Construction of Low Dissipative High Order Well-Balanced Filter Schemes for Non-Equilibrium Flows
NASA Technical Reports Server (NTRS)
Wang, Wei; Yee, H. C.; Sjogreen, Bjorn; Magin, Thierry; Shu, Chi-Wang
2009-01-01
The goal of this paper is to generalize the well-balanced approach for non-equilibrium flow studied by Wang et al. [26] to a class of low dissipative high order shock-capturing filter schemes and to explore more advantages of well-balanced schemes in reacting flows. The class of filter schemes developed by Yee et al. [30], Sjoegreen & Yee [24] and Yee & Sjoegreen [35] consist of two steps, a full time step of spatially high order non-dissipative base scheme and an adaptive nonlinear filter containing shock-capturing dissipation. A good property of the filter scheme is that the base scheme and the filter are stand alone modules in designing. Therefore, the idea of designing a well-balanced filter scheme is straightforward, i.e., choosing a well-balanced base scheme with a well-balanced filter (both with high order). A typical class of these schemes shown in this paper is the high order central difference schemes/predictor-corrector (PC) schemes with a high order well-balanced WENO filter. The new filter scheme with the well-balanced property will gather the features of both filter methods and well-balanced properties: it can preserve certain steady state solutions exactly; it is able to capture small perturbations, e.g., turbulence fluctuations; it adaptively controls numerical dissipation. Thus it shows high accuracy, efficiency and stability in shock/turbulence interactions. Numerical examples containing 1D and 2D smooth problems, 1D stationary contact discontinuity problem and 1D turbulence/shock interactions are included to verify the improved accuracy, in addition to the well-balanced behavior.
High Order Well-Balanced Schemes and Applications to Non-Equilibrium Flow with Stiff Source Terms
Wang, W; Shu, C; Yee, H C; Sjogreen, B
2009-01-14
The stiffness of the source terms in modeling non-equilibrium flow problems containing finite-rate chemistry or combustion poses additional numerical difficulties beyond that for solving non-reacting flows. A well-balanced scheme, which can preserve certain non-trivial steady state solutions exactly, may help to resolve some of these difficulties. In this paper, a simple one dimensional non-equilibrium model with one temperature is considered. We first describe a general strategy to design high order well-balanced finite difference schemes and then study the well-balanced properties of high order finite difference weighted essentially non-oscillatory (WENO) scheme, modified balanced WENO schemes and various TVD schemes. The advantages of using a well-balanced scheme in preserving steady states and in resolving small perturbations of such states will be shown. Additional numerical examples are provided to verify the good resolution, in addition to the well-balancedness, for both smooth and discontinuous solutions as well.
Well-balanced high-order solver for blood flow in networks of vessels with variable properties.
Müller, Lucas O; Toro, Eleuterio F
2013-12-01
We present a well-balanced, high-order non-linear numerical scheme for solving a hyperbolic system that models one-dimensional flow in blood vessels with variable mechanical and geometrical properties along their length. Using a suitable set of test problems with exact solution, we rigorously assess the performance of the scheme. In particular, we assess the well-balanced property and the effective order of accuracy through an empirical convergence rate study. Schemes of up to fifth order of accuracy in both space and time are implemented and assessed. The numerical methodology is then extended to realistic networks of elastic vessels and is validated against published state-of-the-art numerical solutions and experimental measurements. It is envisaged that the present scheme will constitute the building block for a closed, global model for the human circulation system involving arteries, veins, capillaries and cerebrospinal fluid. PMID:23913466
Fuchs, F. G.; McMurry, A. D.; Mishra, S.; Waagan, K. E-mail: a.d.mcmurry@ifi.uio.no E-mail: kwaagan@cscamm.umd.edu
2011-05-10
We consider the propagation of waves in a stratified non-isothermal magnetic atmosphere. The situation of interest corresponds to waves in the outer solar (chromosphere and corona) and other stellar atmospheres. The waves are simulated by using a high-resolution, well-balanced finite-volume-based massively parallel code named SURYA. Numerical experiments in both two and three space dimensions involving realistic temperature distributions, driving forces, and magnetic field configurations are described. Diverse phenomena such as mode conversion, wave acceleration at the transition layer, and driving-dependent wave dynamics are observed. We obtain evidence for the presence of coronal Alfven waves in some three-dimensional configurations. Although some of the incident wave energy is transmitted into the corona, a large proportion of it is accumulated in the chromosphere, providing a possible mechanism for chromospheric heating.
NASA Astrophysics Data System (ADS)
Canestrelli, Alberto; Siviglia, Annunziato; Dumbser, Michael; Toro, Eleuterio F.
2009-06-01
This paper concerns the development of high-order accurate centred schemes for the numerical solution of one-dimensional hyperbolic systems containing non-conservative products and source terms. Combining the PRICE-T method developed in [Toro E, Siviglia A. PRICE: primitive centred schemes for hyperbolic system of equations. Int J Numer Methods Fluids 2003;42:1263-91] with the theoretical insights gained by the recently developed path-conservative schemes [Castro M, Gallardo J, Parés C. High-order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products applications to shallow-water systems. Math Comput 2006;75:1103-34; Parés C. Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM J Numer Anal 2006;44:300-21], we propose the new PRICE-C scheme that automatically reduces to a modified conservative FORCE scheme if the underlying PDE system is a conservation law. The resulting first-order accurate centred method is then extended to high order of accuracy in space and time via the ADER approach together with a WENO reconstruction technique. The well-balanced properties of the PRICE-C method are investigated for the shallow water equations. Finally, we apply the new scheme to the shallow water equations with fix bottom topography and with variable bottom solving an additional sediment transport equation.
NASA Astrophysics Data System (ADS)
Liu, Xin; Mohammadian, Abdolmajid; Kurganov, Alexander; Infante Sedano, Julio Angel
2015-11-01
Intense sediment transport and rapid bed evolution are frequently observed under highly-energetic flows, and bed erosion sometimes is of the same magnitude as the flow itself. Simultaneous simulation of multiple physical processes requires a fully coupled system to achieve an accurate hydraulic and morphodynamical prediction. In this paper, we develop a high-order well-balanced finite-volume method for a new fully coupled two-dimensional hyperbolic system consisting of the shallow water equations with friction terms coupled with the equations modeling the sediment transport and bed evolution. The nonequilibrium sediment transport equation is used to predict the sediment concentration variation. Since bed-load, sediment entrainment and deposition have significant effects on the bed evolution, an Exner-based equation is adopted together with the Grass bed-load formula and sediment entrainment and deposition models to calculate the morphological process. The resulting 5 × 5 hyperbolic system of balance laws is numerically solved using a Godunov-type central-upwind scheme on a triangular grid. A computationally expensive process of finding all of the eigenvalues of the Jacobian matrices is avoided: The upper/lower bounds on the largest/smallest local speeds of propagation are estimated using the Lagrange theorem. A special discretization of the bed-slope term is proposed to guarantee the well-balanced property of the designed scheme. The proposed fully coupled model is verified on a number of numerical experiments.
High order finite volume WENO schemes for the Euler equations under gravitational fields
NASA Astrophysics Data System (ADS)
Li, Gang; Xing, Yulong
2016-07-01
Euler equations with gravitational source terms are used to model many astrophysical and atmospheric phenomena. This system admits hydrostatic balance where the flux produced by the pressure is exactly canceled by the gravitational source term, and two commonly seen equilibria are the isothermal and polytropic hydrostatic solutions. Exact preservation of these equilibria is desirable as many practical problems are small perturbations of such balance. High order finite difference weighted essentially non-oscillatory (WENO) schemes have been proposed in [22], but only for the isothermal equilibrium state. In this paper, we design high order well-balanced finite volume WENO schemes, which can preserve not only the isothermal equilibrium but also the polytropic hydrostatic balance state exactly, and maintain genuine high order accuracy for general solutions. The well-balanced property is obtained by novel source term reformulation and discretization, combined with well-balanced numerical fluxes. Extensive one- and two-dimensional simulations are performed to verify well-balanced property, high order accuracy, as well as good resolution for smooth and discontinuous solutions.
Generalized high order compact methods.
Spotz, William F.; Kominiarczuk, Jakub
2010-09-01
The fundamental ideas of the high order compact method are combined with the generalized finite difference method. The result is a finite difference method that works on unstructured, nonuniform grids, and is more accurate than one would classically expect from the number of grid points employed.
A Well-Balanced Central-Upwind Scheme for the 2D Shallow Water Equations on Triangular Meshes
NASA Technical Reports Server (NTRS)
Bryson, Steve; Levy, Doron
2004-01-01
We are interested in approximating solutions of the two-dimensional shallow water equations with a bottom topography on triangular meshes. We show that there is a certain flexibility in choosing the numerical fluxes in the design of semi-discrete Godunov-type central schemes. We take advantage of this fact to generate a new second-order, central-upwind method for the two-dimensional shallow water equations that is well-balanced. We demonstrate the accuracy of our method as well as its balance properties in a variety of examples.
Building fast well-balanced two-stage numerical schemes for a model of two-phase flows
NASA Astrophysics Data System (ADS)
Thanh, Mai Duc
2014-06-01
We present a set of well-balanced two-stage schemes for an isentropic model of two-phase flows arisen from the modeling of deflagration-to-detonation transition in granular materials. The first stage is to absorb the source term in nonconservative form into equilibria. Then in the second stage, these equilibria will be composed into a numerical flux formed by using a convex combination of the numerical flux of a stable Lax-Friedrichs-type scheme and the one of a higher-order Richtmyer-type scheme. Numerical schemes constructed in such a way are expected to get the interesting property: they are fast and stable. Tests show that the method works out until the parameter takes on the value CFL, and so any value of the parameter between zero and this value is expected to work as well. All the schemes in this family are shown to capture stationary waves and preserves the positivity of the volume fractions. The special values of the parameter 0,1/2,1/(1+CFL), and CFL in this family define the Lax-Friedrichs-type, FAST1, FAST2, and FAST3 schemes, respectively. These schemes are shown to give a desirable accuracy. The errors and the CPU time of these schemes and the Roe-type scheme are calculated and compared. The constructed schemes are shown to be well-balanced and faster than the Roe-type scheme.
High-Order/Low-Order methods for ocean modeling
Newman, Christopher; Womeldorff, Geoff; Chacón, Luis; Knoll, Dana A.
2015-06-01
We examine a High Order/Low Order (HOLO) approach for a z-level ocean model and show that the traditional semi-implicit and split-explicit methods, as well as a recent preconditioning strategy, can easily be cast in the framework of HOLO methods. The HOLO formulation admits an implicit-explicit method that is algorithmically scalable and second-order accurate, allowing timesteps much larger than the barotropic time scale. We demonstrate how HOLO approaches, in particular the implicit-explicit method, can provide a solid route for ocean simulation to heterogeneous computing and exascale environments.
NASA Astrophysics Data System (ADS)
Käppeli, R.; Mishra, S.
2016-03-01
Context. Many problems in astrophysics feature flows which are close to hydrostatic equilibrium. However, standard numerical schemes for compressible hydrodynamics may be deficient in approximating this stationary state, where the pressure gradient is nearly balanced by gravitational forces. Aims: We aim to develop a second-order well-balanced scheme for the Euler equations. The scheme is designed to mimic a discrete version of the hydrostatic balance. It therefore can resolve a discrete hydrostatic equilibrium exactly (up to machine precision) and propagate perturbations, on top of this equilibrium, very accurately. Methods: A local second-order hydrostatic equilibrium preserving pressure reconstruction is developed. Combined with a standard central gravitational source term discretization and numerical fluxes that resolve stationary contact discontinuities exactly, the well-balanced property is achieved. Results: The resulting well-balanced scheme is robust and simple enough to be very easily implemented within any existing computer code that solves time explicitly or implicitly the compressible hydrodynamics equations. We demonstrate the performance of the well-balanced scheme for several astrophysically relevant applications: wave propagation in stellar atmospheres, a toy model for core-collapse supernovae, convection in carbon shell burning, and a realistic proto-neutron star.
Using High-Order Methods on Lower-Order Geometries
NASA Technical Reports Server (NTRS)
Casper, Jay
1997-01-01
The desire to obtain acoustic information from the numerical solution of a nonlinear system of equations is a demanding proposition for a computational algorithm. High-order accuracy is required for the propagation of high-frequency, low-amplitude waves. The accuracy of an algorithm can be compromised by low-order errors that naturally occur in the solution of a particular problem. Such errors arise from two sources: the presence of discontinuities in the flow field or because the geometry on which the problem is defined is not everywhere smooth to the order of the scheme. The performance of high-order accurate essentially non-oscillatory (ENO) schemes on piecewise smooth solutions is well documented. Herein, the performance of these methods on smooth solutions defined on piecewise smooth geometries is investigated. The propagation of sound in a quasi-one-dimensional nozzle is considered as a test case. Some of the issues involved in the extension to two spatial dimensions are discussed.
On the advantage of well-balanced schemes for moving-water equilibria of the shallow water equations
Xing, Yulong; Shu, Chi-wang; Noelle, Sebastian
2011-01-01
This note aims at demonstrating the advantage of moving-water well-balanced schemes over still-water well-balanced schemes for the shallow water equations. We concentrate on numerical examples with solutions near a moving-water equilibrium. For such examples, still-water well-balanced methods are not capable of capturing the small perturbations of the moving-water equilibrium and may generate significant spurious oscillations, unless an extremely refined mesh is used. On the other hand, moving-water well-balanced methods perform well in these tests. The numerical examples in this note clearly demonstrate the importance of utilizing moving-water well-balanced methods for solutions near a moving-water equilibrium.
High-order beam optics: An overview
Heighway, E.A.
1988-01-01
Beam-transport codes have been around for as long as thirty years and high-order codes, second-order at least, for close to twenty years. Before this period of design-code development, there was considerable high-order treatment, but it was almost entirely analytical. History has a way of repeating itself, and the current excitement in the field of high-order optics is based on the application of Lie algebra and the so-called differential algebra to beam-transport codes, both of which are highly analytical in foundation. Some of the main design tools available today will be described, giving a little of their history, and will conclude by trying to convey some of the excitement in the field through a brief description of Lie and differential algebra. 30 refs., 7 figs.
High-Order Energies for Stereo Segmentation.
Peng, Jianteng; Shen, Jianbing; Li, Xuelong
2016-07-01
In this paper, we propose a novel segmentation approach for stereo images using the high-order energy optimization, which utilizes the disparity maps and statistical information of stereo images to enrich the high-order potential functions. To the best of our knowledge, our approach is the first one to formulate the problem of stereo segmentation as a high-order energy optimization problem, which simultaneously segments the foreground objects in left and right images using the proposed high-order potential function. A new method for designing the penalty function in our high-order term is proposed by the corresponding pixels and their neighboring pixels between left and right images. The relationships of stereo correspondence by disparity maps are further employed to enhance the connections between the left and right stereo images. Experimental results demonstrate that the proposed approach can effectively improve the performance of two kinds of stereo segmentation, including the automatic saliency-aware stereocut and the interactive stereo segmentation with user scribbles. PMID:26208377
HODIF:High-Order Discretizations, Interpolations and
Kennedy, Christopher A.; Carpenter, Mark H.; Ray, Jaideen
2006-06-20
This software, a library, contains FORTRAN77 subroutines to calculate first and second derivatives up to 8th order, interpolations (1D and 2D) up to 10th order and filters up to 14th order. Only even orders are addressed and finite-difference stencils are implemented on a vertex-centered mesh. The primary aim of this library is to be used in block-structured adaptive mesh simulations where high order is desired. The interpolants in this library are essentially designed to do prolongations and restrictions between levels of rfinement - however, they assume that the refinement ratio is 2. The filters are provided to remove high wavenumber content from solutions in case Runge phenomenon occurs - a common occurrence in case of marginal resolution of the solution. Details of the derivation and use are to be found in "Using high-order methods on adaptively refined block-structured meshes - discretizations, interpolations and filters", by J. Ray, C.A. Kennedy, S. Lefantzi and H.N. Najm, Sandia Technical Report, SAND2005-7981. The software comes with a User's Guide and examples how to use it.
HODIF:High-Order Discretizations, Interpolations and
Energy Science and Technology Software Center (ESTSC)
2006-06-20
This software, a library, contains FORTRAN77 subroutines to calculate first and second derivatives up to 8th order, interpolations (1D and 2D) up to 10th order and filters up to 14th order. Only even orders are addressed and finite-difference stencils are implemented on a vertex-centered mesh. The primary aim of this library is to be used in block-structured adaptive mesh simulations where high order is desired. The interpolants in this library are essentially designed to domore » prolongations and restrictions between levels of rfinement - however, they assume that the refinement ratio is 2. The filters are provided to remove high wavenumber content from solutions in case Runge phenomenon occurs - a common occurrence in case of marginal resolution of the solution. Details of the derivation and use are to be found in "Using high-order methods on adaptively refined block-structured meshes - discretizations, interpolations and filters", by J. Ray, C.A. Kennedy, S. Lefantzi and H.N. Najm, Sandia Technical Report, SAND2005-7981. The software comes with a User's Guide and examples how to use it.« less
Preference for Well-Balanced Saliency in Details Cropped from Photographs
Abeln, Jonas; Fresz, Leonie; Amirshahi, Seyed Ali; McManus, I. Chris; Koch, Michael; Kreysa, Helene; Redies, Christoph
2016-01-01
Photographic cropping is the act of selecting part of a photograph to enhance its aesthetic appearance or visual impact. It is common practice with both professional (expert) and amateur (non-expert) photographers. In a psychometric study, McManus et al. (2011b) showed that participants cropped photographs confidently and reliably. Experts tended to select details from a wider range of positions than non-experts, but other croppers did not generally prefer details that were selected by experts. It remained unclear, however, on what grounds participants selected particular details from a photograph while avoiding other details. One of the factors contributing to cropping decision may be visual saliency. Indeed, various saliency-based computer algorithms are available for the automatic cropping of photographs. However, careful experimental studies on the relation between saliency and cropping are lacking to date. In the present study, we re-analyzed the data from the studies by McManus et al. (2011a,b), focusing on statistical image properties. We calculated saliency-based measures for details selected and details avoided during cropping. As expected, we found that selected details contain regions of higher saliency than avoided details on average. Moreover, the saliency center-of-mass was closer to the geometrical center in selected details than in avoided details. Results were confirmed in an eye tracking study with the same dataset of images. Interestingly, the observed regularities in cropping behavior were less pronounced for experts than for non-experts. In summary, our results suggest that, during cropping, participants tend to select salient regions and place them in an image composition that is well-balanced with respect to the distribution of saliency. Our study contributes to the knowledge of perceptual bottom-up features that are germane to aesthetic decisions in photography and their variability in non-experts and experts. PMID:26793086
Ordering Transformations in High-Entropy Alloys
NASA Astrophysics Data System (ADS)
Singh, Prashant; Johnson, Duane D.
The high-temperature disordered phase of multi-component alloys, including high-entropy alloys (HEA), generally must experience segregation or else passes through partially-ordered phases to reach the low-temperature, fully-ordered phase. Our first-principles KKR-CPA-based atomic short-range ordering (SRO) calculations (analyzed as concentration-waves) reveal the competing partially and fully ordered phases in HEA, and these phases can be then directly assessed from KKR-CPA results in larger unit cells [Phys. Rev. B 91, 224204 (2015)]. For AlxCrFeNiTi0.25, Liu et al. [J Alloys Compd 619, 610 (2015)] experimentally find FCC+BCC coexistence that changes to BCC with increasing Al (x from 0-to-1), which then exhibits a partially-ordered B2 at low temperatures. CALPHAD (Calculation of Phase Diagrams) predicts a region with L21+B2 coexistence. From KKR-CPA calculations, we find crossover versus Al from FCC+BCC coexistence to BCC, as observed, and regions for partially-order B2+L21 coexistence, as suggest by CALPHAD. Our combined first-principles KKR-CPA method provides a powerful approach in predicting SRO and completing long-range order in HEA and other complex alloys. Supported by the U.S. DOE, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division. Work was performed at Ames Laboratory, which is operated by Iowa State University for the U.S. DOE under Contract #DE-AC02-07CH11358.
George, D.L.
2011-01-01
The simulation of advancing flood waves over rugged topography, by solving the shallow-water equations with well-balanced high-resolution finite volume methods and block-structured dynamic adaptive mesh refinement (AMR), is described and validated in this paper. The efficiency of block-structured AMR makes large-scale problems tractable, and allows the use of accurate and stable methods developed for solving general hyperbolic problems on quadrilateral grids. Features indicative of flooding in rugged terrain, such as advancing wet-dry fronts and non-stationary steady states due to balanced source terms from variable topography, present unique challenges and require modifications such as special Riemann solvers. A well-balanced Riemann solver for inundation and general (non-stationary) flow over topography is tested in this context. The difficulties of modeling floods in rugged terrain, and the rationale for and efficacy of using AMR and well-balanced methods, are presented. The algorithms are validated by simulating the Malpasset dam-break flood (France, 1959), which has served as a benchmark problem previously. Historical field data, laboratory model data and other numerical simulation results (computed on static fitted meshes) are shown for comparison. The methods are implemented in GEOCLAW, a subset of the open-source CLAWPACK software. All the software is freely available at. Published in 2010 by John Wiley & Sons, Ltd.
High-order pulse front tilt caused by high-order angular dispersion.
Nabekawa, Yasuo; Midorikawa, Katsumi
2003-12-15
We have found general expressions relating the high-order pulse front tilt and the high-order angular dispersion in an ultrashort pulse, for the first time to our knowledge. The general formulae based on Fermat's principle are applicable for any ultrashort pulse with angular dispersion in the limit of geometrical optics. By virtue of these formulae, we can calculate the high-order pulse front tilt in the sub-20-fs UV pulse generated in a novel scheme of sum-frequency mixing in a nonlinear crystal accompanied by angular dispersion. It is also demonstrated how the high-order angular dispersion can be eliminated in the calculation. PMID:19471467
High order generalized permutational fractional Fourier transforms
NASA Astrophysics Data System (ADS)
Ran, Qi-Wen; Yuan, Lin; Tan, Li-Ying; Ma, Jing; Wang, Qi
2004-02-01
We generalize the definition of the fractional Fourier transform (FRFT) by extending the new definition proposed by Shih. The generalized FRFT, called the high order generalized permutational fractional Fourier transform (HGPFRFT), is a generalized permutational transform. It is shown to have arbitrary natural number M periodic eigenvalues not only with respect to the order of Hermite-Gaussian functions but also to the order of the transform. This HGPFRFT will be reduced to the original FRFT proposed by Namias and Liu's generalized FRFT and Shih's FRFT at the three limits with M = +infty, M = 4k (k is a natural number) and M = 4, respectively. Therefore the HGPFRFT introduces a comprehensive approach to Shih's FRFT and the original definition. Some important properties of HGPFRFT are discussed. Lastly the results of computer simulations and symbolic representations of the transform are provided.
High-Order Energy Stable WENO Schemes
NASA Technical Reports Server (NTRS)
Yamaleev, Nail K.; Carpenter, Mark H.
2008-01-01
A new third-order Energy Stable Weighted Essentially NonOscillatory (ESWENO) finite difference scheme for scalar and vector linear hyperbolic equations with piecewise continuous initial conditions is developed. The new scheme is proven to be stable in the energy norm for both continuous and discontinuous solutions. In contrast to the existing high-resolution shock-capturing schemes, no assumption that the reconstruction should be total variation bounded (TVB) is explicitly required to prove stability of the new scheme. A rigorous truncation error analysis is presented showing that the accuracy of the 3rd-order ESWENO scheme is drastically improved if the tuning parameters of the weight functions satisfy certain criteria. Numerical results show that the new ESWENO scheme is stable and significantly outperforms the conventional third-order WENO finite difference scheme of Jiang and Shu in terms of accuracy, while providing essentially nonoscillatory solutions near strong discontinuities.
High order WENO scheme for computational cosmology
NASA Astrophysics Data System (ADS)
Roy, Ishani
2010-11-01
This doctoral dissertation is concerned with the formulation and application of a high order accurate numerical algorithm suitable in solving complex multi dimensional equations and the application of this algorithm to a problem in Astrophysics. The algorithm is designed with the aim of resolving solutions of partial differential equations with sharp fronts propagating with time. This high order accurate class of numerical technique is called a Weighted Essentially Non Oscillatory (WENO) method and is well suited for shock capturing in solving conservation laws. The numerical approximation method, in the algorithm, is coupled with high order time marching as well as integration techniques designed to reduce computational cost. This numerical algorithm is used in several applications in computational cosmology to help understand questions about certain physical phenomena which occurred during the formation and evolution of first generation stars. The thesis is divided broadly in terms of the algorithm and its application to the different galactic processes. The first chapter deals with the astrophysical problem and offers an introduction to the numerical algorithm. In chapter 2 we outline the mathematical model and the various functions and parameters associated with the model. We also give a brief description of the relevant physical phenomena and the conservation laws associated with them. In chapter 3, we give a detailed description of the higher order algorithm and its formulation. We also highlight the special techniques incorporated in the algorithm in order to make it more suitable for handling cases which are computationally intensive. In the later chapters, 4-7, we explore in detail the physical processes and the different applications of our numerical scheme. We calculate different results such as the time scale of a temperature coupling mechanism, radiation and intensity changes etc. Different tests are also performed to illustrate the stability and
High-order counting statistics and interactions
NASA Astrophysics Data System (ADS)
Flindt, Christian
2012-02-01
Full counting statistics concerns the stochastic transport of electrons in mesoscopic structures [1]. Recently it has been shown that the charge transport statistics for noninteracting electrons in a two-terminal system is always generalized binomial: it can be decomposed into independent single-particle events, and the zeros of the generating function are real and negative [2]. In this talk I show how the zeros of the generating function move into the complex plane due to interactions and demonstrate how the positions of the zeros can be detected using high-order factorial cumulants [3]. As an illustrative example I discuss electron transport through a Coulomb blockade quantum dot for which the interactions on the quantum dot are clearly visible in the high-order factorial cumulants. These findings are important for understanding the influence of interactions on counting statistics, and the characterization in terms of zeros of the generating function provides a simple interpretation of recent experiments, where high-order statistics have been measured [4]. [4pt] [1] Yu. V. Nazarov, ed., Quantum Noise in Mesoscopic Physics, NATO Science Series, Vol. 97 (Kluwer, Dordrecht, 2003) [2] A. G. Abanov and D. A. Ivanov, Phys. Rev. Lett. 100, 086602 (2008), Phys. Rev. B 79, 205315 (2009) [3] D. Kambly, C. Flindt, and M. B"uttiker, Phys. Rev. B 83, 075432 (2011) -- Editors' Suggestion [4] C. Flindt, C. Fricke, F. Hohls, T. Novotn'y, K. Netocn'y, T. Brandes, and R. J. Haug, Proc. Natl. Acad. Sci. USA 106, 10116 (2009)
On High-Order Radiation Boundary Conditions
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas
1995-01-01
In this paper we develop the theory of high-order radiation boundary conditions for wave propagation problems. In particular, we study the convergence of sequences of time-local approximate conditions to the exact boundary condition, and subsequently estimate the error in the solutions obtained using these approximations. We show that for finite times the Pade approximants proposed by Engquist and Majda lead to exponential convergence if the solution is smooth, but that good long-time error estimates cannot hold for spatially local conditions. Applications in fluid dynamics are also discussed.
High Order Semi-Lagrangian Advection Scheme
NASA Astrophysics Data System (ADS)
Malaga, Carlos; Mandujano, Francisco; Becerra, Julian
2014-11-01
In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).
High phase order transmission demonstration. Final report
Krizauskas, E.; Landers, T.L.; Richeda, R.J.; Oppel, L.J.; Stewart, J.R.
1997-12-01
High-phase-order (HPO), or six-phase, transmission is an extension of line compaction that further increases the power transfer capability of a limited transmission line right-of-way. On July 1, 1992, the first commercially operated six-phase transmission line was energized as a tie line integrated into the New York State Electric and Gas (NYSEG) existing three-phase power system. Previous Empire State Electric Energy Research Corporation (ESEERCO) Project EP 88-23 reports detail the analytical framework and conceptual studies (Phase 1) and the detailed engineering and design/construction (Phase 2) that preceded the 1992 energization. After the six-phase line was constructed, a testing program verified the theoretical predictions of electrical effects due to six-phase construction. This Final Project Report details the results of the Phase 3 testing program and examines steady-state power frequency parameters, partial switching, corona effects, and field effects. In addition, this report details the results of two unplanned unstaged faults, and low-level staged faults. After one year of operation, results led to the identification of aspects that warranted additional study and evaluation. This report summarizes these additional investigations and evaluations of midspan spacers, off-the-shelf microprocessor-based relays for six-phase line protection, live line maintenance, possible standard six-phase station designs, and an economic evaluation of break-even distances for which six-phase is more economical than conventional double-circuit three-phase applications for line upgrades and new construction.
High order harmonic generation in rare gases
Budil, K.S.
1994-05-01
The process of high order harmonic generation in atomic gases has shown great promise as a method of generating extremely short wavelength radiation, extending far into the extreme ultraviolet (XUV). The process is conceptually simple. A very intense laser pulse (I {approximately}10{sup 13}-10{sup 14} W/cm{sup 2}) is focused into a dense ({approximately}10{sup l7} particles/cm{sup 3}) atomic medium, causing the atoms to become polarized. These atomic dipoles are then coherently driven by the laser field and begin to radiate at odd harmonics of the laser field. This dissertation is a study of both the physical mechanism of harmonic generation as well as its development as a source of coherent XUV radiation. Recently, a semiclassical theory has been proposed which provides a simple, intuitive description of harmonic generation. In this picture the process is treated in two steps. The atom ionizes via tunneling after which its classical motion in the laser field is studied. Electron trajectories which return to the vicinity of the nucleus may recombine and emit a harmonic photon, while those which do not return will ionize. An experiment was performed to test the validity of this model wherein the trajectory of the electron as it orbits the nucleus or ion core is perturbed by driving the process with elliptically, rather than linearly, polarized laser radiation. The semiclassical theory predicts a rapid turn-off of harmonic production as the ellipticity of the driving field is increased. This decrease in harmonic production is observed experimentally and a simple quantum mechanical theory is used to model the data. The second major focus of this work was on development of the harmonic {open_quotes}source{close_quotes}. A series of experiments were performed examining the spatial profiles of the harmonics. The quality of the spatial profile is crucial if the harmonics are to be used as the source for experiments, particularly if they must be refocused.
High-order nite volume WENO schemes for the shallow water equations with dry states
Xing, Yulong; Shu, Chi-wang
2011-01-01
The shallow water equations are used to model flows in rivers and coastal areas, and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. These equations have still water steady state solutions in which the flux gradients are balanced by the source term. It is desirable to develop numerical methods which preserve exactly these steady state solutions. Another main difficulty usually arising from the simulation of dam breaks and flood waves flows is the appearance of dry areas where no water is present. If no special attention is paid, standard numerical methods may fail near dry/wet front and produce non-physical negative water height. A high-order accurate finite volume weighted essentially non-oscillatory (WENO) scheme is proposed in this paper to address these difficulties and to provide an efficient and robust method for solving the shallow water equations. A simple, easy-to-implement positivity-preserving limiter is introduced. One- and two-dimensional numerical examples are provided to verify the positivity-preserving property, well-balanced property, high-order accuracy, and good resolution for smooth and discontinuous solutions.
High order accurate solutions of viscous problems
NASA Technical Reports Server (NTRS)
Hayder, M. E.; Turkel, Eli
1993-01-01
We consider a fourth order extension to MacCormack's scheme. The original extension was fourth order only for the inviscid terms but was second order for the viscous terms. We show how to modify the viscous terms so that the scheme is uniformly fourth order in the spatial derivatives. Applications are given to some boundary layer flows. In addition, for applications to shear flows the effect of the outflow boundary conditions are very important. We compare the accuracy of several of these different boundary conditions for both boundary layer and shear flows. Stretching at the outflow usually increases the oscillations in the numerical solution but the addition of a filtered sponge layer (with or without stretching) reduces such oscillations. The oscillations are generated by insufficient resolution of the shear layer. When the shear layer is sufficiently resolved then oscillations are not generated and there is less of a need for a nonreflecting boundary condition.
High-Order Energy Stable WENO Schemes
NASA Technical Reports Server (NTRS)
Yamaleev, Nail K.; Carpenter, Mark H.
2009-01-01
A third-order Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite difference scheme developed by Yamaleev and Carpenter was proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, a systematic approach is presented that enables 'energy stable' modifications for existing WENO schemes of any order. The technique is demonstrated by developing a one-parameter family of fifth-order upwind-biased ESWENO schemes; ESWENO schemes up to eighth order are presented in the appendix. New weight functions are also developed that provide (1) formal consistency, (2) much faster convergence for smooth solutions with an arbitrary number of vanishing derivatives, and (3) improved resolution near strong discontinuities.
High-order tail in Schwarzschild spacetime
NASA Astrophysics Data System (ADS)
Casals, Marc; Ottewill, Adrian
2015-12-01
We present an analysis of the behavior at late times of linear field perturbations of a Schwarzschild black hole spacetime. In particular, we give explicit analytic expressions for the field perturbations (for a specific ℓ-multipole) of general spin up to the first four orders at late times. These expressions are valid at arbitrary radius and include, apart from the well-known power-law tail decay at leading order (˜t-2 ℓ-3), a new logarithmic behavior at third leading order (˜t-2 ℓ-5ln t ). We obtain these late-time results by developing an analytical formalism initially formulated by Mano, Suzuki and Takasugi (MST) [Prog. Theor. Phys. 95, 1079 (1996); 96, 549 (1996)] formalism and by expanding the various MST Fourier-mode quantities for small frequency. While we give explicit expansions up to the first four leading orders (for small frequency for the Fourier modes, for late time for the field perturbation), we give a prescription for obtaining expressions to arbitrary order within a "perturbative regime."
A high performance totally ordered multicast protocol
NASA Technical Reports Server (NTRS)
Montgomery, Todd; Whetten, Brian; Kaplan, Simon
1995-01-01
This paper presents the Reliable Multicast Protocol (RMP). RMP provides a totally ordered, reliable, atomic multicast service on top of an unreliable multicast datagram service such as IP Multicasting. RMP is fully and symmetrically distributed so that no site bears un undue portion of the communication load. RMP provides a wide range of guarantees, from unreliable delivery to totally ordered delivery, to K-resilient, majority resilient, and totally resilient atomic delivery. These QoS guarantees are selectable on a per packet basis. RMP provides many communication options, including virtual synchrony, a publisher/subscriber model of message delivery, an implicit naming service, mutually exclusive handlers for messages, and mutually exclusive locks. It has commonly been held that a large performance penalty must be paid in order to implement total ordering -- RMP discounts this. On SparcStation 10's on a 1250 KB/sec Ethernet, RMP provides totally ordered packet delivery to one destination at 842 KB/sec throughput and with 3.1 ms packet latency. The performance stays roughly constant independent of the number of destinations. For two or more destinations on a LAN, RMP provides higher throughput than any protocol that does not use multicast or broadcast.
Periodicity of high-order neural functions
NASA Technical Reports Server (NTRS)
Kellaway, P.; Borda, R. P.; Frost, J. D.; Carrie, J. R. G.; Coats, A. C.
1973-01-01
The results of recent studies on higher order, integrative processes in the central nervous system are reported. Attempts were made to determine whether these processes exhibit any ongoing rhythmicity which might manifest itself in alterations of attention and alertness. Experiments were also designed to determine if a periodicity approximating that of the REM could be detected in various parameters of brain electrical activity.
Optical waveguides having flattened high order modes
Messerly, Michael Joseph; Beach, Raymond John; Heebner, John Edward; Dawson, Jay Walter; Pax, Paul Henry
2014-08-05
A deterministic methodology is provided for designing optical fibers that support field-flattened, ring-like higher order modes. The effective and group indices of its modes can be tuned by adjusting the widths of the guide's field-flattened layers or the average index of certain groups of layers. The approach outlined here provides a path to designing fibers that simultaneously have large mode areas and large separations between the propagation constants of its modes.
High-order control for symplectic maps
NASA Astrophysics Data System (ADS)
Sansottera, M.; Giorgilli, A.; Carletti, T.
2016-02-01
We revisit the problem of introducing an a priori control for devices that can be modeled via a symplectic map in a neighborhood of an elliptic equilibrium. Using a technique based on Lie transform methods we produce a normal form algorithm that avoids the usual step of interpolating the map with a flow. The formal algorithm is completed with quantitative estimates that bring into evidence the asymptotic character of the normal form transformation. Then we perform an heuristic analysis of the dynamical behavior of the map using the invariant function for the normalized map. Finally, we discuss how control terms of different orders may be introduced so as to increase the size of the stable domain of the map. The numerical examples are worked out on a two dimensional map of Hénon type.
High-order correlation of chaotic bosons and fermions
NASA Astrophysics Data System (ADS)
Liu, Hong-Chao
2016-08-01
We theoretically study the high-order correlation functions of chaotic bosons and fermions. Based on the different parity of the Stirling number, the products of the first-order correlation functions are well classified and employed to represent the high-order correlation function. The correlation of bosons conduces a bunching effect, which will be enhanced as order N increases. Different from bosons, the anticommutation relation of fermions leads to the parity of the Stirling number, which thereby results in a mixture of bunching and antibunching behaviors in high-order correlation. By further investigating third-order ghost diffraction and ghost imaging, the differences between the high-order correlations of bosons and fermions are discussed in detail. A larger N will dramatically improve the ghost image quality for bosons, but a good strategy should be carefully chosen for the fermionic ghost imaging process due to its complex correlation components.
Surface Remeshing with Robust High-Order Reconstruction
Ray, Navamita; Delaney, Tristan; Einstein, Daniel R.; Jiao, Xiangmin
2014-03-26
Remeshing is an important problem in variety of applications, such as finite element methods and geometry processing. Surface remeshing poses some unique challenges, as it must deliver not only good mesh quality but also good geometric accuracy. For applications such as finite elements with high-order elements (quadratic or cubic elements), the geometry must be preserved to high-order (third-order or higher) accuracy, since low-order accuracy may undermine the convergence of numerical computations. The problem is particularly challenging if the CAD model is not available for the underlying geometry, and is even more so if the surface meshes contain some inverted elements. We describe remeshing strategies that can simultaneously produce high-quality triangular meshes, untangling mildly folded triangles and preserve the geometry to high-order of accuracy. Our approach extends our earlier works on high-order surface reconstruction and mesh optimization by enhancing its robustness with a geometric limiter for under-resolved geometries. We also integrate high-order surface reconstruction with surface mesh adaptation techniques, which alter the number of triangles and nodes. We demonstrate the utilization of our method to meshes for high-order finite elements, biomedical image-based surface meshes, and complex interface meshes in fluid simulations.
Generation of intense high-order vortex harmonics.
Zhang, Xiaomei; Shen, Baifei; Shi, Yin; Wang, Xiaofeng; Zhang, Lingang; Wang, Wenpeng; Xu, Jiancai; Yi, Longqiong; Xu, Zhizhan
2015-05-01
This Letter presents for the first time a scheme to generate intense high-order optical vortices that carry orbital angular momentum in the extreme ultraviolet region based on relativistic harmonics from the surface of a solid target. In the three-dimensional particle-in-cell simulation, the high-order harmonics of the high-order vortex mode is generated in both reflected and transmitted light beams when a linearly polarized Laguerre-Gaussian laser pulse impinges on a solid foil. The azimuthal mode of the harmonics scales with its order. The intensity of the high-order vortex harmonics is close to the relativistic region, with the pulse duration down to attosecond scale. The obtained intense vortex beam possesses the combined properties of fine transversal structure due to the high-order mode and the fine longitudinal structure due to the short wavelength of the high-order harmonics. In addition to the application in high-resolution detection in both spatial and temporal scales, it also presents new opportunities in the intense vortex required fields, such as the inner shell ionization process and high energy twisted photons generation by Thomson scattering of such an intense vortex beam off relativistic electrons. PMID:25978234
High Spin-Chern Insulators with Magnetic Order
Ezawa, Motohiko
2013-01-01
As a topological insulator, the quantum Hall (QH) effect is indexed by the Chern and spin-Chern numbers and . We have only in conventional QH systems. We investigate QH effects in generic monolayer honeycomb systems. We search for spin-resolved characteristic patterns by exploring Hofstadter's butterfly diagrams in the lattice theory and fan diagrams in the low-energy Dirac theory. It is shown that the spin-Chern number can takes an arbitrary high value for certain QH systems. This is a new type of topological insulators, which we may call high spin-Chern insulators. Samples may be provided by graphene on the SiC substrate with ferromagnetic order, transition-metal dichalcogenides with ferromagnetic order, transition-metal oxide with antiferromagnetic order and silicene with ferromagnetic order. Actually high spin-Chern insulators are ubiquitous in any systems with magnetic order. Nevertheless, the honeycomb system would provide us with unique materials for practical materialization. PMID:24310394
High Spin-Chern Insulators with Magnetic Order
NASA Astrophysics Data System (ADS)
Ezawa, Motohiko
2013-12-01
As a topological insulator, the quantum Hall (QH) effect is indexed by the Chern and spin-Chern numbers and . We have only in conventional QH systems. We investigate QH effects in generic monolayer honeycomb systems. We search for spin-resolved characteristic patterns by exploring Hofstadter's butterfly diagrams in the lattice theory and fan diagrams in the low-energy Dirac theory. It is shown that the spin-Chern number can takes an arbitrary high value for certain QH systems. This is a new type of topological insulators, which we may call high spin-Chern insulators. Samples may be provided by graphene on the SiC substrate with ferromagnetic order, transition-metal dichalcogenides with ferromagnetic order, transition-metal oxide with antiferromagnetic order and silicene with ferromagnetic order. Actually high spin-Chern insulators are ubiquitous in any systems with magnetic order. Nevertheless, the honeycomb system would provide us with unique materials for practical materialization.
New high order schemes in BATS-R-US
NASA Astrophysics Data System (ADS)
Toth, G.; van der Holst, B.; Daldorff, L.; Chen, Y.; Gombosi, T. I.
2013-12-01
The University of Michigan global magnetohydrodynamics code BATS-R-US has long relied on the block-adaptive mesh refinement (AMR) to increase accuracy in regions of interest, and we used a second order accurate TVD scheme. While AMR can in principle produce arbitrarily accurate results, there are still practical limitations due to computational resources. To further improve the accuracy of the BATS-R-US code, recently, we have implemented a 4th order accurate finite volume scheme (McCorquodale and Colella, 2011}), the 5th order accurate Monotonicity Preserving scheme (MP5, Suresh and Huynh, 1997) and the 5th order accurate CWENO5 scheme (Capdeville, 2008). In the first implementation the high order accuracy is achieved in the uniform parts of the Cartesian grids, and we still use the second order TVD scheme at resolution changes. For spherical grids the new schemes are only second order accurate so far, but still much less diffusive than the TVD scheme. We show a few verification tests that demonstrate the order of accuracy as well as challenging space physics applications. The high order schemes are less robust than the TVD scheme, and it requires some tricks and effort to make the code work. When the high order scheme works, however, we find that in most cases it can obtain similar or better results than the TVD scheme on twice finer grids. For three dimensional time dependent simulations this means that the high order scheme is almost 10 times faster requires 8 times less storage than the second order method.
A High-Order Multiscale Global Atmospheric Model
NASA Astrophysics Data System (ADS)
Nair, Ram
2016-04-01
The High-Order Method Modeling Environment (HOMME), developed at NCAR, is a petascale hydrostatic framework, which employs the cubed-sphere grid system and high-order continuous or discontinuous Galerkin (DG) methods. Recently, the HOMME framework is being extended to a non-hydrostatic dynamical core, named as the "High-Order Multiscale Atmospheric Model (HOMAM)." The spatial discretization is based on DG or high-order finite-volume methods. Orography is handled by the terrain-following height-based coordinate system. To alleviate the stringent CFL stability requirement resulting from the vertical aspects of the dynamics, an operator-splitting time integration scheme based on the horizontally explicit and vertically implicit (HEVI) philosophy is adopted for HOMAM. Preliminary results with the benchmark test cases proposed in the Dynamical Core Model Intercomparison project (DCMIP) test-suite will be presented in the seminar.
Near infrared frequency dependence of high-order sideband generation
Zaks, Benjamin; Banks, Hunter; Sherwin, Mark; Liu, Ren-Bao
2013-12-04
The near infrared frequency dependence of high order sideband generation in InGaAs quantum wells is discussed. The NIR frequency dependence of the sidebands indicates that the HSG phenomenon is excitonic in nature.
A stable 1D multigroup high-order low-order method
Yee, Ben Chung; Wollaber, Allan Benton; Haut, Terry Scot; Park, HyeongKae
2016-07-13
The high-order low-order (HOLO) method is a recently developed moment-based acceleration scheme for solving time-dependent thermal radiative transfer problems, and has been shown to exhibit orders of magnitude speedups over traditional time-stepping schemes. However, a linear stability analysis by Haut et al. (2015 Haut, T. S., Lowrie, R. B., Park, H., Rauenzahn, R. M., Wollaber, A. B. (2015). A linear stability analysis of the multigroup High-Order Low-Order (HOLO) method. In Proceedings of the Joint International Conference on Mathematics and Computation (M&C), Supercomputing in Nuclear Applications (SNA) and the Monte Carlo (MC) Method; Nashville, TN, April 19–23, 2015. American Nuclear Society.)more » revealed that the current formulation of the multigroup HOLO method was unstable in certain parameter regions. Since then, we have replaced the intensity-weighted opacity in the first angular moment equation of the low-order (LO) system with the Rosseland opacity. Furthermore, this results in a modified HOLO method (HOLO-R) that is significantly more stable.« less
Colloquium: Theory of intertwined orders in high temperature superconductors
NASA Astrophysics Data System (ADS)
Fradkin, Eduardo; Kivelson, Steven A.; Tranquada, John M.
2015-04-01
The electronic phase diagrams of many highly correlated systems, and, in particular, the cuprate high temperature superconductors, are complex, with many different phases appearing with similar (sometimes identical) ordering temperatures even as material properties, such as dopant concentration, are varied over wide ranges. This complexity is sometimes referred to as "competing orders." However, since the relation is intimate, and can even lead to the existence of new phases of matter such as the putative "pair-density wave," the general relation is better thought of in terms of "intertwined orders." Some of the experiments in the cuprates which suggest that essential aspects of the physics are reflected in the intertwining of multiple orders, not just in the nature of each order by itself, are selectively analyzed. Several theoretical ideas concerning the origin and implications of this complexity are also summarized and critiqued.
A wavelet-optimized, very high order adaptive grid and order numerical method
NASA Technical Reports Server (NTRS)
Jameson, Leland
1996-01-01
Differencing operators of arbitrarily high order can be constructed by interpolating a polynomial through a set of data followed by differentiation of this polynomial and finally evaluation of the polynomial at the point where a derivative approximation is desired. Furthermore, the interpolating polynomial can be constructed from algebraic, trigonometric, or, perhaps exponential polynomials. This paper begins with a comparison of such differencing operator construction. Next, the issue of proper grids for high order polynomials is addressed. Finally, an adaptive numerical method is introduced which adapts the numerical grid and the order of the differencing operator depending on the data. The numerical grid adaptation is performed on a Chebyshev grid. That is, at each level of refinement the grid is a Chebvshev grid and this grid is refined locally based on wavelet analysis.
High-order disclinations in space-variant polarization
NASA Astrophysics Data System (ADS)
Khajavi, B.; Galvez, E. J.
2016-08-01
We present the investigation of high-order disinclination patterns in the spatially variable polarization of a light beam. The beam was prepared by encoding two distinct high-order optical vortices on each of the circular polarization components of the beam. As a consequence, we were able to produce high-index lemon and star patterns, which have positive and negative indices, respectively. By varying the asymmetry of one of the vortices we were able to transform one symmetric pattern (lemon or star) into another (lemon or star). With one exception, monstar patterns always appear for specific ranges of asymmetry regardless of the end symmetric patterns. Mapping of all disclinations within each case is contained in a spherical space, where monstar regions are cusp-shaped. We found that high-order monstar patterns can have positive or negative index.
CoreSVM: a generalized high-order spectral volume method bearing Conservative Order RElease
NASA Astrophysics Data System (ADS)
Lamouroux, Raphael; Gressier, Jeremie; Joly, Laurent; Grondin, Gilles
2014-11-01
The spectral volume method (SVM) introduced by Wang in 2002 is based on a compact polynomial reconstruction where the interpolation's degree is driven by the partition of the spectral volumes. We propose a generalization of the SVM which releases the polynomial degree from this constraint and more importantly that allows to resort to any polynomial order inferior to the regular stencil order without changing the original spectral volume partition. Using one-dimensional advection and Burgers equation, we prove that the proposed extended method exhibits versatile high-order convergence together with conservativity properties. This new method is thus named the CoreSVM for Conservative Order-REleased SVM and we therefore explore its potential towards the numerical simulation of stiff problems. It is stressed that CoreSVM is indeed particularly suited to handle discontinuities, as the order-reduction serves to damp the numerical oscillations due to Runge's phenomenon. To ensure computational stability, local p-coarsening is used to obtain the highest adequate polynomial degree. It is advocated finally that, since the CoreSVM sets the polynomial order adaptation free from any stencil changes, these features do not come at the expense of any extra remeshing or data adaptation cost. Part of this research was funded by the French DGA.
High order sideband generation in terahertz quantum cascade lasers
NASA Astrophysics Data System (ADS)
Cavalié, P.; Freeman, J.; Maussang, K.; Strupiechonski, E.; Xu, G.; Colombelli, R.; Li, L.; Davies, A. G.; Linfield, E. H.; Tignon, J.; Dhillon, S. S.
2013-06-01
We demonstrate the generation of high order terahertz (THz) frequency sidebands (up to 3rd order) on a near infrared (NIR) optical carrier within a THz quantum cascade laser (QCL). The NIR carrier is resonant with the interband transition of the quantum wells composing the QCL, allowing the nonlinearity to be enhanced and leading to frequency mixing. A phonon depopulation based QCL with a double metal cavity was used to enhance the intracavity power density and to demonstrate the higher order sidebands. The 1st order sideband intensity shows a linear dependence with THz power corresponding to a single THz photon, while the second order sideband has a quadratic dependence implying a two THz photon interaction and hence a third order susceptibility. These measurements are compared to the photoluminescence and the QCL bandstructure to identify the states involved, with the lowest conduction band states contributing the most to the sideband intensity. We also show that the interaction for the second order sideband corresponds to an enhanced direct third order susceptibility χ(3) of ˜7 × 10-16(m/V)2, two orders of magnitude greater than the bulk value.
The Observation of Highly Ordered Domains in Membranes with Cholesterol
Armstrong, Clare L; Marquardt, Drew; Dies, Hannah; Kucerka, Norbert; Yamani, Zahra; Harroun, Thad; Katsaras, John; Shi, A-C; Rheinstadter, Maikel C
2013-01-01
Rafts, or functional domains, are transient nano- or mesoscopic structures in the exoplasmic leaflet of the plasma membrane, and are thought to be essential for many cellular processes. Using neutron diffraction and computer modelling, we present evidence for the existence of highly ordered lipid domains in the cholesterol-rich (32.5 mol%) liquid-ordered (lo) phase of dipalmitoylphosphatidylcholine membranes. The liquid ordered phase in one-component lipid membranes has previously been thought to be a homogeneous phase. The presence of highly ordered lipid domains embedded in a disordered lipid matrix implies non-uniform distribution of cholesterol between the two phases. The experimental results are in excellent agreement with recent computer simulations of DPPC/cholesterol complexes [Meinhardt, Vink and Schmid (2013). Proc Natl Acad Sci USA 110(12): 4476 4481], which reported the existence of nanometer size lo domains in a liquid disordered lipid environment.
The Observation of Highly Ordered Domains in Membranes with Cholesterol
Armstrong, Clare L.; Marquardt, Drew; Dies, Hannah; Kučerka, Norbert; Yamani, Zahra; Harroun, Thad A.; Katsaras, John; Shi, An-Chang; Rheinstädter, Maikel C.
2013-01-01
Rafts, or functional domains, are transient nano- or mesoscopic structures in the exoplasmic leaflet of the plasma membrane, and are thought to be essential for many cellular processes. Using neutron diffraction and computer modelling, we present evidence for the existence of highly ordered lipid domains in the cholesterol-rich (32.5 mol%) liquid-ordered () phase of dipalmitoylphosphatidylcholine membranes. The liquid ordered phase in one-component lipid membranes has previously been thought to be a homogeneous phase. The presence of highly ordered lipid domains embedded in a disordered lipid matrix implies non-uniform distribution of cholesterol between the two phases. The experimental results are in excellent agreement with recent computer simulations of DPPC/cholesterol complexes [Meinhardt, Vink and Schmid (2013). Proc Natl Acad Sci USA 110(12): 4476–4481], which reported the existence of nanometer size domains in a liquid disordered lipid environment. PMID:23823623
Theory of intertwined orders in high temperature superconductors
Fradkin, Eduardo; Tranquada, John M.; Kivelson, Steven A.
2015-03-26
The electronic phase diagrams of many highly correlated systems, and in particular the cuprate high temperature superconductors, are complex, with many different phases appearing with similar—sometimes identical—ordering temperatures even as material properties, such as a dopant concentration, are varied over wide ranges. This complexity is sometimes referred to as “competing orders.” However, since the relation is intimate, and can even lead to the existence of new phases of matter such as the putative “pair-density-wave,” the general relation is better thought of in terms of “intertwined orders.” We selectively analyze some of the experiments in the cuprates which suggest that essentialmore » aspects of the physics are reflected in the intertwining of multiple orders—not just in the nature of each order by itself. We also summarize and critique several theoretical ideas concerning the origin and implications of this complexity.« less
Theory of intertwined orders in high temperature superconductors
Fradkin, Eduardo; Tranquada, John M.; Kivelson, Steven A.
2015-03-26
The electronic phase diagrams of many highly correlated systems, and in particular the cuprate high temperature superconductors, are complex, with many different phases appearing with similar—sometimes identical—ordering temperatures even as material properties, such as a dopant concentration, are varied over wide ranges. This complexity is sometimes referred to as “competing orders.” However, since the relation is intimate, and can even lead to the existence of new phases of matter such as the putative “pair-density-wave,” the general relation is better thought of in terms of “intertwined orders.” We selectively analyze some of the experiments in the cuprates which suggest that essential aspects of the physics are reflected in the intertwining of multiple orders—not just in the nature of each order by itself. We also summarize and critique several theoretical ideas concerning the origin and implications of this complexity.
Separation of High Order Harmonics with Fluoride Windows
Allison, Tom; van Tilborg, Jeroen; Wright, Travis; Hertlein, Marcus; Falcone, Roger; Belkacem, Ali
2010-08-02
The lower orders produced in high order harmonic generation can be effciently temporally separated into monochromatic pulses by propagation in a Fluoride window while still preserving their femtosecond pulse duration. We present calculations for MgF2, CaF2, and LiF windows for the third, fifth, and seventh harmonics of 800 nm. We demonstrate the use of this simple and inexpensive technique in a femtosecond pump/probe experiment using the fifth harmonic.
High-order rogue waves for the Hirota equation
Li, Linjing; Wu, Zhiwei; Wang, Lihong; He, Jingsong
2013-07-15
The Hirota equation is better than the nonlinear Schrödinger equation when approximating deep ocean waves. In this paper, high-order rational solutions for the Hirota equation are constructed based on the parameterized Darboux transformation. Several types of this kind of solutions are classified by their structures. -- Highlights: •The determinant representation of the N-fold Darboux transformation of the Hirota equation. •Properties of the fundamental pattern of the higher order rogue wave. •Ring structure and triangular structure of the higher order rogue waves.
High order ZIP' differencing of convective terms. Memorandum report
Zalesak, S.T.
1980-05-08
The ZIP flux form for differencing the term (wv) sub x, where w is a convected quantity and v is a convective velocity, is observed to be equivalent to differencing the alternative expression wv sub x + w sub x v using centered second order finite differences. Based on this observation, the extension of the ZIP flux concept to arbitrarily high order accuracy is given. Computational examples show the advantage both of the ZIP flux concept itself and of its higher order forms within the context of flux-corrected transport (FCT) algorithms.
Vortices and charge order in high-Tc superconductors
NASA Astrophysics Data System (ADS)
Einenkel, Matthias; Meier, Hendrik; Pépin, Catherine; Efetov, Konstantin B.
2015-03-01
We theoretically investigate the vortex state of the cuprate high-temperature superconductors in the presence of magnetic fields. Assuming the recently derived nonlinear σ-model for fluctuations in the pseudogap phase, we find that the vortex cores consist of two crossed regions of elliptic shape, in which a static charge order emerges. Charge density wave order manifests itself as satellites to the ordinary Bragg peaks directed along the axes of the reciprocal copper lattice. Quadrupole density wave (bond order) satellites, if seen, are predicted to be along the diagonals. The intensity of the satellites should grow linearly with the magnetic field, in agreement with the result of recent experiments.
Vortices and charge order in high-Tc superconductors
NASA Astrophysics Data System (ADS)
Einenkel, M.; Meier, H.; Pépin, C.; Efetov, K. B.
2014-08-01
We theoretically investigate the vortex state of the cuprate high-temperature superconductors in the presence of magnetic fields. Assuming the recently derived nonlinear σ-model for fluctuations in the pseudogap phase, we find that the vortex cores consist of two crossed regions of elliptic shape, in which a static charge order emerges. Charge density wave order manifests itself as satellites to the ordinary Bragg peaks directed along the axes of the reciprocal copper lattice. Quadrupole density wave (bond order) satellites, if seen, are predicted to be along the diagonals. The intensity of the satellites should grow linearly with the magnetic field, in agreement with the result of recent experiments.
High order hybrid numerical simulations of two dimensional detonation waves
NASA Technical Reports Server (NTRS)
Cai, Wei
1993-01-01
In order to study multi-dimensional unstable detonation waves, a high order numerical scheme suitable for calculating the detailed transverse wave structures of multidimensional detonation waves was developed. The numerical algorithm uses a multi-domain approach so different numerical techniques can be applied for different components of detonation waves. The detonation waves are assumed to undergo an irreversible, unimolecular reaction A yields B. Several cases of unstable two dimensional detonation waves are simulated and detailed transverse wave interactions are documented. The numerical results show the importance of resolving the detonation front without excessive numerical viscosity in order to obtain the correct cellular patterns.
A High Order Perturbation Analysis of the Sitnikov Problem
NASA Astrophysics Data System (ADS)
Hagel, Johannes; Lhotka, Christoph
2005-09-01
The Sitnikov problem is one of the most simple cases of the elliptic restricted three body system. A massless body oscillates along a line (z) perpendicular to a plane (x,y) in which two equally massive bodies, called primary masses, perform Keplerian orbits around their common barycentre with a given eccentricity e. The crossing point of the line of motion of the third mass with the plane is equal to the centre of gravity of the entire system. In spite of its simple geometrical structure, the system is nonlinear and explicitly time dependent. It is globally non integrable and therefore represents an interesting application for advanced perturbative methods. In the present work a high order perturbation approach to the problem was performed, by using symbolic algorithms written in Mathematica. Floquet theory was used to derive solutions of the linearized equation up to 17th order in e. In this way precise analytical expressions for the stability of the system were obtained. Then, applying the Courant and Snyder transformation to the nonlinear equation, algebraic solutions of seventh order in z and e were derived using the method of Poincaré Lindstedt. The enormous amount of necessary computations were performed by extensive use of symbolic programming. We developed automated and highly modularized algorithms in order to master the problem of ordering an increasing number of algebraic terms originating from high order perturbation theory.
Highly-Ordered Thin Films from Photocleavable Block Copolymers
NASA Astrophysics Data System (ADS)
Gu, Weiyin; Zhao, Hui; Coughlin, E.; Theato, Patrick; Russell, Thomas; University of Massachusetts at Amherst Team; University of Hamburg Team
2013-03-01
A robust route for the preparation of nanoscopic dot/line patterns with long range lateral order from poly(styrene-block-ethylene oxide) (PS-b-PEO) with an o-nitrobenzyl ester junction (PS-h ν-PEO) is demonstrated. Solvent annealing condition is optimized to achieve the highly ordered cylindrical block copolymer (BCP) microdomains oriented normal or parallel to the silicon substrates. Following a very mild UV exposure and successive washing with methanol, PS-hv-PEO thin films were transformed into highly ordered porous or trench templates. Afterwards the pores or trenches were either filled with PDMS by spin-coating or exposed to direct metal deposition of Au. After a plasma etching or lift-off process to remove the polymer templates, highly ordered arrays of silica or Au nanopatterns were obtained. This represents the first template application example from highly ordered nanoporous thin films derived from block copolymers featuring a photocleavable junction. DOE (DE-FG02-96ER45612), NSF-MRSEC, DFG (TH 1104/4-1), CHE 0924435, R31-10013.
Atomic short-range order and incipient long-range order in high-entropy alloys
NASA Astrophysics Data System (ADS)
Singh, Prashant; Smirnov, A. V.; Johnson, D. D.
2015-06-01
Within density-functional theory, we apply an electronic-structure-based thermodynamic theory to calculate short-ranged order (SRO) in homogeneously disordered substitutional N -component alloys, and its electronic origin. Using the geometric properties of an (N -1 ) simplex that describes the Gibbs (compositional) space, we derive the analytic transform of the SRO eigenvectors that provides a unique description of high-temperature SRO in N -component alloys and the incipient low-temperature long-range order. We apply the electronic-based thermodynamic theory and the new general analysis to ternaries (A 1 Cu-Ni-Zn and A 2 Nb-Al-Ti) for validation, and then to quinary Al-Co-Cr-Fe-Ni high-entropy alloys for predictive assessment.
Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows
NASA Astrophysics Data System (ADS)
Sjoegreen, Bjoern; Yee, Helen C.
2002-11-01
Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes for the compressible Euler and Navier-Stokes equations has been developed and verified by the authors and collaborators. These schemes are suitable for the problems in question. Basically, the scheme consists of sixth-order or higher non-dissipative spatial difference operators as the base scheme. To control the amount of numerical dissipation, multiresolution wavelets are used as sensors to adaptively limit the amount and to aid the selection and/or blending of the appropriate types of numerical dissipation to be used. Magnetohydrodynamics (MHD) waves play a key role in drag reduction in highly maneuverable high speed combat aircraft, in space weather forecasting, and in the understanding of the dynamics of the evolution of our solar system and the main sequence stars. Although there exist a few well-studied second and third-order high-resolution shock-capturing schemes for the MHD in the literature, these schemes are too diffusive and not practical for turbulence/combustion MHD flows. On the other hand, extension of higher than third-order high-resolution schemes to the MHD system of equations is not straightforward. Unlike the hydrodynamic equations, the inviscid MHD system is non-strictly hyperbolic with non-convex fluxes. The wave structures and shock types are different from their hydrodynamic counterparts. Many of the non-traditional hydrodynamic shocks are not fully understood. Consequently, reliable and highly accurate numerical schemes for multiscale MHD equations pose a great
High-order fluorescence fluctuation analysis of model protein clusters.
Palmer, A G; Thompson, N L
1989-01-01
The technique of high-order fluorescence fluctuation autocorrelation for detecting and characterizing protein oligomers was applied to solutions containing two fluorescent proteins in which the more fluorescent proteins were analogues for clusters of the less fluorescent ones. The results show that the model protein clusters can be detected for average numbers of observed subunits (free monomers plus monomers in oligomers) equal to 10-100 and for relative fluorescent yields that correspond to oligomers as small as trimers. High-order fluorescent fluctuation analysis may therefore be applicable to cell surface receptor clusters in natural or model membranes. PMID:2548201
Liu, Chain T.; Inouye, Henry
1979-01-01
Malleable long range ordered alloys having high critical ordering temperatures exist in the V(Fe, Co).sub.3 and V(Fe, Co, Ni).sub.3 systems. These alloys have the following compositions comprising by weight: 22-23% V, 14-30% Fe, and the remainder Co or Co and Ni with an electron density no more than 7.85. The maximum combination of high temperature strength, ductility and creep resistance are manifested in the alloy comprising by weight 22-23% V, 14-20% Fe and the remainder Co and having an atomic composition of V(Fe .sub.0.20-0.26 C Co.sub.0.74-0.80).sub.3. The alloy comprising by weight 22-23% V, 16-17% Fe and 60-62% Co has excellent high temperature properties. The alloys are fabricable into wrought articles by casting, deforming, and annealing for sufficient time to provide ordered structure.
Acoustic centering of sources with high-order radiation patterns.
Shabtai, Noam R; Vorländer, Michael
2015-04-01
Surrounding spherical microphone arrays have recently been used in order to model the radiation pattern of acoustic sources that are assumed to be at the center of the array. Source centering algorithms are applied to the measurements in order to reduce the negative effect of acoustic source misalignment with regard to the physical center of the microphone array. Recent works aim to minimize the energy that is contained in the high-order coefficients of the radiation pattern in the spherical harmonics domain, in order to directly address the problem of increased order and spatial aliasing resulted by this misalignment. However, objective functions which directly minimize the norm of these coefficients were shown to be convex only when employed on sources with low-order radiation patterns. This work presents a source centering algorithm that operates on plane sections and aims to achieve a convex objective function on every plane section. The results of the proposed algorithm are shown to be more convex than the previous algorithms for sources with higher-order radiation pattern, usually at higher frequencies. PMID:25920846
Quantum interference of high-order harmonics from mixed gases
NASA Astrophysics Data System (ADS)
González-Fernández, A.; Velarde, P.
2016-08-01
We present a theoretical study about the interference of the harmonics generated by a mixture of two gases, He-Ne. Our model is based on the electron quantum paths, a discrete number of electron trajectories, and continuum-bound transitions. A laser with intensity around 1014W/cm2 that interacts with a mixture of gases, He-Ne, produces an interference that is destructive at the low-order harmonics and oscillates between constructive and destructive near to cutoff. This destructive interference at high-order harmonics may be used to explore other transitions, which are currently hidden. At low-order harmonic frequencies, our numerical results are in very good agreement with experimental data. At higher-order harmonics, where there are no experimental data, comparison is with a Schrödinger solver.
Massively parallel high-order combinatorial genetics in human cells
Wong, Alan S L; Choi, Gigi C G; Cheng, Allen A; Purcell, Oliver; Lu, Timothy K
2016-01-01
The systematic functional analysis of combinatorial genetics has been limited by the throughput that can be achieved and the order of complexity that can be studied. To enable massively parallel characterization of genetic combinations in human cells, we developed a technology for rapid, scalable assembly of high-order barcoded combinatorial genetic libraries that can be quantified with high-throughput sequencing. We applied this technology, combinatorial genetics en masse (CombiGEM), to create high-coverage libraries of 1,521 two-wise and 51,770 three-wise barcoded combinations of 39 human microRNA (miRNA) precursors. We identified miRNA combinations that synergistically sensitize drug-resistant cancer cells to chemotherapy and/or inhibit cancer cell proliferation, providing insights into complex miRNA networks. More broadly, our method will enable high-throughput profiling of multifactorial genetic combinations that regulate phenotypes of relevance to biomedicine, biotechnology and basic science. PMID:26280411
A New Low Dissipative High Order Schemes for MHD Equations
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sjoegreen, Bjoern; Mansour, Nagi (Technical Monitor)
2002-01-01
The goal of this talk is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls to limit the amount and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids.
Automated Approach to Very High-Order Aeroacoustic Computations. Revision
NASA Technical Reports Server (NTRS)
Dyson, Rodger W.; Goodrich, John W.
2001-01-01
Computational aeroacoustics requires efficient, high-resolution simulation tools. For smooth problems, this is best accomplished with very high-order in space and time methods on small stencils. However, the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewski recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that am located near wall boundaries. These procedures are used to develop automatically and to implement very high-order methods (> 15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.
Attosecond Pulse Trains Using High-Order Harmonics
Antoine, P.; LHuillier, A.; Lewenstein, M.
1996-08-01
We demonstrate that high-order harmonics generated by an atom in intense laser field form trains of ultrashort pulses corresponding to different trajectories of electrons that tunnel out of the atom and recombine. Propagation in an atomic jet allows us to select one of these trajectories, leading to a train of pulses of extremely short duration. {copyright} {ital 1996 The American Physical Society.}
Input cavity for high-order asymmetric-mode gyroklystron
NASA Astrophysics Data System (ADS)
Danilov, Yu. Yu.
2012-06-01
A new input cavity design for a high-order asymmetric-mode gyroklystron is proposed. Methods of the selective excitation of a resonant mode with a rotating field structure and the prevention of cavity self-excitation at harmonics of the gyrofrequency are proposed. Results of experimental investigation of the H711 mode cavity for a multimegawatt pulsed gyroklystron are presented.
Accelerating experimental high-order spatial statistics calculations using GPUs
NASA Astrophysics Data System (ADS)
Li, Xue; Huang, Tao; Lu, De-Tang; Niu, Cong
2014-09-01
High-order spatial statistics have been widely used to describe the spatial phenomena in the field of geology science. Spatial statistics are subject to extremely heavy computational burden for large geostatistical models. To improve the computational efficiency, a parallel approach based on GPU (Graphics Processing Unit) is proposed for the calculation of high-order spatial statistics. The parallel scheme is achieved by utilizing a two-stage method to calculate the replicate of a moment for a given template simultaneously termed as the node-stage parallelism, and transform the spatial moments to cumulants for all lags of a template simultaneously termed as the template-stage parallelism. Also, a series of optimization strategies are proposed to take full advantage of the computational capabilities of GPUs, including the appropriate task allocation to the CUDA (Compute Unified Device Architecture) threads, proper organization of the GPU physical memory, and optimal improvement of the existed parallel routines. Tests are carried out on two training images to compare the performance of the GPU-based method with that of the serial implementation. Error analysis results indicate that the proposed parallel method can generate accurate cumulant maps, and the performance comparisons on various examples show that all the speedups for third-order, fourth-order and fifth-order cumulants calculation are over 17 times.
Anomalies in high-order harmonic generation at relativistic intensities
Teubner, U.; Foerster, E.; Pretzler, G.; Eidmann, K.; Witte, K.; Schlegel, Th.
2003-01-01
High-order harmonic generation from a solid target surface has been investigated using femtosecond laser pulses focused to intensities greater than 10{sup 18} W/cm{sup 2}. The experiments show that the harmonics are very intense, with a conversion efficiency that is one or two orders of magnitude larger than that of harmonics generated in gases. Beside the observation of presently the shortest wavelength harmonics from femtosecond-laser solid target interaction, i.e., down to 22 nm, an anomaly has been observed in the harmonic spectrum. In contrast to the expected well-known continuous 'roll off' of the high-harmonic orders, the harmonic intensity decreases with the increase of harmonic order, but in between shows minima which are significantly less intense than the neighboring harmonics. Furthermore, the order of the harmonic minima depend on target material. Additional calculations using numerical kinetic particle simulations and a simpler oscillating mirror model show that the physical origin of these modulations is an intricate interplay of resonance absorption and ponderomotive force which leads to a complex electron density profile evolution. Furthermore, this is emphasized by a spectral line analysis of the harmonics. In agreement with the theory, broad lines have been observed and, in particular for the harmonics in the minima, a complex interference structure is present.
A Very High Order, Adaptable MESA Implementation for Aeroacoustic Computations
NASA Technical Reports Server (NTRS)
Dydson, Roger W.; Goodrich, John W.
2000-01-01
Since computational efficiency and wave resolution scale with accuracy, the ideal would be infinitely high accuracy for problems with widely varying wavelength scales. Currently, many of the computational aeroacoustics methods are limited to 4th order accurate Runge-Kutta methods in time which limits their resolution and efficiency. However, a new procedure for implementing the Modified Expansion Solution Approximation (MESA) schemes, based upon Hermitian divided differences, is presented which extends the effective accuracy of the MESA schemes to 57th order in space and time when using 128 bit floating point precision. This new approach has the advantages of reducing round-off error, being easy to program. and is more computationally efficient when compared to previous approaches. Its accuracy is limited only by the floating point hardware. The advantages of this new approach are demonstrated by solving the linearized Euler equations in an open bi-periodic domain. A 500th order MESA scheme can now be created in seconds, making these schemes ideally suited for the next generation of high performance 256-bit (double quadruple) or higher precision computers. This ease of creation makes it possible to adapt the algorithm to the mesh in time instead of its converse: this is ideal for resolving varying wavelength scales which occur in noise generation simulations. And finally, the sources of round-off error which effect the very high order methods are examined and remedies provided that effectively increase the accuracy of the MESA schemes while using current computer technology.
Limiters for high-order discontinuous Galerkin methods
NASA Astrophysics Data System (ADS)
Krivodonova, Lilia
2007-09-01
We describe a limiter for the discontinuous Galerkin method that retains as high an order as possible, and does not automatically reduce to first order. The limiter is a generalization of the limiter introduced in [R. Biswas, K. Devine, J.E. Flaherty, Parallel adaptive finite element methods for conservation laws, Applied Numerical Mathematics 14 (1994) 255-284]. We present the one-dimensional case and extend it to two-dimensional problems on tensor-product meshes. Computational results for examples with both smooth and discontinuous solutions are shown.
Effect of Under-Resolved Grids on High Order Methods
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sjoegreen, B.; Mansour, Nagi (Technical Monitor)
2001-01-01
There has been much discussion on verification and validation processes for establishing the credibility of CFD simulations. Since the early 1990s, many of the aeronautical and mechanical engineering related reference journals mandated that any accepted articles in numerical simulations (without known solutions to compared with) need to perform a minimum of one level of grid refinement and time step reduction. Due to the difficulty in analysis, the effect of under-resolved grids and the nonlinear behavior of available spatial discretizations, are scarcely discussed in the literature. Here, an under-resolved numerical simulation is one where the grid spacing being used is too coarse to resolve the smallest physically relevant scales of the chosen continuum governing equations that are of interest to the numerical modeler. With the advent of new developments in fourth-order or higher spatial schemes, it has become common to regard high order schemes as more accurate, reliable and require less grid points. The danger comes when one tries to perform computations with the coarsest grid possible while still hoping to maintain numerical results sufficiently accurate for complex flows, and especially, data-limited problems. On one hand, high order methods when applies to highly coupled multidimensional complex nonlinear problems might have different stability, convergence and reliability behavior than their well studied low order counterparts, especially for nonlinear schemes such as TVD, MUSCL with limiters, ENO, WENO and discrete Galerkin. On the other hand, high order methods involve more operation counts and systematic grid convergence study can be time consuming and prohibitively expansive. At the same time it is difficult to fully understand or categorize the different nonlinear behavior of finite discretizations, especially at the limits of under-resolution when different types of bifurcation phenomena might occur, depending on the combination of grid spacings, time
Research on chromatic properties of high order kinoform
NASA Astrophysics Data System (ADS)
Wegrzyńska, K.; Rachoń, M.; Doch, M.; Siemion, A.; Suszek, J.; Kołodziejczyk, A.; Sypek, M.
2014-09-01
This work is dedicated to the evaluation of the chromatic properties of high order kinoforms. Typical kinoform (of the first order) is a phase only structure having the phase retardation varying in the range 0-2π. Such structures are very commonly used in many practical applications for different ranges of electromagnetic radiation like ultraviolet, visible, infrared, terahertz and millimeter waves. Besides those benefits such structures have one crucial disadvantage - they suffer from big chromatic aberration. This limits their practical application only to the narrowband work, where main wavelength must be well defined (Δλ/λ<<1). This paper presents other type of diffractive structures called high order kinoforms (HOK). They exhibit phase retardation of n2π, where n is an integer number much bigger than 1. Due to this fact they are relatively thin and therefore can be manufactured using laser lithography in thick photoresist (deeply etched). On the other hand they are thick enough to suppress chromatic aberrations. In comparison to the well-known Fresnel lens, the high order kinoform structure has precisely controlled phase retardation between different zones. In the case of the Fresnel lens (known from XVIII/XIX century), phase retardations between different zones are random (designing process is based on the geometrical optics). In the case of the high order kinoform working as the spherical lens - taking into account the real size of the detector - it can be shown that the most of the energy being focused in the focal spot will be registered by the detector for different wavelengths. The paper presents simple theoretical considerations, numerical modeling and their experimental evaluation.
High order methods for elliptic problems in plasma physics
NASA Astrophysics Data System (ADS)
Pataki, Andras
In this dissertation, we develop fast high order solvers for two elliptic problems in plasma physics. The first is the Grad-Shafranov equation, a nonlinear elliptic PDE that describes the magnetohydrodynamic equilibrium of three dimensional, axisymmetric plasmas. A high order solver is desirable to ensure the accurate evaluation of derivatives, required both for the computation of physical quantities and for studying perturbations near equilibrium. Using suitable scaling, we transform the problem from cylindrical coordinates to a nonlinear Poisson problem in Cartesian coordinates. We compute the conformal map from the original domain to the unit circle where we build a separation of variables based solver to obtain a high order, accurate solution. A fixed point or eigenvalue outer iteration is used to solve the nonlinear equation. Our second problem is the computation of the Coulomb collision operator that arises in kinetic models of plasmas. The collision operator can be written in terms of two Rosenbluth potentials obtained by solving a Poisson and a biharmonic problem in the velocity variables. For these PDEs we describe a new class of fast solvers in cylindrical coordinates with free-space radiation conditions. By combining integral equation methods in the radial variable with Fourier methods in the angular and z directions, we show that high-order accuracy can be achieved in both the solution and its derivatives. A weak singularity arises in the Fourier transform with respect to z that is handled with special purpose quadratures. Such solvers are ideally suited to the Rosenbluth potentials, since the collision operator is expressed in terms of up to fourth derivatives of the potentials, placing stringent demands on the computational order. Also, since axisymmetry is generally assumed in the velocity variables, the use of cylindrical coordinates reduces the three dimensional problem to a two dimensional computation.
Technique for Very High Order Nonlinear Simulation and Validation
NASA Technical Reports Server (NTRS)
Dyson, Rodger W.
2001-01-01
Finding the sources of sound in large nonlinear fields via direct simulation currently requires excessive computational cost. This paper describes a simple technique for efficiently solving the multidimensional nonlinear Euler equations that significantly reduces this cost and demonstrates a useful approach for validating high order nonlinear methods. Up to 15th order accuracy in space and time methods were compared and it is shown that an algorithm with a fixed design accuracy approaches its maximal utility and then its usefulness exponentially decays unless higher accuracy is used. It is concluded that at least a 7th order method is required to efficiently propagate a harmonic wave using the nonlinear Euler equations to a distance of 5 wavelengths while maintaining an overall error tolerance that is low enough to capture both the mean flow and the acoustics.
A Low Order and a High Order Solution for a Converging-Diverging Nozzle Problem
NASA Technical Reports Server (NTRS)
Goodrich, John W.
2000-01-01
The Computational Aeroacoustics Workshops on Benchmark problems are conducted in order to generate solutions with a variety of methods for problems that are chosen both to be representative of significant and relevant acoustic phenomena. It is generally recognized that CAA applications require the resolution in time and in space of solution details over a significantly broader range of scales than typical computational fluid dynamics applications. These requirements are forcing the development of new methodologies for CAA applications. This paper presents numerical results from a third and a seventh order algorithm for the propagation of an acoustic signal through a converging-diverging nozzle. These two algorithms are members of a new family of high accuracy methods that have the same order accuracy in both space and time, and are an extension of previous work for linearized Euler equations to fully nonlinear time dependent problems. The simulations are all with the fully nonlinear quasi-1D Euler equations for the total solution, which includes both the fluid dynamics and the acoustics. The acoustic solution is obtained from the time dependent nonlinear solution by subtracting the steady solution.
High Order Difference Method for Low Mach Number Aeroacoustics
NASA Technical Reports Server (NTRS)
Mueller, B.; Yee, H. C.; Mansour, Nagi (Technical Monitor)
2001-01-01
A high order finite difference method with improved accuracy and stability properties for computational aeroacoustics (CAA) at low Mach numbers is proposed. The Euler equations are split into a conservative and a symmetric non- conservative portion to allow the derivation of a generalized energy estimate. Since the symmetrization is based on entropy variables, that splitting of the flux derivatives is referred to as entropy splitting. Its discretization by high order central differences was found to need less numerical dissipation than conventional conservative schemes. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the split Euler equations are formulated in perturbation form. The unknowns are the small changes of the conservative variables with respect to their large stagnation values. All nonlinearities and the conservation form of the conservative portion of the split flux derivatives can be retained, while cancellation errors are avoided with its discretization opposed to the conventional conservative form. The finite difference method is third-order accurate at the boundary and the conventional central sixth-order accurate stencil in the interior. The difference operator satisfies the summation by parts property analogous to the integration by parts in the continuous energy estimate. Thus, strict stability of the difference method follows automatically. Spurious high frequency oscillations are suppressed by a characteristic-based filter similar to but without limiter. The time derivative is approximated by a 4-stage low-storage second-order explicit Runge-Kutta method. The method has been applied to simulate vortex sound at low Mach numbers. We consider the Kirchhoff vortex, which is an elliptical patch of constant vorticity rotating with constant angular frequency in irrotational flow. The acoustic pressure generated by the Kirchhoff vortex is governed by the 2D Helmholtz equation, which can be solved
All-order approach to high-precision atomic calculation
NASA Astrophysics Data System (ADS)
Iskrenova-Tchoukova, Eugeniya
High-precision atomic calculations combined with experiments of matching accuracy provide an excellent opportunity to test our understanding of atomic structure and properties as well as the many-body atomic theories. The relativistic all-order method, which is a linearized version of the coupled-cluster singles-doubles method, has proven to yield high precision results for a variety of atomic properties. In this thesis, we study the atomic properties of neutral atoms and ions by means of the relativistic all-order method. The lifetimes and ground state static polarizabilities of a singly ionized barium atom are studied in comparison with the isoelectronic neutral cesium atom and with a singly ionized calcium atom. The lifetimes of a number of excited states in atomic potassium, rubidium, and francium are theoretically calculated and compared with the available experimental data. The magnetic dipole hyperfine constant of the 9S1/2 state in 210Fr is calculated and the result is combined with the experimental one to extract the value of the 210Fr nuclear magnetic moment. Another part of the thesis work focuses on the development and implementation of an extension of the currently used all-order singles-doubles (SD) method to include all valence triple excitations in an iterative way, all-order SD+vT approximation. Some of the ideas and results presented in Chapters 4, 5, and 6 have been published and are subject to copyright laws. These publications are cited accordingly.
A new local high-order laminate theory
NASA Astrophysics Data System (ADS)
Wu, Chih-Ping; Hsu, Chih-Shun
A new local high-order deformable theory of laminated composite/sandwich plates is presented here. The displacement fields of each discrete layer were assumed in the present theory to be of a high-order polynomial series through layer-thickness. The displacement and traction continuity conditions at the interface between layers and the traction conditions at the outer surfaces were imposed as the constraint conditions, and introduced into the potential energy functional by the Lagrange multiplier method. The equations of motion and admissible boundary conditions were given on the basis of the present theory by using the generalized variational principle. Pagano's 3-D elasticity solutions of generally rectangular laminated composite/sandwich plates, fully simply supported, subjected to transverse sinusoidal loading were used for assessment of the present theory and other theories discussed in previous literature. The present theory was found to agree very closely with 3-D elasticity solutions.
Directed liquid phase assembly of highly ordered metallic nanoparticle arrays
Wu, Yueying; Dong, Nanyi; Fu, Shaofang; Fowlkes, Jason D.; Kondic, Lou; Vincenti, Maria A.; de Ceglia, Domenico; Rack, Philip D.
2014-04-01
Directed assembly of nanomaterials is a promising route for the synthesis of advanced materials and devices. We demonstrate the directed-assembly of highly ordered two-dimensional arrays of hierarchical nanostructures with tunable size, spacing and composition. The directed assembly is achieved on lithographically patterned metal films that are subsequently pulse-laser melted; during the brief liquid lifetime, the pattened nanostructures assemble into highly ordered primary and secondary nanoparticles, with sizes below that which was originally patterned. Complementary fluid-dynamics simulations emulate the resultant patterns and show how the competition of capillary forces and liquid metal–solid substrate interaction potential drives the directed assembly. Lastly, asmore » an example of the enhanced functionality, a full-wave electromagnetic analysis has been performed to identify the nature of the supported plasmonic resonances.« less
Directed liquid phase assembly of highly ordered metallic nanoparticle arrays
Wu, Yueying; Dong, Nanyi; Fu, Shaofang; Fowlkes, Jason D.; Kondic, Lou; Vincenti, Maria A.; de Ceglia, Domenico; Rack, Philip D.
2014-04-01
Directed assembly of nanomaterials is a promising route for the synthesis of advanced materials and devices. We demonstrate the directed-assembly of highly ordered two-dimensional arrays of hierarchical nanostructures with tunable size, spacing and composition. The directed assembly is achieved on lithographically patterned metal films that are subsequently pulse-laser melted; during the brief liquid lifetime, the pattened nanostructures assemble into highly ordered primary and secondary nanoparticles, with sizes below that which was originally patterned. Complementary fluid-dynamics simulations emulate the resultant patterns and show how the competition of capillary forces and liquid metal–solid substrate interaction potential drives the directed assembly. Lastly, as an example of the enhanced functionality, a full-wave electromagnetic analysis has been performed to identify the nature of the supported plasmonic resonances.
Spectrally Resolved Maker Fringes in High-Order Harmonic Generation
NASA Astrophysics Data System (ADS)
Heyl, C. M.; Güdde, J.; Höfer, U.; L'Huillier, A.
2011-07-01
We investigate macroscopic interference effects in high-order harmonic generation using a Ti:sapphire laser operating at a 100 kHz repetition rate. The structure and behavior of spectral and spatial interference fringes are explained and analytically described by transient phase matching of the long electron trajectory contribution. Time-frequency mapping due to the temporal chirp of the harmonic emission allows us to observe Maker fringes directly in the spectral domain.
A highly ordered cubic mesoporous silica/graphene nanocomposite.
Lee, Chang-Wook; Roh, Kwang Chul; Kim, Kwang-Bum
2013-10-21
A highly ordered cubic mesoporous silica (KIT-6)/graphene nanocomposite and 2D KIT-6 nanoflakes were synthesized using a novel synthesis methodology. The non-ionic triblock copolymer, P123, played a dual role as a structure-directing agent in the formation of the cubic mesoporous structure and as a cross-linking agent between mesoporous silica and graphene. The prepared (KIT-6)/graphene nanocomposite could act as a template for the preparation of mesoporous material/graphene nanocomposites. PMID:24057016
High order Nyström method for elastodynamic scattering
NASA Astrophysics Data System (ADS)
Chen, Kun; Gurrala, Praveen; Song, Jiming; Roberts, Ron
2016-02-01
Elastic waves in solids find important applications in ultrasonic non-destructive evaluation. The scattering of elastic waves has been treated using many approaches like the finite element method, boundary element method and Kirchhoff approximation. In this work, we propose a novel accurate and efficient high order Nyström method to solve the boundary integral equations for elastodynamic scattering problems. This approach employs high order geometry description for the element, and high order interpolation for fields inside each element. Compared with the boundary element method, this approach makes the choice of the nodes for interpolation based on the Gaussian quadrature, which renders matrix elements for far field interaction free from integration, and also greatly simplifies the process for singularity and near singularity treatment. The proposed approach employs a novel efficient near singularity treatment that makes the solver able to handle extreme geometries like very thin penny-shaped crack. Numerical results are presented to validate the approach. By using the frequency domain response and performing the inverse Fourier transform, we also report the time domain response of flaw scattering.
High-order species interactions shape ecosystem diversity.
Bairey, Eyal; Kelsic, Eric D; Kishony, Roy
2016-01-01
Classical theory shows that large communities are destabilized by random interactions among species pairs, creating an upper bound on ecosystem diversity. However, species interactions often occur in high-order combinations, whereby the interaction between two species is modulated by one or more other species. Here, by simulating the dynamics of communities with random interactions, we find that the classical relationship between diversity and stability is inverted for high-order interactions. More specifically, while a community becomes more sensitive to pairwise interactions as its number of species increases, its sensitivity to three-way interactions remains unchanged, and its sensitivity to four-way interactions actually decreases. Therefore, while pairwise interactions lead to sensitivity to the addition of species, four-way interactions lead to sensitivity to species removal, and their combination creates both a lower and an upper bound on the number of species. These findings highlight the importance of high-order species interactions in determining the diversity of natural ecosystems. PMID:27481625
High-order species interactions shape ecosystem diversity
Bairey, Eyal; Kelsic, Eric D.; Kishony, Roy
2016-01-01
Classical theory shows that large communities are destabilized by random interactions among species pairs, creating an upper bound on ecosystem diversity. However, species interactions often occur in high-order combinations, whereby the interaction between two species is modulated by one or more other species. Here, by simulating the dynamics of communities with random interactions, we find that the classical relationship between diversity and stability is inverted for high-order interactions. More specifically, while a community becomes more sensitive to pairwise interactions as its number of species increases, its sensitivity to three-way interactions remains unchanged, and its sensitivity to four-way interactions actually decreases. Therefore, while pairwise interactions lead to sensitivity to the addition of species, four-way interactions lead to sensitivity to species removal, and their combination creates both a lower and an upper bound on the number of species. These findings highlight the importance of high-order species interactions in determining the diversity of natural ecosystems. PMID:27481625
Spatial Mode Control of High-Order Harmonics
Mercer, I.; Mevel, E.; Zerne, R.; LHuillier, A.; Antoine, P.; Wahlstroem, C.
1996-08-01
We demonstrate that the spatial mode of high-order harmonics can be continuously controlled. The control is achieved by spatially modulating the degree of elliptical polarization of the fundamental field using birefringent optics. A highly sensitive relationship between the efficiency of harmonic generation and the degree of laser elliptical polarization leads to atoms emitting harmonics only in regions of linear polarization. The harmonics are emitted as annular beams whose angles of divergence can be continuously varied. {copyright} {ital 1996 The American Physical Society.}
Fast calibration of high-order adaptive optics systems
NASA Astrophysics Data System (ADS)
Kasper, Markus; Fedrigo, Enrico; Looze, Douglas P.; Bonnet, Henri; Ivanescu, Liviu; Oberti, Sylvain
2004-06-01
We present a new method of calibrating adaptive optics systems that greatly reduces the required calibration time or, equivalently, improves the signal-to-noise ratio. The method uses an optimized actuation scheme with Hadamard patterns and does not scale with the number of actuators for a given noise level in the wave-front sensor channels. It is therefore highly desirable for high-order systems and/or adaptive secondary systems on a telescope without a Gregorian focal plane. In the latter case, the measurement noise is increased by the effects of the turbulent atmosphere when one is calibrating on a natural guide star.
Fast calibration of high-order adaptive optics systems.
Kasper, Markus; Fedrigo, Enrico; Looze, Douglas P; Bonnet, Henri; Ivanescu, Liviu; Oberti, Sylvain
2004-06-01
We present a new method of calibrating adaptive optics systems that greatly reduces the required calibration time or, equivalently, improves the signal-to-noise ratio. The method uses an optimized actuation scheme with Hadamard patterns and does not scale with the number of actuators for a given noise level in the wavefront sensor channels. It is therefore highly desirable for high-order systems and/or adaptive secondary systems on a telescope without a Gregorian focal plane. In the latter case, the measurement noise is increased by the effects of the turbulent atmosphere when one is calibrating on a natural guide star. PMID:15191182
Probing non local order parameters in highly correlated Bose insulators
NASA Astrophysics Data System (ADS)
Altman, Ehud
2008-03-01
Ground states of integer spin chains are known since the late 80's to sustain highly non local order described by infinite string operators of the spins. Such states defy the usual Landau theory description and can be considered simple prototypes of topological order. Recently we showed that spinless Bose insulators with nearest neighbor or longer range repulsion in one dimension can exhibit similar string order in terms of the boson density [1]. The tunability of cold atomic systems would allow much more flexibility in probing the non local order than spin systems do. For example the bosons can be tuned across a quantum phase transition between the exotic insulator, which we term Haldane insulator, and the usual Mott insulator. Investigating how the transition responds to external perturbations lends direct access to properties of the string order parameter. I will demonstrate this with several new results obtained from a field theoretic description of the phases and confirmed by numerical calculations using DMRG. Particularly revealing of the unusual character of the string order is the prediction that any external perturbation, which breaks the lattice inversion symmetry, would eliminate the distinction between the Haldane and Mott phases and allow a fully gapped adiabatic connection between them. This is remarkable given that neither phase involves spontaneous breaking of lattice inversion symmetry. We also predict that inter-chain tunneling destroys the direct phase transition between the two insulators by establishing an intermediate superfluid phase. Finally I will discuss how the new phases and phase transitions may be realized and probed in actual experiments with ultra cold atoms or polar molecules. [1] E. G. Dalla Torre, E. Berg and E. Altman, Phys. Rev. Lett. 97, 260401 (2006)
TWave: high-order analysis of functional MRI.
Barnathan, Michael; Megalooikonomou, Vasileios; Faloutsos, Christos; Faro, Scott; Mohamed, Feroze B
2011-09-15
The traditional approach to functional image analysis models images as matrices of raw voxel intensity values. Although such a representation is widely utilized and heavily entrenched both within neuroimaging and in the wider data mining community, the strong interactions among space, time, and categorical modes such as subject and experimental task inherent in functional imaging yield a dataset with "high-order" structure, which matrix models are incapable of exploiting. Reasoning across all of these modes of data concurrently requires a high-order model capable of representing relationships between all modes of the data in tandem. We thus propose to model functional MRI data using tensors, which are high-order generalizations of matrices equivalent to multidimensional arrays or data cubes. However, several unique challenges exist in the high-order analysis of functional medical data: naïve tensor models are incapable of exploiting spatiotemporal locality patterns, standard tensor analysis techniques exhibit poor efficiency, and mixtures of numeric and categorical modes of data are very often present in neuroimaging experiments. Formulating the problem of image clustering as a form of Latent Semantic Analysis and using the WaveCluster algorithm as a baseline, we propose a comprehensive hybrid tensor and wavelet framework for clustering, concept discovery, and compression of functional medical images which successfully addresses these challenges. Our approach reduced runtime and dataset size on a 9.3GB finger opposition motor task fMRI dataset by up to 98% while exhibiting improved spatiotemporal coherence relative to standard tensor, wavelet, and voxel-based approaches. Our clustering technique was capable of automatically differentiating between the frontal areas of the brain responsible for task-related habituation and the motor regions responsible for executing the motor task, in contrast to a widely used fMRI analysis program, SPM, which only detected the
High-order primordial perturbations with quantum gravitational effects
NASA Astrophysics Data System (ADS)
Zhu, Tao; Wang, Anzhong; Kirsten, Klaus; Cleaver, Gerald; Sheng, Qin
2016-06-01
In this paper, we provide a systematic investigation of high-order primordial perturbations with nonlinear dispersion relations due to quantum gravitational effects in the framework of uniform asymptotic approximations. Because of these effects, the equation of motion of the mode function in general has multiple turning points. After obtaining analytically approximated solutions to any order in different regions, associated with different types of turning points, we match them to the third one. To this order the errors are less than 0.15%. General expressions of the power spectra of the primordial tensor and scalar perturbations are derived explicitly. We also investigate effects of backreactions of the quantum gravitational corrections, and make sure that inflation lasts long enough in order to solve the underlying problems, such as flatness, horizon, and monopole. Then we study various features of the spectra that are observationally relevant. In particular, under a moderate assumption about the energy scale of the underlying theory of quantum gravity, we have shown that the quantum gravitational effects may alter significantly the ratio between the tensor and scalar power spectra, thereby providing a natural mechanism to alleviate the tension between observations and certain inflationary models, including the one with a quadratic potential.
Integrated high-order surface diffraction gratings for diode lasers
NASA Astrophysics Data System (ADS)
Zolotarev, V. V.; Leshko, A. Yu; Pikhtin, N. A.; Slipchenko, S. O.; Sokolova, Z. N.; Lubyanskiy, Ya V.; Voronkova, N. V.; Tarasov, I. S.
2015-12-01
High-order surface diffraction gratings acting as a distributed Bragg reflector (DBR) in mesa stripe semiconductor lasers (λ = 1030 nm) have been studied theoretically and experimentally. Higher order interfering radiation modes (IRMs), which propagate off the plane of the waveguide, have been shown to have a crucial effect on the reflection and transmission spectra of the DBR. The decrease in the reflectivity of the DBR in response to the increase in the diffraction efficiency of these modes may reach 80% and more. According to theoretical analysis results, the intensity of the higher order IRMs is determined by the geometry of the DBR groove profile. Experimental data demonstrate that the noncavity modes are responsible for parasitic light leakage losses in the laser cavity. It has been shown that, in the case of nonoptimal geometry of the grating groove profile, the overall external differential quantum efficiency of the parasitic laser emission may exceed 45%, which is more than half of the laser output power. The optimal geometry of the DBR groove profile is trapezoidal, with the smallest possible lower base. Experimental evidence has been presented that this geometry considerably reduces the power of the higher order IRMs and minimises the parasitic light leakage loss.
A Multilevel Parallelization Framework for High-Order Stencil Computations
NASA Astrophysics Data System (ADS)
Dursun, Hikmet; Nomura, Ken-Ichi; Peng, Liu; Seymour, Richard; Wang, Weiqiang; Kalia, Rajiv K.; Nakano, Aiichiro; Vashishta, Priya
Stencil based computation on structured grids is a common kernel to broad scientific applications. The order of stencils increases with the required precision, and it is a challenge to optimize such high-order stencils on multicore architectures. Here, we propose a multilevel parallelization framework that combines: (1) inter-node parallelism by spatial decomposition; (2) intra-chip parallelism through multithreading; and (3) data-level parallelism via single-instruction multiple-data (SIMD) techniques. The framework is applied to a 6 th order stencil based seismic wave propagation code on a suite of multicore architectures. Strong-scaling scalability tests exhibit superlinear speedup due to increasing cache capacity on Intel Harpertown and AMD Barcelona based clusters, whereas weak-scaling parallel efficiency is 0.92 on 65,536 BlueGene/P processors. Multithreading+SIMD optimizations achieve 7.85-fold speedup on a dual quad-core Intel Clovertown, and the data-level parallel efficiency is found to depend on the stencil order.
High-order harmonics from laser-irradiated plasma surfaces
Teubner, U.; Gibbon, P.
2009-04-15
The investigation of high-order harmonic generation (HHG) of femtosecond laser pulses by means of laser-produced plasmas is surveyed. This kind of harmonic generation is an alternative to the HHG in gases and shows significantly higher conversion efficiency. Furthermore, with plasma targets there is no limitation on applicable laser intensity and thus the generated harmonics can be much more intense. In principle, harmonic light may also be generated at relativistic laser intensity, in which case their harmonic intensities may even exceed that of the focused laser pulse by many orders of magnitude. This phenomenon presents new opportunities for applications such as nonlinear optics in the extreme ultraviolet region, photoelectron spectroscopy, and opacity measurements of high-density matter with high temporal and spatial resolution. On the other hand, HHG is strongly influenced by the laser-plasma interaction itself. In particular, recent results show a strong correlation with high-energy electrons generated during the interaction process. The harmonics are a promising tool for obtaining information not only on plasma parameters such as the local electron density, but also on the presence of large electric and magnetic fields, plasma waves, and the (electron) transport inside the target. This paper reviews the theoretical and experimental progress on HHG via laser-plasma interactions and discusses the prospects for applying HHG as a short-wavelength, coherent optical tool.
Shaping Neural Circuits by High Order Synaptic Interactions.
Ravid Tannenbaum, Neta; Burak, Yoram
2016-08-01
Spike timing dependent plasticity (STDP) is believed to play an important role in shaping the structure of neural circuits. Here we show that STDP generates effective interactions between synapses of different neurons, which were neglected in previous theoretical treatments, and can be described as a sum over contributions from structural motifs. These interactions can have a pivotal influence on the connectivity patterns that emerge under the influence of STDP. In particular, we consider two highly ordered forms of structure: wide synfire chains, in which groups of neurons project to each other sequentially, and self connected assemblies. We show that high order synaptic interactions can enable the formation of both structures, depending on the form of the STDP function and the time course of synaptic currents. Furthermore, within a certain regime of biophysical parameters, emergence of the ordered connectivity occurs robustly and autonomously in a stochastic network of spiking neurons, without a need to expose the neural network to structured inputs during learning. PMID:27517461
Shaping Neural Circuits by High Order Synaptic Interactions
Ravid Tannenbaum, Neta; Burak, Yoram
2016-01-01
Spike timing dependent plasticity (STDP) is believed to play an important role in shaping the structure of neural circuits. Here we show that STDP generates effective interactions between synapses of different neurons, which were neglected in previous theoretical treatments, and can be described as a sum over contributions from structural motifs. These interactions can have a pivotal influence on the connectivity patterns that emerge under the influence of STDP. In particular, we consider two highly ordered forms of structure: wide synfire chains, in which groups of neurons project to each other sequentially, and self connected assemblies. We show that high order synaptic interactions can enable the formation of both structures, depending on the form of the STDP function and the time course of synaptic currents. Furthermore, within a certain regime of biophysical parameters, emergence of the ordered connectivity occurs robustly and autonomously in a stochastic network of spiking neurons, without a need to expose the neural network to structured inputs during learning. PMID:27517461
Rad-Hydro with a High-Order, Low-Order Method
Wollaber, Allan Benton; Park, HyeongKae; Lowrie, Robert Byron; Rauenzahn, Rick M.; Cleveland, Mathew Allen
2015-08-04
Moment-based acceleration via the development of “high-order, low-order” (HO-LO) algorithms has provided substantial accuracy and efficiency enhancements for solutions of the nonlinear, thermal radiative transfer equations by CCS-2 and T-3 staff members. Accuracy enhancements over traditional, linearized methods are obtained by solving a nonlinear, timeimplicit HO-LO system via a Jacobian-free Newton Krylov procedure. This also prevents the appearance of non-physical maximum principle violations (“temperature spikes”) associated with linearization. Efficiency enhancements are obtained in part by removing “effective scattering” from the linearized system. In this highlight, we summarize recent work in which we formally extended the HO-LO radiation algorithm to include operator-split radiation-hydrodynamics.
High order parallel numerical schemes for solving incompressible flows
NASA Technical Reports Server (NTRS)
Lin, Avi; Milner, Edward J.; Liou, May-Fun; Belch, Richard A.
1992-01-01
The use of parallel computers for numerically solving flow fields has gained much importance in recent years. This paper introduces a new high order numerical scheme for computational fluid dynamics (CFD) specifically designed for parallel computational environments. A distributed MIMD system gives the flexibility of treating different elements of the governing equations with totally different numerical schemes in different regions of the flow field. The parallel decomposition of the governing operator to be solved is the primary parallel split. The primary parallel split was studied using a hypercube like architecture having clusters of shared memory processors at each node. The approach is demonstrated using examples of simple steady state incompressible flows. Future studies should investigate the secondary split because, depending on the numerical scheme that each of the processors applies and the nature of the flow in the specific subdomain, it may be possible for a processor to seek better, or higher order, schemes for its particular subcase.
High Precision Superconducting Cavity Diagnostics With Higher Order Mode Measurements
Molloy, S.; Frisch, J.; McCormick, D.; May, J.; Ross, M.; Smith, T.; Baboi, N.; Hensler, O.; Petrosian, L.; Napoly, O.; Paparella, R.C.; Simon, C.; Eddy, N.; Nagaitsev, S.; Wendt, M.; /Fermilab
2007-02-12
Experiments at the FLASH facility at DESY have demonstrated that the higher order modes induced in superconducting cavities can be used to provide a variety of beam and cavity diagnostics. The axes of the modes can be determined from the beam orbit that produces minimum power in the dipole HOM modes. The phase and amplitude of the dipole modes can be used to obtain high resolution beam position information, and the phase of the monopole modes to measure the beam phase relative to the accelerator rf. For most superconducting accelerators, the existing higher order mode couplers provide the necessary signals, and the downmix and digitizing electronics are straightforward, similar to those for a conventional beam position monitor.
Hybrid overlay metrology for high order correction by using CDSEM
NASA Astrophysics Data System (ADS)
Leray, Philippe; Halder, Sandip; Lorusso, Gian; Baudemprez, Bart; Inoue, Osamu; Okagawa, Yutaka
2016-03-01
Overlay control has become one of the most critical issues for semiconductor manufacturing. Advanced lithographic scanners use high-order corrections or correction per exposure to reduce the residual overlay. It is not enough in traditional feedback of overlay measurement by using ADI wafer because overlay error depends on other process (etching process and film stress, etc.). It needs high accuracy overlay measurement by using AEI wafer. WIS (Wafer Induced Shift) is the main issue for optical overlay, IBO (Image Based Overlay) and DBO (Diffraction Based Overlay). We design dedicated SEM overlay targets for dual damascene process of N10 by i-ArF multi-patterning. The pattern is same as device-pattern locally. Optical overlay tools select segmented pattern to reduce the WIS. However segmentation has limit, especially the via-pattern, for keeping the sensitivity and accuracy. We evaluate difference between the viapattern and relaxed pitch gratings which are similar to optical overlay target at AEI. CDSEM can estimate asymmetry property of target from image of pattern edge. CDSEM can estimate asymmetry property of target from image of pattern edge. We will compare full map of SEM overlay to full map of optical overlay for high order correction ( correctables and residual fingerprints).
High-order harmonic generation in a capillary discharge
Rocca, Jorge J.; Kapteyn, Henry C.; Mumane, Margaret M.; Gaudiosi, David; Grisham, Michael E.; Popmintchev, Tenio V.; Reagan, Brendan A.
2010-06-01
A pre-ionized medium created by a capillary discharge results in more efficient use of laser energy in high-order harmonic generation (HHG) from ions. It extends the cutoff photon energy, and reduces the distortion of the laser pulse as it propagates down the waveguide. The observed enhancements result from a combination of reduced ionization energy loss and reduced ionization-induced defocusing of the driving laser as well as waveguiding of the driving laser pulse. The discharge plasma also provides a means to spectrally tune the harmonics by tailoring the initial level of ionization of the medium.
High order harmonic generation in dual gas multi-jets
Tosa, Valer E-mail: calin.hojbota@itim-cj.ro; Hojbota, Calin E-mail: calin.hojbota@itim-cj.ro
2013-11-13
High order harmonic generation (HHG) in gas media suffers from a low conversion efficiency that has its origins in the interaction of the atom/molecule with the laser field. Phase matching is the main way to enhance the harmonic flux and several solutions have been designed to achieve it. Here we present numerical results modeling HHG in a system of multi-jets in which two gases alternate: the first gas jet (for example Ne) generates harmonics and the second one which ionizes easier, recover the phase matching condition. We obtain configurations which are experimentally feasible with respect to pressures and dimensions of the jets.
High Precision SC Cavity alignment Measurements with Higher Order Modes
Molloy, Stephen; Frisch, Josef; Hendrickson, Linda; McCormick, Douglas; May, Justin; Ross, Marc; Smith, Tonee; Eddy, Nathan; Nagaitsev, Sergei; Baboi, Nicoleta; Hensler, Olaf; Petrosyan, Lyudvig; Napoly, Olivier; Paparella, Rita; Simon, Claire; /DSM, DAPNIA, Saclay
2007-06-14
Experiments at the FLASH linac at DESY have demonstrated that the higher order modes (HOMs) induced in superconducting cavities can be used to provide a variety of beam and cavity diagnostics. The centers of the cavities can be determined from the beam orbit which produces minimum power in the dipole HOM modes. The phase and amplitude of the dipole modes can be used as a high resolution beam position monitor. For most superconducting accelerators, the existing HOM couplers provide the necessary signals, and the downmix and digitizing electronics are straightforward, similar to those for a conventional BPM.
High-order momentum modes by resonant superradiant scattering
Zhou Xiaoji; Fu Jiageng; Chen Xuzong
2009-12-15
The spatial and time evolutions of superradiant scattering are studied theoretically for a weak pump beam with different frequency components traveling along the long axis of an elongated Bose-Einstein condensate. Resulting from the analysis for mode competition between the different resonant channels and the local depletion of the spatial distribution in the superradiant Rayleigh scattering, a method of getting a large number of high-order forward modes by resonant frequency components of the pump beam is provided, which is beneficial to a lager momentum transfer in atom manipulation for the atom interferometry and atomic optics.
Optimization of High-order Wave Equations for Multicore CPUs
Energy Science and Technology Software Center (ESTSC)
2011-11-01
This is a simple benchmark to guage the performance of a high-order isotropic wave equation grid. The code is optimized for both SSE and AVX and is parallelized using OpenMP (see Optimization section). Structurally, the benchmark begins, reads a few command-line parameters, allocates and pads the four arrays (current, last, next wave fields, and the spatially varying but isotropic velocity), initializes these arrays, then runs the benchmark proper. The code then benchmarks the naive, SSEmore » (if supported), and AVX (if supported implementations) by applying the wave equation stencil 100 times and taking the average performance. Boundary conditions are ignored and would noiminally be implemented by the user. THus, the benchmark measures only the performance of the wave equation stencil and not a full simulation. The naive implementation is a quadruply (z,y,x, radius) nested loop that can handle arbitrarily order wave equations. The optimized (SSE/AVX) implentations are somewhat more complex as they operate on slabs and include a case statement to select an optimized inner loop depending on wave equation order.« less
Optimization of High-order Wave Equations for Multicore CPUs
Williams, Samuel
2011-11-01
This is a simple benchmark to guage the performance of a high-order isotropic wave equation grid. The code is optimized for both SSE and AVX and is parallelized using OpenMP (see Optimization section). Structurally, the benchmark begins, reads a few command-line parameters, allocates and pads the four arrays (current, last, next wave fields, and the spatially varying but isotropic velocity), initializes these arrays, then runs the benchmark proper. The code then benchmarks the naive, SSE (if supported), and AVX (if supported implementations) by applying the wave equation stencil 100 times and taking the average performance. Boundary conditions are ignored and would noiminally be implemented by the user. THus, the benchmark measures only the performance of the wave equation stencil and not a full simulation. The naive implementation is a quadruply (z,y,x, radius) nested loop that can handle arbitrarily order wave equations. The optimized (SSE/AVX) implentations are somewhat more complex as they operate on slabs and include a case statement to select an optimized inner loop depending on wave equation order.
Genesis of charge orders in high temperature superconductors
NASA Astrophysics Data System (ADS)
Tu, Wei-Lin; Lee, Ting-Kuo
2016-01-01
One of the most puzzling facts about cuprate high-temperature superconductors in the lightly doped regime is the coexistence of uniform superconductivity and/or antiferromagnetism with many low-energy charge-ordered states in a unidirectional charge density wave or a bidirectional checkerboard structure. Recent experiments have discovered that these charge density waves exhibit different symmetries in their intra-unit-cell form factors for different cuprate families. Using a renormalized mean-field theory for a well-known, strongly correlated model of cuprates, we obtain a number of charge-ordered states with nearly degenerate energies without invoking special features of the Fermi surface. All of these self-consistent solutions have a pair density wave intertwined with a charge density wave and sometimes a spin density wave. Most of these states vanish in the underdoped regime, except for one with a large d-form factor that vanishes at approximately 19% doping of the holes, as reported by experiments. Furthermore, these states could be modified to have a global superconducting order, with a nodal-like density of states at low energy.
Genesis of charge orders in high temperature superconductors
Tu, Wei-Lin; Lee, Ting-Kuo
2016-01-01
One of the most puzzling facts about cuprate high-temperature superconductors in the lightly doped regime is the coexistence of uniform superconductivity and/or antiferromagnetism with many low-energy charge-ordered states in a unidirectional charge density wave or a bidirectional checkerboard structure. Recent experiments have discovered that these charge density waves exhibit different symmetries in their intra-unit-cell form factors for different cuprate families. Using a renormalized mean-field theory for a well-known, strongly correlated model of cuprates, we obtain a number of charge-ordered states with nearly degenerate energies without invoking special features of the Fermi surface. All of these self-consistent solutions have a pair density wave intertwined with a charge density wave and sometimes a spin density wave. Most of these states vanish in the underdoped regime, except for one with a large d-form factor that vanishes at approximately 19% doping of the holes, as reported by experiments. Furthermore, these states could be modified to have a global superconducting order, with a nodal-like density of states at low energy. PMID:26732076
High Variability of Mitochondrial Gene Order among Fungi
Aguileta, Gabriela; de Vienne, Damien M.; Ross, Oliver N.; Hood, Michael E.; Giraud, Tatiana; Petit, Elsa; Gabaldón, Toni
2014-01-01
From their origin as an early alpha proteobacterial endosymbiont to their current state as cellular organelles, large-scale genomic reorganization has taken place in the mitochondria of all main eukaryotic lineages. So far, most studies have focused on plant and animal mitochondrial (mt) genomes (mtDNA), but fungi provide new opportunities to study highly differentiated mtDNAs. Here, we analyzed 38 complete fungal mt genomes to investigate the evolution of mtDNA gene order among fungi. In particular, we looked for evidence of nonhomologous intrachromosomal recombination and investigated the dynamics of gene rearrangements. We investigated the effect that introns, intronic open reading frames (ORFs), and repeats may have on gene order. Additionally, we asked whether the distribution of transfer RNAs (tRNAs) evolves independently to that of mt protein-coding genes. We found that fungal mt genomes display remarkable variation between and within the major fungal phyla in terms of gene order, genome size, composition of intergenic regions, and presence of repeats, introns, and associated ORFs. Our results support previous evidence for the presence of mt recombination in all fungal phyla, a process conspicuously lacking in most Metazoa. Overall, the patterns of rearrangements may be explained by the combined influences of recombination (i.e., most likely nonhomologous and intrachromosomal), accumulated repeats, especially at intergenic regions, and to a lesser extent, mobile element dynamics. PMID:24504088
NMR study of new ruthenates with high magnetic ordering
NASA Astrophysics Data System (ADS)
Paulose, P. L.; Chakrabarty, Tanmoy
The Ru based compounds, Ca3LiRuO6 and Ca3NaRuO6 show unusually high magnetic ordering temperature. Extended super exchange model is invoked to explain the magnetic behavior in the isostructural compound Ca3LiOsO6. We have carried out NMR investigation on these two Ru-based compounds. Ca3LiRuO6 is a weak ferromagnet with a magnetic ordering temperature (TC) of 115 K which is explored by the temperature dependence of 7Li NMR line shift, line-width and spin-lattice relaxation rate (1/T1) . Above TC, a broad maximum is observed in the evolution of line-width of the spectra. We speculate that this feature might be attributed to some low-dimensional magnetic behavior. Contrastingly, Ca3NaRuO6 with similar structure and local geometry of the Ru5+ ions is a conventional antiferromagnet with a transition temperature of 90 K. The temperature dependence of 23Na NMR line shift and 1/T1 is studied across magnetic transition in Ca3NaRuO6. The temperature variation of line-width is found to be different compared to Ca3LiRuO6. In both these systems, 1/T1 decreases significantly below ordering temperature, characteristic of many antiferromagnetic systems.
High-order finite element methods for cardiac monodomain simulations.
Vincent, Kevin P; Gonzales, Matthew J; Gillette, Andrew K; Villongco, Christopher T; Pezzuto, Simone; Omens, Jeffrey H; Holst, Michael J; McCulloch, Andrew D
2015-01-01
Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori. PMID:26300783
High-order finite element methods for cardiac monodomain simulations
Vincent, Kevin P.; Gonzales, Matthew J.; Gillette, Andrew K.; Villongco, Christopher T.; Pezzuto, Simone; Omens, Jeffrey H.; Holst, Michael J.; McCulloch, Andrew D.
2015-01-01
Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori. PMID:26300783
Clinical Risk Prediction by Exploring High-Order Feature Correlations
Wang, Fei; Zhang, Ping; Wang, Xiang; Hu, Jianying
2014-01-01
Clinical risk prediction is one important problem in medical informatics, and logistic regression is one of the most widely used approaches for clinical risk prediction. In many cases, the number of potential risk factors is fairly large and the actual set of factors that contribute to the risk is small. Therefore sparse logistic regression is proposed, which can not only predict the clinical risk but also identify the set of relevant risk factors. The inputs of logistic regression and sparse logistic regression are required to be in vector form. This limits the applicability of these models in the problems when the data cannot be naturally represented vectors (e.g., medical images are two-dimensional matrices). To handle the cases when the data are in the form of multi-dimensional arrays, we propose HOSLR: High-Order Sparse Logistic Regression, which can be viewed as a high order extension of sparse logistic regression. Instead of solving one classification vector as in conventional logistic regression, we solve for K classification vectors in HOSLR (K is the number of modes in the data). A block proximal descent approach is proposed to solve the problem and its convergence is guaranteed. Finally we validate the effectiveness of HOSLR on predicting the onset risk of patients with Alzheimer’s disease and heart failure. PMID:25954428
High-order unified symplectic FDTD scheme for the metamaterials
NASA Astrophysics Data System (ADS)
Ren, Xingang; Huang, Zhixiang; Wu, Xianliang; Lu, Silong; Wang, Hui; Wu, Lei; Li, Shen
2012-06-01
A high-order unified symplectic finite-difference time-domain (US-FDTD) method, which is energy conserved, for modeling the metamaterials is proposed. The lossless Drude dispersive model is taken into account in US-FDTD scheme, and the detailed formulations of the proposed US-FDTD method are also provided. The high-order split perfectly matched layers (SPML) are used as the absorbing boundary conditions (ABCs) to terminate the computational domain. The analysis of Courant stability and numerical dispersion demonstrate that US-FDTD scheme is more efficient than the traditional time domain numerical methods. Focusing and refocusing of the electromagnetic wave in target detection is validated using the normal incident Gaussian beam with a matched slab. Oblique incidence results associated with the inverse Snell effect and the phase compensation effect of the composite slab further demonstrated the efficiency of the method. Numerical results for a more realistic structure are also included. All the results agree well with the theoretical prediction. The method proposed here can be directly put into using as a time-domain full-wave simulation tool for applications in metamaterials.
Highly ordered periodic mesoporous organosilica nanoparticles with controllable pore structures
NASA Astrophysics Data System (ADS)
Guan, Buyuan; Cui, Yan; Ren, Zhongyuan; Qiao, Zhen-An; Wang, Li; Liu, Yunling; Huo, Qisheng
2012-09-01
A general synthetic procedure for highly ordered and well-dispersed periodic mesoporous organosilica (PMO) nanoparticles is reported based on a single cationic surfactant cetyltrimethylammonium bromide (CTAB) and simple silica sources with organic bridging groups via an ammonia-catalyzed sol-gel reaction. By changing the bridging group in the silica sources, the pore structures of the as-made particles with three-dimensional hexagonal (P63/mmc), cubic (Pm3n), two-dimensional hexagonal (P6mm), and wormlike structure were evidenced by powder X-ray diffraction analysis (XRD) and transmission electron microscopy (TEM). The size range of the nanoparticles can be adjusted from 30 nm to 500 nm by variation of the ammonia concentration or the co-solvent content of the reaction medium. The PMO nanoparticles with high concentration of organic groups in the framework offered good thermal stability, good dispersion in low polarity solvent and high adsorption of small hydrophobic molecules. Finally, the dye functionalized PMO nanoparticles show low cytotoxicity and excellent cell permeability, which offers great potential for biomedical applications.A general synthetic procedure for highly ordered and well-dispersed periodic mesoporous organosilica (PMO) nanoparticles is reported based on a single cationic surfactant cetyltrimethylammonium bromide (CTAB) and simple silica sources with organic bridging groups via an ammonia-catalyzed sol-gel reaction. By changing the bridging group in the silica sources, the pore structures of the as-made particles with three-dimensional hexagonal (P63/mmc), cubic (Pm3n), two-dimensional hexagonal (P6mm), and wormlike structure were evidenced by powder X-ray diffraction analysis (XRD) and transmission electron microscopy (TEM). The size range of the nanoparticles can be adjusted from 30 nm to 500 nm by variation of the ammonia concentration or the co-solvent content of the reaction medium. The PMO nanoparticles with high concentration of organic
Resistively detected high-order magnetoplasmons in a high-quality 2D electron gas
NASA Astrophysics Data System (ADS)
Zudov, M. A.; Shi, Q.; Pfeiffer, L. N.; West, K. W.; Watson, J. D.; Manfra, M. J.
We report on high-order magnetoplasmon resonances detected in photoresistance in high-mobility GaAs quantum wells. These resonances manifest themselves as a series of resistance extrema in the regime of Shubnikov-de Haas oscillations. Extending to orders above 20, the extrema exhibit alternating strength, being less (more) pronounced at even (odd) order magnetoplasmon modes. The lower magnetoplasmon modes reveal the importance of retardation effects.
The high-order quantum coherence of thermal light
NASA Astrophysics Data System (ADS)
Chen, Hui
Thermal light, such as sunlight, is usually considered classical light. In a macroscopic picture, classical theory successfully explained the first-order coherence phenomena of thermal light. The macroscopic theory, based on the statistical behavior of light intensity fluctuations, however, can only phenomenologically explain the second- or higher-order coherence phenomena of thermal light. This thesis introduces a microscopic quantum picture, based on the interferences of a large number of randomly distributed and randomly radiated subfields, wavepackets or photons, to the study of high-order coherence of thermal light. This thesis concludes that the second-order intensity fluctuation correlation is caused by nonlocal interference: a pair of wavepackets, which are randomly paired together, interferes with the pair itself at two distant space-time coordinates. This study has the following practical motivations: (1) to simulate N-qbits. Practical quantum computing requires quantum bits(qubits) of N-digit to represent all possible integers from 0 to 2N-1 simultaneously. A large number of independent particles can be prepared to represent a large set of N orthogonal |0> and |1> bits. In fact, based on our recent experiments of simulating the high-order correlation of entangled photons, thermal radiation is suggested as a promising source for quantum information processing. (2) to achieve sunlight ghost imaging. Ghost imaging has three attractive non-classical features: (a) the ghost camera can "see" targets that can never be seen by a classic camera; (2) it is turbulence-free; and (3) its spatial resolution is mainly determined by the angular diameter of the light source. For example, a sunlight ghost image of an object on earth may achieve a spatial resolution of 200 micrometer because the angular diameter of sun is 0.53 degree with respect to Earth. Although ghost imaging has been experimental demonstrated by using entangled photon pairs and "pseudo-thermal light
Global Monte Carlo Simulation with High Order Polynomial Expansions
William R. Martin; James Paul Holloway; Kaushik Banerjee; Jesse Cheatham; Jeremy Conlin
2007-12-13
The functional expansion technique (FET) was recently developed for Monte Carlo simulation. The basic idea of the FET is to expand a Monte Carlo tally in terms of a high order expansion, the coefficients of which can be estimated via the usual random walk process in a conventional Monte Carlo code. If the expansion basis is chosen carefully, the lowest order coefficient is simply the conventional histogram tally, corresponding to a flat mode. This research project studied the applicability of using the FET to estimate the fission source, from which fission sites can be sampled for the next generation. The idea is that individual fission sites contribute to expansion modes that may span the geometry being considered, possibly increasing the communication across a loosely coupled system and thereby improving convergence over the conventional fission bank approach used in most production Monte Carlo codes. The project examined a number of basis functions, including global Legendre polynomials as well as “local” piecewise polynomials such as finite element hat functions and higher order versions. The global FET showed an improvement in convergence over the conventional fission bank approach. The local FET methods showed some advantages versus global polynomials in handling geometries with discontinuous material properties. The conventional finite element hat functions had the disadvantage that the expansion coefficients could not be estimated directly but had to be obtained by solving a linear system whose matrix elements were estimated. An alternative fission matrix-based response matrix algorithm was formulated. Studies were made of two alternative applications of the FET, one based on the kernel density estimator and one based on Arnoldi’s method of minimized iterations. Preliminary results for both methods indicate improvements in fission source convergence. These developments indicate that the FET has promise for speeding up Monte Carlo fission source
Rapid removal of bisphenol A on highly ordered mesoporous carbon.
Sui, Qian; Huang, Jun; Liu, Yousong; Chang, Xiaofeng; Ji, Guangbin; Deng, Shubo; Xie, Tao; Yu, Gang
2011-01-01
Bisphenol A (BPA) is of global concern due to its disruption of endocrine systems and ubiquity in the aquatic environment. It is important, therefore, that efforts are made to remove it from the aqueous phase. A novel adsorbent, mesoporous carbon CMK-3, prepared from hexagonal SBA-15 mesoporous silica was studied for BPA removal from aqueous phase, and compared with conventional powdered activated carbon (PAC). Characterization of CMK-3 by transmission electron microscopy (TEM), X-ray diffraction, and nitrogen adsorption indicated that prepared CMK-3 had an ordered mesoporous structure with a high specific surface area of 920 m2/g and a pore-size of about 4.9 nm. The adsorption of BPA on CMK-3 followed a pseudo second-order kinetic model. The kinetic constant was 0.00049 g/(mg x min), much higher than the adsorption of BPA on PAC. The adsorption isotherm fitted slightly better with the Freundlich model than the Langmuir model, and adsorption capacity decreased as temperature increased from 10 to 40 degrees C. No significant influence of pH on adsorption was observed at pH 3 to 9; however, adsorption capacity decreased dramatically from pH 9 to 13. PMID:21516989
High-order social interactions in groups of mice
Shemesh, Yair; Sztainberg, Yehezkel; Forkosh, Oren; Shlapobersky, Tamar; Chen, Alon; Schneidman, Elad
2013-01-01
Social behavior in mammals is often studied in pairs under artificial conditions, yet groups may rely on more complicated social structures. Here, we use a novel system for tracking multiple animals in a rich environment to characterize the nature of group behavior and interactions, and show strongly correlated group behavior in mice. We have found that the minimal models that rely only on individual traits and pairwise correlations between animals are not enough to capture group behavior, but that models that include third-order interactions give a very accurate description of the group. These models allow us to infer social interaction maps for individual groups. Using this approach, we show that environmental complexity during adolescence affects the collective group behavior of adult mice, in particular altering the role of high-order structure. Our results provide new experimental and mathematical frameworks for studying group behavior and social interactions. DOI: http://dx.doi.org/10.7554/eLife.00759.001 PMID:24015357
Self assembly of highly-ordered nanoparticle monolayers.
Bigioni, T. P.; Lin, X.-M.; Nguyen, T. T.; Corwin, E. I.; Witten, T. A.; Jaeger, H. M.; Univ. of Chicago
2006-01-01
When a drop of a colloidal solution of nanoparticles dries on a surface, it leaves behind coffee-stain-like rings of material with lace-like patterns or clumps of particles in the interior. These non-uniform mass distributions are manifestations of far-from-equilibrium effects, such as fluid flows and solvent fluctuations during late-stage drying. However, recently a strikingly different drying regime promising highly uniform, long-range-ordered nanocrystal monolayers has been found. Here we make direct, real-time and real-space observations of nanocrystal self-assembly to reveal the mechanism. We show how the morphology of drop-deposited nanoparticle films is controlled by evaporation kinetics and particle interactions with the liquid-air interface. In the presence of an attractive particle-interface interaction, rapid early-stage evaporation dynamically produces a two-dimensional solution of nanoparticles at the liquid-air interface, from which nanoparticle islands nucleate and grow. This self-assembly mechanism produces monolayers with exceptional long-range ordering that are compact over macroscopic areas, despite the far-from-equilibrium evaporation process. This new drop-drying regime is simple, robust and scalable, is insensitive to the substrate material and topography, and has a strong preference for forming monolayer films. As such, it stands out as an excellent candidate for the fabrication of technologically important ultra thin film materials for sensors, optical devices and magnetic storage media.
High-order harmonic generation enhanced by XUV light
Buth, Christian; Kohler, Markus C.; Ullrich, Joachim; Keitel, Christoph H.
2012-03-19
The combination of high-order harmonic generation (HHG) with resonant XUV excitation of a core electron into the transient valence vacancy that is created in the course of the HHG process is investigated theoretically. In this setup, the first electron performs a HHG three-step process, whereas the second electron Rabi flops between the core and the valence vacancy. The modified HHG spectrum due to recombination with the valence and the core is determined and analyzed for krypton on the 3d {yields} 4p resonance in the ion. We assume an 800 nm laser with an intensity of about 10{sup 14} Wcm{sup 2} and XUV radiation from the Free Electron Laser in Hamburg (FLASH) with an intensity in the range 10{sup 13}-10{sup 16} Wcm{sup 2}. Our prediction opens perspectives for nonlinear XUV physics, attosecond x rays, and HHG-based spectroscopy involving core orbitals.
High-order jamming crossovers and density anomalies.
Pica Ciamarra, Massimo; Sollich, Peter
2013-10-28
We demonstrate that particles interacting via core-softened potentials exhibit a series of successive density anomalies upon isothermal compression, leading to oscillations in the diffusivity and thermal expansion coefficient, with the latter reaching negative values. These finite-temperature density anomalies are then shown to correspond to zero-temperature high-order jamming crossovers. These occur when particles are forced to come into contact with neighbours in successive coordination shells upon increasing the density. The crossovers induce anomalous behavior of the bulk modulus, which oscillates with density. We rationalize the dependence of these crossovers on the softness of the interaction potential, and relate the jamming crossovers and the anomalous diffusivity via the properties of the vibrational spectrum. PMID:26029762
Transparent boundary conditions for iterative high-order parabolic equations
NASA Astrophysics Data System (ADS)
Petrov, P. S.; Ehrhardt, M.
2016-05-01
Recently a new approach to the construction of high-order parabolic approximations for the Helmholtz equation was developed. These approximations have the form of the system of iterative parabolic equations, where the solution of the n-th equation is used as an input term for the (n + 1)-th equation. In this study the transparent boundary conditions for such systems of coupled parabolic equations are derived. The existence and uniqueness of the solution of the initial boundary value problem for the system of iterative parabolic equations with the derived boundary conditions are proved. The well-posedness of this problem is also established and an unconditionally stable finite difference scheme for its solution is proposed.
High-order harmonic generation enhanced by XUV light
NASA Astrophysics Data System (ADS)
Buth, Christian; Kohler, Markus C.; Ullrich, Joachim; Keitel, Christoph H.
2011-09-01
The combination of high-order harmonic generation (HHG) with resonant XUV excitation of a core electron into the transient valence vacancy that is created in the course of the HHG process is investigated theoretically. In this setup, the first electron performs a HHG three-step process, whereas the second electron Rabi flops between the core and the valence vacancy. The modified HHG spectrum due to recombination with the valence and the core is determined and analyzed for krypton on the 3d→4p resonance in the ion. We assume an 800nm laser with an intensity of about 1014Wcm2 and XUV radiation from the Free Electron Laser in Hamburg (FLASH) with an intensity in the range 1013--1016Wcm2. Our prediction opens perspectives for nonlinear XUV physics, attosecond x rays, and HHG-basedspectroscopy involving core orbitals.
A robust high-order ideal magnetohydrodynamic solver
NASA Astrophysics Data System (ADS)
Seal, David; Christlieb, Andrew; Feng, Xiao; Tang, Qi
In this work we present a robust high-order numerical method for the ideal magnetohydrodynamics (MHD) equations. Our method is single-stage and single-step, and hence amenable to adaptive mesh refinement (AMR) technology. The numerical robustness of the scheme is realized by accomplishing a total of two unrelated tasks: we retain positivity of the density and pressure by limiting fluxes similar to what happens in a flux corrected transport method, and we obtain divergence free magnetic fields by implementing an unstaggered transport method for the evolution of the magnetic potential. We present numerical results in two and three dimensions that indicate the utility of the scheme. These results include several classical test problems such as Orzag-Tang, cloud shock interactions and blast wave problems.
High-order multiphoton photoelectric effect at midinfrared laser wavelengths
Georges, A.T.
2002-12-01
A theoretical model that predicts the unexpectedly high photocurrents that were reported by Farkas et al. [J. Phys. B 31, L461 (1998)] for the photoelectric effect in gold at midinfrared laser wavelengths (12 {mu}m) is presented. It is shown that the observed effect, a nominally 46-photon process at threshold, is a stepwise and multiple-order process, which is strongly saturated at the moderate laser intensity of about {approx}10 MW/cm{sup 2}. The {approx_equal}30-photon-wide energy spectrum of the observed photoelectron current is due to above threshold photoemission. This relatively efficient above threshold effect is due to laser absorption in the long range Coulombic image surface potential.
Emission times in high-order harmonic generation
Chirila, C. C.; Dreissigacker, I.; Lein, M.; Zwan, E. V. van der
2010-03-15
We calculate the emission times of the radiation in high-order harmonic generation using the Gabor transform of numerical data obtained from solving the time-dependent Schroedinger equation in one, two, and three dimensions. Both atomic and molecular systems, including nuclear motion, are investigated. Lewenstein model calculations are used to gauge the performance of the Gabor method. The resulting emission times are compared against the classical simple man's model as well as against the more accurate quantum orbit model based on complex trajectories. The influence of the range of the binding potential (long or short) on the level of agreement is assessed. Our analysis reveals that the short-trajectory harmonics are emitted slightly earlier than predicted by the quantum orbit model. This partially explains recent experimental observations for atoms and molecules. Furthermore, we observe a distinct signature of two-center interference in the emission times for H{sub 2} and D{sub 2}.
High-order harmonic generation and Fano resonances
NASA Astrophysics Data System (ADS)
Strelkov, V. V.; Khokhlova, M. A.; Shubin, N. Yu
2014-05-01
We present a high-order harmonic generation theory which generalizes the strong-field approximation to the resonant case when the harmonic frequency is close to that of the transition from the ground state to an autoionizing state of the generating system. We show that the line shape of the resonant harmonic is a product of the Fano-like factor and the harmonic line which would be emitted in the absence of the resonance. The theory predicts rapid variation of the harmonic phase in the vicinity of the resonance. The calculated resonant harmonic phase is in reasonable agreement with recent measurements. Predicting the phase locking of a group of resonantly enhanced harmonics, our theory allows us to study the perspectives of producing an attosecond pulse train using such harmonics.
High-Order Space-Time Methods for Conservation Laws
NASA Technical Reports Server (NTRS)
Huynh, H. T.
2013-01-01
Current high-order methods such as discontinuous Galerkin and/or flux reconstruction can provide effective discretization for the spatial derivatives. Together with a time discretization, such methods result in either too small a time step size in the case of an explicit scheme or a very large system in the case of an implicit one. To tackle these problems, two new high-order space-time schemes for conservation laws are introduced: the first is explicit and the second, implicit. The explicit method here, also called the moment scheme, achieves a Courant-Friedrichs-Lewy (CFL) condition of 1 for the case of one-spatial dimension regardless of the degree of the polynomial approximation. (For standard explicit methods, if the spatial approximation is of degree p, then the time step sizes are typically proportional to 1/p(exp 2)). Fourier analyses for the one and two-dimensional cases are carried out. The property of super accuracy (or super convergence) is discussed. The implicit method is a simplified but optimal version of the discontinuous Galerkin scheme applied to time. It reduces to a collocation implicit Runge-Kutta (RK) method for ordinary differential equations (ODE) called Radau IIA. The explicit and implicit schemes are closely related since they employ the same intermediate time levels, and the former can serve as a key building block in an iterative procedure for the latter. A limiting technique for the piecewise linear scheme is also discussed. The technique can suppress oscillations near a discontinuity while preserving accuracy near extrema. Preliminary numerical results are shown
A highly ordered cubic mesoporous silica/graphene nanocomposite
NASA Astrophysics Data System (ADS)
Lee, Chang-Wook; Roh, Kwang Chul; Kim, Kwang-Bum
2013-09-01
A highly ordered cubic mesoporous silica (KIT-6)/graphene nanocomposite and 2D KIT-6 nanoflakes were synthesized using a novel synthesis methodology. The non-ionic triblock copolymer, P123, played a dual role as a structure-directing agent in the formation of the cubic mesoporous structure and as a cross-linking agent between mesoporous silica and graphene. The prepared (KIT-6)/graphene nanocomposite could act as a template for the preparation of mesoporous material/graphene nanocomposites.A highly ordered cubic mesoporous silica (KIT-6)/graphene nanocomposite and 2D KIT-6 nanoflakes were synthesized using a novel synthesis methodology. The non-ionic triblock copolymer, P123, played a dual role as a structure-directing agent in the formation of the cubic mesoporous structure and as a cross-linking agent between mesoporous silica and graphene. The prepared (KIT-6)/graphene nanocomposite could act as a template for the preparation of mesoporous material/graphene nanocomposites. Electronic supplementary information (ESI) available: S1: TEM images of disordered mesoporous silica/graphene nanocomposite; S2: TEM images of KIT-6/GO nanocomposite; S3: Thermogravimetric analysis of KIT-6/GO and KG-400-700; S4: SEM and TEM images of KIT-6; S5: Low angle XRD, Raman spectra, N2 adsorption isotherms, pore size distribution and photographic images of the prepared samples; S6: TEM image and N2 adsorption isotherms of mesoporous carbon/graphene nanocomposite; S7: XPS C1s spectra of the prepared samples. See DOI: 10.1039/c3nr03108j
NASA Astrophysics Data System (ADS)
Vater, Stefan; Beisiegel, Nicole; Behrens, Jörn
2015-11-01
An important part in the numerical simulation of tsunami and storm surge events is the accurate modeling of flooding and the appearance of dry areas when the water recedes. This paper proposes a new algorithm to model inundation events with piecewise linear Runge-Kutta discontinuous Galerkin approximations applied to the shallow water equations. This study is restricted to the one-dimensional case and shows a detailed analysis and the corresponding numerical treatment of the inundation problem. The main feature is a velocity based "limiting" of the momentum distribution in each cell, which prevents instabilities in case of wetting or drying situations. Additional limiting of the fluid depth ensures its positivity while preserving local mass conservation. A special flux modification in cells located at the wet/dry interface leads to a well-balanced method, which maintains the steady state at rest. The discontinuous Galerkin scheme is formulated in a nodal form using a Lagrange basis. The proposed wetting and drying treatment is verified with several numerical simulations. These test cases demonstrate the well-balancing property of the method and its stability in case of rapid transition of the wet/dry interface. We also verify the conservation of mass and investigate the convergence characteristics of the scheme.
High-order computational fluid dynamics tools for aircraft design.
Wang, Z J
2014-08-13
Most forecasts predict an annual airline traffic growth rate between 4.5 and 5% in the foreseeable future. To sustain that growth, the environmental impact of aircraft cannot be ignored. Future aircraft must have much better fuel economy, dramatically less greenhouse gas emissions and noise, in addition to better performance. Many technical breakthroughs must take place to achieve the aggressive environmental goals set up by governments in North America and Europe. One of these breakthroughs will be physics-based, highly accurate and efficient computational fluid dynamics and aeroacoustics tools capable of predicting complex flows over the entire flight envelope and through an aircraft engine, and computing aircraft noise. Some of these flows are dominated by unsteady vortices of disparate scales, often highly turbulent, and they call for higher-order methods. As these tools will be integral components of a multi-disciplinary optimization environment, they must be efficient to impact design. Ultimately, the accuracy, efficiency, robustness, scalability and geometric flexibility will determine which methods will be adopted in the design process. This article explores these aspects and identifies pacing items. PMID:25024419
Phase properties of the cutoff high-order harmonics
NASA Astrophysics Data System (ADS)
Khokhlova, M. A.; Strelkov, V. V.
2016-04-01
The cutoff regime of high-order harmonic generation (HHG) by atoms in an intense laser field is studied numerically and analytically. We find that the cutoff regime is characterized by equal dephasing between the successive harmonics. The change of the harmonic phase locking when HHG evolves from the cutoff to the plateau regime determines the optimal bandwidth of the spectral region which should be used for attosecond pulse generation via the amplitude gating technique. The minimal pulse duration which can be obtained with this technique in argon without using dispersion elements is approximately 0.08-0.1 of the laser cycle for different intensities and frequencies of the fundamental. The cutoff regime is also characterized by a linear dependence of the harmonic phase on the fundamental intensity. The proportionality coefficient grows as the cube of the fundamental wavelength, thus this dependence becomes very important for the HHG by midinfrared fields. Moreover, for every high harmonic there is a range of laser intensities providing the generation in the cutoff regime and the atomic response magnitude in this regime can be greater than that in the plateau regime. Thus, the cutoff regime substantially contributes to the harmonic energy emitted under typical experimental conditions where the laser intensity varies in time and space.
High-order computational fluid dynamics tools for aircraft design
Wang, Z. J.
2014-01-01
Most forecasts predict an annual airline traffic growth rate between 4.5 and 5% in the foreseeable future. To sustain that growth, the environmental impact of aircraft cannot be ignored. Future aircraft must have much better fuel economy, dramatically less greenhouse gas emissions and noise, in addition to better performance. Many technical breakthroughs must take place to achieve the aggressive environmental goals set up by governments in North America and Europe. One of these breakthroughs will be physics-based, highly accurate and efficient computational fluid dynamics and aeroacoustics tools capable of predicting complex flows over the entire flight envelope and through an aircraft engine, and computing aircraft noise. Some of these flows are dominated by unsteady vortices of disparate scales, often highly turbulent, and they call for higher-order methods. As these tools will be integral components of a multi-disciplinary optimization environment, they must be efficient to impact design. Ultimately, the accuracy, efficiency, robustness, scalability and geometric flexibility will determine which methods will be adopted in the design process. This article explores these aspects and identifies pacing items. PMID:25024419
Resistively detected high-order magnetoplasmons in a high-quality two-dimensional electron gas
NASA Astrophysics Data System (ADS)
Shi, Q.; Zudov, M. A.; Pfeiffer, L. N.; West, K. W.; Watson, J. D.; Manfra, M. J.
2016-04-01
We report on high-order magnetoplasmon resonances detected in photoresistance in high-mobility GaAs quantum wells. These resonances manifest themselves as a series of photoresistance extrema in the regime of Shubnikov-de Haas oscillations. Extending to orders as high as 25, the extrema exhibit alternating strength, being less (more) pronounced at even- (odd)-order magnetoplasmon modes. This experimental technique provides a sensitive and elegant means to detect and investigate multiple magnetoplasmon modes and could be applied to other systems.
High Order And High Resolution Methods For a Model CAA Problem
NASA Technical Reports Server (NTRS)
Goodrich, John W.
2004-01-01
The initial value problem for the first order linear wave equation in one space dimension is treated for two cases with specified initial data and grid, and data from solutions at t = 400 and t = 800 are presented, as prescribed for Problem 1 in Category 1. Results are shown from computations with a sequence of recently developed high order and high resolution methods which combine Hermite interpolation, Cauchy-Kowaleskya recursion for time derivatives, and Taylor series time advancement. These methods have the same order of accuracy in time as in space. Results are shown from methods that range from third to nineteenth order. The stated problems with the prescribed coarse grid can be simulated with errors that are at the level of machine accuracy if the method is sufficiently high order. In addition, the growth of the maximum absolute error out to t = 100,000 is given for simulations with the stated problem data.
Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence
NASA Technical Reports Server (NTRS)
Sandham, N. D.; Yee, H. C.; Kwak, Dochan (Technical Monitor)
2000-01-01
A stable high order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy splitting approach splits the inviscid flux derivatives into conservative and non-conservative portions. The spatial difference operators satisfy a summation by parts condition leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier-Stokes equations is used to ensure that any tendency to odd-even decoupling associated with central schemes can be countered by the fluid viscosity. A special formulation of the continuity equation is used, based on similar arguments. The resulting methods are able to minimize spurious high frequency oscillation producing nonlinear instability associated with pure central schemes, especially for long time integration simulation such as DNS. For validation purposes, the methods are tested in a DNS of compressible turbulent plane channel flow at a friction Mach number of 0.1 where a very accurate turbulence data base exists. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with incompressible channel data, as expected at this Mach number. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.
Analytical and experimental study of high phase order induction motors
NASA Astrophysics Data System (ADS)
Klingshirn, Eugene A.
1989-08-01
Induction motors having more than three phases were investigated to determine their suitability for electric vehicle applications. The objective was to have a motor with a current rating lower than that of a three-phase motor. The name chosen for these is high phase order (HPO) motors. Motors having six phases and nine phases were given the most attention. It was found that HPO motors are quite suitable for electric vehicles, and for many other applications as well. They have characteristics which are as good as or better than three-phase motors for practically all applications where polyphase induction motors are appropriate. Some of the analysis methods are presented, and several of the equivalent circuits which facilitate the determination of harmonic currents and losses, or currents with unbalanced sources, are included. The sometimes large stator currents due to harmonics in the source voltages are pointed out. Filters which can limit these currents were developed. An analysis and description of these filters is included. Experimental results which confirm and illustrate much of the theory are also included. These include locked rotor test results and full-load performance with an open phase. Also shown are oscillograms which display the reduction in harmonic currents when a filter is used with the experimental motor supplied by a non-sinusoidal source.
Analytical and experimental study of high phase order induction motors
NASA Technical Reports Server (NTRS)
Klingshirn, Eugene A.
1989-01-01
Induction motors having more than three phases were investigated to determine their suitability for electric vehicle applications. The objective was to have a motor with a current rating lower than that of a three-phase motor. The name chosen for these is high phase order (HPO) motors. Motors having six phases and nine phases were given the most attention. It was found that HPO motors are quite suitable for electric vehicles, and for many other applications as well. They have characteristics which are as good as or better than three-phase motors for practically all applications where polyphase induction motors are appropriate. Some of the analysis methods are presented, and several of the equivalent circuits which facilitate the determination of harmonic currents and losses, or currents with unbalanced sources, are included. The sometimes large stator currents due to harmonics in the source voltages are pointed out. Filters which can limit these currents were developed. An analysis and description of these filters is included. Experimental results which confirm and illustrate much of the theory are also included. These include locked rotor test results and full-load performance with an open phase. Also shown are oscillograms which display the reduction in harmonic currents when a filter is used with the experimental motor supplied by a non-sinusoidal source.
Template synthesis and characterization of highly ordered lamellar hydroxyapatite
NASA Astrophysics Data System (ADS)
Liu, Chao; Ji, Xiujie; Cheng, Guoxiang
2007-06-01
Surfactant template synthesis attracts great attention in the fields of biomaterials and functional materials. In this study, highly ordered lamellar hydroxyapatite (Lα-HA) powder was synthesized by a surfactant templating method in water-ethanol. Ca(NO 3) 2 and (NH 4) 2HPO 4 were used as calcium and phosphorus sources, respectively. Sodium dodecyl sulphonate (SDS, C 12H 25SO 3Na) acted as the template. X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR) analyses showed that HA is the only crystal phase in Lα-HA. Transmission electron microscope (TEM) observation further proved this regular lamellar structure detected by XRD. The repeat periodicity of the structure is about 3.6 nm observed by TEM, which is in well accordance with the XRD data (3.16 nm). The selected area electron diffraction (SAED) results indicated that Lα-HA was a polycrystalline structure. The formation of Lα-HA could be explained by a surfactant template.
Nonlinear high-order mode locking in stochastic sensory neurons
NASA Astrophysics Data System (ADS)
Rowe, Michael; Afghan, Muhammad; Neiman, Alexander
2004-03-01
Excitable systems demonstrate various mode locking regimes when driven by periodic external signals. With noise taken into account, such regimes represent complex nonlinear responses which depend crucially on the frequency and amplitude of the periodic drive as well as on the noise intensity. We study this using a computational model of a stochastic Hodgkin-Huxley neuron in combination with the turtle vestibular sensory system as an experimental model. A bifurcation analysis of the model is performed. Extracellular recordings from primary vestibular afferent neurons with two types of stimuli are used in the experimental study. First, mechanical stimuli applied to the labyrinth allow us to study the responses of the entire system, including transduction by the hair cells and spike generation in the primary afferents. Second, a galvanic stimuli applied directly to an afferent are used to study the responses of afferent spike generator directly. The responses to galvanic stimuli reveal multiple high-order mode locking regimes which are well reproduced in numerical simulation. Responses to mechanical stimulation are characterized by larger variability so that fewer mode-locking regimes can be observed.
Stirling Analysis Comparison of Commercial vs. High-Order Methods
NASA Technical Reports Server (NTRS)
Dyson, Rodger W.; Wilson, Scott D.; Tew, Roy C.; Demko, Rikako
2007-01-01
Recently, three-dimensional Stirling engine simulations have been accomplished utilizing commercial Computational Fluid Dynamics software. The validations reported can be somewhat inconclusive due to the lack of precise time accurate experimental results from engines, export control/ proprietary concerns, and the lack of variation in the methods utilized. The last issue may be addressed by solving the same flow problem with alternate methods. In this work, a comprehensive examination of the methods utilized in the commercial codes is compared with more recently developed high-order methods. Specifically, Lele's Compact scheme and Dyson s Ultra Hi-Fi method will be compared with the SIMPLE and PISO methods currently employed in CFD-ACE, FLUENT, CFX, and STAR-CD (all commercial codes which can in theory solve a three-dimensional Stirling model although sliding interfaces and their moving grids limit the effective time accuracy). We will initially look at one-dimensional flows since the current standard practice is to design and optimize Stirling engines with empirically corrected friction and heat transfer coefficients in an overall one-dimensional model. This comparison provides an idea of the range in which commercial CFD software for modeling Stirling engines may be expected to provide accurate results. In addition, this work provides a framework for improving current one-dimensional analysis codes.
Stirling Analysis Comparison of Commercial Versus High-Order Methods
NASA Technical Reports Server (NTRS)
Dyson, Rodger W.; Wilson, Scott D.; Tew, Roy C.; Demko, Rikako
2005-01-01
Recently, three-dimensional Stirling engine simulations have been accomplished utilizing commercial Computational Fluid Dynamics software. The validations reported can be somewhat inconclusive due to the lack of precise time accurate experimental results from engines, export control/proprietary concerns, and the lack of variation in the methods utilized. The last issue may be addressed by solving the same flow problem with alternate methods. In this work, a comprehensive examination of the methods utilized in the commercial codes is compared with more recently developed high-order methods. Specifically, Lele's compact scheme and Dyson's Ultra Hi-Fi method will be compared with the SIMPLE and PISO methods currently employed in CFD-ACE, FLUENT, CFX, and STAR-CD (all commercial codes which can in theory solve a three-dimensional Stirling model with sliding interfaces and their moving grids limit the effective time accuracy). We will initially look at one-dimensional flows since the current standard practice is to design and optimize Stirling engines with empirically corrected friction and heat transfer coefficients in an overall one-dimensional model. This comparison provides an idea of the range in which commercial CFD software for modeling Stirling engines may be expected to provide accurate results. In addition, this work provides a framework for improving current one-dimensional analysis codes.
Central Command Architecture for High Order Autonomous Unmanned Systems
NASA Astrophysics Data System (ADS)
Bieber, Chad Michael
This dissertation describes a High-Order Central Command (HOCC) architecture and presents a flight demonstration where a single user coordinates 4 unmanned fixed-wing aircraft. HOCC decouples the user from control of individual vehicles, eliminating human limits on the size of the system, and uses a non-iterative sequence of algorithms that permit easy estimation of how computational complexity scales. The Hungarian algorithm used to solve a min-sum assignment with a one-task planning horizon becomes the limiting complexity, scaling at O(x3) where x is the larger number of vehicles or tasks in the assignment. This method is shown to have a unique property of creating non-intersecting routes which is used to drastically reduce the computational cost of deconflicting planned routes. Results from several demonstration flights are presented where a single user commands a system of 4 fixed-wing aircraft. The results confirm that autonomous flight of a large number of UAVs is a bona fide engineering sub-discipline, which is expected to be of interest to engineers who will find its utility in the aviation industry and in other emerging markets.
Highly ordered ultralong magnetic nanowires wrapped in stacked graphene layers
El Mel, Abdel-Aziz; Duvail, Jean-Luc; Gautron, Eric; Xu, Wei; Choi, Chang-Hwan; Angleraud, Benoit; Granier, Agnès
2012-01-01
Summary We report on the synthesis and magnetic characterization of ultralong (1 cm) arrays of highly ordered coaxial nanowires with nickel cores and graphene stacking shells (also known as metal-filled carbon nanotubes). Carbon-containing nickel nanowires are first grown on a nanograted surface by magnetron sputtering. Then, a post-annealing treatment favors the metal-catalyzed crystallization of carbon into stacked graphene layers rolled around the nickel cores. The observed uniaxial magnetic anisotropy field oriented along the nanowire axis is an indication that the shape anisotropy dominates the dipolar coupling between the wires. We further show that the thermal treatment induces a decrease in the coercivity of the nanowire arrays. This reflects an enhancement of the quality of the nickel nanowires after annealing attributed to a decrease of the roughness of the nickel surface and to a reduction of the defect density. This new type of graphene–ferromagnetic-metal nanowire appears to be an interesting building block for spintronic applications. PMID:23365798
NASA Astrophysics Data System (ADS)
Mazaheri, Alireza; Nishikawa, Hiroaki
2016-09-01
We propose arbitrary high-order discontinuous Galerkin (DG) schemes that are designed based on a first-order hyperbolic advection-diffusion formulation of the target governing equations. We present, in details, the efficient construction of the proposed high-order schemes (called DG-H), and show that these schemes have the same number of global degrees-of-freedom as comparable conventional high-order DG schemes, produce the same or higher order of accuracy solutions and solution gradients, are exact for exact polynomial functions, and do not need a second-derivative diffusion operator. We demonstrate that the constructed high-order schemes give excellent quality solution and solution gradients on irregular triangular elements. We also construct a Weighted Essentially Non-Oscillatory (WENO) limiter for the proposed DG-H schemes and apply it to discontinuous problems. We also make some accuracy comparisons with conventional DG and interior penalty schemes. A relative qualitative cost analysis is also reported, which indicates that the high-order schemes produce orders of magnitude more accurate results than the low-order schemes for a given CPU time. Furthermore, we show that the proposed DG-H schemes are nearly as efficient as the DG and Interior-Penalty (IP) schemes as these schemes produce results that are relatively at the same error level for approximately a similar CPU time.
NASA Technical Reports Server (NTRS)
Mankbadi, M. R.; Georgiadis, N. J.; DeBonis, J. R.
2015-01-01
The objective of this work is to compare a high-order solver with a low-order solver for performing large-eddy simulations (LES) of a compressible mixing layer. The high-order method is the Wave-Resolving LES (WRLES) solver employing a Dispersion Relation Preserving (DRP) scheme. The low-order solver is the Wind-US code, which employs the second-order Roe Physical scheme. Both solvers are used to perform LES of the turbulent mixing between two supersonic streams at a convective Mach number of 0.46. The high-order and low-order methods are evaluated at two different levels of grid resolution. For a fine grid resolution, the low-order method produces a very similar solution to the high-order method. At this fine resolution the effects of numerical scheme, subgrid scale modeling, and filtering were found to be negligible. Both methods predict turbulent stresses that are in reasonable agreement with experimental data. However, when the grid resolution is coarsened, the difference between the two solvers becomes apparent. The low-order method deviates from experimental results when the resolution is no longer adequate. The high-order DRP solution shows minimal grid dependence. The effects of subgrid scale modeling and spatial filtering were found to be negligible at both resolutions. For the high-order solver on the fine mesh, a parametric study of the spanwise width was conducted to determine its effect on solution accuracy. An insufficient spanwise width was found to impose an artificial spanwise mode and limit the resolved spanwise modes. We estimate that the spanwise depth needs to be 2.5 times larger than the largest coherent structures to capture the largest spanwise mode and accurately predict turbulent mixing.
NASA Technical Reports Server (NTRS)
Mankbadi, Mina R.; Georgiadis, Nicholas J.; DeBonis, James R.
2015-01-01
The objective of this work is to compare a high-order solver with a low-order solver for performing Large-Eddy Simulations (LES) of a compressible mixing layer. The high-order method is the Wave-Resolving LES (WRLES) solver employing a Dispersion Relation Preserving (DRP) scheme. The low-order solver is the Wind-US code, which employs the second-order Roe Physical scheme. Both solvers are used to perform LES of the turbulent mixing between two supersonic streams at a convective Mach number of 0.46. The high-order and low-order methods are evaluated at two different levels of grid resolution. For a fine grid resolution, the low-order method produces a very similar solution to the highorder method. At this fine resolution the effects of numerical scheme, subgrid scale modeling, and filtering were found to be negligible. Both methods predict turbulent stresses that are in reasonable agreement with experimental data. However, when the grid resolution is coarsened, the difference between the two solvers becomes apparent. The low-order method deviates from experimental results when the resolution is no longer adequate. The high-order DRP solution shows minimal grid dependence. The effects of subgrid scale modeling and spatial filtering were found to be negligible at both resolutions. For the high-order solver on the fine mesh, a parametric study of the spanwise width was conducted to determine its effect on solution accuracy. An insufficient spanwise width was found to impose an artificial spanwise mode and limit the resolved spanwise modes. We estimate that the spanwise depth needs to be 2.5 times larger than the largest coherent structures to capture the largest spanwise mode and accurately predict turbulent mixing.
High-Order Harmonic And Fast Ion Generation In High Intensity Laser-Solid Interactions
Loch, R. A.; Boller, K.-J.; Martin, Ph.; Ceccotti, T.; Monot, P.; Quere, F.; George, H.; Bougeard, M.; Reau, F.; D'Oliveira, P.
2009-07-25
Experiments on high-order harmonic generation and ion acceleration are performed with the new installed 100 TW, 25 fs laser in Saclay (UHI100). These experiments require a very high laser pulse contrast. The suppression of prepulse energy is achieved by using a double plasma mirror, which results in a contrast of 10{sup 13}.
High-order harmonic generation using a high-repetition-rate turnkey laser.
Lorek, E; Larsen, E W; Heyl, C M; Carlström, S; Paleček, D; Zigmantas, D; Mauritsson, J
2014-12-01
We generate high-order harmonics at high pulse repetition rates using a turnkey laser. High-order harmonics at 400 kHz are observed when argon is used as target gas. In neon, we achieve generation of photons with energies exceeding 90 eV (∼13 nm) at 20 kHz. We measure a photon flux of up to 4.4 × 10(10) photons per second per harmonic in argon at 100 kHz. Many experiments employing high-order harmonics would benefit from higher repetition rates, and the user-friendly operation opens up for applications of coherent extreme ultra-violet pulses in new research areas. PMID:25554271
High-order harmonic generation using a high-repetition-rate turnkey laser
Lorek, E. Larsen, E. W.; Heyl, C. M.; Carlström, S.; Mauritsson, J.; Paleček, D.; Zigmantas, D.
2014-12-15
We generate high-order harmonics at high pulse repetition rates using a turnkey laser. High-order harmonics at 400 kHz are observed when argon is used as target gas. In neon, we achieve generation of photons with energies exceeding 90 eV (∼13 nm) at 20 kHz. We measure a photon flux of up to 4.4 × 10{sup 10} photons per second per harmonic in argon at 100 kHz. Many experiments employing high-order harmonics would benefit from higher repetition rates, and the user-friendly operation opens up for applications of coherent extreme ultra-violet pulses in new research areas.
Low Dissipative High Order Numerical Simulations of Supersonic Reactive Flows
NASA Technical Reports Server (NTRS)
Sjoegreen, B.; Yee, H. C.; Mansour, Nagi (Technical Monitor)
2001-01-01
The objective of this paper is to evaluate the performance of a newly developed low dissipative sixth-order spatial and fourth-order temporal scheme for viscous reactive flows interacting with shock waves that contain fine scale flow structures. The accuracy and efficiency of the scheme, and to what degree the scheme can capture the correct physical wave speeds of stiff reactive flows will be included.
High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order
NASA Technical Reports Server (NTRS)
Mazaheri, Alireza R.; Nishikawa, Hiroaki
2014-01-01
In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.
A Very Important Lesson: Respect and the Socialization of Order(s) in High School ESL
ERIC Educational Resources Information Center
Talmy, Steven
2009-01-01
The "stigma" associated with ESL in K-12 public schools is a widely referenced if little explored topic. In this paper, I consider how this "stigma" was produced in a high school ESL class in Hawai'i, specifically, as it was licensed by and framed in terms of teaching students "respect." Based on analysis of two extended teacher-fronted…
High-order numerical solutions using cubic splines
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1975-01-01
The cubic spline collocation procedure for the numerical solution of partial differential equations was reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a nonuniform mesh and overall fourth-order accuracy for a uniform mesh. Application of the technique was made to the Burger's equation, to the flow around a linear corner, to the potential flow over a circular cylinder, and to boundary layer problems. The results confirmed the higher-order accuracy of the spline method and suggest that accurate solutions for more practical flow problems can be obtained with relatively coarse nonuniform meshes.
Compact high-order schemes for the Euler equations
NASA Technical Reports Server (NTRS)
Abarbanel, Saul; Kumar, Ajay
1988-01-01
An implicit approximate factorization (AF) algorithm is constructed which has the following characteristics. In 2-D: the scheme is unconditionally stable, has a 3 x 3 stencil and at steady state has a fourth order spatial accuracy. The temporal evolution is time accurate either to first or second order through choice of parameter. In 3-D: the scheme has almost the same properties as in 2-D except that it is now only conditionally stable, with the stability condition (the CFL number) being dependent on the cell aspect ratios, delta y/delta x and delta z/delta x. The stencil is still compact and fourth order accuracy at steady state is maintained.
High-Order Noise Filtering in Nontrivial Quantum Logic Gates
NASA Astrophysics Data System (ADS)
Green, Todd; Uys, Hermann; Biercuk, Michael J.
2012-07-01
Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of noncommuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. We present a general method to calculate the ensemble-averaged entanglement fidelity to arbitrary order in terms of noise filter functions, and provide explicit expressions to fourth order in the noise strength. In the weak noise limit we derive explicit filter functions for a broad class of piecewise-constant control sequences, and use them to study the performance of dynamically corrected gates, yielding good agreement with brute-force numerics.
High-order noise filtering in nontrivial quantum logic gates.
Green, Todd; Uys, Hermann; Biercuk, Michael J
2012-07-13
Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of noncommuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. We present a general method to calculate the ensemble-averaged entanglement fidelity to arbitrary order in terms of noise filter functions, and provide explicit expressions to fourth order in the noise strength. In the weak noise limit we derive explicit filter functions for a broad class of piecewise-constant control sequences, and use them to study the performance of dynamically corrected gates, yielding good agreement with brute-force numerics. PMID:23030139
High-order harmonics from bow wave caustics driven by a high-intensity laser
NASA Astrophysics Data System (ADS)
Esirkepov, T. Zh.; Pirozhkov, A. S.; Kando, M.; Gallegos, P.; Ahmed, H.; Ragozin, E. N.; Faenov, A. Ya.; Pikuz, T. A.; Kawachi, T.; Sagisaka, A.; Koga, J. K.; Coury, M.; Green, J.; Foster, P.; Brenner, C.; Dromey, B.; Symes, D. R.; Mori, M.; Kawase, K.; Kameshima, T.; Fukuda, Y.; Chen, L. M.; Daito, I.; Ogura, K.; Hayashi, Y.; Kotaki, H.; Kiriyama, H.; Okada, H.; Nishimori, N.; Imazono, T.; Kondo, K.; Kimura, T.; Tajima, T.; Daido, H.; Rajeev, P.; Mckenna, P.; Borghesi, M.; Neely, D.; Kato, Y.; Bulanov, S. V.
2012-07-01
We propose a new mechanism of high-order harmonic generation during an interaction of a high-intensity laser pulse with underdense plasma. A tightly focused laser pulse creates a cavity in plasma pushing electrons aside and exciting the wake wave and the bow wave. At the joint of the cavity wall and the bow wave boundary, an annular spike of electron density is formed. This spike surrounds the cavity and moves together with the laser pulse. Collective motion of electrons in the spike driven by the laser field generates high-order harmonics. A strong localization of the electron spike, its robustness to oscillations imposed by the laser field and, consequently, its ability to produce high-order harmonics is explained by catastrophe theory. The proposed mechanism explains the experimental observations of high-order harmonics with the 9 TW J-KAREN laser (JAEA, Japan) and the 120 TW Astra Gemini laser (CLF RAL, UK) [A. S. Pirozhkov, et al., arXiv:1004.4514 (2010); A. S. Pirozhkov et al, AIP Proceedings, this volume]. The theory is corroborated by high-resolution two-and three-dimensional particle-in-cell simulations.
Interaction of high-order solitons with external dispersive waves.
Oreshnikov, I; Driben, R; Yulin, A V
2015-12-01
The effect of mutual interaction between second-order soliton and dispersive waves (DWs) is investigated. It is predicted analytically and confirmed numerically that DWs (both transmitted and reflected components) become polychromatic after interaction with the soliton. Collision with DWs of considerable intensity can lead to acceleration/deceleration and central frequency shift of the soliton, while still preserving the soliton's oscillating structure. Two second-order solitons with resonant DWs trapped between them can form an effective solitonic cavity with "flat" or "concave mirrors," depending on the intensity of the input. PMID:26625049
AMR vs High Order Schemes Wavelets as a Guide
Jameson, L.
2000-10-04
The final goal behind any numerical method is give the smallest wall-clock time for a given final time error or, conversely, the smallest run-time error for a given wall clock time, etc. Here a comparison will be given between adaptive mesh refinement schemes and non-adaptive schemes of higher order. It will be shown that in three dimension calculations that in order for AMR schemes to be competitive that the finest scale must be restricted to an extremely, and unrealistic, small percentage of the computational domain.
Compact high order schemes for the Euler equations
NASA Technical Reports Server (NTRS)
Abarbanel, Saul; Kumar, Ajay
1988-01-01
An implicit approximate factorization (AF) algorithm is constructed which has the following characteistics. In 2-D: The scheme is unconditionally stable, has a 3 x 3 stencil and at steady state has a fourth order spatial accuracy. The temporal evolution is time accurate either to first or second order through choice of parameter. In 3-D: The scheme has almost the same properties as in 2-D except that it is now only conditionally stable, with the stability condition (the CFL number) being dependent on the cell aspect ratios, delta y/delta x and delta z/delta x. The stencil is still compact and fourth order accuracy at steady state is maintained. Numerical experiments on a 2-D shock-reflection problem show the expected improvement over lower order schemes, not only in accuracy (measured by the L sub 2 error) but also in the dispersion. It is also shown how the same technique is immediately extendable to Runge-Kutta type schemes resulting in improved stability in addition to the enhanced accuracy.
Uniformly high-order accurate non-oscillatory schemes, 1
NASA Technical Reports Server (NTRS)
Harten, A.; Osher, S.
1985-01-01
The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws was begun. These schemes share many desirable properties with total variation diminishing schemes (TVD), but TVD schemes have at most first order accuracy, in the sense of truncation error, at extreme of the solution. A uniformly second order approximation was constucted, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.
High order software - A methodology for defining software
NASA Technical Reports Server (NTRS)
Hamilton, M.; Zeldin, S.
1975-01-01
Higher order software (HOS) is a formal methodology for reliable systems specification and development. HOS is concerned only with computable functions and their relationships for any given system. Questions of methodology are considered, taking into account aspects of formulation meta-language principles, and HOS analyzers. Details of system design are discussed, giving attention to aspects of immediate self-control and indirect self-control. A description is given of the approaches used for software management.
Fabrication and structural characterization of highly ordered titania nanotube arrays
NASA Astrophysics Data System (ADS)
Shi, Hongtao; Ordonez, Rosita
Titanium (Ti) dioxide nanotubes have drawn much attention in the past decade due to the fact that titania is an extremely versatile material with a variety of technological applications. Anodizing Ti in different electrolytes has proved to be quite successful so far in creating the nanotubes, however, their degree of order is still not nearly as good as nanoporous anodic alumina. In this work, we first deposit a thin layer of aluminum (Al) onto electropolished Ti substrates, using thermal evaporation. Such an Al layer is then anodized in 0.3 M oxalic acid, forming an ordered nanoporous alumina mask on top of Ti. Afterwards, the anodization of Ti is accomplished at 20 V in solutions containing 1 M NaH2PO4 and 0.5% HF or H2SO4, which results in the creation of ordered titania nanotube arrays. The inner pore diameter of the nanotubes can be tuned from ~50 nm to ~75 nm, depending on the anodization voltage applied to Al or Ti. X-ray diffractometry shows the as-grown titania nanotubes are amorphous. Samples annealed at different temperatures in ambient atmosphere will be also reported.
High-Order Entropy Stable Formulations for Computational Fluid Dynamics
NASA Technical Reports Server (NTRS)
Carpenter, Mark H.; Fisher, Travis C.
2013-01-01
A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.
A New Approach for Constructing Highly Stable High Order CESE Schemes
NASA Technical Reports Server (NTRS)
Chang, Sin-Chung
2010-01-01
A new approach is devised to construct high order CESE schemes which would avoid the common shortcomings of traditional high order schemes including: (a) susceptibility to computational instabilities; (b) computational inefficiency due to their local implicit nature (i.e., at each mesh points, need to solve a system of linear/nonlinear equations involving all the mesh variables associated with this mesh point); (c) use of large and elaborate stencils which complicates boundary treatments and also makes efficient parallel computing much harder; (d) difficulties in applications involving complex geometries; and (e) use of problem-specific techniques which are needed to overcome stability problems but often cause undesirable side effects. In fact it will be shown that, with the aid of a conceptual leap, one can build from a given 2nd-order CESE scheme its 4th-, 6th-, 8th-,... order versions which have the same stencil and same stability conditions of the 2nd-order scheme, and also retain all other advantages of the latter scheme. A sketch of multidimensional extensions will also be provided.
Effects of high-order deformation on high-K isomers in superheavy nuclei
Liu, H. L.; Bertulani, C. A.; Xu, F. R.; Walker, P. M.
2011-01-15
Using, for the first time, configuration-constrained potential-energy-surface calculations with the inclusion of {beta}{sub 6} deformation, we find remarkable effects of the high-order deformation on the high-K isomers in {sup 254}No, the focus of recent spectroscopy experiments on superheavy nuclei. For shapes with multipolarity six, the isomers are more tightly bound and, microscopically, have enhanced deformed shell gaps at N=152 and Z=100. The inclusion of {beta}{sub 6} deformation significantly improves the description of the very heavy high-K isomers.
Highly Ordered Single Conjugated Polymer Chain Rod Morphologies
Adachi, Takuji; Brazard, Johanna; Chokshi, Paresh; Ganesan, Venkat; Bolinger, Joshua; Barbara, Paul F.
2010-10-15
We have reexamined the fluorescence polarization anisotropy of single polymer chains of the prototypical conjugated polymer poly[2-methoxy-5-(2'-ethylhexyloxy)-1,4-phenylenevinylene] (MEH-PPV) isolated in a poly(methyl methacrylate) (PMMA) matrix employing improved synthetic samples that contain a much smaller number of tetrahedral chemical defects per chain. The new measurements reveal a much larger fraction of highly anisotropic MEH-PPV chains, with >70% of the chains exhibiting polarization anisotropy values falling in the range of 0.6-0.9. High anisotropy is strong evidence for a rod-shaped conformation. A comparison of the experimental results with coarse grain, beads on a chain simulations reveals that simulations with the usual bead-bead pairwise additive potentials cannot reproduce the observed large fraction of high polarization values. Apparently, this type of potential lacks some yet to be identified molecular feature that is necessary to accurately simulate the experimental results.
Electrodeposition of highly uniform magnetic nanoparticle arrays in ordered alumite
NASA Astrophysics Data System (ADS)
Sun, Ming; Zangari, Giovanni; Shamsuzzoha, Mohammad; Metzger, Robert M.
2001-05-01
We report the fabrication of nanometer scale ordered arrays of magnetic cylindrical nanoparticles with low aspect ratio (height/radius a=0.2-7) and ultrahigh uniformity. Anodization and electrochemical deposition are employed for template synthesis and metal particle growth, respectively. Particle uniformity is achieved by an electrodeposition scheme, utilizing pulse reverse voltage wave forms to control nucleation and growth of the particles. The resulting nanoparticles are polycrystalline and grains are randomly oriented. The magnetic properties of the array are dominated by particle shape and by interparticle magnetostatic interactions. A very clear transition of the anisotropy from perpendicular to in plane is observed at an aspect ratio a of about two. The arrays exhibit good thermal stability, demonstrating a great potential of these structures as future recording media in a patterned scheme. The pulse reverse electrodeposition technique shows great promise for the synthesis of nanostructures of various nature.
Physician orders contribute to high-tech imaging slowdown.
Levin, David C; Rao, Vijay M; Parker, Laurence
2010-01-01
The utilization rate of advanced diagnostic imaging (magnetic resonance imaging, computed tomography, and nuclear medicine) in Medicare outpatients rose 72.7 percent between 2000 and 2005, sparking concern among policymakers. However, analysis of discretionary use of these exams indicates that their use largely stabilized after 2005. Some have credited the Deficit Reduction Act of 2005, which sharply reduced reimbursements for advanced imaging done in physicians' offices. But the fact that the leveling was more pronounced in hospital outpatient facilities than in physicians' offices indicates that the explanation lies elsewhere. More likely, there has been a change in physicians' ordering patterns, possibly due to the influence of radiology business management companies (RBMs) and imaging guidelines promulgated by specialty societies. PMID:20048376
Induced Goldstone mode in a highly ordered ferroelectric phase
NASA Astrophysics Data System (ADS)
Wrobel, S.; Fafara, A.; Haase, Wolfgang; Kilian, D.; Nguyen, H. T.; Saxena, K.
1998-02-01
Dielectric, electrooptic and pyroelectric properties of unknown SmX* phase of (S)-(1-propyl-oxycarbonyl) ethyl 4(dodecyloxythiobenzyloxy) benzoate are studied. Low frequency dielectric studies performed with a 10micrometers EHC cell show that this SmX* phase exhibits an induced Goldstone mode dielectric spectrum. The spectrum is a single Debye-Type process with the relaxation time of the order of 10-5 s. The intensity of the spectrum increases non- linearly with the bias field strength. Studies of pyroelectric coefficient in the vicinity SmA*-SmX* transition show, that the SmX* phase is not a typical ferroelectric or antiferroelectric phase, and that the character of the transition depends on the field strength applied.
High level waste facilities -- Continuing operation or orderly shutdown
Decker, L.A.
1998-04-01
Two options for Environmental Impact Statement No action alternatives describe operation of the radioactive liquid waste facilities at the Idaho Chemical Processing Plant at the Idaho National Engineering and Environmental Laboratory. The first alternative describes continued operation of all facilities as planned and budgeted through 2020. Institutional control for 100 years would follow shutdown of operational facilities. Alternatively, the facilities would be shut down in an orderly fashion without completing planned activities. The facilities and associated operations are described. Remaining sodium bearing liquid waste will be converted to solid calcine in the New Waste Calcining Facility (NWCF) or will be left in the waste tanks. The calcine solids will be stored in the existing Calcine Solids Storage Facilities (CSSF). Regulatory and cost impacts are discussed.
Highly swelling hydrogels from ordered galactose-based polyacrylates.
Martin, B D; Linhardt, R J; Dordick, J S
1998-01-01
High swelling galactose-based hydrogels have been prepared using a chemoenzymatic procedure. Regioselective acylation of beta-O-methyl-galactopyranoside in nearly anhydrous pyridine with lipase from Pseudomonas cepacia yields the 6-acryloyl derivative (Compound I). Further lipase-catalysed acylation of the monoacrylate derivative in nearly anhydrous acetone yielded 2,6-diacryloyl-beta-O-methyl galactopyranoside (Compound II) that can act as a cross-linker with a structure similar to that of the sugar-based monomer. The high selectivity of enzyme catalysis yielded apparently highly regular hydrogel networks with swelling ratios at equilibrium ranging from 170 to 1100. elastic moduli ranging from 0.005 to 0.088 MPa and calculated mesh sizes ranging from 1160 to 6600 A. These values are far higher than conventional uncharged or lightly charged hydrogels at similar elastic moduli. Gel swelling was fast, with 75% of the equilibrium swelling value reached in a fractional time of 0.17. Non-selective chemical acryloylation of beta-O-methyl galactopyranoside followed by polymerization yielded a far lower-swelling hydrogel than that obtained using selective enzyme catalysis. These results indicate that the highly regular polymer structure achieved by regioselective enzyme-catalysed acylation yields relatively strong and highly swellable materials. Sugar-based hydrogels, such as those described herein, may find particular use as biomaterials because of their high water content, homogeneity, stability and expected non-toxicity. A wide range of pore sizes can be attained, suggesting that they may also be especially useful as matrices for enzyme immobilization and controlled delivery of biological macromolecules. PMID:9678852
High order mode damping in a pill box cavity
Voelker, F.; Lambertson, G.; Rimmer, R.
1991-04-01
We have substantially damped the higher order modes (HOM's) in a pill box cavity with attached beam pipe, while reducing the Q of the principal mode by less that 10%. This was accomplished by cutting slots in the cavity end wall at a radius at which the magnetic field of the lowest frequency HOM's is large. The slots couple energy from the cavity into waveguides which are below cut off for the principal mode, but which propagate energy at the HOM frequencies. Three slots 120 degrees apart couple HOM energy to three waveguides. We are concerned primarily with accelerating and deflecting modes: i.e. the TM{sub mnp} modes of order m=0 and m=1. For the strongest damping, only three m=0 and m=1 modes were detectable. These were the principal TM{sub 010} mode, the TM{sub 011} longitudinal mode, and the TM{sub 110} deflecting mode. In addition the HOM Q's and the reduction of Q for the principal mode were determined by computer calculation. The principal mode Q for an actual rf cavity could not be measured because the bolted joints used in the construction of the cavity were not sufficiently good to support Q's above 6000. The measured Q of the first longitudinal mode was 31 and of the first transverse mode 37. Our maximum damping was limited by how well we could terminated the waveguides, and indeed, the computer calculations for the TM{sub 011} and TM{sub 110} modes give values in the range we measured. 2 refs., 2 figs.
UNCERTAINTY AND SENSITIVITY ANALYSES FOR VERY HIGH ORDER MODELS
While there may in many cases be high potential for exposure of humans and ecosystems to chemicals released from a source, the degree to which this potential is realized is often uncertain. Conceptually, uncertainties are divided among parameters, model, and modeler during simula...
Stability of gyrotron operation in very high-order modes
Sinitsyn, O. V.; Nusinovich, G. S.; Antonsen, T. M. Jr.
2012-06-15
This study was motivated by the desire to increase the power, which can be delivered by gyrotrons in long pulse and continuous regimes. Since the admissible power level is determined by the density of ohmic losses in resonator walls, to increase the radiated power a gyrotron should operate in higher order modes. Using an existing gyrotron developed for plasma experiments in the International Thermonuclear Experimental Reactor as a base model, the stability of operation of such a gyrotron in modes with larger number of radial variations was studied. It is shown that the power level achievable in such gyrotrons in stable single mode regimes is close to 1.5 MW. The power level 1.7-1.8 MW can be realized in regimes where the oscillations of the desired mode are accompanied by excitation of distant sidebands whose power is about 1% level of the power of the operating mode. Finally, in the case of operation at the 2-MW level, either the desired mode loses its stability and is replaced by less efficient oscillations of a mode with a smaller azimuthal index or oscillations of the operating mode are accompanied by excitation of sidebands with equally spaced frequencies.
NASA Astrophysics Data System (ADS)
Ersoy, Mehmet; Lakkis, Omar; Townsend, Philip
2016-04-01
The flow of water in rivers and oceans can, under general assumptions, be efficiently modelled using Saint-Venant's shallow water system of equations (SWE). SWE is a hyperbolic system of conservation laws (HSCL) which can be derived from a starting point of incompressible Navier-Stokes. A common difficulty in the numerical simulation of HSCLs is the conservation of physical entropy. Work by Audusse, Bristeau, Perthame (2000) and Perthame, Simeoni (2001), proposed numerical SWE solvers known as kinetic schemes (KSs), which can be shown to have desirable entropy-consistent properties, and are thus called well-balanced schemes. A KS is derived from kinetic equations that can be integrated into the SWE. In flood risk assessment models the SWE must be coupled with other equations describing interacting meteorological and hydrogeological phenomena such as rain and groundwater flows. The SWE must therefore be appropriately modified to accommodate source and sink terms, so kinetic schemes are no longer valid. While modifications of SWE in this direction have been recently proposed, e.g., Delestre (2010), we depart from the extant literature by proposing a novel model that is "entropy-consistent" and naturally extends the SWE by respecting its kinetic formulation connections. This allows us to derive a system of partial differential equations modelling flow of a one-dimensional river with both a precipitation term and a groundwater flow model to account for potential infiltration and recharge. We exhibit numerical simulations of the corresponding kinetic schemes. These simulations can be applied to both real world flood prediction and the tackling of wider issues on how climate and societal change are affecting flood risk.
High-intensity attosecond high-order harmonic generation driven by a synthesized laser field
Zeng Zhinan; Li Ruxin; Xie Xinhua; Xu Zhizhan
2004-11-01
The scheme of high-intensity attosecond high-order harmonic generation driven by a synthesized laser field is proposed. The synthesized laser field is obtained by an appropriate superposition of a few-cycle laser pulse and a relatively long pulse of several tens of femtoseconds. Calculated results show that the intensity of the attosecond high-order harmonic pulse in helium driven by the synthesized laser field with a 8.8x10{sup 13} W/cm{sup 2}/5 fs laser pulse and a 3.51x10{sup 14} W/cm{sup 2}/50 fs laser pulse is several orders of magnitude higher than that driven by a single 8.8x10{sup 13} W/cm{sup 2}/5 fs laser pulse, and it is even stronger than that driven by a single 7.9x10{sup 14} W/cm{sup 2}/5 fs laser pulse, although the single and the synthesized pulses have the same peak electric-field strength.
Harmonic gyrotrons operating in high-order symmetric modes
Nusinovich, Gregory S.; Kashyn, Dmytro G.; Antonsen, T. M.
2015-01-05
It is shown that gyrotrons operating at cyclotron harmonics can be designed for operation in symmetric TE{sub 0,p}-modes. Such operation in fundamental harmonic gyrotrons is possible only at small radial indices (p≤3) because of the severe mode competition with TE{sub 2,p}-modes, which are equally coupled to annular beams as the symmetric modes. At cyclotron harmonics, however, this “degeneracy” of coupling is absent, and there is a region in the parameter space where harmonic gyrotrons can steadily operate in symmetric modes. This fact is especially important for sub-THz and THz-range gyrotrons where ohmic losses limit the power achievable in continuous-wave and high duty cycle regimes.
Highly ordered thin films prepared with octabutoxy copper phthalocyanine complexes.
Stevenson, Kelly; Miyashita, Naoko; Smieja, Joanne; Mazur, Ursula
2003-01-01
Langmuir-Blodgett (LB) films of copper (II) 1,4,8,11,15,18,22,25-octabutoxyphthalocyanine, nCuPc(OBu)(8), (non-peripheral substitution) and copper (II) 2,3,9,10,16,17,23,24-octabutoxyphthalocyanine, pCuPc(OBu)(8), (peripheral substitution), were fabricated and characterized by optical spectroscopy and scanning probe microscopy. The LB films were transferred onto hydrophilic substrates by vertical dipping. Although they posses relatively short polar substituents both compounds form smooth, uniform, dense, and highly stable LB monolayers composed of linear arrays of cofacial oligomers. The long range discotic assemblies of LB and spun cast films of pCuPc(OBu)(8) and nCuPc(OBu)(8) posses physical and chemical properties favorable for molecular electronic device application. PMID:12801680
NASA Technical Reports Server (NTRS)
Mukhopadhyay, V.; Newsom, J. R.; Abel, I.
1981-01-01
A method of synthesizing reduced-order optimal feedback control laws for a high-order system is developed. A nonlinear programming algorithm is employed to search for the control law design variables that minimize a performance index defined by a weighted sum of mean-square steady-state responses and control inputs. An analogy with the linear quadractic Gaussian solution is utilized to select a set of design variables and their initial values. To improve the stability margins of the system, an input-noise adjustment procedure is used in the design algorithm. The method is applied to the synthesis of an active flutter-suppression control law for a wind tunnel model of an aeroelastic wing. The reduced-order controller is compared with the corresponding full-order controller and found to provide nearly optimal performance. The performance of the present method appeared to be superior to that of two other control law order-reduction methods. It is concluded that by using the present algorithm, nearly optimal low-order control laws with good stability margins can be synthesized.
NASA Astrophysics Data System (ADS)
Sherer, Scott Eric
Various high-order and optimized interpolation procedures have been developed for use in a high-order overset grid computational fluid dynamics solver. Because of the high spatial order of accuracy of the solver, second-order accurate trilinear interpolation typically used in low-order overset grid flow solvers is insufficient to maintain overall order of accuracy, and thus high-order interpolation methods must be employed. Candidate interpolation methods, including a generalized Lagrangian method and a method based on the use of B-splines, were formulated. The coefficients for the generalized Lagrangian method may be found strictly from constraints on the formal order of accuracy of the method, in which case the method is non-optimized, or through constraints arising from the minimization of a one-dimensional integrated error, in which case the method is considered optimized. The interpolation methods were investigated using a one-dimensional Fourier error analysis, and their spectral behavior studied. They also were examined in multiple dimensions for the problem of grid-to-grid interpolation of various two- and three-dimensional analytical test functions. The high-order non-optimized explicit Lagrangian method was found to be the most robust and accurate of the interpolation methods considered. The fourth-order B-spline method was very competitive when the interpolation points were located in the middle of the stencil, but was shown to be weak when the interpolation points were located near the boundary of the stencil. The complete high-order overset grid method was validated for several fluid flow problems including flat-plate boundary-layer flow, an inviscid convecting vortex, and the unsteady flow past a circular cylinder at a low Reynolds number. Results indicate that second-order interpolation was insufficient to maintain a high-order rate of grid convergence, and that explicit high-order interpolation methods are superior to optimized, implicit or B
Moosavifard, Seyyed E; El-Kady, Maher F; Rahmanifar, Mohammad S; Kaner, Richard B; Mousavi, Mir F
2015-03-01
The increasing demand for energy has triggered tremendous research efforts for the development of lightweight and durable energy storage devices. Herein, we report a simple, yet effective, strategy for high-performance supercapacitors by building three-dimensional pseudocapacitive CuO frameworks with highly ordered and interconnected bimodal nanopores, nanosized walls (∼4 nm) and large specific surface area of 149 m(2) g(-1). This interesting electrode structure plays a key role in providing facilitated ion transport, short ion and electron diffusion pathways and more active sites for electrochemical reactions. This electrode demonstrates excellent electrochemical performance with a specific capacitance of 431 F g(-1) (1.51 F cm(-2)) at 3.5 mA cm(-2) and retains over 70% of this capacitance when operated at an ultrafast rate of 70 mA cm(-2). When this highly ordered CuO electrode is assembled in an asymmetric cell with an activated carbon electrode, the as-fabricated device demonstrates remarkable performance with an energy density of 19.7 W h kg(-1), power density of 7 kW kg(-1), and excellent cycle life. This work presents a new platform for high-performance asymmetric supercapacitors for the next generation of portable electronics and electric vehicles. PMID:25671715
High-Intensity High-order Harmonics Generated from Low-Density Plasma
Ozaki, T.; Bom, L. B. Elouga; Abdul-Hadi, J.; Ganeev, R. A.; Haessler, S.; Salieres, P.
2009-07-25
We study the generation of high-order harmonics from lowly ionized plasma, using the 10 TW, 10 Hz laser of the Advanced Laser Light Source (ALLS). We perform detailed studies on the enhancement of a single order of the high-order harmonic spectrum generated in plasma using the fundamental and second harmonic of the ALLS beam line. We observe quasi-monochromatic harmonics for various targets, including Mn, Cr, Sn, and In. We identify most of the ionic/neutral transitions responsible for the enhancement, which all have strong oscillator strengths. We demonstrate intensity enhancements of the 13th, 17th, 29th, and 33rd harmonics from these targets using the 800 nm pump laser and varying its chirp. We also characterized the attosecond nature of such plasma harmonics, measuring attosecond pulse trains with 360 as duration for chromium plasma, using the technique of 'Reconstruction of Attosecond Beating by Interference of Two-photon Transitions'(RABBIT). These results show that plasma harmonics are intense source of ultrashort coherent soft x-rays.
NASA Astrophysics Data System (ADS)
Rooms, F.; Camet, S.; Curis, J. F.
2010-02-01
A new technology of deformable mirror will be presented. Based on magnetic actuators, these deformable mirrors feature record strokes (more than +/- 45μm of astigmatism and focus correction) with an optimized temporal behavior. Furthermore, the development has been made in order to have a large density of actuators within a small clear aperture (typically 52 actuators within a diameter of 9.0mm). We will present the key benefits of this technology for vision science: simultaneous correction of low and high order aberrations, AO-SLO image without artifacts due to the membrane vibration, optimized control, etc. Using recent papers published by Doble, Thibos and Miller, we show the performances that can be achieved by various configurations using statistical approach. The typical distribution of wavefront aberrations (both the low order aberration (LOA) and high order aberration (HOA)) have been computed and the correction applied by the mirror. We compare two configurations of deformable mirrors (52 and 97 actuators) and highlight the influence of the number of actuators on the fitting error, the photon noise error and the effective bandwidth of correction.
Convergency analysis of the high-order mimetic finite difference method
Lipnikov, Konstantin; Veiga Da Beirao, L; Manzini, G
2008-01-01
We prove second-order convergence of the conservative variable and its flux in the high-order MFD method. The convergence results are proved for unstructured polyhedral meshes and full tensor diffusion coefficients. For the case of non-constant coefficients, we also develop a new family of high-order MFD methods. Theoretical result are confirmed through numerical experiments.
High Order Entropy-Constrained Residual VQ for Lossless Compression of Images
NASA Technical Reports Server (NTRS)
Kossentini, Faouzi; Smith, Mark J. T.; Scales, Allen
1995-01-01
High order entropy coding is a powerful technique for exploiting high order statistical dependencies. However, the exponentially high complexity associated with such a method often discourages its use. In this paper, an entropy-constrained residual vector quantization method is proposed for lossless compression of images. The method consists of first quantizing the input image using a high order entropy-constrained residual vector quantizer and then coding the residual image using a first order entropy coder. The distortion measure used in the entropy-constrained optimization is essentially the first order entropy of the residual image. Experimental results show very competitive performance.
NASA Astrophysics Data System (ADS)
Deng, Guo; Pan, Wei; Zou, Xihua
2010-09-01
Optical pulse compression using high-order dispersion compensation is proposed and theoretically analyzed. Firstly, the required dispersion profile for the high-order dispersion compensation is derived, according to the linear chirp and the nonlinear chirp of a phase-modulated continuous-wave (CW) laser source. With the use of the high-order dispersion compensation, such as the combination compensation of the second order dispersion (SOD) and the fourth order dispersion (FOD), an efficient pulse compression having a less time-bandwidth product and a greater peak power is realized. A sampled fiber Bragg grating (FBG) with both the SOD and the FOD is then designed using the equivalent chirp and the reconstruction algorithm. Finally, in the numerical simulation an optical pulse with a time-bandwidth product of 0.79 is generated via high-order dispersion compensation that is performed by using the sampled FBG.
High-order central ENO finite-volume scheme for ideal MHD
NASA Astrophysics Data System (ADS)
Susanto, A.; Ivan, L.; De Sterck, H.; Groth, C. P. T.
2013-10-01
A high-order accurate finite-volume scheme for the compressible ideal magnetohydrodynamics (MHD) equations is proposed. The high-order MHD scheme is based on a central essentially non-oscillatory (CENO) method combined with the generalized Lagrange multiplier divergence cleaning method for MHD. The CENO method uses k-exact multidimensional reconstruction together with a monotonicity procedure that switches from a high-order reconstruction to a limited low-order reconstruction in regions of discontinuous or under-resolved solution content. Both reconstructions are performed on central stencils, and the switching procedure is based on a smoothness indicator. The proposed high-order accurate MHD scheme can be used on general polygonal grids. A highly sophisticated parallel implementation of the scheme is described that is fourth-order accurate on two-dimensional dynamically-adaptive body-fitted structured grids. The hierarchical multi-block body-fitted grid permits grid lines to conform to curved boundaries. High-order accuracy is maintained at curved domain boundaries by employing high-order spline representations and constraints at the Gauss quadrature points for flux integration. Detailed numerical results demonstrate high-order convergence for smooth flows and robustness against oscillations for problems with shocks. A new MHD extension of the well-known Shu-Osher test problem is proposed to test the ability of the high-order MHD scheme to resolve small-scale flow features in the presence of shocks. The dynamic mesh adaptation capabilities of the approach are demonstrated using adaptive time-dependent simulations of the Orszag-Tang vortex problem with high-order accuracy and unprecedented effective resolution.
Zheng, Juan; Wang, Kun; Liang, Yeru; Zhu, Fang; Wu, Dingcai; Ouyang, Gangfeng
2016-05-21
Due to unique high-surface-area ordered mesoporous channels interconnected with 3D network-like mesopores and π-π interactions between carbon frameworks and analytes, the as-prepared ordered mesoporous carbon-coated fiber exhibited a large adsorption amount, fast mass transport and high sensitivity. PMID:27137527
Functional optical devices using highly ordered hole array architectures of anodic porous alumina
NASA Astrophysics Data System (ADS)
Masuda, Hideki; Kondo, Toshiaki; Nishio, Kazuyuki
2011-12-01
The fabrication of highly ordered anodic porous alumina and its application to the fabrication of several types of functional optical devices are described. Highly ordered hole array structures of anodic porous alumina, which were formed under appropriate anodizing conditions, were applied as a starting structure in several processes for the fabrication of ordered structures used for the functional optical devices. On the basis of these processes, twodimensional photonic crystals and localized surface plasmonic devices were prepared.
High-order harmonic generation in carbon-nanotube-containing plasma plumes
Ganeev, R. A.; Naik, P. A.; Singhal, H.; Chakera, J. A.; Kumar, M.; Joshi, M. P.; Srivastava, A. K.; Gupta, P. D.
2011-01-15
High-order harmonic generation (HHG) in carbon-nanotube (CNT)-containing plasma plumes has been demonstrated. Various targets were ablated to produce the plasma plumes containing nanotubes for the HHG in these media. Harmonics up to the 29th order were generated. Odd and even harmonics were generated using a two-color pump. The integrity of CNTs within the plasma plume, indicating nanotubes as the source of high-order harmonics, was confirmed by structural studies of plasma debris.
NASA Technical Reports Server (NTRS)
Balas, Mark J.
1989-01-01
Partially constructed/assembled structures in space are complicated enough but their dynamics will also be operating in closed-loop with feedback controllers. The dynamics of such structures are modeled by large-scale finite element models. The model dimension L is extremely large (approximately 10,000) while the numbers of actuators (M) and sensors (P) are small. The model parameters M(sub m) mass matrix, D(sub o) damping matrix, and K(sub o) stiffness matrix, are all symmetric and sparse (banded). Thus simulation of open-loop structure models of very large dimension can be accomplished by special integration techniques for sparse matrices. The problem of simulation of closed-loop control of such structures is complicated by the addition of controllers. Simulation of closed-loop controlled structures is an essential part of the controller design and evaluation process. Current research in the following areas is presented: high-order simulation of actively controlled aerospace structures; low-order controller design and SCI compensation for unmodeled dynamics; prediction of closed-loop stability using asymptotic eigenvalue series; and flexible robot manipulator control experiment.
NASA Astrophysics Data System (ADS)
Severt, T.; Troß, J.; Timilisina, P.; Kolliopoulos, G.; Buczek, S.; Trallero-Herrero, C.; Ben-Itzhak, I.
2016-05-01
In the past decade, there has been a drive to produce intense tabletop XUV laser sources to study ultrafast dynamics in atoms and molecules. One promising technique is high-order harmonic generation (HHG) driven by two-color laser fields, which has been shown to enhance the harmonic yield over harmonics generated by only the fundamental single-color field, depending on the wavelengths' relationship. In preliminary data, we observe more than two orders of magnitude enhancement of harmonics produced by the two-color (800/400-nm) laser field over the 800-nm field. We also explore the enhancement's dependence on the relative intensities between the two colors. This work and T.S. are partially supported by the National Science Foundation under Award No. IIA-1430493. JRML personnel and operations are funded by the Chemical Sciences, Geosciences, and Biosciences Division, Office of Basic Energy Sciences, Office for Science, U.S. Department of Energy. S.B. was also supported by NSF-REU program Grant No. PHYS-1461251.
Yu, P.Y.; Martinez, G.; Zeman, J.; Uchida, K.
2000-12-31
Photoluminescence upconversion (PLU) is a phenomenon in which a sample emits photons with energy higher than that of the excitation photon. This effect has been observed in many materials including rare earth ions doped in insulating hosts and semiconductor heterostructures without using high power lasers as the excitation source. Recently, this effect has been observed also in partially CuPt-ordered GaInP{sub 2} epilayers grown on GaAs substrates. As a spectroscopic technique photoluminescence upconversion is particularly well suited for studying band alignment at heterojunction interface. The value of band-offset has been determined with meV precision using magneto-photoluminescence. Using the fact that the pressure coefficient of electrons in GaAs is higher than those in GaInP{sub 2} they have been able to manipulate the band-offset at the GaInP/GaAs interface. By converting the band-offset from Type I to Type II they were able to demonstrate that the efficiency of the upconversion process is greatly enhanced by a Type II band-offset.
Ray, Jaideep; Lefantzi, Sophia; Najm, Habib N.; Kennedy, Christopher A.
2006-01-01
Block-structured adaptively refined meshes (SAMR) strive for efficient resolution of partial differential equations (PDEs) solved on large computational domains by clustering mesh points only where required by large gradients. Previous work has indicated that fourth-order convergence can be achieved on such meshes by using a suitable combination of high-order discretizations, interpolations, and filters and can deliver significant computational savings over conventional second-order methods at engineering error tolerances. In this paper, we explore the interactions between the errors introduced by discretizations, interpolations and filters. We develop general expressions for high-order discretizations, interpolations, and filters, in multiple dimensions, using a Fourier approach, facilitating the high-order SAMR implementation. We derive a formulation for the necessary interpolation order for given discretization and derivative orders. We also illustrate this order relationship empirically using one and two-dimensional model problems on refined meshes. We study the observed increase in accuracy with increasing interpolation order. We also examine the empirically observed order of convergence, as the effective resolution of the mesh is increased by successively adding levels of refinement, with different orders of discretization, interpolation, or filtering.
Extension of Efficient Low Dissipative High Order Schemes for 3-D Curvilinear Moving Grids
NASA Technical Reports Server (NTRS)
Vinokur, Marcel; Yee H. C.; Koga, Dennis (Technical Monitor)
2000-01-01
The efficient low dissipative high order schemes proposed by Yee et al. is formulated for 3-D curvilinear moving grids. These schemes consists of a high order base schemes combined with nonlinear characteristic filters. The amount of numerical dissipation is minimized by applying the schemes to the entropy splitting form of the inviscid flux derivatives. The analysis is given for a thermally perfect gas. The main difficulty in the extension of higher order schemes that were formulated in Cartesian coordinates to curvilinear moving grids is the higher order transformed metric evaluations. The higher order numerical evaluation of the transformed metric terms to insure freestream preservation is done in a coordinate invariant manner. The formulation is an improvement over existing formulation of high order scheme in curvilinear moving grids.
Technical Training on High-Order Spectral Analysis and Thermal Anemometry Applications
NASA Technical Reports Server (NTRS)
Maslov, A. A.; Shiplyuk, A. N.; Sidirenko, A. A.; Bountin, D. A.
2003-01-01
The topics of thermal anemometry and high-order spectral analyses were the subject of the technical training. Specifically, the objective of the technical training was to study: (i) the recently introduced constant voltage anemometer (CVA) for high-speed boundary layer; and (ii) newly developed high-order spectral analysis techniques (HOSA). Both CVA and HOSA are relevant tools for studies of boundary layer transition and stability.
High-order spoof localized surface plasmons supported on a complementary metallic spiral structure
NASA Astrophysics Data System (ADS)
Gao, Zhen; Gao, Fei; Zhang, Baile
2016-04-01
We experimentally demonstrate that multiple high-order spoof localized surface plasmons (spoof-LSPs) modes can be supported on a complementary metallic spiral structure, which were absent in the previously reported spoof-LSPs modes. Through exact numerical simulations and near-field imaging experiments, we directly observe these high-order spoof-LSPs modes at microwave frequencies. We also show that these higher-order spoof-LSPs modes exhibit larger frequency shifts caused by the local environmental refractive index change than the previously reported low-order spoof-LSPs modes. Hence the complementary MSS may find potential applications as plasmonic sensor in the microwave and terahertz frequencies.
An adaptive high-order hybrid scheme for compressive, viscous flows with detailed chemistry
NASA Astrophysics Data System (ADS)
Ziegler, Jack L.; Deiterding, Ralf; Shepherd, Joseph E.; Pullin, D. I.
2011-08-01
A hybrid weighted essentially non-oscillatory (WENO)/centered-difference numerical method, with low numerical dissipation, high-order shock-capturing, and structured adaptive mesh refinement (SAMR), has been developed for the direct numerical simulation of the multicomponent, compressible, reactive Navier-Stokes equations. The method enables accurate resolution of diffusive processes within reaction zones. The approach combines time-split reactive source terms with a high-order, shock-capturing scheme specifically designed for diffusive flows. A description of the order-optimized, symmetric, finite difference, flux-based, hybrid WENO/centered-difference scheme is given, along with its implementation in a high-order SAMR framework. The implementation of new techniques for discontinuity flagging, scheme-switching, and high-order prolongation and restriction is described. In particular, the refined methodology does not require upwinded WENO at grid refinement interfaces for stability, allowing high-order prolongation and thereby eliminating a significant source of numerical diffusion within the overall code performance. A series of one-and two-dimensional test problems is used to verify the implementation, specifically the high-order accuracy of the diffusion terms. One-dimensional benchmarks include a viscous shock wave and a laminar flame. In two-space dimensions, a Lamb-Oseen vortex and an unstable diffusive detonation are considered, for which quantitative convergence is demonstrated. Further, a two-dimensional high-resolution simulation of a reactive Mach reflection phenomenon with diffusive multi-species mixing is presented.
High-order harmonic spectroscopy of the Cooper minimum in argon: Experimental and theoretical study
Higuet, J.; Ruf, H.; Constant, E.; Cormier, E.; Descamps, D.; Mevel, E.; Petit, S.; Pons, B.; Mairesse, Y.; Fabre, B.; Thire, N.; Cireasa, R.
2011-05-15
We study the Cooper minimum in high-order-harmonic generation from argon atoms by using long wavelength laser pulses. We find that the minimum in high-order-harmonic spectra is systematically shifted with respect to total photoionization cross section measurements. We use a semiclassical theoretical approach based on classical trajectory Monte Carlo and quantum electron scattering methods to model the experiment. Our study reveals that the shift between photoionization and high-order-harmonic emission is due to several effects: the directivity of the recombining electrons and emitted polarization, and the shape of the recolliding electron wave packet.
High Order Schemes in BATS-R-US: Is it OK to Simplify Them?
NASA Astrophysics Data System (ADS)
Tóth, G.; Chen, Y.; van der Holst, B.; Daldorff, L. K. S.
2014-09-01
We describe a number of high order schemes and their simplified variants that have been implemented into the University of Michigan global magnetohydrodynamics code BATS-R-US. We compare the various schemes with each other and the legacy 2nd order TVD scheme for various test problems and two space physics applications. We find that the simplified schemes are often quite competitive with the more complex and expensive full versions, despite the fact that the simplified versions are only high order accurate for linear systems of equations. We find that all the high order schemes require some fixes to ensure positivity in the space physics applications. On the other hand, they produce superior results as compared with the second order scheme and/or produce the same quality of solution at a much reduced computational cost.
Pencil lead plasma for generating multimicrojoule high-order harmonics with a broad spectrum
Pertot, Y.; Elouga Bom, L. B.; Ozaki, T.; Bhardwaj, V. R.
2011-03-07
Using the plasma harmonic method, we show the generation of efficient and intense high-order harmonics from plasma of pencil lead. We demonstrate multimicrojoule energy in each harmonic order for the 11th to the 17th order of a Ti:sapphire laser. By analyzing the target morphology and the plasma composition, we conclude that these intense harmonics are generated from nanoparticles of graphitic carbon.
High-Order Central WENO Schemes for 1D Hamilton-Jacobi Equations
NASA Technical Reports Server (NTRS)
Bryson, Steve; Levy, Doron; Biegel, Bryan A. (Technical Monitor)
2002-01-01
In this paper we derive fully-discrete Central WENO (CWENO) schemes for approximating solutions of one dimensional Hamilton-Jacobi (HJ) equations, which combine our previous works. We introduce third and fifth-order accurate schemes, which are the first central schemes for the HJ equations of order higher than two. The core ingredient is the derivation of our schemes is a high-order CWENO reconstructions in space.
Developing Student-Centered Learning Model to Improve High Order Mathematical Thinking Ability
ERIC Educational Resources Information Center
Saragih, Sahat; Napitupulu, Elvis
2015-01-01
The purpose of this research was to develop student-centered learning model aiming to improve high order mathematical thinking ability of junior high school students of based on curriculum 2013 in North Sumatera, Indonesia. The special purpose of this research was to analyze and to formulate the purpose of mathematics lesson in high order…
High order mode damping in the NSLS accelerating RF cavities by the use of damping antennae
NASA Astrophysics Data System (ADS)
Fewell, N.; Wen, Z.
High order modes were successfully damped in the existing NSLS accelerating cavities by the insertion of damping antennae. The location of the antennae was aided by cavity field plots using superfish and their lengths determined experimentally. A description of their construction is presented together with the results of their insertion upon higher order cavity modes and beam stability.
NASA Astrophysics Data System (ADS)
Hirata, So; Nooijen, Marcel; Bartlett, Rodney J.
2000-10-01
General-order equation-of-motion coupled-cluster methods for ionization potentials and electron affinities (IP-EOM-CC and EA-EOM-CC) are developed by employing a determinantal algorithm. With these, principal ionization potentials or electron affinities of diatomic molecules and the excitation energies of their ionized or electron-attached counterparts are computed across different approximations of the cluster operator and the ionization (electron-attachment) operator. IP-EOM-CC(2,2h-1p)=IP-EOM-CCSD and EA-EOM-CC(2,1h-2p)=EA-EOM-CCSD or EA-EOM-CC(2,2h-3p) prove to be well-balanced models for principal ionization potentials and electron affinities, whereas for the quantitative descriptions of non-Koopmans ionization or electron-attachment processes IP-EOM-CC(3,3h-2p)=IP-EOM-CCSDT and EA-EOM-CC(2,2h-3p) appear to be the minimal levels.
Stability and periodicity of high-order Lorenz–Stenflo equations
NASA Astrophysics Data System (ADS)
Park, Junho; Han, Beom-Soon; Lee, Hyunho; Jeon, Ye-Lim; Baik, Jong-Jin
2016-06-01
In this paper, we derive high-order Lorenz–Stenflo equations with 6 variables and investigate periodic behaviors as well as stability of the equations. The stability of the high-order Lorenz–Stenflo equations is investigated by the linear stability analysis for various parameters. A periodicity diagram is also computed and it shows that the high-order Lorenz–Stenflo equations exhibit very different behaviors from the original Lorenz–Stenflo equations for both periodic and chaotic solutions. For example, period 3 regime for large parameters and scattered periodic regime are newly observed, and chaotic regimes exist for smaller values of r but for larger values of s than the original equations. In contrast, similarities such as the enclosure of the chaotic regime by the periodic regime or complex periodic regimes inside the chaotic regime are also observed for both the original and high-order Lorenz–Stenflo equations.
ASYMPTOTICALLY OPTIMAL HIGH-ORDER ACCURATE ALGORITHMS FOR THE SOLUTION OF CERTAIN ELLIPTIC PDEs
Leonid Kunyansky, PhD
2008-11-26
The main goal of the project, "Asymptotically Optimal, High-Order Accurate Algorithms for the Solution of Certain Elliptic PDE's" (DE-FG02-03ER25577) was to develop fast, high-order algorithms for the solution of scattering problems and spectral problems of photonic crystals theory. The results we obtained lie in three areas: (1) asymptotically fast, high-order algorithms for the solution of eigenvalue problems of photonics, (2) fast, high-order algorithms for the solution of acoustic and electromagnetic scattering problems in the inhomogeneous media, and (3) inversion formulas and fast algorithms for the inverse source problem for the acoustic wave equation, with applications to thermo- and opto- acoustic tomography.
NASA Astrophysics Data System (ADS)
Moiseev, N. Ya.
2011-04-01
An approach to the construction of high-order accurate monotone difference schemes for solving gasdynamic problems by Godunov's method with antidiffusion is proposed. Godunov's theorem on monotone schemes is used to construct a new antidiffusion flux limiter in high-order accurate difference schemes as applied to linear advection equations with constant coefficients. The efficiency of the approach is demonstrated by solving linear advection equations with constant coefficients and one-dimensional gasdynamic equations.
High-Energy Amplitudes in the Next-to-Leading Order
Ian Balitsky
2011-03-01
High-energy scattering in the saturation region is described by the evolution of color dipoles. In the leading order this evolution is governed by the non-linear BK equation. To see if this equation is relevant for existing or future accelerators (like EIC or LHeC) one needs to know how big are the next-to-leading order (NLO) corrections. I review the calculation of the NLO corrections to high-energy amplitudes in QCD.
A High-Order Finite Spectral Volume Method for Conservation Laws on Unstructured Grids
NASA Technical Reports Server (NTRS)
Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)
2001-01-01
A time accurate, high-order, conservative, yet efficient method named Finite Spectral Volume (FSV) is developed for conservation laws on unstructured grids. The concept of a 'spectral volume' is introduced to achieve high-order accuracy in an efficient manner similar to spectral element and multi-domain spectral methods. In addition, each spectral volume is further sub-divided into control volumes (CVs), and cell-averaged data from these control volumes is used to reconstruct a high-order approximation in the spectral volume. Riemann solvers are used to compute the fluxes at spectral volume boundaries. Then cell-averaged state variables in the control volumes are updated independently. Furthermore, TVD (Total Variation Diminishing) and TVB (Total Variation Bounded) limiters are introduced in the FSV method to remove/reduce spurious oscillations near discontinuities. A very desirable feature of the FSV method is that the reconstruction is carried out only once, and analytically, and is the same for all cells of the same type, and that the reconstruction stencil is always non-singular, in contrast to the memory and CPU-intensive reconstruction in a high-order finite volume (FV) method. Discussions are made concerning why the FSV method is significantly more efficient than high-order finite volume and the Discontinuous Galerkin (DG) methods. Fundamental properties of the FSV method are studied and high-order accuracy is demonstrated for several model problems with and without discontinuities.
Amplification of high-order rainbows of a cylinder with an elliptical cross section.
Lock, J A; Adler, C L; Stone, B R; Zajak, P D
1998-03-20
The intensity of high-order rainbows for normally incident light and certain rotation angles of a cylinder with an elliptical cross section is greatly amplified with respect to the intensity for a circular cross-sectional cylinder. The amplification is due to a number of the internal reflections occurring past the critical angle for total internal reflection, and the effect is especially strong for odd-order rainbows, beginning with the third order. Experimentally, the fourth- and the fifth-order rainbows of a nearly elliptical cross-sectional glass rod were observed and analyzed. PMID:18268744
A high-order gas-kinetic Navier-Stokes flow solver
Li Qibing; Xu Kun; Fu Song
2010-09-20
The foundation for the development of modern compressible flow solver is based on the Riemann solution of the inviscid Euler equations. The high-order schemes are basically related to high-order spatial interpolation or reconstruction. In order to overcome the low-order wave interaction mechanism due to the Riemann solution, the temporal accuracy of the scheme can be improved through the Runge-Kutta method, where the dynamic deficiencies in the first-order Riemann solution is alleviated through the sub-step spatial reconstruction in the Runge-Kutta process. The close coupling between the spatial and temporal evolution in the original nonlinear governing equations seems weakened due to its spatial and temporal decoupling. Many recently developed high-order methods require a Navier-Stokes flux function under piece-wise discontinuous high-order initial reconstruction. However, the piece-wise discontinuous initial data and the hyperbolic-parabolic nature of the Navier-Stokes equations seem inconsistent mathematically, such as the divergence of the viscous and heat conducting terms due to initial discontinuity. In this paper, based on the Boltzmann equation, we are going to present a time-dependent flux function from a high-order discontinuous reconstruction. The theoretical basis for such an approach is due to the fact that the Boltzmann equation has no specific requirement on the smoothness of the initial data and the kinetic equation has the mechanism to construct a dissipative wave structure starting from an initially discontinuous flow condition on a time scale being larger than the particle collision time. The current high-order flux evaluation method is an extension of the second-order gas-kinetic BGK scheme for the Navier-Stokes equations (BGK-NS). The novelty for the easy extension from a second-order to a higher order is due to the simple particle transport and collision mechanism on the microscopic level. This paper will present a hierarchy to construct such
High-aspect-ratio and highly ordered 15-nm porous alumina templates.
Martín, Jaime; Manzano, Cristina V; Caballero-Calero, Olga; Martín-González, Marisol
2013-01-01
Ordered anodic aluminum oxide (AAO) templates with pores <15 nm in diameter and an aspect ratio (length-to-diameter ratio) above 3 × 10(3) have been fabricated using a nonlithographic approach; specifically, by anodizing aluminum in an ethylene-glycol-containing sulfuric acid electrolyte. The pores are the smallest in diameter reported for a self-ordered AAO without pore aspect-ratio limitations and good ordering, which opens up the possibility of obtaining nanowire arrays in the quantum confinement regime that is of interest for efficient thermoelectric generators. The effect of the ethylene glycol addition on both the pore diameter and the ordering is evaluated and discussed. Moreover, 15-nm-diameter Bi(2)Te(3) and poly(3-hexyl thiophene) (P3HT) nanowires have been prepared using these AAO templates. As known, Bi(2)Te(3) is currently the most efficient thermoelectric bulk material for room-temperature operations and, according with theory, its Seebeck coefficient should be increased when it is confined to nanowires with diameters close to 10 nm. On the other hand, P3HT is one of the main candidates for integrating organic photovoltaic and thermoelectric devices, and its properties are also proposed to increase when it is confined to nanoscale structures, mainly due to molecular orientation effects. PMID:23215033
Robust high-order space-time conservative schemes for solving conservation laws on hybrid meshes
NASA Astrophysics Data System (ADS)
Shen, Hua; Wen, Chih-Yung; Liu, Kaixin; Zhang, Deliang
2015-01-01
In this paper, the second-order space-time conservation element and solution element (CE/SE) method proposed by Chang (1995) [3] is implemented on hybrid meshes for solving conservation laws. In addition, the present scheme has been extended to high-order versions including third and fourth order. Most methodologies of proposed schemes are consistent with that of the original CE/SE method, including: (i) a unified treatment of space and time (thereby ensuring good conservation in both space and time); (ii) a highly compact node stencil (the solution node is calculated using only the neighboring mesh nodes) regardless of the order of accuracy at the cost of storing all derivatives. A staggered time marching strategy is adopted and the solutions are updated alternatively between cell centers and vertexes. To construct explicit high-order schemes, second- and third-order derivatives are calculated by a modified finite-difference/weighted-average procedure which is different from that used to calculate the first-order derivatives. The present schemes can be implemented on a wide variety of meshes, including triangular, quadrilateral and hybrid (consisting of both triangular and quadrilateral elements). Beyond that, it can be easily extended to arbitrary-order schemes and arbitrary shape of polygonal elements by using the present methodologies. A series of common benchmark examples are used to confirm the accuracy and robustness of the proposed schemes.
High-order rogue waves in vector nonlinear Schrödinger equations.
Ling, Liming; Guo, Boling; Zhao, Li-Chen
2014-04-01
We study the dynamics of high-order rogue waves (RWs) in two-component coupled nonlinear Schrödinger equations. We find that four fundamental rogue waves can emerge from second-order vector RWs in the coupled system, in contrast to the high-order ones in single-component systems. The distribution shape can be quadrilateral, triangle, and line structures by varying the proper initial excitations given by the exact analytical solutions. The distribution pattern for vector RWs is more abundant than that for scalar rogue waves. Possibilities to observe these new patterns for rogue waves are discussed for a nonlinear fiber. PMID:24827185
Concurrent constant modulus algorithm and multi-modulus algorithm scheme for high-order QAM signals
NASA Astrophysics Data System (ADS)
Rao, Wei
2011-10-01
In order to overcome the slow convergence rate and large steady-state mean square error of constant modulus algorithm (CMA), a concurrent constant modulus algorithm and multi-modulus algorithm scheme for high-order QAM signals is proposed, which makes full use of the character which is that the high-order QAM signals locate in the different modulus. This algorithm uses the CMA as the basal mode. And in the second mode it uses the multi-modulus algorithm. Furthermore, the two modes operate concurrently. The efficiency of the method is proved by computer simulations in underwater acoustic channels.
Wave-mixing with high-order harmonics in extreme ultraviolet region
Dao, Lap Van; Dinh, Khuong Ba; Le, Hoang Vu; Gaffney, Naylyn; Hannaford, Peter
2015-01-12
We report studies of the wave-mixing process in the extreme ultraviolet region with two near-infrared driving and controlling pulses with incommensurate frequencies (at 1400 nm and 800 nm). A non-collinear scheme for the two beams is used in order to spatially separate and to characterise the properties of the high-order wave-mixing field. We show that the extreme ultraviolet frequency mixing can be treated by perturbative, very high-order nonlinear optics; the modification of the wave-packet of the free electron needs to be considered in this process.
Forward-smooth high-order uniform Aharonov–Bohm asymptotics
NASA Astrophysics Data System (ADS)
Berry, M. V.
2016-07-01
The Aharonov–Bohm (AB) function, describing a plane wave scattered by a flux line, is expanded asymptotically in a Fresnel-integral based series whose terms are smooth in the forward direction and uniformly valid in angle and flux. Successive approximations are valid for large distance r from the flux (or short wavelength) but are accurate even within one wavelength of it. Coefficients of all the terms are exhibited explicitly for the forward direction, enabling the high-order asymptotics to be understood in detail. The series is factorally divergent, with optimal truncation error exponentially small in r. Systematic resummation gives further exponential improvement. Terms of the series satisfy a resurgence relation: the high orders are related to the low orders. Discontinuities in the backward direction get smaller order by order, with systematic cancellation by successive terms. The relation to an earlier scheme based on the Cornu spiral is discussed.
Manipulating the wavefront of light by plasmonic metasurfaces operating in high order modes.
Li, Zhiwei; Hao, Jiaming; Huang, Lirong; Li, Hu; Xu, Hao; Sun, Yan; Dai, Ning
2016-04-18
In this work, plasmonic metasurfaces with abrupt phase discontinuities operating in high order modes are investigated for manipulating the wavefront of light. We first design two types of meta-super-cells consisting of V-shaped antennas with the phase shift coverage larger than 2π. And then, we create two linear gradient phased metasurfaces using the designed cells, which exhibit exceptional abilities for light-steering functioned as meta-echelette gratings operating in high order diffraction modes, may be valuable for using in high resolution spectrographs and advantage to achieve high numerical aperture plasmonic lenses. Based on the new designed super cells we further build another two azimuthal gradient phased metasurfaces that are able to generate high order optical vortex beams. Our results could lead to wide applications in photonic research. PMID:27137313
Sjogreen, B; Yee, H C
2007-12-12
Flows containing steady or nearly steady strong shocks in parts of the flow field, and unsteady turbulence with shocklets on other parts of the flow field are difficult to capture accurately and efficiently employing the same numerical scheme even under the multiblock grid or adaptive grid refinement framework. On one hand, sixth-order or higher shock-capturing methods are appropriate for unsteady turbulence with shocklets. On the other hand, lower order shock-capturing methods are more effective for strong steady shocks in terms of convergence. In order to minimize the shortcomings of low order and high order shock-capturing schemes for the subject flows, a multi-block overlapping grid with different orders of accuracy on different blocks is proposed. Test cases to illustrate the performance of the new solver are included.
Generation of high-order optical vortices using directly machined spiral phase mirrors.
Campbell, Geoff; Hage, Boris; Buchler, Ben; Lam, Ping Koy
2012-03-01
We report on the generation of high-order optical vortices by spiral phase mirrors (SPMs). The mirrors are produced by direct machining with a diamond tool and are shown to produce high-quality optical vortices with topological charges ranging from 1 to upwards of 100 at a wavelength of 532 nm. The direct machining technique is flexible and offers the promise of high-precision, large-diameter SPMs that are compatible with high optical powers. PMID:22410888
Multipass relativistic high-order-harmonic generation for intense attosecond pulses
NASA Astrophysics Data System (ADS)
Edwards, Matthew R.; Mikhailova, Julia M.
2016-02-01
We demonstrate that the total reflected field produced by the interaction of a moderately relativistic laser with dense plasma is itself an efficient driver of high-order-harmonic generation. A system of two or more successive interactions of an incident laser beam on solid targets may therefore be an experimentally realizable method of optimizing conversion of laser energy to high-order harmonics. Particle-in-cell simulations suggest that attosecond pulse intensity may be increased by up to four orders of magnitude in a multipass system, with decreased duration of the attosecond pulse train. We discuss high-order-harmonic wave-form engineering for enhanced attosecond pulse generation with an electron trajectory model, present the behavior of multipass systems over a range of parameters, and offer possible routes towards experimental implementation of a two-pass system.
NASA Astrophysics Data System (ADS)
Evans, W. A. B.; Torre, A.
2012-11-01
The paper focusses on the advantages of using high-order Gauss-Legendre quadratures for the precise evaluation of integrals with both smooth and rapidly changing integrands. Aspects of their precision are analysed in the light of Gauss' error formula. Some "test examples" are considered and evaluated in multiple precision to ≈ 200 significant decimal digits with David Bailey's multiprecision package to eliminate truncation/rounding errors. The increase of precision on doubling the number of subintervals is analysed, the relevant quadrature attribute being the precision increment. In order to exemplify the advantages that high-order quadrature afford, the technique is then used to evaluate several plots of the Rayleigh-Sommerfeld diffraction integral for axi-symmetric source fields defined on a planar aperture. A comparison of the high-order quadrature method against various FFT-based methods is finally given.
NASA Technical Reports Server (NTRS)
Weinan, E.; Shu, Chi-Wang
1992-01-01
High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth order central differences through Fast Fourier Transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large-scale features, such as the total circulation around the roll-up region, are adequately resolved.
Compact high order schemes with gradient-direction derivatives for absorbing boundary conditions
NASA Astrophysics Data System (ADS)
Gordon, Dan; Gordon, Rachel; Turkel, Eli
2015-09-01
We consider several compact high order absorbing boundary conditions (ABCs) for the Helmholtz equation in three dimensions. A technique called "the gradient method" (GM) for ABCs is also introduced and combined with the high order ABCs. GM is based on the principle of using directional derivatives in the direction of the wavefront propagation. The new ABCs are used together with the recently introduced compact sixth order finite difference scheme for variable wave numbers. Experiments on problems with known analytic solutions produced very accurate results, demonstrating the efficacy of the high order schemes, particularly when combined with GM. The new ABCs are then applied to the SEG/EAGE Salt model, showing the advantages of the new schemes.
High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes
NASA Technical Reports Server (NTRS)
Barth, Timothy (Editor); Deconinck, Herman (Editor)
1999-01-01
The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists
Efficient High Order Central Schemes for Multi-Dimensional Hamilton-Jacobi Equations: Talk Slides
NASA Technical Reports Server (NTRS)
Bryson, Steve; Levy, Doron; Biegel, Brian R. (Technical Monitor)
2002-01-01
This viewgraph presentation presents information on the attempt to produce high-order, efficient, central methods that scale well to high dimension. The central philosophy is that the equations should evolve to the point where the data is smooth. This is accomplished by a cyclic pattern of reconstruction, evolution, and re-projection. One dimensional and two dimensional representational methods are detailed, as well.
High-order resting-state functional connectivity network for MCI classification.
Chen, Xiaobo; Zhang, Han; Gao, Yue; Wee, Chong-Yaw; Li, Gang; Shen, Dinggang
2016-09-01
Brain functional connectivity (FC) network, estimated with resting-state functional magnetic resonance imaging (RS-fMRI) technique, has emerged as a promising approach for accurate diagnosis of neurodegenerative diseases. However, the conventional FC network is essentially low-order in the sense that only the correlations among brain regions (in terms of RS-fMRI time series) are taken into account. The features derived from this type of brain network may fail to serve as an effective disease biomarker. To overcome this drawback, we propose extraction of novel high-order FC correlations that characterize how the low-order correlations between different pairs of brain regions interact with each other. Specifically, for each brain region, a sliding window approach is first performed over the entire RS-fMRI time series to generate multiple short overlapping segments. For each segment, a low-order FC network is constructed, measuring the short-term correlation between brain regions. These low-order networks (obtained from all segments) describe the dynamics of short-term FC along the time, thus also forming the correlation time series for every pair of brain regions. To overcome the curse of dimensionality, we further group the correlation time series into a small number of different clusters according to their intrinsic common patterns. Then, the correlation between the respective mean correlation time series of different clusters is calculated to represent the high-order correlation among different pairs of brain regions. Finally, we design a pattern classifier, by combining features of both low-order and high-order FC networks. Experimental results verify the effectiveness of the high-order FC network on disease diagnosis. Hum Brain Mapp 37:3282-3296, 2016. © 2016 Wiley Periodicals, Inc. PMID:27144538
High-order harmonic generation at a repetition rate of 100 kHz
Lindner, F.; Stremme, W.; Schaetzel, M. G.; Grasbon, F.; Paulus, G. G.; Walther, H.; Hartmann, R.; Strueder, L.
2003-07-01
We report high-order harmonic generation (HHG) in rare gases using a femtosecond laser system with a very high repetition rate (100 kHz) and low pulse energy (7 {mu}J). To our knowledge, this is the highest repetition rate reported to date for HHG. The tight focusing geometry required to reach sufficiently high intensities implies low efficiency of the process. Harmonics up to the 45th order are nevertheless generated and detected. We show evidence of clear separation and selection of quantum trajectories by moving the gas jet with respect to the focus, in agreement with the theoretical predictions of the semiclassical model of HHG.
Room temperature NO2 sensor based on highly ordered porphyrin nanotubes.
Song, Feifei; Ma, Pan; Chen, Changlong; Jia, Jingna; Wang, Yucheng; Zhu, Peihua
2016-07-15
Highly ordered nanotubes of 5, 10, 15, 20-tetrakis(4-aminophenyl)porphyrin zinc (ZnTAP) are fabricated by using nanoporous anodized aluminum oxide (AAO) membrane as the template. Electronic absorption spectra, fluorescence spectra, transmission electron microscope (TEM), scanning electronic microscopy (SEM), low-angle X-ray diffraction (XRD) techniques are adopted to characterize these nanotubes. The highly ordered nanotubes of ZnTAP show good conductivity and present an efficient gas sensor platform for the ultrasensitive detection of NO2 under room temperature. The proposed sensor shows high sensitivity, reproducibility and fast response/recovery behavior, and provides a promising avenue for improving the sensing performance. PMID:27100904
Implementation of the high-order schemes QUICK and LECUSSO in the COMMIX-1C Program
Sakai, K.; Sun, J.G.; Sha, W.T.
1995-08-01
Multidimensional analysis computer programs based on the finite volume method, such as COMMIX-1C, have been commonly used to simulate thermal-hydraulic phenomena in engineering systems such as nuclear reactors. In COMMIX-1C, the first-order schemes with respect to both space and time are used. In many situations such as flow recirculations and stratifications with steep gradient of velocity and temperature fields, however, high-order difference schemes are necessary for an accurate prediction of the fields. For these reasons, two second-order finite difference numerical schemes, QUICK (Quadratic Upstream Interpolation for Convective Kinematics) and LECUSSO (Local Exact Consistent Upwind Scheme of Second Order), have been implemented in the COMMIX-1C computer code. The formulations were derived for general three-dimensional flows with nonuniform grid sizes. Numerical oscillation analyses for QUICK and LECUSSO were performed. To damp the unphysical oscillations which occur in calculations with high-order schemes at high mesh Reynolds numbers, a new FRAM (Filtering Remedy and Methodology) scheme was developed and implemented. To be consistent with the high-order schemes, the pressure equation and the boundary conditions for all the conservation equations were also modified to be of second order. The new capabilities in the code are listed. Test calculations were performed to validate the implementation of the high-order schemes. They include the test of the one-dimensional nonlinear Burgers equation, two-dimensional scalar transport in two impinging streams, von Karmann vortex shedding, shear driven cavity flow, Couette flow, and circular pipe flow. The calculated results were compared with available data; the agreement is good.
Adaptive Numerical Dissipative Control in High Order Schemes for Multi-D Non-Ideal MHD
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sjoegreen, B.
2004-01-01
The goal is to extend our adaptive numerical dissipation control in high order filter schemes and our new divergence-free methods for ideal MHD to non-ideal MHD that include viscosity and resistivity. The key idea consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free of numerical dissipation contamination. These scheme-independent detectors are capable of distinguishing shocks/shears, flame sheets, turbulent fluctuations and spurious high-frequency oscillations. The detection algorithm is based on an artificial compression method (ACM) (for shocks/shears), and redundant multi-resolution wavelets (WAV) (for the above types of flow feature). These filter approaches also provide a natural and efficient way for the minimization of Div(B) numerical error. The filter scheme consists of spatially sixth order or higher non-dissipative spatial difference operators as the base scheme for the inviscid flux derivatives. If necessary, a small amount of high order linear dissipation is used to remove spurious high frequency oscillations. For example, an eighth-order centered linear dissipation (AD8) might be included in conjunction with a spatially sixth-order base scheme. The inviscid difference operator is applied twice for the viscous flux derivatives. After the completion of a full time step of the base scheme step, the solution is adaptively filtered by the product of a 'flow detector' and the 'nonlinear dissipative portion' of a high-resolution shock-capturing scheme. In addition, the scheme independent wavelet flow detector can be used in conjunction with spatially compact, spectral or spectral element type of base schemes. The ACM and wavelet filter schemes using the dissipative portion of a second-order shock-capturing scheme with sixth-order spatial central base scheme for both the inviscid and viscous MHD flux
Reaching a consensus in networks of high-order integral agents under switching directed topologies
NASA Astrophysics Data System (ADS)
Cheng, Long; Wang, Hanlei; Hou, Zeng-Guang; Tan, Min
2016-06-01
Consensus problem of high-order integral multi-agent systems under switching directed topology is considered in this study. Depending on whether the agent's full state is available or not, two distributed protocols are proposed to ensure that states of all agents can be convergent to a same stationary value. In the proposed protocols, the gain vector associated with the agent's (estimated) state and the gain vector associated with the relative (estimated) states between agents are designed in a sophisticated way. By this particular design, the high-order integral multi-agent system can be transformed into a first-order integral multi-agent system. Also, the convergence of the transformed first-order integral agent's state indicates the convergence of the original high-order integral agent's state, if and only if all roots of the polynomial, whose coefficients are the entries of the gain vector associated with the relative (estimated) states between agents, are in the open left-half complex plane. Therefore, many analysis techniques in the first-order integral multi-agent system can be directly borrowed to solve the problems in the high-order integral multi-agent system. Due to this property, it is proved that to reach a consensus, the switching directed topology of multi-agent system is only required to be 'uniformly jointly quasi-strongly connected', which seems the mildest connectivity condition in the literature. In addition, the consensus problem of discrete-time high-order integral multi-agent systems is studied. The corresponding consensus protocol and performance analysis are presented. Finally, three simulation examples are provided to show the effectiveness of the proposed approach.
High Order Schemes in Bats-R-US for Faster and More Accurate Predictions
NASA Astrophysics Data System (ADS)
Chen, Y.; Toth, G.; Gombosi, T. I.
2014-12-01
BATS-R-US is a widely used global magnetohydrodynamics model that originally employed second order accurate TVD schemes combined with block based Adaptive Mesh Refinement (AMR) to achieve high resolution in the regions of interest. In the last years we have implemented fifth order accurate finite difference schemes CWENO5 and MP5 for uniform Cartesian grids. Now the high order schemes have been extended to generalized coordinates, including spherical grids and also to the non-uniform AMR grids including dynamic regridding. We present numerical tests that verify the preservation of free-stream solution and high-order accuracy as well as robust oscillation-free behavior near discontinuities. We apply the new high order accurate schemes to both heliospheric and magnetospheric simulations and show that it is robust and can achieve the same accuracy as the second order scheme with much less computational resources. This is especially important for space weather prediction that requires faster than real time code execution.
Optimization of thermal ghost imaging: high-order correlations vs. background subtraction.
Chan, Kam Wai C; O'Sullivan, Malcolm N; Boyd, Robert W
2010-03-15
We compare the performance of high-order thermal ghost imaging with that of conventional (that is, lowest-order) thermal ghost imaging for different data processing methods. Particular attention is given to high-order thermal ghost imaging with background normalization and conventional ghost imaging with background subtraction. The contrast-to-noise ratio (CNR) of the ghost image is used as the figure of merit for the comparison.We find analytically that the CNR of the normalized high-order ghost image is inversely proportional to the square root of the number of transmitting pixels of the object. This scaling law is independent of the exponents used in calculating the high-order correlation and is the same as that of conventional ghost imaging with background subtraction. We find that no data processing procedure performs better than lowest-order ghost imaging with background subtraction. Our results are found to be able to explain the observations of a recent experiment [Chen et al., arXiv:0902.3713v3 [quant-ph
Comparative Study of Three High Order Schemes for LES of Temporally Evolving Mixing Layers
NASA Technical Reports Server (NTRS)
Yee, Helen M. C.; Sjogreen, Biorn Axel; Hadjadj, C.
2012-01-01
Three high order shock-capturing schemes are compared for large eddy simulations (LES) of temporally evolving mixing layers (TML) for different convective Mach numbers (Mc) ranging from the quasi-incompressible regime to highly compressible supersonic regime. The considered high order schemes are fifth-order WENO (WENO5), seventh-order WENO (WENO7) and the associated eighth-order central spatial base scheme with the dissipative portion of WENO7 as a nonlinear post-processing filter step (WENO7fi). This high order nonlinear filter method (H.C. Yee and B. Sjogreen, Proceedings of ICOSAHOM09, June 22-26, 2009, Trondheim, Norway) is designed for accurate and efficient simulations of shock-free compressible turbulence, turbulence with shocklets and turbulence with strong shocks with minimum tuning of scheme parameters. The LES results by WENO7fi using the same scheme parameter agree well with experimental results of Barone et al. (2006), and published direct numerical simulations (DNS) work of Rogers & Moser (1994) and Pantano & Sarkar (2002), whereas results by WENO5 and WENO7 compare poorly with experimental data and DNS computations.
High order curvilinear finite elements for elastic–plastic Lagrangian dynamics
Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.
2014-01-15
This paper presents a high-order finite element method for calculating elastic–plastic flow on moving curvilinear meshes and is an extension of our general high-order curvilinear finite element approach for solving the Euler equations of gas dynamics in a Lagrangian frame [1,2]. In order to handle transition to plastic flow, we formulate the stress–strain relation in rate (or incremental) form and augment our semi-discrete equations for Lagrangian hydrodynamics with an additional evolution equation for the deviatoric stress which is valid for arbitrary order spatial discretizations of the kinematic and thermodynamic variables. The semi-discrete equation for the deviatoric stress rate is developed for 2D planar, 2D axisymmetric and full 3D geometries. For each case, the strain rate is approximated via a collocation method at zone quadrature points while the deviatoric stress is approximated using an L{sub 2} projection onto the thermodynamic basis. We apply high order, energy conserving, explicit time stepping methods to the semi-discrete equations to develop the fully discrete method. We conclude with numerical results from an extensive series of verification tests that demonstrate several practical advantages of using high-order finite elements for elastic–plastic flow.