unstructured Grids
NASA Astrophysics Data System (ADS)
Xu, Tianhao; Chen, Long
2016-06-01
Graphics processing units have gained popularities in scientific computing over past several years due to their outstanding parallel computing capability. Computational fluid dynamics applications involve large amounts of calculations, therefore a latest GPU card is preferable of which the peak computing performance and memory bandwidth are much better than a contemporary high-end CPU. We herein focus on the detailed implementation of our GPU targeting Reynolds-averaged Navier-Stokes equations solver based on finite-volume method. The solver employs a vertex-centered scheme on unstructured grids for the sake of being capable of handling complex topologies. Multiple optimizations are carried out to improve the memory accessing performance and kernel utilization. Both steady and unsteady flow simulation cases are carried out using explicit Runge-Kutta scheme. The solver with GPU acceleration in this paper is demonstrated to have competitive advantages over the CPU targeting one.
Two Solvers for Tractable Temporal Constraints with Preferences
NASA Technical Reports Server (NTRS)
Rossi, F.; Khatib,L.; Morris, P.; Morris, R.; Clancy, Daniel (Technical Monitor)
2002-01-01
A number of reasoning problems involving the manipulation of temporal information can naturally be viewed as implicitly inducing an ordering of potential local decisions involving time on the basis of preferences. Soft temporal constraints problems allow to describe in a natural way scenarios where events happen over time and preferences are associated to event distances and durations. In general, solving soft temporal problems require exponential time in the worst case, but there are interesting subclasses of problems which are polynomially solvable. We describe two solvers based on two different approaches for solving the same tractable subclass. For each solver we present the theoretical results it stands on, a description of the algorithm and some experimental results. The random generator used to build the problems on which tests are performed is also described. Finally, we compare the two solvers highlighting the tradeoff between performance and representational power.
Generation of ion temperature anisotropy in kinetic hybrid-Vlasov simulations (Invited)
NASA Astrophysics Data System (ADS)
Perrone, D.; Valentini, F.; Servidio, S.; Dalena, S.; Veltri, P.
2013-12-01
The interplanetary medium is a multi-component and weakly collisional system generally observed to be in a fully turbulent regime [1,2]. The system dynamics at short spatial scales appears to be dominated by kinetic effects that drive the interstellar gas far from the configuration of thermodynamic equilibrium [3-5]. We present a numerical analysis of a turbulent plasma composed of kinetic ions (protons and alpha particles) and fluid electrons in the typical conditions of the solar-wind environment, developed by using a low-noise hybrid Vlasov-Maxwell code [6,7] in a five dimensional phase space configuration (two dimensions in physical space and three dimensions in velocity space) [8]. The ion dynamics at short spatial scales (shorter than the proton skin depth) display several interesting aspects, mainly consisting in the departure of the distribution functions from the typical Maxwellian configuration, which has been systematically quantified through the evalutation of the temperature anisotropy ratio (perpendicular to parallel temperature ratio) with respect to the local magnetic field. This temperature anisotropy appears to be a direct effect of the turbulent nature of the system dynamics. Moreover, the turbulent activity leads to the generation of coherent structures, such as vortices and current sheets. Conditioned ion temperature distributions suggest heating associated with coherent structures; the distribution of ion temperatures moves towards higher values with increasing PVI threshold for the upper inertial range in the turbulent spectra. This behavior is more evident for alpha particles than for protons. The physical phenomenology recovered in these numerical simulations reproduces very common features recovered in 'in situ' measurements in the turbulent solar wind [9-11], suggesting that the multi-ion Vlasov model represents a valid approach to the understanding of the nature of complex kinetic effects in astrophysical plasmas. [1] R. Bruno and V
Correlated Electron Phenomena in 2D Materials
NASA Astrophysics Data System (ADS)
Lambert, Joseph G.
In this thesis, I present experimental results on coherent electron phenomena in layered two-dimensional materials: single layer graphene and van der Waals coupled 2D TiSe2. Graphene is a two-dimensional single-atom thick sheet of carbon atoms first derived from bulk graphite by the mechanical exfoliation technique in 2004. Low-energy charge carriers in graphene behave like massless Dirac fermions, and their density can be easily tuned between electron-rich and hole-rich quasiparticles with electrostatic gating techniques. The sharp interfaces between regions of different carrier densities form barriers with selective transmission, making them behave as partially reflecting mirrors. When two of these interfaces are set at a separation distance within the phase coherence length of the carriers, they form an electronic version of a Fabry-Perot cavity. I present measurements and analysis of multiple Fabry-Perot modes in graphene with parallel electrodes spaced a few hundred nanometers apart. Transition metal dichalcogenide (TMD) TiSe2 is part of the family of materials that coined the term "materials beyond graphene". It contains van der Waals coupled trilayer stacks of Se-Ti-Se. Many TMD materials exhibit a host of interesting correlated electronic phases. In particular, TiSe2 exhibits chiral charge density waves (CDW) below TCDW ˜ 200 K. Upon doping with copper, the CDW state gets suppressed with Cu concentration, and CuxTiSe2 becomes superconducting with critical temperature of T c = 4.15 K. There is still much debate over the mechanisms governing the coexistence of the two correlated electronic phases---CDW and superconductivity. I will present some of the first conductance spectroscopy measurements of proximity coupled superconductor-CDW systems. Measurements reveal a proximity-induced critical current at the Nb-TiSe2 interfaces, suggesting pair correlations in the pure TiSe2. The results indicate that superconducting order is present concurrently with CDW in
Strichartz Estimates and Moment Bounds for the Relativistic Vlasov-Maxwell System
NASA Astrophysics Data System (ADS)
Luk, Jonathan; Strain, Robert M.
2016-01-01
We consider the relativistic Vlasov-Maxwell system with data of unrestricted size and without compact support in momentum space. In the two-dimensional and the two-and-a-half-dimensional cases, Glassey-Schaeffer proved (Commun Math Phys 185:257-284, 1997; Arch Ration Mech Anal 141:331-354, 1998; Arch Ration Mech Anal. 141:355-374, 1998) that for regular initial data with compact momentum support this system has unique global in time classical solutions. In this work we do not assume compact momentum support for the initial data and instead require only that the data have polynomial decay in momentum space. In the two-dimensional and the two-and-a-half-dimensional cases, we prove the global existence, uniqueness and regularity for solutions arising from this class of initial data. To this end we use Strichartz estimates and prove that suitable moments of the solution remain bounded. Moreover, we obtain a slight improvement of the temporal growth of the {L^∞_x} norms of the electromagnetic fields compared to Glassey and Schaeffer (Commun Math Phys 185:257-284, 1997; Arch Ration Mech Anal 141:355-374, 1998). In the three-dimensional case, we apply Strichartz estimates and moment bounds to show that a regular solution can be extended as long as {{|p_0^{θ} f |_{LqxL^1p}}} remains bounded for {θ > 2/q}, {2 < q ≤q ∞}. This improves previous results of Pallard (Indiana Univ Math J 54(5):1395-1409, 2005; Commun Math Sci 13(2):347-354, 2015).
LAPACKrc: Fast linear algebra kernels/solvers for FPGA accelerators
NASA Astrophysics Data System (ADS)
Gonzalez, Juan; Núñez, Rafael C.
2009-07-01
We present LAPACKrc, a family of FPGA-based linear algebra solvers able to achieve more than 100x speedup per commodity processor on certain problems. LAPACKrc subsumes some of the LAPACK and ScaLAPACK functionalities, and it also incorporates sparse direct and iterative matrix solvers. Current LAPACKrc prototypes demonstrate between 40x-150x speedup compared against top-of-the-line hardware/software systems. A technology roadmap is in place to validate current performance of LAPACKrc in HPC applications, and to increase the computational throughput by factors of hundreds within the next few years.
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.
Profile solver in C for finite element equations
NASA Astrophysics Data System (ADS)
Hededal, O.; Krenk, S.
1994-08-01
This paper presents an efficient, pointer based profile solver with standard matrix indexing. Constrained equations Ax = b where x contains known and unknown values are solved and the full vectors x and b are obtained. Pseudo-code algorithms are formulated for a row oriented form of the LDL(sup T) factorization and implemented directly as a C code. The solver is implemented in C because of the close relation between two-dimensional arrays and pointers which makes it possible to write a clear and efficient code.
CYP2D7 Sequence Variation Interferes with TaqMan CYP2D6*15 and *35 Genotyping
Riffel, Amanda K.; Dehghani, Mehdi; Hartshorne, Toinette; Floyd, Kristen C.; Leeder, J. Steven; Rosenblatt, Kevin P.; Gaedigk, Andrea
2016-01-01
TaqMan™ genotyping assays are widely used to genotype CYP2D6, which encodes a major drug metabolizing enzyme. Assay design for CYP2D6 can be challenging owing to the presence of two pseudogenes, CYP2D7 and CYP2D8, structural and copy number variation and numerous single nucleotide polymorphisms (SNPs) some of which reflect the wild-type sequence of the CYP2D7 pseudogene. The aim of this study was to identify the mechanism causing false-positive CYP2D6*15 calls and remediate those by redesigning and validating alternative TaqMan genotype assays. Among 13,866 DNA samples genotyped by the CompanionDx® lab on the OpenArray platform, 70 samples were identified as heterozygotes for 137Tins, the key SNP of CYP2D6*15. However, only 15 samples were confirmed when tested with the Luminex xTAG CYP2D6 Kit and sequencing of CYP2D6-specific long range (XL)-PCR products. Genotype and gene resequencing of CYP2D6 and CYP2D7-specific XL-PCR products revealed a CC>GT dinucleotide SNP in exon 1 of CYP2D7 that reverts the sequence to CYP2D6 and allows a TaqMan assay PCR primer to bind. Because CYP2D7 also carries a Tins, a false-positive mutation signal is generated. This CYP2D7 SNP was also responsible for generating false-positive signals for rs769258 (CYP2D6*35) which is also located in exon 1. Although alternative CYP2D6*15 and *35 assays resolved the issue, we discovered a novel CYP2D6*15 subvariant in one sample that carries additional SNPs preventing detection with the alternate assay. The frequency of CYP2D6*15 was 0.1% in this ethnically diverse U.S. population sample. In addition, we also discovered linkage between the CYP2D7 CC>GT dinucleotide SNP and the 77G>A (rs28371696) SNP of CYP2D6*43. The frequency of this tentatively functional allele was 0.2%. Taken together, these findings emphasize that regardless of how careful genotyping assays are designed and evaluated before being commercially marketed, rare or unknown SNPs underneath primer and/or probe regions can impact
CYP2D7 Sequence Variation Interferes with TaqMan CYP2D6 (*) 15 and (*) 35 Genotyping.
Riffel, Amanda K; Dehghani, Mehdi; Hartshorne, Toinette; Floyd, Kristen C; Leeder, J Steven; Rosenblatt, Kevin P; Gaedigk, Andrea
2015-01-01
TaqMan™ genotyping assays are widely used to genotype CYP2D6, which encodes a major drug metabolizing enzyme. Assay design for CYP2D6 can be challenging owing to the presence of two pseudogenes, CYP2D7 and CYP2D8, structural and copy number variation and numerous single nucleotide polymorphisms (SNPs) some of which reflect the wild-type sequence of the CYP2D7 pseudogene. The aim of this study was to identify the mechanism causing false-positive CYP2D6 (*) 15 calls and remediate those by redesigning and validating alternative TaqMan genotype assays. Among 13,866 DNA samples genotyped by the CompanionDx® lab on the OpenArray platform, 70 samples were identified as heterozygotes for 137Tins, the key SNP of CYP2D6 (*) 15. However, only 15 samples were confirmed when tested with the Luminex xTAG CYP2D6 Kit and sequencing of CYP2D6-specific long range (XL)-PCR products. Genotype and gene resequencing of CYP2D6 and CYP2D7-specific XL-PCR products revealed a CC>GT dinucleotide SNP in exon 1 of CYP2D7 that reverts the sequence to CYP2D6 and allows a TaqMan assay PCR primer to bind. Because CYP2D7 also carries a Tins, a false-positive mutation signal is generated. This CYP2D7 SNP was also responsible for generating false-positive signals for rs769258 (CYP2D6 (*) 35) which is also located in exon 1. Although alternative CYP2D6 (*) 15 and (*) 35 assays resolved the issue, we discovered a novel CYP2D6 (*) 15 subvariant in one sample that carries additional SNPs preventing detection with the alternate assay. The frequency of CYP2D6 (*) 15 was 0.1% in this ethnically diverse U.S. population sample. In addition, we also discovered linkage between the CYP2D7 CC>GT dinucleotide SNP and the 77G>A (rs28371696) SNP of CYP2D6 (*) 43. The frequency of this tentatively functional allele was 0.2%. Taken together, these findings emphasize that regardless of how careful genotyping assays are designed and evaluated before being commercially marketed, rare or unknown SNPs underneath primer
An algorithm for computing the 2D structure of fast rotating stars
NASA Astrophysics Data System (ADS)
Rieutord, Michel; Espinosa Lara, Francisco; Putigny, Bertrand
2016-08-01
Stars may be understood as self-gravitating masses of a compressible fluid whose radiative cooling is compensated by nuclear reactions or gravitational contraction. The understanding of their time evolution requires the use of detailed models that account for a complex microphysics including that of opacities, equation of state and nuclear reactions. The present stellar models are essentially one-dimensional, namely spherically symmetric. However, the interpretation of recent data like the surface abundances of elements or the distribution of internal rotation have reached the limits of validity of one-dimensional models because of their very simplified representation of large-scale fluid flows. In this article, we describe the ESTER code, which is the first code able to compute in a consistent way a two-dimensional model of a fast rotating star including its large-scale flows. Compared to classical 1D stellar evolution codes, many numerical innovations have been introduced to deal with this complex problem. First, the spectral discretization based on spherical harmonics and Chebyshev polynomials is used to represent the 2D axisymmetric fields. A nonlinear mapping maps the spheroidal star and allows a smooth spectral representation of the fields. The properties of Picard and Newton iterations for solving the nonlinear partial differential equations of the problem are discussed. It turns out that the Picard scheme is efficient on the computation of the simple polytropic stars, but Newton algorithm is unsurpassed when stellar models include complex microphysics. Finally, we discuss the numerical efficiency of our solver of Newton iterations. This linear solver combines the iterative Conjugate Gradient Squared algorithm together with an LU-factorization serving as a preconditioner of the Jacobian matrix.
Neukirch, T.; Wilson, F.; Harrison, M. G.
2009-12-15
A detailed discussion is presented of the Vlasov-Maxwell equilibrium for the force-free Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)]. The derivation of the distribution function and a discussion of its general properties and their dependence on the distribution function parameters will be given. In particular, the distribution function can be single-peaked or multipeaked in two of the velocity components, with possible implications for stability. The dependence of the shape of the distribution function on the values of its parameters will be investigated and the relation to macroscopic quantities such as the current sheet thickness will be discussed.
NASA Technical Reports Server (NTRS)
Roberts, Dana Aaron; Abraham-Shrauner, Barbara
1987-01-01
The phase trajectories of particles in a plasma described by the one-dimensional Vlasov-Maxwell equations are determined qualitatively, analyzing exact general similarity solutions for the cases of temporally damped and growing (sinusoidal or localized) electric fields. The results of numerical integration in both untransformed and Lie-group point-transformed coordinates are presented in extensive graphs and characterized in detail. The implications of the present analysis for the stability of BGK equilibria are explored, and the existence of nonlinear solutions arbitrarily close to and significantly different from the BGK solutions is demonstrated.
Albrecht-Marc, M.; Ghizzo, A.; Johnston, T. W.; Reveille, T.; Del Sarto, D.; Bertrand, P.
2007-07-15
The influence of low-frequency nonlinear Bernstein-Greene-Kruskal (BGK)-type waves induced by trapped electrons in backward stimulated Raman scattering is investigated in optical mixing. Semi-Lagrangian Vlasov-Maxwell simulations show two nonlinear behaviors. First, there is a Morales-O'Neil plasma wave frequency downshift retuned by a small wavenumber shift which maintains the Stimulated Raman Scattering (SRS) resonance. The saturation of Raman backscattering begins with phase space vortex merging followed by a transition to lower wavenumbers following the (nonlinear) dispersion relation, resembling weak turbulence.
Mechanical characterization of 2D, 2D stitched, and 3D braided/RTM materials
NASA Technical Reports Server (NTRS)
Deaton, Jerry W.; Kullerd, Susan M.; Portanova, Marc A.
1993-01-01
Braided composite materials have potential for application in aircraft structures. Fuselage frames, floor beams, wing spars, and stiffeners are examples where braided composites could find application if cost effective processing and damage tolerance requirements are met. Another important consideration for braided composites relates to their mechanical properties and how they compare to the properties of composites produced by other textile composite processes being proposed for these applications. Unfortunately, mechanical property data for braided composites do not appear extensively in the literature. Data are presented in this paper on the mechanical characterization of 2D triaxial braid, 2D triaxial braid plus stitching, and 3D (through-the-thickness) braid composite materials. The braided preforms all had the same graphite tow size and the same nominal braid architectures, (+/- 30 deg/0 deg), and were resin transfer molded (RTM) using the same mold for each of two different resin systems. Static data are presented for notched and unnotched tension, notched and unnotched compression, and compression after impact strengths at room temperature. In addition, some static results, after environmental conditioning, are included. Baseline tension and compression fatigue results are also presented, but only for the 3D braided composite material with one of the resin systems.
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).
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)
Coordinate Projection-based Solver for ODE with Invariants
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.
Computational Screening of 2D Materials for Photocatalysis.
Singh, Arunima K; Mathew, Kiran; Zhuang, Houlong L; Hennig, Richard G
2015-03-19
Two-dimensional (2D) materials exhibit a range of extraordinary electronic, optical, and mechanical properties different from their bulk counterparts with potential applications for 2D materials emerging in energy storage and conversion technologies. In this Perspective, we summarize the recent developments in the field of solar water splitting using 2D materials and review a computational screening approach to rapidly and efficiently discover more 2D materials that possess properties suitable for solar water splitting. Computational tools based on density-functional theory can predict the intrinsic properties of potential photocatalyst such as their electronic properties, optical absorbance, and solubility in aqueous solutions. Computational tools enable the exploration of possible routes to enhance the photocatalytic activity of 2D materials by use of mechanical strain, bias potential, doping, and pH. We discuss future research directions and needed method developments for the computational design and optimization of 2D materials for photocatalysis.
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).
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)
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.
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
Synthetic Covalent and Non-Covalent 2D Materials.
Boott, Charlotte E; Nazemi, Ali; Manners, Ian
2015-11-16
The creation of synthetic 2D materials represents an attractive challenge that is ultimately driven by their prospective uses in, for example, electronics, biomedicine, catalysis, sensing, and as membranes for separation and filtration. This Review illustrates some recent advances in this diverse field with a focus on covalent and non-covalent 2D polymers and frameworks, and self-assembled 2D materials derived from nanoparticles, homopolymers, and block copolymers.
Kandrup, H.E. ); Morrison, P.J. . Inst. for Fusion Studies)
1992-11-01
The Hamiltonian formulation of the Vlasov-Einstein system, which is appropriate for collisionless, self-gravitating systems like clusters of stars that are so dense that gravity must be described by the Einstein equation, is presented. In particular, it is demonstrated explicitly in the context of a 3 + 1 splitting that, for spherically symmetric configurations, the Vlasov-Einstein system can be viewed as a Hamiltonian system, where the dynamics is generated by a noncanonical Poisson bracket, with the Hamiltonian generating the evolution of the distribution function f (a noncanonical variable) being the conserved ADM mass-energy H[sub ADM]. An explicit expression is derived for the energy [delta]([sup 2])H[sub ADM] associated with an arbitrary phase space preserving perturbation of an arbitrary spherical equilibrium, and it is shown that the equilibrium must be linearly stable if [delta]([sup 2])H[sub ADM] is positive semi-definite. Insight into the Hamiltonian reformulation is provided by a description of general finite degree of freedom systems.
Kandrup, H.E.; Morrison, P.J.
1992-11-01
The Hamiltonian formulation of the Vlasov-Einstein system, which is appropriate for collisionless, self-gravitating systems like clusters of stars that are so dense that gravity must be described by the Einstein equation, is presented. In particular, it is demonstrated explicitly in the context of a 3 + 1 splitting that, for spherically symmetric configurations, the Vlasov-Einstein system can be viewed as a Hamiltonian system, where the dynamics is generated by a noncanonical Poisson bracket, with the Hamiltonian generating the evolution of the distribution function f (a noncanonical variable) being the conserved ADM mass-energy H{sub ADM}. An explicit expression is derived for the energy {delta}({sup 2})H{sub ADM} associated with an arbitrary phase space preserving perturbation of an arbitrary spherical equilibrium, and it is shown that the equilibrium must be linearly stable if {delta}({sup 2})H{sub ADM} is positive semi-definite. Insight into the Hamiltonian reformulation is provided by a description of general finite degree of freedom systems.
Lund, S M; Kikuchi, T; Davidson, R C
2007-04-12
Self-consistent Vlasov simulations of beams with high space-charge intensity often require specification of initial phase-space distributions that reflect properties of a beam that is well adapted to the transport channel, both in terms of low-order rms (envelope) properties as well as the higher-order phase-space structure. Here, we first review broad classes of distributions commonly in use as initial Vlasov distributions in simulations of beams with intense space-charge fields including: the Kapchinskij-Vladimirskij (KV) equilibrium, continuous-focusing equilibria with specific detailed examples, and various non-equilibrium distributions, such as the semi-Gaussian distribution and distributions formed from specified functions of linear-field Courant-Snyder invariants. Important practical details necessary to specify these distributions in terms of usual accelerator inputs are presented in a unified format. Building on this presentation, a new class of approximate initial distributions are constructed using transformations that preserve linear-focusing single-particle Courant-Snyder invariants to map initial continuous-focusing equilibrium distributions to a form more appropriate for non-continuous focusing channels. Self-consistent particle-in-cell simulations are employed to show that the approximate initial distributions generated in this manner are better adapted to the focusing channels for beams with high space-charge intensity. This improved capability enables simulation applications that more precisely probe intrinsic stability properties and machine performance.
A Geometric Boolean Library for 2D Objects
2006-01-05
The 2D Boolean Library is a collection of C++ classes -- which primarily represent 2D geometric data and relationships, and routines -- which contain algorithms for 2D geometric Boolean operations and utility functions. Classes are provided for 2D points, lines, arcs, edgeuses, loops, surfaces and mask sets. Routines are provided that incorporate the Boolean operations Union(OR), XOR, Intersection and Difference. Various analytical geometry routines and routines for importing and exporting the data in various filemore » formats, are also provided in the library.« less
New Insight into Short-Wavelength Solar Wind Fluctuations from Vlasov Theory
NASA Technical Reports Server (NTRS)
Sahraoui, Fouad; Belmont, G.; Goldstein, M. L.
2012-01-01
The nature of solar wind (SW) turbulence below the proton gyroscale is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations gave evidence of the dominance of kinetic Alfven waves (KAWs) at sub-ion scales with omega < omega(sub ci), other studies suggest that the KAW mode cannot carry the turbulence cascade down to electron scales and that the whistler mode (i.e., omega > omega (sub ci)) is more relevant. Here, we study key properties of the short-wavelength plasma modes under limited, but realistic, SW conditions, Typically Beta(sub i) approx. > Beta (sub e) 1 and for high oblique angles of propagation 80 deg <= Theta (sub kB) < 90 deg as observed from the Cluster spacecraft data. The linear properties of the plasma modes under these conditions are poorly known, which contrasts with the well-documented cold plasma limit and/or moderate oblique angles of propagation (Theta (sub kB) < 80 deg). Based on linear solutions of the Vlasov kinetic theory, we discuss the relevance of each plasma mode (fast, Bernstein, KAW, whistler) in carrying the energy cascade down to electron scales. We show, in particular, that the shear Alfven mode (known in the magnetohydrodynamic limit) extends at scales kappa rho (sub i) approx. > 1 to frequencies either larger or smaller than omega (sub ci), depending on the anisotropy kappa (parallel )/ kappa(perpendicular). This extension into small scales is more readily called whistler (omega > omega (sub ci)) or KAW (omega < omega (sub ci)) although the mode is essentially the same. This contrasts with the well-accepted idea that the whistler branch always develops as a continuation at high frequencies of the fast magnetosonic mode. We show, furthermore, that the whistler branch is more damped than the KAW one, which makes the latter the more relevant candidate to carry the energy cascade down to electron scales. We discuss how these new findings may facilitate resolution
NEW INSIGHT INTO SHORT-WAVELENGTH SOLAR WIND FLUCTUATIONS FROM VLASOV THEORY
Sahraoui, F.; Belmont, G.; Goldstein, M. L.
2012-04-01
The nature of solar wind (SW) turbulence below the proton gyroscale is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations gave evidence of the dominance of kinetic Alfven waves (KAWs) at sub-ion scales with {omega} < {omega}{sub ci}, other studies suggest that the KAW mode cannot carry the turbulence cascade down to electron scales and that the whistler mode (i.e., {omega} > {omega}{sub ci}) is more relevant. Here, we study key properties of the short-wavelength plasma modes under limited, but realistic, SW conditions, typically {beta}{sub i} {approx}> {beta}{sub e} {approx} 1 and for high oblique angles of propagation 80 Degree-Sign {<=} {Theta}{sub kB} < 90 Degree-Sign as observed from the Cluster spacecraft data. The linear properties of the plasma modes under these conditions are poorly known, which contrasts with the well-documented cold plasma limit and/or moderate oblique angles of propagation ({Theta}{sub kB} < 80 Degree-Sign ). Based on linear solutions of the Vlasov kinetic theory, we discuss the relevance of each plasma mode (fast, Bernstein, KAW, whistler) in carrying the energy cascade down to electron scales. We show, in particular, that the shear Alfven mode (known in the magnetohydrodynamic limit) extends at scales k{rho}{sub i} {approx}> 1 to frequencies either larger or smaller than {omega}{sub ci}, depending on the anisotropy k{sub ||}/k . This extension into small scales is more readily called whistler ({omega} > {omega}{sub ci}) or KAW ({omega} < {omega}{sub ci}), although the mode is essentially the same. This contrasts with the well-accepted idea that the whistler branch always develops as a continuation at high frequencies of the fast magnetosonic mode. We show, furthermore, that the whistler branch is more damped than the KAW one, which makes the latter the more relevant candidate to carry the energy cascade down to electron scales. We discuss how these new findings
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.
VizieR Online Data Catalog: The 2dF Galaxy Redshift Survey (2dFGRS) (2dFGRS Team, 1998-2003)
NASA Astrophysics Data System (ADS)
Colless, M.; Dalton, G.; Maddox, S.; Sutherland, W.; Norberg, P.; Cole, S.; Bland-Hawthorn, J.; Bridges, T.; Cannon, R.; Collins, C.; Couch, W.; Cross, N.; Deeley, K.; de Propris, R.; Driver, S. P.; Efstathiou, G.; Ellis, R. S.; Frenk, C. S.; Glazebrook, K.; Jackson, C.; Lahav, O.; Lewis, I.; Lumsden, S.; Madgwick, D.; Peacock, J. A.; Peterson, B. A.; Price, I.; Seaborne, M.; Taylor, K.
2007-11-01
The 2dF Galaxy Redshift Survey (2dFGRS) is a major spectroscopic survey taking full advantage of the unique capabilities of the 2dF facility built by the Anglo-Australian Observatory. The 2dFGRS is integrated with the 2dF QSO survey (2QZ, Cat. VII/241). The 2dFGRS obtained spectra for 245591 objects, mainly galaxies, brighter than a nominal extinction-corrected magnitude limit of bJ=19.45. Reliable (quality>=3) redshifts were obtained for 221414 galaxies. The galaxies cover an area of approximately 1500 square degrees selected from the extended APM Galaxy Survey in three regions: a North Galactic Pole (NGP) strip, a South Galactic Pole (SGP) strip, and random fields scattered around the SGP strip. Redshifts are measured from spectra covering 3600-8000 Angstroms at a two-pixel resolution of 9.0 Angstrom and a median S/N of 13 per pixel. All redshift identifications are visually checked and assigned a quality parameter Q in the range 1-5; Q>=3 redshifts are 98.4% reliable and have an rms uncertainty of 85 km/s. The overall redshift completeness for Q>=3 redshifts is 91.8% but this varies with magnitude from 99% for the brightest galaxies to 90% for objects at the survey limit. The 2dFGRS data base is available on the World Wide Web at http://www.mso.anu.edu.au/2dFGRS/. (6 data files).
Klassifikation von Standardebenen in der 2D-Echokardiographie mittels 2D-3D-Bildregistrierung
NASA Astrophysics Data System (ADS)
Bergmeir, Christoph; Subramanian, Navneeth
Zum Zweck der Entwicklung eines Systems, das einen unerfahrenen Anwender von Ultraschall (US) zur Aufnahme relevanter anatomischer Strukturen leitet, untersuchen wir die Machbarkeit von 2D-US zu 3D-CT Registrierung. Wir verwenden US-Aufnahmen von Standardebenen des Herzens, welche zu einem 3D-CT-Modell registriert werden. Unser Algorithmus unterzieht sowohl die US-Bilder als auch den CT-Datensatz Vorverarbeitungsschritten, welche die Daten durch Segmentierung auf wesentliche Informationen in Form von Labein für Muskel und Blut reduzieren. Anschließend werden diese Label zur Registrierung mittels der Match-Cardinality-Metrik genutzt. Durch mehrmaliges Registrieren mit verschiedenen Initialisierungen ermitteln wir die im US-Bild sichtbare Standardebene. Wir evaluierten die Methode auf sieben US-Bildern von Standardebenen. Fünf davon wurden korrekt zugeordnet.
Epitaxial 2D SnSe2/ 2D WSe2 van der Waals Heterostructures.
Aretouli, Kleopatra Emmanouil; Tsoutsou, Dimitra; Tsipas, Polychronis; Marquez-Velasco, Jose; Aminalragia Giamini, Sigiava; Kelaidis, Nicolaos; Psycharis, Vassilis; Dimoulas, Athanasios
2016-09-01
van der Waals heterostructures of 2D semiconductor materials can be used to realize a number of (opto)electronic devices including tunneling field effect devices (TFETs). It is shown in this work that high quality SnSe2/WSe2 vdW heterostructure can be grown by molecular beam epitaxy on AlN(0001)/Si(111) substrates using a Bi2Se3 buffer layer. A valence band offset of 0.8 eV matches the energy gap of SnSe2 in such a way that the VB edge of WSe2 and the CB edge of SnSe2 are lined up, making this materials combination suitable for (nearly) broken gap TFETs. PMID:27537619
CVMAC 2D Program: A method of converting 3D to 2D
Lown, J.
1990-06-20
This paper presents the user with a method of converting a three- dimensional wire frame model into a technical illustration, detail, or assembly drawing. By using the 2D Program, entities can be mapped from three-dimensional model space into two-dimensional model space, as if they are being traced. Selected entities to be mapped can include circles, arcs, lines, and points. This program prompts the user to digitize the view to be mapped, specify the layers in which the new two-dimensional entities will reside, and select the entities, either by digitizing or windowing. The new two-dimensional entities are displayed in a small view which the program creates in the lower left corner of the drawing. 9 figs.
NASA Technical Reports Server (NTRS)
Thompson David S.; Soni, Bharat K.
2001-01-01
An integrated geometry/grid/simulation software package, ICEG2D, is being developed to automate computational fluid dynamics (CFD) simulations for single- and multi-element airfoils with ice accretions. The current version, ICEG213 (v2.0), was designed to automatically perform four primary functions: (1) generate a grid-ready surface definition based on the geometrical characteristics of the iced airfoil surface, (2) generate high-quality structured and generalized grids starting from a defined surface definition, (3) generate the input and restart files needed to run the structured grid CFD solver NPARC or the generalized grid CFD solver HYBFL2D, and (4) using the flow solutions, generate solution-adaptive grids. ICEG2D (v2.0) can be operated in either a batch mode using a script file or in an interactive mode by entering directives from a command line within a Unix shell. This report summarizes activities completed in the first two years of a three-year research and development program to address automation issues related to CFD simulations for airfoils with ice accretions. As well as describing the technology employed in the software, this document serves as a users manual providing installation and operating instructions. An evaluation of the software is also presented.
2D Four-Channel Perfect Reconstruction Filter Bank Realized with the 2D Lattice Filter Structure
NASA Astrophysics Data System (ADS)
Sezen, S.; Ertüzün, A.
2006-12-01
A novel orthogonal 2D lattice structure is incorporated into the design of a nonseparable 2D four-channel perfect reconstruction filter bank. The proposed filter bank is obtained by using the polyphase decomposition technique which requires the design of an orthogonal 2D lattice filter. Due to constraint of perfect reconstruction, each stage of this lattice filter bank is simply parameterized by two coefficients. The perfect reconstruction property is satisfied regardless of the actual values of these parameters and of the number of the lattice stages. It is also shown that a separable 2D four-channel perfect reconstruction lattice filter bank can be constructed from the 1D lattice filter and that this is a special case of the proposed 2D lattice filter bank under certain conditions. The perfect reconstruction property of the proposed 2D lattice filter approach is verified by computer simulations.
Destabilization of 2D magnetic current sheets by resonance with bouncing electron - a new theory
NASA Astrophysics Data System (ADS)
Fruit, Gabriel; Louarn, Philippe; Tur, Anatoly
2016-07-01
In the general context of understanding the possible destabilization of the magnetotail before a substorm, we propose a kinetic model for electromagnetic instabilities in resonant interaction with trapped bouncing electrons. The geometry is clearly 2D and uses Harris sheet profile. Fruit et al. 2013 already used this model to investigate the possibilities of electrostatic instabilities. Tur et al. 2014 generalizes the model for full electromagnetic perturbations. Starting with a modified Harris sheet as equilibrium state, the linearized gyrokinetic Vlasov equation is solved for electromagnetic fluctuations with period of the order of the electron bounce period (a few seconds). The particle motion is restricted to its first Fourier component along the magnetic field and this allows the complete time integration of the non local perturbed distribution functions. The dispersion relation for electromagnetic modes is finally obtained through the quasi neutrality condition and the Ampere's law for the current density. The present talk will focus on the main results of this theory. The electrostatic version of the model may be applied to the near-Earth environment (8-12 R_{E}) where beta is rather low. It is showed that inclusion of bouncing electron motion may enhance strongly the growth rate of the classical drift wave instability. This model could thus explain the generation of strong parallel electric fields in the ionosphere and the formation of aurora beads with wavelength of a few hundreds of km. In the electromagnetic version, it is found that for mildly stretched current sheet (B_{z} > 0.1 B _{lobes}) undamped modes oscillate at typical electron bounce frequency with wavelength of the order of the plasma sheet thickness. As the stretching of the plasma sheet becomes more intense, the frequency of these normal modes decreases and beyond a certain threshold in B_{z}/B _{lobes}, the mode becomes explosive (pure imaginary frequency) with typical growing rate of a few
Functional characterization of CYP2D6 enhancer polymorphisms
Wang, Danxin; Papp, Audrey C.; Sun, Xiaochun
2015-01-01
CYP2D6 metabolizes nearly 25% of clinically used drugs. Genetic polymorphisms cause large inter-individual variability in CYP2D6 enzyme activity and are currently used as biomarker to predict CYP2D6 metabolizer phenotype. Previously, we had identified a region 115 kb downstream of CYP2D6 as enhancer for CYP2D6, containing two completely linked single nucleotide polymorphisms (SNPs), rs133333 and rs5758550, associated with enhanced transcription. However, the enhancer effect on CYP2D6 expression, and the causative variant, remained to be ascertained. To characterize the CYP2D6 enhancer element, we applied chromatin conformation capture combined with the next-generation sequencing (4C assays) and chromatin immunoprecipitation with P300 antibody, in HepG2 and human primary culture hepatocytes. The results confirmed the role of the previously identified enhancer region in CYP2D6 expression, expanding the number of candidate variants to three highly linked SNPs (rs133333, rs5758550 and rs4822082). Among these, only rs5758550 demonstrated regulating enhancer activity in a reporter gene assay. Use of clustered regularly interspaced short palindromic repeats mediated genome editing in HepG2 cells targeting suspected enhancer regions decreased CYP2D6 mRNA expression by 70%, only upon deletion of the rs5758550 region. These results demonstrate robust effects of both the enhancer element and SNP rs5758550 on CYP2D6 expression, supporting consideration of rs5758550 for CYP2D6 genotyping panels to yield more accurate phenotype prediction. PMID:25381333
NASA Astrophysics Data System (ADS)
Chae, Dongho; Constantin, Peter; Wu, Jiahong
2014-09-01
We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to be the first such example. Further, we construct explicit solutions of the 2D Boussinesq equations whose gradients grow exponentially in time for all time. In addition, we introduce a variant of the 2D Boussinesq equations which is perhaps a more faithful companion of the 3D axisymmetric Euler equations than the usual 2D Boussinesq equations.
NASA Astrophysics Data System (ADS)
Daude, F.; Galon, P.
2016-01-01
Computation of compressible two-phase flows with the unsteady compressible Baer-Nunziato model in conjunction with the moving grid approach is discussed in this paper. Both HLL- and HLLC-type Finite-Volume methods are presented and implemented in the context of Arbitrary Lagrangian-Eulerian formulation in a multidimensional framework. The construction of suitable numerical methods is linked to proper approximations of the non-conservative terms on moving grids. The HLL discretization follows global conservation properties such as free-stream preservation and uniform pressure and velocity profiles preservation on moving grids. The HLLC solver initially proposed by Tokareva and Toro [1] for the Baer-Nunziato model is based on an approximate solution of local Riemann problems containing all the characteristic fields present in the exact solution. Both "subsonic" and "supersonic" configurations are considered in the construction of the present HLLC solver. In addition, an adaptive 6-wave HLLC scheme is also proposed for computational efficiency. The methods are first assessed on a variety of 1-D Riemann problems including both fixed and moving grids applications. The methods are finally tested on 2-D and 3-D applications: 2-D Riemann problems, a 2-D shock-bubble interaction and finally a 3-D fluid-structure interaction problem with a good agreement with the experiments.
Adaptation algorithms for 2-D feedforward neural networks.
Kaczorek, T
1995-01-01
The generalized weight adaptation algorithms presented by J.G. Kuschewski et al. (1993) and by S.H. Zak and H.J. Sira-Ramirez (1990) are extended for 2-D madaline and 2-D two-layer feedforward neural nets (FNNs).
Integrating Mobile Multimedia into Textbooks: 2D Barcodes
ERIC Educational Resources Information Center
Uluyol, Celebi; Agca, R. Kagan
2012-01-01
The major goal of this study was to empirically compare text-plus-mobile phone learning using an integrated 2D barcode tag in a printed text with three other conditions described in multimedia learning theory. The method examined in the study involved modifications of the instructional material such that: a 2D barcode was used near the text, the…
Efficient Visible Quasi-2D Perovskite Light-Emitting Diodes.
Byun, Jinwoo; Cho, Himchan; Wolf, Christoph; Jang, Mi; Sadhanala, Aditya; Friend, Richard H; Yang, Hoichang; Lee, Tae-Woo
2016-09-01
Efficient quasi-2D-structure perovskite light-emitting diodes (4.90 cd A(-1) ) are demonstrated by mixing a 3D-structured perovskite material (methyl ammonium lead bromide) and a 2D-structured perovskite material (phenylethyl ammonium lead bromide), which can be ascribed to better film uniformity, enhanced exciton confinement, and reduced trap density. PMID:27334788
CYP2D6: novel genomic structures and alleles
Kramer, Whitney E.; Walker, Denise L.; O’Kane, Dennis J.; Mrazek, David A.; Fisher, Pamela K.; Dukek, Brian A.; Bruflat, Jamie K.; Black, John L.
2010-01-01
Objective CYP2D6 is a polymorphic gene. It has been observed to be deleted, to be duplicated and to undergo recombination events involving the CYP2D7 pseudogene and surrounding sequences. The objective of this study was to discover the genomic structure of CYP2D6 recombinants that interfere with clinical genotyping platforms that are available today. Methods Clinical samples containing rare homozygous CYP2D6 alleles, ambiguous readouts, and those with duplication signals and two different alleles were analyzed by long-range PCR amplification of individual genes, PCR fragment analysis, allele-specific primer extension assay, and DNA sequencing to characterize alleles and genomic structure. Results Novel alleles, genomic structures, and the DNA sequence of these structures are described. Interestingly, in 49 of 50 DNA samples that had CYP2D6 gene duplications or multiplications where two alleles were detected, the chromosome containing the duplication or multiplication had identical tandem alleles. Conclusion Several new CYP2D6 alleles and genomic structures are described which will be useful for CYP2D6 genotyping. The findings suggest that the recombination events responsible for CYP2D6 duplications and multiplications are because of mechanisms other than interchromosomal crossover during meiosis. PMID:19741566
Efficient Visible Quasi-2D Perovskite Light-Emitting Diodes.
Byun, Jinwoo; Cho, Himchan; Wolf, Christoph; Jang, Mi; Sadhanala, Aditya; Friend, Richard H; Yang, Hoichang; Lee, Tae-Woo
2016-09-01
Efficient quasi-2D-structure perovskite light-emitting diodes (4.90 cd A(-1) ) are demonstrated by mixing a 3D-structured perovskite material (methyl ammonium lead bromide) and a 2D-structured perovskite material (phenylethyl ammonium lead bromide), which can be ascribed to better film uniformity, enhanced exciton confinement, and reduced trap density.
A parallel-vector equation solver for unsymmetric matrices on supercomputers
NASA Technical Reports Server (NTRS)
Qin, J.; Mei, C.; Nguyen, D. T.; Gray, C. E., Jr.
1991-01-01
A parallel-vector unsymmetric equation solver is presented. The solver exploits both vector and parallel capabilities provided by modern, high-performance supercomputers. A special storage scheme and loop-unrolling technique are used to optimize the vector performance. A parallel FORTRAN language is used to develop the solver on the CRAY 2 and CRAY Y-MP multiple processing computer environment. Three numerical examples are presented which demonstrate the efficiency and accuracy of this equation solver. The first two examples demonstrate the improved performance, and the third example utilizes the proposed solver to solve a highly nonlinear, unsymmetric finite element formulation for panel flutter.
2D materials and van der Waals heterostructures.
Novoselov, K S; Mishchenko, A; Carvalho, A; Castro Neto, A H
2016-07-29
The physics of two-dimensional (2D) materials and heterostructures based on such crystals has been developing extremely fast. With these new materials, truly 2D physics has begun to appear (for instance, the absence of long-range order, 2D excitons, commensurate-incommensurate transition, etc.). Novel heterostructure devices--such as tunneling transistors, resonant tunneling diodes, and light-emitting diodes--are also starting to emerge. Composed from individual 2D crystals, such devices use the properties of those materials to create functionalities that are not accessible in other heterostructures. Here we review the properties of novel 2D crystals and examine how their properties are used in new heterostructure devices.
Van der Waals stacked 2D layered materials for optoelectronics
NASA Astrophysics Data System (ADS)
Zhang, Wenjing; Wang, Qixing; Chen, Yu; Wang, Zhuo; Wee, Andrew T. S.
2016-06-01
The band gaps of many atomically thin 2D layered materials such as graphene, black phosphorus, monolayer semiconducting transition metal dichalcogenides and hBN range from 0 to 6 eV. These isolated atomic planes can be reassembled into hybrid heterostructures made layer by layer in a precisely chosen sequence. Thus, the electronic properties of 2D materials can be engineered by van der Waals stacking, and the interlayer coupling can be tuned, which opens up avenues for creating new material systems with rich functionalities and novel physical properties. Early studies suggest that van der Waals stacked 2D materials work exceptionally well, dramatically enriching the optoelectronics applications of 2D materials. Here we review recent progress in van der Waals stacked 2D materials, and discuss their potential applications in optoelectronics.
Estrogen-Induced Cholestasis Leads to Repressed CYP2D6 Expression in CYP2D6-Humanized Mice
Pan, Xian
2015-01-01
Cholestasis activates bile acid receptor farnesoid X receptor (FXR) and subsequently enhances hepatic expression of small heterodimer partner (SHP). We previously demonstrated that SHP represses the transactivation of cytochrome P450 2D6 (CYP2D6) promoter by hepatocyte nuclear factor (HNF) 4α. In this study, we investigated the effects of estrogen-induced cholestasis on CYP2D6 expression. Estrogen-induced cholestasis occurs in subjects receiving estrogen for contraception or hormone replacement, or in susceptible women during pregnancy. In CYP2D6-humanized transgenic (Tg-CYP2D6) mice, cholestasis triggered by administration of 17α-ethinylestradiol (EE2) at a high dose led to 2- to 3-fold decreases in CYP2D6 expression. This was accompanied by increased hepatic SHP expression and subsequent decreases in the recruitment of HNF4α to CYP2D6 promoter. Interestingly, estrogen-induced cholestasis also led to increased recruitment of estrogen receptor (ER) α, but not that of FXR, to Shp promoter, suggesting a predominant role of ERα in transcriptional regulation of SHP in estrogen-induced cholestasis. EE2 at a low dose (that does not cause cholestasis) also increased SHP (by ∼50%) and decreased CYP2D6 expression (by 1.5-fold) in Tg-CYP2D6 mice, the magnitude of differences being much smaller than that shown in EE2-induced cholestasis. Taken together, our data indicate that EE2-induced cholestasis increases SHP and represses CYP2D6 expression in Tg-CYP2D6 mice in part through ERα transactivation of Shp promoter. PMID:25943116
Rethinking Electrostatic Solvers in Particle Simulations for the Exascale Era
NASA Astrophysics Data System (ADS)
Deca, Jan; Markidis, Stefano; Lapenta, Giovanni; Járleberg, Erik; Apostolov, Rossen; Laure, Erwin
2012-10-01
In preparation to the exascale era, an alternative approach to calculate the electrostatic forces in Particle Mesh (PM) methods is proposed. While the traditional techniques are based on the calculation of the electrostatic potential by solving the Poisson equation, in the new approach the electric field is calculated by solving Ampère's law. When the Ampere's law is discretized explicitly in time, the electric field values on the mesh are simply updated from the previous values. In this way, the electrostatic solver becomes an embarrassingly parallel problem, making the algorithm extremely scalable and suitable for exascale computing platforms. An implementation PM code with the new electrostatic solver is presented to show that the proposed method produces correct results. It is a very promising algorithm for exascale PM simulations.
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.
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.
An exact solver for the DCJ median problem.
Zhang, Meng; Arndt, William; Tang, Jijun
2009-01-01
The "double-cut-and-join" (DCJ) model of genome rearrangement proposed by Yancopoulos et al. uses the single DCJ operation to account for all genome rearrangement events. Given three signed permutations, the DCJ median problem is to find a fourth permutation that minimizes the sum of the pairwise DCJ distances between it and the three others. In this paper, we present a branch-and-bound method that provides accurate solution to the multichromosomal DCJ median problems. We conduct extensive simulations and the results show that the DCJ median solver performs better than other median solvers for most of the test cases. These experiments also suggest that DCJ model is more suitable for real datasets where both reversals and transpositions occur.
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.
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.
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.
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 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.
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.
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.
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.
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.
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
Reynolds-Averaged Navier-Stokes Simulation of a 2D Circulation Control Wind Tunnel Experiment
NASA Technical Reports Server (NTRS)
Allan, Brian G.; Jones, Greg; Lin, John C.
2011-01-01
Numerical simulations are performed using a Reynolds-averaged Navier-Stokes (RANS) flow solver for a circulation control airfoil. 2D and 3D simulation results are compared to a circulation control wind tunnel test conducted at the NASA Langley Basic Aerodynamics Research Tunnel (BART). The RANS simulations are compared to a low blowing case with a jet momentum coefficient, C(sub u), of 0:047 and a higher blowing case of 0.115. Three dimensional simulations of the model and tunnel walls show wall effects on the lift and airfoil surface pressures. These wall effects include a 4% decrease of the midspan sectional lift for the C(sub u) 0.115 blowing condition. Simulations comparing the performance of the Spalart Allmaras (SA) and Shear Stress Transport (SST) turbulence models are also made, showing the SST model compares best to the experimental data. A Rotational/Curvature Correction (RCC) to the turbulence model is also evaluated demonstrating an improvement in the CFD predictions.
Rise characteristics of gas bubbles in a 2D rectangular column: VOF simulations vs experiments
Krishna, R.; Baten, J.M. van
1999-10-01
About five centuries ago, Leonardo da Vinci described the sinuous motion of gas bubbles rising in water. The authors have attempted to simulate the rise trajectories of bubbles of 4, 5, 7, 8, 9, 12, and 20 mm in diameter rising in a 2D rectangular column filled with water. The simulations were carried out using the volume-of-fluid (VOF) technique developed by Hirt and Nichols (J. Computational Physics, 39, 201--225 (1981)). To solve the Navier-Stokes equations of motion the authors used a commercial solver, CFX 4.1c of AEA Technology, UK. They developed their own bubble-tracking algorithm to capture sinuous bubble motions. The 4 and 5 mm bubbles show large lateral motions observed by Da Vinci. The 7, 8 and 9 mm bubble behave like jellyfish. The 12 mm bubble flaps its wings like a bird. The extent of lateral motion of the bubbles decreases with increasing bubble size. Bubbles larger than 20 mm in size assume a spherical cap form and simulations of the rise characteristics match experiments exactly. VOF simulations are powerful tools for a priori determination of the morphology and rise characteristics of bubbles rising in a liquid. Bubble-bubble interactions are also properly modeled by the VOF technique.
2D electrostatic PIC algorithm for laser induced studying plasma in vacuum
NASA Astrophysics Data System (ADS)
Álvarez, C. A.; Riascos, H.; Gonzalez, C.
2016-02-01
Particle-In-Cell(PIC) method is widely used for simulating plasma kinetic models. A 2D-PIC electrostatic algorithm is implemented for simulating the expansion of a laser- induced plasma plume. For potential and Electric Field calculation, Dirichlet and periodic boundary conditions are used in the X (perpendicular to the ablated material) and Y directions, respectively. Poisson-solver employs FFTW3 library and the five-point Laplacian to compute the electric potential. Electric field calculation is made by central finite differences method. Leap-frog scheme updates particle positions and velocities at each iteration. Plume expansion anlysis is done for the Emission and Post-Emission stages. In the Emission phase (while the laser is turned on), fast electron expansion is observed and ion particles remain near the surface of the ablated material. In the post-emission stage (with the laser turned off) the charge separation produces an electric field that accelerates the ions leading to the formation of a KeV per particle Ion-Front. At the end of the expansion, fastest electrons escape from the simulation space; an almost homogeneous ion-electron distribution is observed, decreasing the electric field value and the Coulomb interactions.
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.
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
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.
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.
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.
Direct linear programming solver in C for structural applications
NASA Astrophysics Data System (ADS)
Damkilde, L.; Hoyer, O.; Krenk, S.
1994-08-01
An optimization problem can be characterized by an object-function, which is maximized, and restrictions, which limit the variation of the variables. A subclass of optimization is Linear Programming (LP), where both the object-function and the restrictions are linear functions of the variables. The traditional solution methods for LP problems are based on the simplex method, and it is customary to allow only non-negative variables. Compared to other optimization routines the LP solvers are more robust and the optimum is reached in a finite number of steps and is not sensitive to the starting point. For structural applications many optimization problems can be linearized and solved by LP routines. However, the structural variables are not always non-negative, and this requires a reformation, where a variable x is substituted by the difference of two non-negative variables, x(sup + ) and x(sup - ). The transformation causes a doubling of the number of variables, and in a computer implementation the memory allocation doubles and for a typical problem the execution time at least doubles. This paper describes a LP solver written in C, which can handle a combination of non-negative variables and unlimited variables. The LP solver also allows restart, and this may reduce the computational costs if the solution to a similar LP problem is known a priori. The algorithm is based on the simplex method, and differs only in the logical choices. Application of the new LP solver will at the same time give both a more direct problem formulation and a more efficient program.
Xie, Donghao; Ji, Ding-Kun; Zhang, Yue; Cao, Jun; Zheng, Hu; Liu, Lin; Zang, Yi; Li, Jia; Chen, Guo-Rong; James, Tony D; He, Xiao-Peng
2016-08-01
Here we demonstrate that 2D MoS2 can enhance the receptor-targeting and imaging ability of a fluorophore-labelled ligand. The 2D MoS2 has an enhanced working concentration range when compared with graphene oxide, resulting in the improved imaging of both cell and tissue samples.
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.
Fast linear solvers for variable density turbulent flows
NASA Astrophysics Data System (ADS)
Pouransari, Hadi; Mani, Ali; Darve, Eric
2015-11-01
Variable density flows are ubiquitous in variety of natural and industrial systems. Two-phase and multi-phase flows in natural and industrial processes, astrophysical flows, and flows involved in combustion processes are such examples. For an ideal gas subject to low-Mach approximation, variations in temperature can lead to a non-uniform density field. In this work, we consider radiatively heated particle-laden turbulent flows as an example application in which density variability is resulted from inhomogeneities in the heat absorption by an inhomogeneous particle field. Under such conditions, the divergence constraint of the fluid is enforced through a variable coefficient Poisson equation. Inversion of the discretized variable coefficient Poisson operator is difficult using the conventional linear solvers as the size of the problem grows. We apply a novel hierarchical linear solve algorithm based on low-rank approximations. The proposed linear solver could be applied to variety of linear systems arising from discretized partial differential equations. It can be used as a standalone direct-solver with tunable accuracy and linear complexity, or as a high-accuracy pre-conditioner in conjunction with other iterative methods.
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.
QED multi-dimensional vacuum polarization finite-difference solver
NASA Astrophysics Data System (ADS)
Carneiro, Pedro; Grismayer, Thomas; Silva, Luís; Fonseca, Ricardo
2015-11-01
The Extreme Light Infrastructure (ELI) is expected to deliver peak intensities of 1023 - 1024 W/cm2 allowing to probe nonlinear Quantum Electrodynamics (QED) phenomena in an unprecedented regime. Within the framework of QED, the second order process of photon-photon scattering leads to a set of extended Maxwell's equations [W. Heisenberg and H. Euler, Z. Physik 98, 714] effectively creating nonlinear polarization and magnetization terms that account for the nonlinear response of the vacuum. To model this in a self-consistent way, we present a multi dimensional generalized Maxwell equation finite difference solver with significantly enhanced dispersive properties, which was implemented in the OSIRIS particle-in-cell code [R.A. Fonseca et al. LNCS 2331, pp. 342-351, 2002]. We present a detailed numerical analysis of this electromagnetic solver. As an illustration of the properties of the solver, we explore several examples in extreme conditions. We confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field [arXiv:1301.4918 [quant-ph
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.
NASA Astrophysics Data System (ADS)
Su, Xiaohui; Cao, Yuanwei; Zhao, Yong
2016-06-01
In this paper, an unstructured mesh Arbitrary Lagrangian-Eulerian (ALE) incompressible flow solver is developed to investigate the aerodynamics of insect hovering flight. The proposed finite-volume ALE Navier-Stokes solver is based on the artificial compressibility method (ACM) with a high-resolution method of characteristics-based scheme on unstructured grids. The present ALE model is validated and assessed through flow passing over an oscillating cylinder. Good agreements with experimental results and other numerical solutions are obtained, which demonstrates the accuracy and the capability of the present model. The lift generation mechanisms of 2D wing in hovering motion, including wake capture, delayed stall, rapid pitch, as well as clap and fling are then studied and illustrated using the current ALE model. Moreover, the optimized angular amplitude in symmetry model, 45°, is firstly reported in details using averaged lift and the energy power method. Besides, the lift generation of complete cyclic clap and fling motion, which is simulated by few researchers using the ALE method due to large deformation, is studied and clarified for the first time. The present ALE model is found to be a useful tool to investigate lift force generation mechanism for insect wing flight.
Efficient 2D MRI relaxometry using compressed sensing
NASA Astrophysics Data System (ADS)
Bai, Ruiliang; Cloninger, Alexander; Czaja, Wojciech; Basser, Peter J.
2015-06-01
Potential applications of 2D relaxation spectrum NMR and MRI to characterize complex water dynamics (e.g., compartmental exchange) in biology and other disciplines have increased in recent years. However, the large amount of data and long MR acquisition times required for conventional 2D MR relaxometry limits its applicability for in vivo preclinical and clinical MRI. We present a new MR pipeline for 2D relaxometry that incorporates compressed sensing (CS) as a means to vastly reduce the amount of 2D relaxation data needed for material and tissue characterization without compromising data quality. Unlike the conventional CS reconstruction in the Fourier space (k-space), the proposed CS algorithm is directly applied onto the Laplace space (the joint 2D relaxation data) without compressing k-space to reduce the amount of data required for 2D relaxation spectra. This framework is validated using synthetic data, with NMR data acquired in a well-characterized urea/water phantom, and on fixed porcine spinal cord tissue. The quality of the CS-reconstructed spectra was comparable to that of the conventional 2D relaxation spectra, as assessed using global correlation, local contrast between peaks, peak amplitude and relaxation parameters, etc. This result brings this important type of contrast closer to being realized in preclinical, clinical, and other applications.
Practical Algorithm For Computing The 2-D Arithmetic Fourier Transform
NASA Astrophysics Data System (ADS)
Reed, Irving S.; Choi, Y. Y.; Yu, Xiaoli
1989-05-01
Recently, Tufts and Sadasiv [10] exposed a method for computing the coefficients of a Fourier series of a periodic function using the Mobius inversion of series. They called this method of analysis the Arithmetic Fourier Transform(AFT). The advantage of the AFT over the FN 1' is that this method of Fourier analysis needs only addition operations except for multiplications by scale factors at one stage of the computation. The disadvantage of the AFT as they expressed it originally is that it could be used effectively only to compute finite Fourier coefficients of a real even function. To remedy this the AFT developed in [10] is extended in [11] to compute the Fourier coefficients of both the even and odd components of a periodic function. In this paper, the improved AFT [11] is extended to a two-dimensional(2-D) Arithmetic Fourier Transform for calculating the Fourier Transform of two-dimensional discrete signals. This new algorithm is based on both the number-theoretic method of Mobius inversion of double series and the complex conjugate property of Fourier coefficients. The advantage of this algorithm over the conventional 2-D FFT is that the corner-turning problem needed in a conventional 2-D Discrete Fourier Transform(DFT) can be avoided. Therefore, this new 2-D algorithm is readily suitable for VLSI implementation as a parallel architecture. Comparing the operations of 2-D AFT of a MxM 2-D data array with the conventional 2-D FFT, the number of multiplications is significantly reduced from (2log2M)M2 to (9/4)M2. Hence, this new algorithm is faster than the FFT algorithm. Finally, two simulation results of this new 2-D AFT algorithm for 2-D artificial and real images are given in this paper.
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.
2D electron cyclotron emission imaging at ASDEX Upgrade (invited)
Classen, I. G. J.; Boom, J. E.; Vries, P. C. de; Suttrop, W.; Schmid, E.; Garcia-Munoz, M.; Schneider, P. A.; Tobias, B.; Domier, C. W.; Luhmann, N. C. Jr.; Donne, A. J. H.; Jaspers, R. J. E.; Park, H. K.; Munsat, T.
2010-10-15
The newly installed electron cyclotron emission imaging diagnostic on ASDEX Upgrade provides measurements of the 2D electron temperature dynamics with high spatial and temporal resolution. An overview of the technical and experimental properties of the system is presented. These properties are illustrated by the measurements of the edge localized mode and the reversed shear Alfven eigenmode, showing both the advantage of having a two-dimensional (2D) measurement, as well as some of the limitations of electron cyclotron emission measurements. Furthermore, the application of singular value decomposition as a powerful tool for analyzing and filtering 2D data is presented.
Comparison of 2D and 3D gamma analyses
Pulliam, Kiley B.; Huang, Jessie Y.; Howell, Rebecca M.; Followill, David; Kry, Stephen F.; Bosca, Ryan; O’Daniel, Jennifer
2014-02-15
Purpose: As clinics begin to use 3D metrics for intensity-modulated radiation therapy (IMRT) quality assurance, it must be noted that these metrics will often produce results different from those produced by their 2D counterparts. 3D and 2D gamma analyses would be expected to produce different values, in part because of the different search space available. In the present investigation, the authors compared the results of 2D and 3D gamma analysis (where both datasets were generated in the same manner) for clinical treatment plans. Methods: Fifty IMRT plans were selected from the authors’ clinical database, and recalculated using Monte Carlo. Treatment planning system-calculated (“evaluated dose distributions”) and Monte Carlo-recalculated (“reference dose distributions”) dose distributions were compared using 2D and 3D gamma analysis. This analysis was performed using a variety of dose-difference (5%, 3%, 2%, and 1%) and distance-to-agreement (5, 3, 2, and 1 mm) acceptance criteria, low-dose thresholds (5%, 10%, and 15% of the prescription dose), and data grid sizes (1.0, 1.5, and 3.0 mm). Each comparison was evaluated to determine the average 2D and 3D gamma, lower 95th percentile gamma value, and percentage of pixels passing gamma. Results: The average gamma, lower 95th percentile gamma value, and percentage of passing pixels for each acceptance criterion demonstrated better agreement for 3D than for 2D analysis for every plan comparison. The average difference in the percentage of passing pixels between the 2D and 3D analyses with no low-dose threshold ranged from 0.9% to 2.1%. Similarly, using a low-dose threshold resulted in a difference between the mean 2D and 3D results, ranging from 0.8% to 1.5%. The authors observed no appreciable differences in gamma with changes in the data density (constant difference: 0.8% for 2D vs 3D). Conclusions: The authors found that 3D gamma analysis resulted in up to 2.9% more pixels passing than 2D analysis. It must
Recent advances in 2D materials for photocatalysis.
Luo, Bin; Liu, Gang; Wang, Lianzhou
2016-04-01
Two-dimensional (2D) materials have attracted increasing attention for photocatalytic applications because of their unique thickness dependent physical and chemical properties. This review gives a brief overview of the recent developments concerning the chemical synthesis and structural design of 2D materials at the nanoscale and their applications in photocatalytic areas. In particular, recent progress on the emerging strategies for tailoring 2D material-based photocatalysts to improve their photo-activity including elemental doping, heterostructure design and functional architecture assembly is discussed.
Xiao, Jianyuan; Liu, Jian; Qin, Hong; Yu, Zhi
2013-10-15
Smoothing functions are commonly used to reduce numerical noise arising from coarse sampling of particles in particle-in-cell (PIC) plasma simulations. When applying smoothing functions to symplectic algorithms, the conservation of symplectic structure should be guaranteed to preserve good conservation properties. In this paper, we show how to construct a variational multi-symplectic PIC algorithm with smoothing functions for the Vlasov-Maxwell system. The conservation of the multi-symplectic structure and the reduction of numerical noise make this algorithm specifically suitable for simulating long-term dynamics of plasmas, such as those in the steady-state operation or long-pulse discharge of a super-conducting tokamak. The algorithm has been implemented in a 6D large scale PIC code. Numerical examples are given to demonstrate the good conservation properties of the multi-symplectic algorithm and the reduction of the noise due to the application of smoothing function.
Kasahara, Kento; Sato, Hirofumi
2014-06-28
Site-site Smoluchowski-Vlasov (SSSV) equation enables us to directly calculate van Hove time correlation function, which describes diffusion process in molecular liquids. Recently, the theory had been extended to treat solute-solvent system by Iida and Sato [J. Chem. Phys. 137, 034506 (2012)]. Because the original framework of SSSV equation is based on conventional pair correlation function, time evolution of system is expressed in terms of one-dimensional solvation structure. Here, we propose a new SSSV equation to calculate time evolution of solvation structure in three-dimensional space. The proposed theory was applied to analyze diffusion processes in 1M NaCl aqueous solution and in lithium ion battery electrolyte solution. The results demonstrate that these processes are properly described with the theory, and the computed van Hove functions are in good agreement with those in previous works.
Maruca, Bennett A.; Kasper, Justin C.; Gary, S. Peter
2012-04-01
Kinetic microinstabilities in the solar wind arise when the plasma deviates too far from thermal equilibrium. Previously published work has provided strong evidence that the cyclotron, mirror, and parallel and oblique firehose instabilities limit proton (i.e., ionized hydrogen) temperature anisotropy. However, few studies have thoroughly explored whether a less-abundant ion species can also trigger these instabilities. This study considered the possibility of similar instability-driven limits on {alpha}-particle (i.e., fully ionized helium) temperature anisotropy. Linear Vlasov analysis was used to derive the expected threshold conditions for instabilities driven by {alpha}-particle temperature anisotropy. Measurements in situ of {alpha}-particle temperature anisotropy from the Wind spacecraft's Faraday cups were found to be consistent with the limits imposed by these instability thresholds. This strongly suggests that {alpha}-particles, which only constitute {approx}5% of ions in the solar wind, can drive an instability if their temperature anisotropy becomes sufficiently extreme.
Hamiltonian fluid closures of the Vlasov-Ampère equations: From water-bags to N moment models
Perin, M.; Chandre, C.; Tassi, E.; Morrison, P. J.
2015-09-15
Moment closures of the Vlasov-Ampère system, whereby higher moments are represented as functions of lower moments with the constraint that the resulting fluid system remains Hamiltonian, are investigated by using water-bag theory. The link between the water-bag formalism and fluid models that involve density, fluid velocity, pressure and higher moments is established by introducing suitable thermodynamic variables. The cases of one, two, and three water-bags are treated and their Hamiltonian structures are provided. In each case, we give the associated fluid closures and we discuss their Casimir invariants. We show how the method can be extended to an arbitrary number of fields, i.e., an arbitrary number of water-bags and associated moments. The thermodynamic interpretation of the resulting models is discussed. Finally, a general procedure to derive Hamiltonian N-field fluid models is proposed.
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.
The value of continuity: Refined isogeometric analysis and fast direct solvers
Garcia, Daniel; Pardo, David; Dalcin, Lisandro; Paszynski, Maciej; Collier, Nathan; Calo, Victor M.
2016-08-24
Here, we propose the use of highly continuous finite element spaces interconnected with low continuity hyperplanes to maximize the performance of direct solvers. Starting from a highly continuous Isogeometric Analysis (IGA) discretization, we introduce C0-separators to reduce the interconnection between degrees of freedom in the mesh. By doing so, both the solution time and best approximation errors are simultaneously improved. We call the resulting method “refined Isogeometric Analysis (rIGA)”. To illustrate the impact of the continuity reduction, we analyze the number of Floating Point Operations (FLOPs), computational times, and memory required to solve the linear system obtained by discretizing themore » Laplace problem with structured meshes and uniform polynomial orders. Theoretical estimates demonstrate that an optimal continuity reduction may decrease the total computational time by a factor between p2 and p3, with pp being the polynomial order of the discretization. Numerical results indicate that our proposed refined isogeometric analysis delivers a speed-up factor proportional to p2. In a 2D mesh with four million elements and p=5, the linear system resulting from rIGA is solved 22 times faster than the one from highly continuous IGA. In a 3D mesh with one million elements and p=3, the linear system is solved 15 times faster for the refined than the maximum continuity isogeometric analysis.« less
Alloyed 2D Metal-Semiconductor Atomic Layer Junctions.
Kim, Ah Ra; Kim, Yonghun; Nam, Jaewook; Chung, Hee-Suk; Kim, Dong Jae; Kwon, Jung-Dae; Park, Sang Won; Park, Jucheol; Choi, Sun Young; Lee, Byoung Hun; Park, Ji Hyeon; Lee, Kyu Hwan; Kim, Dong-Ho; Choi, Sung Mook; Ajayan, Pulickel M; Hahm, Myung Gwan; Cho, Byungjin
2016-03-01
Heterostructures of compositionally and electronically variant two-dimensional (2D) atomic layers are viable building blocks for ultrathin optoelectronic devices. We show that the composition of interfacial transition region between semiconducting WSe2 atomic layer channels and metallic NbSe2 contact layers can be engineered through interfacial doping with Nb atoms. WxNb1-xSe2 interfacial regions considerably lower the potential barrier height of the junction, significantly improving the performance of the corresponding WSe2-based field-effect transistor devices. The creation of such alloyed 2D junctions between dissimilar atomic layer domains could be the most important factor in controlling the electronic properties of 2D junctions and the design and fabrication of 2D atomic layer devices.
Emerging and potential opportunities for 2D flexible nanoelectronics
NASA Astrophysics Data System (ADS)
Zhu, Weinan; Park, Saungeun; Akinwande, Deji
2016-05-01
The last 10 years have seen the emergence of two-dimensional (2D) nanomaterials such as graphene, transition metal dichalcogenides (TMDs), and black phosphorus (BP) among the growing portfolio of layered van der Waals thin films. Graphene, the prototypical 2D material has advanced rapidly in device, circuit and system studies that has resulted in commercial large-area applications. In this work, we provide a perspective of the emerging and potential translational applications of 2D materials including semiconductors, semimetals, and insulators that comprise the basic material set for diverse nanosystems. Applications include RF transceivers, smart systems, the so-called internet of things, and neurotechnology. We will review the DC and RF electronic performance of graphene and BP thin film transistors. 2D materials at sub-um channel length have so far enabled cut-off frequencies from baseband to 100GHz suitable for low-power RF and sub-THz concepts.
2D hexagonal quaternion Fourier transform in color image processing
NASA Astrophysics Data System (ADS)
Grigoryan, Artyom M.; Agaian, Sos S.
2016-05-01
In this paper, we present a novel concept of the quaternion discrete Fourier transform on the two-dimensional hexagonal lattice, which we call the two-dimensional hexagonal quaternion discrete Fourier transform (2-D HQDFT). The concept of the right-side 2D HQDFT is described and the left-side 2-D HQDFT is similarly considered. To calculate the transform, the image on the hexagonal lattice is described in the tensor representation when the image is presented by a set of 1-D signals, or splitting-signals which can be separately processed in the frequency domain. The 2-D HQDFT can be calculated by a set of 1-D quaternion discrete Fourier transforms (QDFT) of the splitting-signals.
Technical Review of the UNET2D Hydraulic Model
Perkins, William A.; Richmond, Marshall C.
2009-05-18
The Kansas City District of the US Army Corps of Engineers is engaged in a broad range of river management projects that require knowledge of spatially-varied hydraulic conditions such as velocities and water surface elevations. This information is needed to design new structures, improve existing operations, and assess aquatic habitat. Two-dimensional (2D) depth-averaged numerical hydraulic models are a common tool that can be used to provide velocity and depth information. Kansas City District is currently using a specific 2D model, UNET2D, that has been developed to meet the needs of their river engineering applications. This report documents a tech- nical review of UNET2D.
Double resonance rotational spectroscopy of CH2D+
NASA Astrophysics Data System (ADS)
Töpfer, Matthias; Jusko, Pavol; Schlemmer, Stephan; Asvany, Oskar
2016-09-01
Context. Deuterated forms of CH are thought to be responsible for deuterium enrichment in lukewarm astronomical environments. There is no unambiguous detection of CH2D+ in space to date. Aims: Four submillimetre rotational lines of CH2D+ are documented in the literature. Our aim is to present a complete dataset of highly resolved rotational lines, including millimetre (mm) lines needed for a potential detection. Methods: We used a low-temperature ion trap and applied a novel IR-mm-wave double resonance method to measure the rotational lines of CH2D+. Results: We measured 21 low-lying (J ≤ 4) rotational transitions of CH2D+ between 23 GHz and 1.1 THz with accuracies close to 2 ppb.
Alloyed 2D Metal-Semiconductor Atomic Layer Junctions.
Kim, Ah Ra; Kim, Yonghun; Nam, Jaewook; Chung, Hee-Suk; Kim, Dong Jae; Kwon, Jung-Dae; Park, Sang Won; Park, Jucheol; Choi, Sun Young; Lee, Byoung Hun; Park, Ji Hyeon; Lee, Kyu Hwan; Kim, Dong-Ho; Choi, Sung Mook; Ajayan, Pulickel M; Hahm, Myung Gwan; Cho, Byungjin
2016-03-01
Heterostructures of compositionally and electronically variant two-dimensional (2D) atomic layers are viable building blocks for ultrathin optoelectronic devices. We show that the composition of interfacial transition region between semiconducting WSe2 atomic layer channels and metallic NbSe2 contact layers can be engineered through interfacial doping with Nb atoms. WxNb1-xSe2 interfacial regions considerably lower the potential barrier height of the junction, significantly improving the performance of the corresponding WSe2-based field-effect transistor devices. The creation of such alloyed 2D junctions between dissimilar atomic layer domains could be the most important factor in controlling the electronic properties of 2D junctions and the design and fabrication of 2D atomic layer devices. PMID:26839956
ORION96. 2-d Finite Element Code Postprocessor
Sanford, L.A.; Hallquist, J.O.
1992-02-02
ORION is an interactive program that serves as a postprocessor for the analysis programs NIKE2D, DYNA2D, TOPAZ2D, and CHEMICAL TOPAZ2D. ORION reads binary plot files generated by the two-dimensional finite element codes currently used by the Methods Development Group at LLNL. Contour and color fringe plots of a large number of quantities may be displayed on meshes consisting of triangular and quadrilateral elements. ORION can compute strain measures, interface pressures along slide lines, reaction forces along constrained boundaries, and momentum. ORION has been applied to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.
Phylogenetic tree construction based on 2D graphical representation
NASA Astrophysics Data System (ADS)
Liao, Bo; Shan, Xinzhou; Zhu, Wen; Li, Renfa
2006-04-01
A new approach based on the two-dimensional (2D) graphical representation of the whole genome sequence [Bo Liao, Chem. Phys. Lett., 401(2005) 196.] is proposed to analyze the phylogenetic relationships of genomes. The evolutionary distances are obtained through measuring the differences among the 2D curves. The fuzzy theory is used to construct phylogenetic tree. The phylogenetic relationships of H5N1 avian influenza virus illustrate the utility of our approach.
Generating a 2D Representation of a Complex Data Structure
NASA Technical Reports Server (NTRS)
James, Mark
2006-01-01
A computer program, designed to assist in the development and debugging of other software, generates a two-dimensional (2D) representation of a possibly complex n-dimensional (where n is an integer >2) data structure or abstract rank-n object in that other software. The nature of the 2D representation is such that it can be displayed on a non-graphical output device and distributed by non-graphical means.
Anisotropic 2D Materials for Tunable Hyperbolic Plasmonics.
Nemilentsau, Andrei; Low, Tony; Hanson, George
2016-02-12
Motivated by the recent emergence of a new class of anisotropic 2D materials, we examine their electromagnetic modes and demonstrate that a broad class of the materials can host highly directional hyperbolic plasmons. Their propagation direction can be manipulated on the spot by gate doping, enabling hyperbolic beam reflection, refraction, and bending. The realization of these natural 2D hyperbolic media opens up a new avenue in dynamic control of hyperbolic plasmons not possible in the 3D version.
A simultaneous 2D/3D autostereo workstation
NASA Astrophysics Data System (ADS)
Chau, Dennis; McGinnis, Bradley; Talandis, Jonas; Leigh, Jason; Peterka, Tom; Knoll, Aaron; Sumer, Aslihan; Papka, Michael; Jellinek, Julius
2012-03-01
We present a novel immersive workstation environment that scientists can use for 3D data exploration and as their everyday 2D computer monitor. Our implementation is based on an autostereoscopic dynamic parallax barrier 2D/3D display, interactive input devices, and a software infrastructure that allows client/server software modules to couple the workstation to scientists' visualization applications. This paper describes the hardware construction and calibration, software components, and a demonstration of our system in nanoscale materials science exploration.
QUENCH2D. Two-Dimensional IHCP Code
Osman, A.; Beck, J.V.
1995-01-01
QUENCH2D* is developed for the solution of general, non-linear, two-dimensional inverse heat transfer problems. This program provides estimates for the surface heat flux distribution and/or heat transfer coefficient as a function of time and space by using transient temperature measurements at appropriate interior points inside the quenched body. Two-dimensional planar and axisymmetric geometries such as turnbine disks and blades, clutch packs, and many other problems can be analyzed using QUENCH2D*.
Simulating MEMS Chevron Actuator for Strain Engineering 2D Materials
NASA Astrophysics Data System (ADS)
Vutukuru, Mounika; Christopher, Jason; Bishop, David; Swan, Anna
2D materials pose an exciting paradigm shift in the world of electronics. These crystalline materials have demonstrated high electric and thermal conductivities and tensile strength, showing great potential as the new building blocks of basic electronic circuits. However, strain engineering 2D materials for novel devices remains a difficult experimental feat. We propose the integration of 2D materials with MEMS devices to investigate the strain dependence on material properties such as electrical and thermal conductivity, refractive index, mechanical elasticity, and band gap. MEMS Chevron actuators, provides the most accessible framework to study strain in 2D materials due to their high output force displacements for low input power. Here, we simulate Chevron actuators on COMSOL to optimize actuator design parameters and accurately capture the behavior of the devices while under the external force of a 2D material. Through stationary state analysis, we analyze the response of the device through IV characteristics, displacement and temperature curves. We conclude that the simulation precisely models the real-world device through experimental confirmation, proving that the integration of 2D materials with MEMS is a viable option for constructing novel strain engineered devices. The authors acknowledge support from NSF DMR1411008.
Bond Order Correlations in the 2D Hubbard Model
NASA Astrophysics Data System (ADS)
Moore, Conrad; Abu Asal, Sameer; Yang, Shuxiang; Moreno, Juana; Jarrell, Mark
We use the dynamical cluster approximation to study the bond correlations in the Hubbard model with next nearest neighbor (nnn) hopping to explore the region of the phase diagram where the Fermi liquid phase is separated from the pseudogap phase by the Lifshitz line at zero temperature. We implement the Hirsch-Fye cluster solver that has the advantage of providing direct access to the computation of the bond operators via the decoupling field. In the pseudogap phase, the parallel bond order susceptibility is shown to persist at zero temperature while it vanishes for the Fermi liquid phase which allows the shape of the Lifshitz line to be mapped as a function of filling and nnn hopping. Our cluster solver implements NVIDIA's CUDA language to accelerate the linear algebra of the Quantum Monte Carlo to help alleviate the sign problem by allowing for more Monte Carlo updates to be performed in a reasonable amount of computation time. Work supported by the NSF EPSCoR Cooperative Agreement No. EPS-1003897 with additional support from the Louisiana Board of Regents.
Use of the 'Precessions' process for prepolishing and correcting 2D & 2(1/2)D form.
Walker, David D; Freeman, Richard; Morton, Roger; McCavana, Gerry; Beaucamp, Anthony
2006-11-27
The Precessions process polishes complex surfaces from the ground state preserving the ground-in form, and subsequently rectifies measured form errors. Our first paper introduced the technology and focused on the novel tooling. In this paper we describe the unique CNC machine tools and how they operate in polishing and correcting form. Experimental results demonstrate both the '2D' and '2(1/2)D' form-correction modes, as applied to aspheres with rotationally-symmetric target-form.
A new 3D Eikonal solver for accurate traveltimes, take-off angles and amplitudes
NASA Astrophysics Data System (ADS)
Noble, Mark; Gesret, Alexandrine
2013-04-01
The finite-difference approximation to the eikonal equation was first introduced by J.Vidale in 1988 to propagate first-arrival times throughout a 2D or 3D gridded velocity model. Even today this method is still very attractive from a computational point of view when dealing with large datasets. Among many domains of application, the eikonal solver may be used for 2-D or 3-D depth migration, tomography or microseismicity data analysis. The original 3D method proposed by Vidale in 1990 did exhibit some degree of travel time error that may lead to poor image focusing in migration or inaccurate velocities estimated via tomographic inversion. The method even failed when large and sharp velocity contrasts were encountered. To try and overcome these limitations many authors proposed alternative algorithms, incorporating new finite-difference operators and/or new schemes of implementing the operators to propagate the travel times through the velocity model. If many recently published algorithms for resolving the 3D eikonal equation do yield fairly accurate travel times for most applications, the spatial derivatives of travel times remain very approximate and prevent reliable computation of auxiliary quantities such as take-off angle and amplitude. This limitation is due to the fact that the finite-difference operators locally assume that the wavefront is flat (plane wave). This assumption is in particularly wrong when close to the source where a spherical approximation would be more suitable. To overcome this singularity at the source, some authors proposed an adaptive method that reduces inaccuracies, however, the cost is more algorithmic complexity. The objective of this study is to develop an efficient simple 3D eikonal solver that is able to: overcome the problem of the source singularity, handle velocity models that exhibit strong vertical and horizontal velocity variations, use different grid spacing in x, y and z axis of model. The final goal is of course to
NASA Astrophysics Data System (ADS)
Guo, Xiaocheng
2015-06-01
By revisiting the derivation of the previously developed HLLC Riemann solver for magneto-hydrodynamics (MHD), the paper presents an extended HLLC Riemann solver specifically designed for the MHD system in which the magnetic field can be decomposed into a strong internal magnetic field and an external component. The derived HLLC Riemann solver satisfies the conservation laws. The numerical tests show that the extended solver deals with the global MHD simulation of the Earth's magnetosphere well, and maintains high numerical resolution. It recovers the previously developed HLLC Riemann solver for the MHD as long as the internal field is set to zero. Thus, it is backward compatible with the previous HLLC solver, and suitable for the MHD simulations no matter whether a strong internal magnetic field is included or not.
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
A New Robust Solver for Saturated-Unsaturated Richards' Equation
NASA Astrophysics Data System (ADS)
Barajas-Solano, D. A.; Tartakovsky, D. M.
2012-12-01
We present a novel approach for the numerical integration of the saturated-unsaturated Richards' equation, a degenerate parabolic partial differential equation that models flow in porous media. The method is based on the mixed (pore pressure-water content) form of RE, written as a set of differential algebraic equations (DAEs) of index-1 for the fully saturated case and index-2 for the partially saturated case. A DAE-based approach allows us to overcome the numerical challenges posed by the degenerate nature of the Richards' equation. The resulting set of DAEs is solved using the stiffly-accurate, single-step, 3-stage implicit Runge-Kutta method Radau IIA, chosen for its favorable accuracy and stability properties, and its ease of implementation. For each time step a nonlinear system of equations on the intermediate Runge-Kutta states of the pore pressure is solved, written so to ensure that the next step pore pressure and water content correspond to one another correctly. The implementation of our approach compares favorably to state-of-the-art DAE-based solvers in both one- and two-dimensional simulations. These solvers use multi-step backward difference formulas together with a pressure-based form of Richards' equation. To the best of our knowledge, our method is the first instance of a successful DAE-based solver that uses the mixed form of Richards' equation. We consider this a promising line of research, with future work to be done on the use of globally convergent methods for the solution of the occurring nonlinear systems of equations.
A computationally efficient Multicomponent Equilibrium Solver for Aerosols (MESA)
NASA Astrophysics Data System (ADS)
Zaveri, Rahul A.; Easter, Richard C.; Peters, Leonard K.
2005-12-01
Development and application of a new Multicomponent Equilibrium Solver for Aerosols (MESA) is described for systems containing H+, NH4+, Na+, Ca2+, SO42-, HSO4-, NO3-, and Cl- ions. The equilibrium solution is obtained by integrating a set of pseudo-transient ordinary differential equations describing the precipitation and dissolution reactions for all the possible salts to steady state. A comprehensive temperature dependent mutual deliquescence relative humidity (MDRH) parameterization is developed for all the possible salt mixtures, thereby eliminating the need for a rigorous numerical solution when ambient RH is less than MDRH(T). The solver is unconditionally stable, mass conserving, and shows robust convergence. Performance of MESA was evaluated against the Web-based AIM Model III, which served as a benchmark for accuracy, and the EQUISOLV II solver for speed. Important differences in the convergence and thermodynamic errors in MESA and EQUISOLV II are discussed. The average ratios of speeds of MESA over EQUISOLV II ranged between 1.4 and 5.8, with minimum and maximum ratios of 0.6 and 17, respectively. Because MESA directly diagnoses MDRH, it is significantly more efficient when RH < MDRH. MESA's superior performance is partially due to its "hard-wired" code for the present system as opposed to EQUISOLV II, which has a more generalized structure for solving any number and type of reactions at temperatures down to 190 K. These considerations suggest that MESA is highly attractive for use in 3-D aerosol/air-quality models for lower tropospheric applications (T > 240 K) in which both accuracy and computational efficiency are critical.
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.
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.
Some fast elliptic solvers on parallel architectures and their complexities
NASA Technical Reports Server (NTRS)
Gallopoulos, E.; Saad, Y.
1989-01-01
The discretization of separable elliptic partial differential equations leads to linear systems with special block tridiagonal matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconstant coefficients. A method was recently proposed to parallelize and vectorize BCR. In this paper, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational compelxity lower than that of parallel BCR.
Some fast elliptic solvers on parallel architectures and their complexities
NASA Technical Reports Server (NTRS)
Gallopoulos, E.; Saad, Youcef
1989-01-01
The discretization of separable elliptic partial differential equations leads to linear systems with special block triangular matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconsistant coefficients. A method was recently proposed to parallelize and vectorize BCR. Here, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches, including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational complexity lower than that of parallel BCR.
Algorithms for parallel flow solvers on message passing architectures
NASA Astrophysics Data System (ADS)
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
Hierarchically parallelized constrained nonlinear solvers with automated substructuring
NASA Technical Reports Server (NTRS)
Padovan, J.; Kwang, A.
1991-01-01
This paper develops a parallelizable multilevel 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, both sequential, 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 capacity to yield significant reductions in memory utilization and calculational effort due both to updating and inversion.
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.
Advances in the hydrodynamics solver of CO5BOLD
NASA Astrophysics Data System (ADS)
Freytag, Bernd
Many features of the Roe solver used in the hydrodynamics module of CO5BOLD have recently been added or overhauled, including the reconstruction methods (by adding the new second-order ``Frankenstein's method''), the treatment of transversal velocities, energy-flux averaging and entropy-wave treatment at small Mach numbers, the CTU scheme to combine the one-dimensional fluxes, and additional safety measures. All this results in a significantly better behavior at low Mach number flows, and an improved stability at larger Mach numbers requiring less (or no) additional tensor viscosity, which then leads to a noticeable increase in effective resolution.
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.
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.
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.
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.
Novel accurate and scalable 3-D MT forward solver based on a contracting integral equation method
NASA Astrophysics Data System (ADS)
Kruglyakov, M.; Geraskin, A.; Kuvshinov, A.
2016-11-01
We present a novel, open source 3-D MT forward solver based on a method of integral equations (IE) with contracting kernel. Special attention in the solver is paid to accurate calculations of Green's functions and their integrals which are cornerstones of any IE solution. The solver supports massive parallelization and is able to deal with highly detailed and contrasting models. We report results of a 3-D numerical experiment aimed at analyzing the accuracy and scalability of the code.
A 2D/1D coupling neutron transport method based on the matrix MOC and NEM methods
Zhang, H.; Zheng, Y.; Wu, H.; Cao, L.
2013-07-01
A new 2D/1D coupling method based on the matrix MOC method (MMOC) and nodal expansion method (NEM) is proposed for solving the three-dimensional heterogeneous neutron transport problem. The MMOC method, used for radial two-dimensional calculation, constructs a response matrix between source and flux with only one sweep and then solves the linear system by using the restarted GMRES algorithm instead of the traditional trajectory sweeping process during within-group iteration for angular flux update. Long characteristics are generated by using the customization of commercial software AutoCAD. A one-dimensional diffusion calculation is carried out in the axial direction by employing the NEM method. The 2D and ID solutions are coupled through the transverse leakage items. The 3D CMFD method is used to ensure the global neutron balance and adjust the different convergence properties of the radial and axial solvers. A computational code is developed based on these theories. Two benchmarks are calculated to verify the coupling method and the code. It is observed that the corresponding numerical results agree well with references, which indicates that the new method is capable of solving the 3D heterogeneous neutron transport problem directly. (authors)
Efficient 2D and 3D multiparameters frequency-domain full waveform inversion (Invited)
NASA Astrophysics Data System (ADS)
Virieux, J.; Operto, S.; Ribodetti, A.; Ben Hadj Ali, H.; Brossier, R.; Etienne, V.; Gholami, Y.; Hu, G.; Jia, Y.; Pageot, D.; Prieux, V.
2010-12-01
With the tremendous increase of the computational power provided by large-scale distributed-memory platforms and the development of dense 3D multi-component wide-aperture/wide-azimuth surveys, full waveform inversion (FWI) introduced in geophysics by Albert Tarantola has become a re-emerging technique to build high-resolution velocity models of the subsurface. Because of the cost of the forward modeling and the high dimensionality of the model space, full waveform inversion is actually a local optimization problem, the aim of which is the minimization of the misfit between the recorded and modeled seismic wavefields. Among all possible minimization criteria, the L1 norm provides the most robust and easy-to-tune criterion. With such criterion, white noise in all seismograms with outliers does not prevent the convergence to the nearly same minimum as for noise-free data. The frequency formulation of the FWI allows coarse sampling of the frequencies data over few frequencies for the reconstruction of the medium when wide-aperture geometries are considered. A preconditioned quasi-Newton L-BFGS modified algorithm provides scaled gradients of the misfit function for each class of parameters. The gradient is computed by the adjoint-state method where the forward field is stored in the core memory of the computer while computing the backpropagation of residuals for cross-correlation at each point of the medium, thanks to the frequency-domain approach. We are using a sequential multiscale hierarchical inversion algorithm with two nested levels of data preconditioning with respect to frequency and first-arrival time. We are able to reconstruct both Vp and Vs velocity structures in various offshore and onshore environments various configurations of crustal investigation where both body waves (and surface) waves are progressively included in the inversion scheme. Solving the forward problem for 2D geometry could be efficiently performed in frequency by using a direct solver
2D nanostructures for water purification: graphene and beyond.
Dervin, Saoirse; Dionysiou, Dionysios D; Pillai, Suresh C
2016-08-18
Owing to their atomically thin structure, large surface area and mechanical strength, 2D nanoporous materials are considered to be suitable alternatives for existing desalination and water purification membrane materials. Recent progress in the development of nanoporous graphene based materials has generated enormous potential for water purification technologies. Progress in the development of nanoporous graphene and graphene oxide (GO) membranes, the mechanism of graphene molecular sieve action, structural design, hydrophilic nature, mechanical strength and antifouling properties and the principal challenges associated with nanopore generation are discussed in detail. Subsequently, the recent applications and performance of newly developed 2D materials such as 2D boron nitride (BN) nanosheets, graphyne, molybdenum disulfide (MoS2), tungsten chalcogenides (WS2) and titanium carbide (Ti3C2Tx) are highlighted. In addition, the challenges affecting 2D nanostructures for water purification are highlighted and their applications in the water purification industry are discussed. Though only a few 2D materials have been explored so far for water treatment applications, this emerging field of research is set to attract a great deal of attention in the near future.
Ultrafast 2D-IR spectroelectrochemistry of flavin mononucleotide
NASA Astrophysics Data System (ADS)
El Khoury, Youssef; Van Wilderen, Luuk J. G. W.; Bredenbeck, Jens
2015-06-01
We demonstrate the coupling of ultrafast two-dimensional infrared (2D-IR) spectroscopy to electrochemistry in solution and apply it to flavin mononucleotide, an important cofactor of redox proteins. For this purpose, we designed a spectroelectrochemical cell optimized for 2D-IR measurements in reflection and measured the time-dependent 2D-IR spectra of the oxidized and reduced forms of flavin mononucleotide. The data show anharmonic coupling and vibrational energy transfer between different vibrational modes in the two redox species. Such information is inaccessible with redox-controlled steady-state FTIR spectroscopy. The wide range of applications offered by 2D-IR spectroscopy, such as sub-picosecond structure determination, IR band assignment via energy transfer, disentangling reaction mixtures through band connectivity in the 2D spectra, and the measurement of solvation dynamics and chemical exchange can now be explored under controlled redox potential. The development of this technique furthermore opens new horizons for studying the dynamics of redox proteins.
Ultrafast 2D-IR spectroelectrochemistry of flavin mononucleotide.
El Khoury, Youssef; Van Wilderen, Luuk J G W; Bredenbeck, Jens
2015-06-01
We demonstrate the coupling of ultrafast two-dimensional infrared (2D-IR) spectroscopy to electrochemistry in solution and apply it to flavin mononucleotide, an important cofactor of redox proteins. For this purpose, we designed a spectroelectrochemical cell optimized for 2D-IR measurements in reflection and measured the time-dependent 2D-IR spectra of the oxidized and reduced forms of flavin mononucleotide. The data show anharmonic coupling and vibrational energy transfer between different vibrational modes in the two redox species. Such information is inaccessible with redox-controlled steady-state FTIR spectroscopy. The wide range of applications offered by 2D-IR spectroscopy, such as sub-picosecond structure determination, IR band assignment via energy transfer, disentangling reaction mixtures through band connectivity in the 2D spectra, and the measurement of solvation dynamics and chemical exchange can now be explored under controlled redox potential. The development of this technique furthermore opens new horizons for studying the dynamics of redox proteins.
Mean flow and anisotropic cascades in decaying 2D turbulence
NASA Astrophysics Data System (ADS)
Liu, Chien-Chia; Cerbus, Rory; Gioia, Gustavo; Chakraborty, Pinaki
2015-11-01
Many large-scale atmospheric and oceanic flows are decaying 2D turbulent flows embedded in a non-uniform mean flow. Despite its importance for large-scale weather systems, the affect of non-uniform mean flows on decaying 2D turbulence remains unknown. In the absence of mean flow it is well known that decaying 2D turbulent flows exhibit the enstrophy cascade. More generally, for any 2D turbulent flow, all computational, experimental and field data amassed to date indicate that the spectrum of longitudinal and transverse velocity fluctuations correspond to the same cascade, signifying isotropy of cascades. Here we report experiments on decaying 2D turbulence in soap films with a non-uniform mean flow. We find that the flow transitions from the usual isotropic enstrophy cascade to a series of unusual and, to our knowledge, never before observed or predicted, anisotropic cascades where the longitudinal and transverse spectra are mutually independent. We discuss implications of our results for decaying geophysical turbulence.
Sparse radar imaging using 2D compressed sensing
NASA Astrophysics Data System (ADS)
Hou, Qingkai; Liu, Yang; Chen, Zengping; Su, Shaoying
2014-10-01
Radar imaging is an ill-posed linear inverse problem and compressed sensing (CS) has been proved to have tremendous potential in this field. This paper surveys the theory of radar imaging and a conclusion is drawn that the processing of ISAR imaging can be denoted mathematically as a problem of 2D sparse decomposition. Based on CS, we propose a novel measuring strategy for ISAR imaging radar and utilize random sub-sampling in both range and azimuth dimensions, which will reduce the amount of sampling data tremendously. In order to handle 2D reconstructing problem, the ordinary solution is converting the 2D problem into 1D by Kronecker product, which will increase the size of dictionary and computational cost sharply. In this paper, we introduce the 2D-SL0 algorithm into the reconstruction of imaging. It is proved that 2D-SL0 can achieve equivalent result as other 1D reconstructing methods, but the computational complexity and memory usage is reduced significantly. Moreover, we will state the results of simulating experiments and prove the effectiveness and feasibility of our method.
Ultrafast 2D NMR: an emerging tool in analytical spectroscopy.
Giraudeau, Patrick; Frydman, Lucio
2014-01-01
Two-dimensional nuclear magnetic resonance (2D NMR) spectroscopy is widely used in chemical and biochemical analyses. Multidimensional NMR is also witnessing increased use in quantitative and metabolic screening applications. Conventional 2D NMR experiments, however, are affected by inherently long acquisition durations, arising from their need to sample the frequencies involved along their indirect domains in an incremented, scan-by-scan nature. A decade ago, a so-called ultrafast (UF) approach was proposed, capable of delivering arbitrary 2D NMR spectra involving any kind of homo- or heteronuclear correlation, in a single scan. During the intervening years, the performance of this subsecond 2D NMR methodology has been greatly improved, and UF 2D NMR is rapidly becoming a powerful analytical tool experiencing an expanded scope of applications. This review summarizes the principles and main developments that have contributed to the success of this approach and focuses on applications that have been recently demonstrated in various areas of analytical chemistry--from the real-time monitoring of chemical and biochemical processes, to extensions in hyphenated techniques and in quantitative applications. PMID:25014342
2D nanostructures for water purification: graphene and beyond.
Dervin, Saoirse; Dionysiou, Dionysios D; Pillai, Suresh C
2016-08-18
Owing to their atomically thin structure, large surface area and mechanical strength, 2D nanoporous materials are considered to be suitable alternatives for existing desalination and water purification membrane materials. Recent progress in the development of nanoporous graphene based materials has generated enormous potential for water purification technologies. Progress in the development of nanoporous graphene and graphene oxide (GO) membranes, the mechanism of graphene molecular sieve action, structural design, hydrophilic nature, mechanical strength and antifouling properties and the principal challenges associated with nanopore generation are discussed in detail. Subsequently, the recent applications and performance of newly developed 2D materials such as 2D boron nitride (BN) nanosheets, graphyne, molybdenum disulfide (MoS2), tungsten chalcogenides (WS2) and titanium carbide (Ti3C2Tx) are highlighted. In addition, the challenges affecting 2D nanostructures for water purification are highlighted and their applications in the water purification industry are discussed. Though only a few 2D materials have been explored so far for water treatment applications, this emerging field of research is set to attract a great deal of attention in the near future. PMID:27506268
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.
NASA Technical Reports Server (NTRS)
Abraham-Shrauner, B.
1986-01-01
Upper hybrid drift waves are found as a special solution to a Vlasov-Maxwell plasma which has a longitudinal electric field and a perpendicular uniform magnetic field. A single-species plasma with a constant-density mobile neutralizing background supports spatially varying disturbances that oscillate at the upper hybrid frequency. The general functional dependences of the electric field, the plasma number density, and the one-particle distribution function for the special case are found from more general Vlasov-Maxwell equations invariant under a Lie group point transformation. The one-particle distribution function for the plasma is a function of the Liouville invariant, which is the energy in the generalized Bernstein-Greene-Kruskal (BGK) reference frame, and the momentum in the drift direction.
Davidson, R.C.; Chen, C.
1997-08-01
A kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field B{sup sol}({rvec x}) is developed. The analysis is carried out for a thin beam with characteristic beam radius r{sub b} {much_lt} S, and directed axial momentum {gamma}{sub b}m{beta}{sub b}c (in the z-direction) large compared with the transverse momentum and axial momentum spread of the beam particles. Making use of the nonlinear Vlasov-Maxwell equations for general distribution function f{sub b}({rvec x},{rvec p},t) and self-consistent electrostatic field consistent with the thin-beam approximation, the kinetic model is used to investigate detailed beam equilibrium properties for a variety of distribution functions. Examples are presented both for the case of a uniform solenoidal focusing field B{sub z}(z) = B{sub 0} = const. and for the case of a periodic solenoidal focusing field B{sub z}(z + S) = B{sub z}(z). The nonlinear Vlasov-Maxwell equations are simplified in the thin-beam approximation, and an alternative Hamiltonian formulation is developed that is particularly well-suited to intense beam propagation in periodic focusing systems. Based on the present analysis, the Vlasov-Maxwell description of intense nonneutral beam propagation through a periodic solenoidal focusing field {rvec B}{sup sol}({rvec x}) is found to be remarkably tractable and rich in physics content. The Vlasov-Maxwell formalism developed here can be extended in a straightforward manner to investigate detailed stability behavior for perturbations about specific choices of beam equilibria.
Graphene based 2D-materials for supercapacitors
NASA Astrophysics Data System (ADS)
Palaniselvam, Thangavelu; Baek, Jong-Beom
2015-09-01
Ever-increasing energy demands and the depletion of fossil fuels are compelling humanity toward the development of suitable electrochemical energy conversion and storage devices to attain a more sustainable society with adequate renewable energy and zero environmental pollution. In this regard, supercapacitors are being contemplated as potential energy storage devices to afford cleaner, environmentally friendly energy. Recently, a great deal of attention has been paid to two-dimensional (2D) nanomaterials, including 2D graphene and its inorganic analogues (transition metal double layer hydroxides, chalcogenides, etc), as potential electrodes for the development of supercapacitors with high electrochemical performance. This review provides an overview of the recent progress in using these graphene-based 2D materials as potential electrodes for supercapacitors. In addition, future research trends including notable challenges and opportunities are also discussed.
Perception-based reversible watermarking for 2D vector maps
NASA Astrophysics Data System (ADS)
Men, Chaoguang; Cao, Liujuan; Li, Xiang
2010-07-01
This paper presents an effective and reversible watermarking approach for digital copyright protection of 2D-vector maps. To ensure that the embedded watermark is insensitive for human perception, we only select the noise non-sensitive regions for watermark embedding by estimating vertex density within each polyline. To ensure the exact recovery of original 2D-vector map after watermark extraction, we introduce a new reversible watermarking scheme based on reversible high-frequency wavelet coefficients modification. Within the former-selected non-sensitive regions, our watermarking operates on the lower-order vertex coordinate decimals with integer wavelet transform. Such operation further reduces the visual distortion caused by watermark embedding. We have validated the effectiveness of our scheme on our real-world city river/building 2D-vector maps. We give extensive experimental comparisons with state-of-the-art methods, including embedding capability, invisibility, and robustness over watermark attacking.
Secretory pathways generating immunosuppressive NKG2D ligands
Baragaño Raneros, Aroa; Suarez-Álvarez, Beatriz; López-Larrea, Carlos
2014-01-01
Natural Killer Group 2 member D (NKG2D) activating receptor, present on the surface of various immune cells, plays an important role in activating the anticancer immune response by their interaction with stress-inducible NKG2D ligands (NKG2DL) on transformed cells. However, cancer cells have developed numerous mechanisms to evade the immune system via the downregulation of NKG2DL from the cell surface, including the release of NKG2DL from the cell surface in a soluble form. Here, we review the mechanisms involved in the production of soluble NKG2DL (sNKG2DL) and the potential therapeutic strategies aiming to block the release of these immunosuppressive ligands. Therapeutically enabling the NKG2D-NKG2DL interaction would promote immunorecognition of malignant cells, thus abrogating disease progression. PMID:25050215
2D bifurcations and Newtonian properties of memristive Chua's circuits
NASA Astrophysics Data System (ADS)
Marszalek, W.; Podhaisky, H.
2016-01-01
Two interesting properties of Chua's circuits are presented. First, two-parameter bifurcation diagrams of Chua's oscillatory circuits with memristors are presented. To obtain various 2D bifurcation images a substantial numerical effort, possibly with parallel computations, is needed. The numerical algorithm is described first and its numerical code for 2D bifurcation image creation is available for free downloading. Several color 2D images and the corresponding 1D greyscale bifurcation diagrams are included. Secondly, Chua's circuits are linked to Newton's law φ ''= F(t,φ,φ')/m with φ=\\text{flux} , constant m > 0, and the force term F(t,φ,φ') containing memory terms. Finally, the jounce scalar equations for Chua's circuits are also discussed.
Focusing surface wave imaging with flexible 2D array
NASA Astrophysics Data System (ADS)
Zhou, Shiyuan; Fu, Junqiang; Li, Zhe; Xu, Chunguang; Xiao, Dingguo; Wang, Shaohan
2016-04-01
Curved surface is widely exist in key parts of energy and power equipment, such as, turbine blade cylinder block and so on. Cycling loading and harsh working condition of enable fatigue cracks appear on the surface. The crack should be found in time to avoid catastrophic damage to the equipment. A flexible 2D array transducer was developed. 2D Phased Array focusing method (2DPA), Mode-Spatial Double Phased focusing method (MSDPF) and the imaging method using the flexible 2D array probe are studied. Experiments using these focusing and imaging method are carried out. Surface crack image is obtained with both 2DPA and MSDPF focusing method. It have been proved that MSDPF can be more adaptable for curved surface and more calculate efficient than 2DPA.
Riemann solvers and Alfven waves in black hole magnetospheres
NASA Astrophysics Data System (ADS)
Punsly, Brian; Balsara, Dinshaw; Kim, Jinho; Garain, Sudip
2016-09-01
In the magnetosphere of a rotating black hole, an inner Alfven critical surface (IACS) must be crossed by inflowing plasma. Inside the IACS, Alfven waves are inward directed toward the black hole. The majority of the proper volume of the active region of spacetime (the ergosphere) is inside of the IACS. The charge and the totally transverse momentum flux (the momentum flux transverse to both the wave normal and the unperturbed magnetic field) are both determined exclusively by the Alfven polarization. Thus, it is important for numerical simulations of black hole magnetospheres to minimize the dissipation of Alfven waves. Elements of the dissipated wave emerge in adjacent cells regardless of the IACS, there is no mechanism to prevent Alfvenic information from crossing outward. Thus, numerical dissipation can affect how simulated magnetospheres attain the substantial Goldreich-Julian charge density associated with the rotating magnetic field. In order to help minimize dissipation of Alfven waves in relativistic numerical simulations we have formulated a one-dimensional Riemann solver, called HLLI, which incorporates the Alfven discontinuity and the contact discontinuity. We have also formulated a multidimensional Riemann solver, called MuSIC, that enables low dissipation propagation of Alfven waves in multiple dimensions. The importance of higher order schemes in lowering the numerical dissipation of Alfven waves is also catalogued.
A massively parallel fractional step solver for incompressible flows
Houzeaux, G. Vazquez, M. Aubry, R. Cela, J.M.
2009-09-20
This paper presents a parallel implementation of fractional solvers for the incompressible Navier-Stokes equations using an algebraic approach. Under this framework, predictor-corrector and incremental projection schemes are seen as sub-classes of the same class, making apparent its differences and similarities. An additional advantage of this approach is to set a common basis for a parallelization strategy, which can be extended to other split techniques or to compressible flows. The predictor-corrector scheme consists in solving the momentum equation and a modified 'continuity' equation (namely a simple iteration for the pressure Schur complement) consecutively in order to converge to the monolithic solution, thus avoiding fractional errors. On the other hand, the incremental projection scheme solves only one iteration of the predictor-corrector per time step and adds a correction equation to fulfill the mass conservation. As shown in the paper, these two schemes are very well suited for massively parallel implementation. In fact, when compared with monolithic schemes, simpler solvers and preconditioners can be used to solve the non-symmetric momentum equations (GMRES, Bi-CGSTAB) and to solve the symmetric continuity equation (CG, Deflated CG). This gives good speedup properties of the algorithm. The implementation of the mesh partitioning technique is presented, as well as the parallel performances and speedups for thousands of processors.
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.
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.
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.
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