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.
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.
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."
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.
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
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 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
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.
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.
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
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.
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.
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 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.
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.
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 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 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 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.
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 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
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
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 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
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
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 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
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 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
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.
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 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.
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.
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.
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.
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
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.
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.
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…
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 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.
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.
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.
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
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
A family of high-order targeted ENO schemes for compressible-fluid simulations
NASA Astrophysics Data System (ADS)
Fu, Lin; Hu, Xiangyu Y.; Adams, Nikolaus A.
2016-01-01
Although classical WENO schemes have achieved great success and are widely accepted, they exhibit several shortcomings. They are too dissipative for direct simulations of turbulence and lack robustness when very-high-order versions are applied to complex flows. In this paper, we propose a family of high-order targeted ENO schemes which are applicable for compressible-fluid simulations involving a wide range of flow scales. In order to increase the numerical robustness as compared to very-high-order classical WENO schemes, the reconstruction dynamically assembles a set of low-order candidate stencils with incrementally increasing width. While discontinuities and small-scale fluctuations are efficiently separated, the numerical dissipation is significantly diminished by an ENO-like stencil selection, which either applies a candidate stencil with its original linear weight, or removes its contribution when it is crossed by a discontinuity. The background linear scheme is optimized under the constraint of preserving an approximate dispersion-dissipation relation. By means of quasi-linear analyses and practical numerical experiments, a set of case-independent parameters is determined. The general formulation of arbitrarily high-order schemes is presented in a straightforward way. A variety of benchmark-test problems, including broadband waves, strong shock and contact discontinuities are studied. Compared to well-established classical WENO schemes, the present schemes exhibit significantly improved robustness, low numerical dissipation and sharp discontinuity capturing. They are particularly suitable for DNS and LES of shock-turbulence interactions.
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.
Rieben, R N
2004-07-20
The goal of this dissertation is twofold. The first part concerns the development of a numerical method for solving Maxwell's equations on unstructured hexahedral grids that employs both high order spatial and high order temporal discretizations. The second part involves the use of this method as a computational tool to perform high fidelity simulations of various electromagnetic devices such as optical transmission lines and photonic crystal structures to yield a level of accuracy that has previously been computationally cost prohibitive. This work is based on the initial research of Daniel White who developed a provably stable, charge and energy conserving method for solving Maxwell's equations in the time domain that is second order accurate in both space and time. The research presented here has involved the generalization of this procedure to higher order methods. High order methods are capable of yielding far more accurate numerical results for certain problems when compared to corresponding h-refined first order methods , and often times at a significant reduction in total computational cost. The first half of this dissertation presents the method as well as the necessary mathematics required for its derivation. The second half addresses the implementation of the method in a parallel computational environment, its validation using benchmark problems, and finally its use in large scale numerical simulations of electromagnetic transmission devices.
Stability Switches of Arbitrary High-Order Consensus in Multiagent Networks with Time Delays
2013-01-01
High-order consensus seeking, in which individual high-order dynamic agents share a consistent view of the objectives and the world in a distributed manner, finds its potential broad applications in the field of cooperative control. This paper presents stability switches analysis of arbitrary high-order consensus in multiagent networks with time delays. By employing a frequency domain method, we explicitly derive analytical equations that clarify a rigorous connection between the stability of general high-order consensus and the system parameters such as the network topology, communication time-delays, and feedback gains. Particularly, our results provide a general and a fairly precise notion of how increasing communication time-delay causes the stability switches of consensus. Furthermore, under communication constraints, the stability and robustness problems of consensus algorithms up to third order are discussed in details to illustrate our central results. Numerical examples and simulation results for fourth-order consensus are provided to demonstrate the effectiveness of our theoretical results. PMID:24109207
High-energy amplitudes in N = 4 SYM in the next-to-leading order
Chirilli, Giovanni; Balitsky, Ian
2010-03-16
In this study, the high-energy behavior of the N = 4 SYM amplitudes in the Regge limit can be calculated order by order in perturbation theory using the high-energy operator expansion in Wilson lines. At large $N_c$, a typical four-point amplitude is determined by a single BFKL pomeron. The conformal structure of the four-point amplitude is fixed in terms of two functions: pomeron intercept and the coefficient function in front of the pomeron (the product of two residues). The pomeron intercept is universal while the coefficient function depends on the correlator in question. The intercept is known in the first two orders in coupling constant: BFKL intercept and NLO BFKL intercept calculated in Ref. 1. As an example of using the Wilson-line OPE, we calculate the coefficient function in front of the pomeron for the correlator of four $Z^2$ currents in the first two orders in perturbation theory.
High Order Numerical Simulation of Sound Generated by the Kirchhoff Vortex
NASA Technical Reports Server (NTRS)
Mueller, Bernhard; Yee, H. C.
2001-01-01
An improved high order finite difference method for low Mach number computational aeroacoustics (CAA) is described. The improvements involve the conditioning of the Euler equations in perturbation form to minimize numerical cancellation error, and the use of a stable non-dissipative sixth-order central spatial differencing for the interior points and third-order at the boundary points. The spatial difference operator satisfies the summation-by-parts property to guarantee strict stability for linear hyperbolic systems. Spurious high frequency oscillations are damped by a third-order characteristic-based filter. The objective of this paper is to apply these improvements in the simulation of sound generated by the Kirchhoff vortex.
High-order spoof localized surface plasmons supported on a complementary metallic spiral structure.
Gao, Zhen; Gao, Fei; Zhang, Baile
2016-01-01
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. PMID:27079658
Design of high-order elliptic filter from a versatile mode generic OTA-C structure
NASA Astrophysics Data System (ADS)
Ghosh, K.; Ray, B. N.
2015-03-01
A new synthesis methodology for high-order versatile mode programmable Operational transconductance amplifier and capacitor (OTA-C) generic filter structure is proposed. The structure fulfills the three main criteria of high frequency operation i.e it uses (1) less number of components (2) only single ended input OTAs (3) only grounded capacitors. Any nth order transfer function can be realised from it. Elliptic filter is designed from the generic structure using optimisation technique to reduce the number of OTAs. SPICE simulation with BSIM level 53 model and 0.13 μm process confirms the theoretical analysis. Frequency response of third-order and fourth-order elliptic filter is shown as representative set of simulated result. Sensitivity and non-ideal effect of the designed filter are studied.
Design and performance analysis of high-order optical temporal differentiator with twin-core fiber
NASA Astrophysics Data System (ADS)
You, Haidong; Ning, Tigang; Li, Jing; Jian, Wei; Wen, Xiaodong; Pei, Li
2013-08-01
A simple and general approach for implementing all-fiber high-order optical temporal differentiator based on twin-core fiber (TCF) is presented and demonstrated. Specifically, the core 2 (or core 1) of the TCF should be cut in N sections with the same length for achieving N'th-order optical temporal differentiator, which can be considered to consist of N cascaded first-order optical temporal differentiators based on TCF. Our simulations show that the proposed approach can provide optical operation bandwidths in the several THz regime, which is capable of accurately processing time features as short as subpicoseconds. Performance analysis results show a good accuracy calculating the high-order time differentiation of the optical signal launched at core 2 (or core 1).
High-order spoof localized surface plasmons supported on a complementary metallic spiral structure
Gao, Zhen; Gao, Fei; Zhang, Baile
2016-01-01
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. PMID:27079658
BOTDA sensors enhanced using high-efficiency second-order distributed Brillouin amplification.
Jia, Xin-Hong; Chang, Han-Qing; Ao, Lei; Ji, Xiao-Ling; Xu, Cong; Zhang, Wei-Li
2016-06-27
A novel approach for long-distance sensing through Brillouin optical time-domain analysis (BOTDA) assisted by second-order distributed Brillouin amplification (DBA) was proposed and experimentally demonstrated. To the best of our knowledge, this is the first BOTDA study that used second-order DBA. Compared with BOTDA assisted by first-order DBA, the proposed approach enhanced the signal-to-noise ratio of the Brillouin trace by ~3 dB for a range featuring minimum sensing intensity. Long-distance sensing with ~5 m spatial resolution and ± 1.6°C measurement uncertainty over ~99 km fiber was successfully realized by employing high-efficiency pumping using ~6 dBm second-order and ~1.5 dBm first-order pumps. PMID:27410568
Facile route to high-density, ordered ZnO nanowire arrays and their photoluminescence properties
NASA Astrophysics Data System (ADS)
Chen, Wei; Tao, Xiaoming; Liu, Yuyang; Sun, Xiaohong; Hu, Zhigang; Fei, Bin
2006-10-01
A simple template-directed wet chemistry route based on traditional thermal decomposition technique has been developed for the preparation of high-density, ordered ZnO nanowire arrays. The fabrication was performed at relative low temperature without involving complex procedures, sophisticated equipment and rigorous experiment conditions, thereby providing a straightforward and mild method to produce metal/metal oxide ordered nanostructures. The nanowire array system was evaluated by SEM, XRD, TEM and PL. A stable luminescence at 425 nm was present.
Local Box-Counting to Determine Fractal Dimension of High-Order Chaos
NASA Astrophysics Data System (ADS)
Osaka, Motohisa; Ito, Nobuyasu
To determine the attractor dimension of chaotic dynamics, the box-counting method has the difficulty in getting accurate estimates because the boxes are not weighted by their relative probabilities. We present a new method to minimize this difficulty. The local box-counting method can be quite effective in determining the attractor dimension of high-order chaos as well as low-order chaos.
An Investigation of High-Order Shock-Capturing Methods for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Casper, Jay; Baysal, Oktay
1997-01-01
Topics covered include: Low-dispersion scheme for nonlinear acoustic waves in nonuniform flow; Computation of acoustic scattering by a low-dispersion scheme; Algorithmic extension of low-dispersion scheme and modeling effects for acoustic wave simulation; The accuracy of shock capturing in two spatial dimensions; Using high-order methods on lower-order geometries; and Computational considerations for the simulation of discontinuous flows.
High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids
NASA Technical Reports Server (NTRS)
Mazaheri, Alireza; Nishikawa, Hiroaki
2015-01-01
In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.
High-order diffraction gratings for high-power semiconductor lasers
Vasil'eva, V. V.; Vinokurov, D. A.; Zolotarev, V. V.; Leshko, A. Yu.; Petrunov, A. N.; Pikhtin, N. A.; Rastegaeva, M. G.; Sokolova, Z. N. Shashkin, I. S.; Tarasov, I. S.
2012-02-15
A deep diffraction grating with a large period ({approx}2 {mu}m) within one of the cladding layers is proposed for the implementation of selective feedback in a semiconductor laser. Frequency dependences of reflectance in the 12th diffraction order for rectangular, triangular, and trapezoidal diffraction gratings are calculated. It is shown that the maximum reflectance of the waveguide mode is attained using a rectangular or trapezoidal grating {approx}2 {mu}m deep in the laser structure. Deep trapezoidal diffraction gratings with large periods are fabricated in the Al{sub 0.3}Ga{sub 0.7}As cladding layer of a GaAs/AlGaAs laser structure using photolithography and reactive ion etching.
A High-Order Accurate Parallel Solver for Maxwell's Equations on Overlapping Grids
Henshaw, W D
2005-09-23
A scheme for the solution of the time dependent Maxwell's equations on composite overlapping grids is described. The method uses high-order accurate approximations in space and time for Maxwell's equations written as a second-order vector wave equation. High-order accurate symmetric difference approximations to the generalized Laplace operator are constructed for curvilinear component grids. The modified equation approach is used to develop high-order accurate approximations that only use three time levels and have the same time-stepping restriction as the second-order scheme. Discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed. The implementation is optimized for component grids that are Cartesian, resulting in a fast and efficient method. The solver runs on parallel machines with each component grid distributed across one or more processors. Numerical results in two- and three-dimensions are presented for the fourth-order accurate version of the method. These results demonstrate the accuracy and efficiency of the approach.
Estimate Low and High Order Wavefront Using P1640 Calibrator Measurements
NASA Technical Reports Server (NTRS)
Zhai, C.; Vasisht, G.; Shao, M.; Lockhart, T.; Cady, E.; Oppenheimer, B.; Burruss, R.; Roberts, J.; Beichman, C.; Brenner, D.; Crepp, J.; Dekany, R.; Hillenbrand, L.; Hinkley, S.; Parry, I.; Pueyo, L.; Rice, E.; Roberts, L. C. Jr.; Sivaramakrishnan, A.; Soummer, R.; Tang, H.; Vescelus, F.; Wallace, K.; Zimmerman, N.
2013-01-01
P1640 high contrast imaging system on the Palomar 200 inch Telescope consists of an apodized-pupil Lyot coronagraph, the PALM-3000 adaptive optics (P3K-AO), and P1640 Calibrator (CAL). Science images are recorded by an integral field spectrograph covering J-H bands for detecting and characterizing stellar companions. With aberrations from atmosphere corrected by the P3K-AO, instrument performance is limited mainly by the quasi-static speckles due to noncommon path wavefront aberrations for the light to propagate to the P3K-AO wavefront sensor and to the coronagraph mask. The non-common path wavefront aberrations are sensed by CAL, which measures the post-coronagraph E-field using interferometry, and can be effectively corrected by offsetting the P3K-AO deformable mirror target position accordingly. Previously, we have demonstrated using CAL measurements to correct high order wavefront aberrations, which is directly connected to the static speckles in the image plane. Low order wavefront, on the other hand, usually of larger amplitudes, causes light to leak through the coronagraph making the whole image plane brighter. Knowledge error in low order wavefront aberrations can also affect the estimation of the high order wavefront. Even though, CAL is designed to sense efficiently high order wavefront aberrations, the low order wavefront front can be inferred with less sensitivity. Here, we describe our method for estimating both low and high order wavefront aberrations using CAL measurements by propagating the post-coronagraph E-field to a pupil before the coronagraph. We present the results from applying this method to both simulated and experiment data.
Highly ordered three-dimensional macroporous carbon spheres for determination of heavy metal ions
Zhang, Yuxiao; Zhang, Jianming; Liu, Yang; Huang, Hui; Kang, Zhenhui
2012-04-15
Highlights: Black-Right-Pointing-Pointer Highly ordered three dimensional macroporous carbon spheres (MPCSs) were prepared. Black-Right-Pointing-Pointer MPCS was covalently modified by cysteine (MPCS-CO-Cys). Black-Right-Pointing-Pointer MPCS-CO-Cys was first time used in electrochemical detection of heavy metal ions. Black-Right-Pointing-Pointer Heavy metal ions such as Pb{sup 2+} and Cd{sup 2+} can be simultaneously determined. -- Abstract: An effective voltammetric method for detection of trace heavy metal ions using chemically modified highly ordered three dimensional macroporous carbon spheres electrode surfaces is described. The highly ordered three dimensional macroporous carbon spheres were prepared by carbonization of glucose in silica crystal bead template, followed by removal of the template. The highly ordered three dimensional macroporous carbon spheres were covalently modified by cysteine, an amino acid with high affinities towards some heavy metals. The materials were characterized by physical adsorption of nitrogen, scanning electron microscopy, and transmission electron microscopy techniques. While the Fourier-transform infrared spectroscopy was used to characterize the functional groups on the surface of carbon spheres. High sensitivity was exhibited when this material was used in electrochemical detection (square wave anodic stripping voltammetry) of heavy metal ions due to the porous structure. And the potential application for simultaneous detection of heavy metal ions was also investigated.
High order filtering methods for approximating hyberbolic systems of conservation laws
NASA Technical Reports Server (NTRS)
Lafon, F.; Osher, S.
1990-01-01
In the computation of discontinuous solutions of hyperbolic systems of conservation laws, the recently developed essentially non-oscillatory (ENO) schemes appear to be very useful. However, they are computationally costly compared to simple central difference methods. A filtering method which is developed uses simple central differencing of arbitrarily high order accuracy, except when a novel local test indicates the development of spurious oscillations. At these points, the full ENO apparatus is used, maintaining the high order of accuracy, but removing spurious oscillations. Numerical results indicate the success of the method. High order of accuracy was obtained in regions of smooth flow without spurious oscillations for a wide range of problems and a significant speed up of generally a factor of almost three over the full ENO method.
Madsen, C. B.; Abu-samha, M.; Madsen, L. B.
2010-04-15
We present a generic approach for treating the effect of nuclear motion in high-order harmonic generation from polyatomic molecules. Our procedure relies on a separation of nuclear and electron dynamics where we account for the electronic part using the Lewenstein model and nuclear motion enters as a nuclear correlation function. We express the nuclear correlation function in terms of Franck-Condon factors, which allows us to decompose nuclear motion into modes and identify the modes that are dominant in the high-order harmonic generation process. We show results for the isotopes CH{sub 4} and CD{sub 4} and thereby provide direct theoretical support for a recent experiment [S. Baker et al., Science 312, 424 (2006)] that uses high-order harmonic generation to probe the ultrafast structural nuclear rearrangement of ionized methane.
NASA Astrophysics Data System (ADS)
Madsen, C. B.; Abu-Samha, M.; Madsen, L. B.
2010-04-01
We present a generic approach for treating the effect of nuclear motion in high-order harmonic generation from polyatomic molecules. Our procedure relies on a separation of nuclear and electron dynamics where we account for the electronic part using the Lewenstein model and nuclear motion enters as a nuclear correlation function. We express the nuclear correlation function in terms of Franck-Condon factors, which allows us to decompose nuclear motion into modes and identify the modes that are dominant in the high-order harmonic generation process. We show results for the isotopes CH4 and CD4 and thereby provide direct theoretical support for a recent experiment [S. Baker , Science 312, 424 (2006)] that uses high-order harmonic generation to probe the ultrafast structural nuclear rearrangement of ionized methane.
Giant Faraday Rotation of High-Order Plasmonic Modes in Graphene-Covered Nanowires.
Kuzmin, Dmitry A; Bychkov, Igor V; Shavrov, Vladimir G; Temnov, Vasily V
2016-07-13
Plasmonic Faraday rotation in nanowires manifests itself in the rotation of the spatial intensity distribution of high-order surface plasmon polariton (SPP) modes around the nanowire axis. Here we predict theoretically the giant Faraday rotation for SPPs propagating on graphene-coated magneto-optically active nanowires. Upon the reversal of the external magnetic field pointing along the nanowire axis some high-order plasmonic modes may be rotated by up to ∼100° on the length scale of about 500 nm at mid-infrared frequencies. Tuning the carrier concentration in graphene by chemical doping or gate voltage allows for controlling SPP-properties and notably the rotation angle of high-order azimuthal modes. Our results open the door to novel plasmonic applications ranging from nanowire-based Faraday isolators to the magnetic control in quantum-optical applications. PMID:27348746
Efficient nonlinear generation of high power, higher order, ultrafast "perfect" vortices in green.
Apurv Chaitanya, N; Jabir, M V; Samanta, G K
2016-04-01
We report on efficient nonlinear generation of ultrafast, higher order "perfect" vortices at the green wavelength. Based on Fourier transformation of the higher order Bessel-Gauss (BG) beam generated through the combination of the spiral phase plate and axicon, we have transformed the Gaussian beam of the ultrafast Yb-fiber laser at 1060 nm into perfect vortices of power 4.4 W and order up to 6. Using single-pass second-harmonic generation (SHG) of such vortices in 5 mm long chirped MgO-doped, periodically poled congruent LiNbO_{3} crystal, we have generated perfect vortices at green wavelength (530 nm) with output power of 1.2 W and vortex order up to 12 at a single-pass conversion efficiency of 27%, independent of the orders. This is the highest single-pass SHG efficiency of any optical beams other than Gaussian beams. Unlike the disintegration of higher order vortices due to spatial walk-off effect in birefringent crystals, here, the use of the quasi-phase-matching process enables generation of high-quality vortices, even at higher orders. The green perfect vortices of all orders have temporal and spectral widths of 507 fs and 1.9 nm, respectively, corresponding to a time-bandwidth product of 1.02. PMID:27192233
NASA Astrophysics Data System (ADS)
Pan, Weichun; Kolomeisky, Anatoly B.; Vekilov, Peter G.
2005-05-01
Nucleation of ordered solid phases of proteins triggers numerous phenomena in laboratory, industry, and in healthy and sick organisms. Recent simulations and experiments with protein crystals suggest that the formation of an ordered crystalline nucleus is preceded by a disordered high-density cluster, akin to a droplet of high-density liquid that has been observed with some proteins; this mechanism allowed a qualitative explanation of recorded complex nucleation kinetics curves. Here, we present a simple phenomenological theory that takes into account intermediate high-density metastable states in the nucleation process. Nucleation rate data at varying temperature and protein concentration are reproduced with high fidelity using literature values of the thermodynamic and kinetic parameters of the system. Our calculations show that the growth rate of the near-critical and supercritical ordered clusters within the dense intermediate is a major factor for the overall nucleation rate. This highlights the role of viscosity within the dense intermediate for the formation of the ordered nucleus. The model provides an understanding of the action of additives that delay or accelerate nucleation and presents a framework within which the nucleation of other ordered protein solid phases, e.g., the sickle cell hemoglobin polymers, can be analyzed.
A high-order external distributed feedback polymer laser with low working threshold
NASA Astrophysics Data System (ADS)
Huang, Wenbin; Pu, Donglin; Yang, Xiaofei; Wei, Guojun; Fang, Zongbao; Zhou, Xiaohong; Qiao, Wen; Chen, Linsen
2016-05-01
In this paper, we report a high-order distributed feedback (DFB) polymer laser with low working threshold. Using the high-order grating increases the lithographic tolerances, providing coherent light sources that are more amenable to mass-manufacturing techniques, such as laser direct writing lithography and roll-to-roll processing. To enable high-order DFB lasing, an unconventional working configuration is designed in which the grating is situated on top of the uniform conjugated polymer film. In addition, a novel Forster energy transfer blend of two conjugated polymers is used as the gain medium. Upon pumping, the device emits lasing around 603.6 nm with a bandwidth of 0.5 nm. The threshold is around 20.5 μJ cm‑2 (~2.56 kW cm‑2), about to enter the regime of inexpensive LED pumping. A further increase in pump energy results in simultaneous oscillations at the 29th and 30th Bragg orders. Operating principles of the high-order DFB polymer laser, including spectral performance and threshold dependence on pump length, are investigated. This approach represents a step towards low-cost, even ‘disposable’ polymer lasers.
High-order ENO schemes for unstructured meshes based on least-squares reconstruction
Ollivier-Gooch, C.F.
1997-03-01
High-order accurate schemes for conservation laws for unstructured meshes are not nearly so well advanced as such schemes for structured meshes. Consequently, little or nothing is known about the possible practical advantages of high-order discretization on unstructured meshes. This article is part of an ongoing effort to develop high-order schemes for unstructured meshes to the point where meaningful information can be obtained about the trade-offs involved in using spatial discretizations of higher than second-order accuracy on unstructured meshes. This article describes a high-order accurate ENO reconstruction scheme, called DD-L{sub 2}-ENO, for use with vertex-centered upwind flow solution algorithms on unstructured meshes. The solution of conservation equations in this context can be broken naturally into three phases: (1) solution reconstruction, in which a polynomial approximation of the solution is obtained in each control volume. (2) Flux integration around each control volume, using an appropriate flux function and a quadrature rule with accuracy commensurate with that of the reconstruction. (3) Time evolution, which may be implicit, explicit, multigrid, or some hybrid.
Nonlinear filtering and limiting in high order methods for ideal and non-ideal MHD
NASA Technical Reports Server (NTRS)
Yee,H. C.; Sjogreen, B.
2004-01-01
The various filtering mechanisms and base scheme options of the newly developed adaptive numerical dissipation control in spatially high order filter schemes for the ideal and non-ideal magnetohydrodynamics (MHD) equations are investigated. These filter schemes are applicable to complex unsteady MHD high-speed shock/shear/turbulence problems. They also provide a natural and efficient way for the minimization of Div(B) numerical error. The type of spatial base scheme to be used in conjunction with our filter idea is very general. For example, spectral, compact and non-compact spatially central finite difference schemes are possible candidates. The adaptive numerical dissipation mechanism 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 to leave the rest of the region free from numerical dissipation contamination. The numerical dissipation considered consists of high order linear dissipation for the suppression of high frequency oscillation and the nonlinear dissipative portion of high-resolution shock-capturing methods for discontinuity capturing. The applicable nonlinear dissipative portion of high-resolution shock-capturing methods is also very general. The objective of this paper is to investigate the performance of using compact and non-compact central base schemes in conjunction with three commonly used types of nonlinear numerical dissipation for both the ideal and non-ideal MHD. This extended abstract shows the performance of three nonlinear filters in conjunction with a sixth-order non-compact spatial central base scheme. In the final paper, the high order compact spatial central base scheme will be illustrated and compared with the non-compact base scheme. The reason for the investigation of the high order compact spatial central base scheme over the non-compact base scheme is to evaluate if additional accuracy can be gained in regions of
Guiding of low-energy electrons by highly ordered Al2O3 nanocapillaries
NASA Astrophysics Data System (ADS)
Milosavljević, A. R.; Víkor, Gy.; Pešić, Z. D.; Kolarž, P.; Šević, D.; Marinković, B. P.; Mátéfi-Tempfli, S.; Mátéfi-Tempfli, M.; Piraux, L.
2007-03-01
We report an experimental study of guided transmission of low-energy (200 350eV) electrons through highly ordered Al2O3 nanocapillaries with large aspect ratio ( 140nm diameter and 15μm length). The nanochannel array was prepared using self-ordering phenomena during a two-step anodization process of a high-purity aluminum foil. The experimental results clearly show the existence of the guiding effect, as found for highly charged ions. The guiding of the electron beam was observed for tilt angles up to 12° . As seen for highly charged ions, the guiding efficiency increases with decreasing electron incident energy. The transmission efficiency appeared to be significantly lower than observed for highly charged ions and, moreover, the intensity of transmitted electrons significantly decreases with decreasing impact energy.
High temperature sensing using higher-order-mode rejected sapphire-crystal fiber gratings
NASA Astrophysics Data System (ADS)
Zhan, Chun; Kim, Jae Hun; Lee, Jon; Yin, Stuart; Ruffin, Paul; Luo, Claire
2007-09-01
In this paper, we report the fabrication of higher-order-mode rejected fiber Bragg gratings (FBGs) in sapphire crystal fiber using infrared (IR) femtosecond laser illumination. The grating is tested in high temperature furnace up to 1600 degree Celsius. As sapphire fiber is only available as highly multimode fiber, a scheme to filter out higher order modes in favor for the fundamental mode is theoretically evaluated and experimentally demonstrated. The approach is to use an ultra thin sapphire crystal fiber (60 micron in diameter) to decrease the number of modes. The small diameter fiber also enables bending the fiber to certain radius which is carefully chosen to provide low loss for the fundamental mode LP01 and high loss for the other high-order modes. After bending, less-than-2-nm resonant peak bandwidth is achieved. The grating spectrum is improved, and higher resolution sensing measurement can be achieved. This mode filtering method is very easy to implement. Furthermore, the sapphire fiber is sealed with hi-purity alumina ceramic cement inside a flexible high temperature titanium tube, and the highly flexible titanium tube offers a robust packaging to sapphire fiber. Our high temperature sapphire grating sensor is very promising in extremely high temperature sensing application.
Multielectron signatures in the polarization of high-order harmonic radiation
Zhao Zengxiu; Yuan Jianmin; Brabec, Thomas
2007-09-15
The polarization of high-order harmonic radiation emitted from N{sub 2} molecules interacting with a linearly polarized laser pulse is investigated theoretically. We find that the exchange effect between the recombining electron and the bound core electrons imprints a clear signature onto the high-order harmonic polarization and its dependence on the alignment angle between the molecular axis and driving laser electric field. Our analysis reveals an observable for the experimental investigation of many-electron dynamics in intense laser fields.
High order filtering methods for approximating hyperbolic systems of conservation laws
NASA Technical Reports Server (NTRS)
Lafon, F.; Osher, S.
1991-01-01
The essentially nonoscillatory (ENO) schemes, while potentially useful in the computation of discontinuous solutions of hyperbolic conservation-law systems, are computationally costly relative to simple central-difference methods. A filtering technique is presented which employs central differencing of arbitrarily high-order accuracy except where a local test detects the presence of spurious oscillations and calls upon the full ENO apparatus to remove them. A factor-of-three speedup is thus obtained over the full-ENO method for a wide range of problems, with high-order accuracy in regions of smooth flow.
High-order localized spoof surface plasmon resonances and experimental verifications
Liao, Zhen; Luo, Yu; Fernández-Domínguez, Antonio I.; Shen, Xiaopeng; Maier, Stefan A.; Cui, Tie Jun
2015-01-01
We theoretically demonstrated and experimentally verified high-order radial spoof localized surface plasmon resonances supported by textured metal particles. Through an effective medium theory and exact numerical simulations, we show the emergence of these geometrically-originated electromagnetic modes at microwave frequencies. The occurrence of high-order radial spoof plasmon resonances is experimentally verified in ultrathin disks. Their spectral and near-field properties are characterized experimentally, showing an excellent agreement with theoretical predictions. Our findings shed light into the nature of spoof localized surface plasmons, and open the way to the design of broadband plasmonic devices able to operate at very different frequency regimes. PMID:25873523
R. M. Ferrer; Y. Y. Azmy
2009-05-01
We present a robust arbitrarily high order transport method of the characteristic type for unstructured tetrahedral grids. Previously encountered difficulties have been addressed through the reformulation of the method based on coordinate transformations, evaluation of the moments balance relation as a linear system of equations involving the expansion coefficients of the projected basis, and the asymptotic expansion of the integral kernels in the thin cell limit. The proper choice of basis functions for the high-order spatial expansion of the solution is discussed and its effect on problems involving scattering discussed. Numerical tests are presented to illustrate the beneficial effect of these improvements, and the improved robustness they yield.
Zhang, Xinyi; Lu, Wei; Dai, Jiyan; Bourgeois, Laure; Yao, Jianfeng; Wang, Huanting; Friend, James R.; Zhao, Dongyuan; MacFarlane, Douglas R.
2014-01-01
The synthesis of metal frameworks perforated with nanotunnels is a challenge because metals have high surface energies that favor low surface area structures; traditional liquid-crystal templating techniques cannot achieve the synthetic control required. We report a synthetic strategy to fabricate metal nanomaterials with highly ordered, tunable mesostructures in confined systems based on a new quasi-hard-templating liquid-crystals mechanism. The resulting platinum nanowires exhibit long range two-dimensional hexagonally ordered mesopore structures. In addition, single crystalline hexagonal mesoporous platinum nanowires with dominant {110} facets have been synthesized. Finally, we demonstrate that the mesostructures of metal nanomaterials can be tuned from hexagonal to lamellar mesostructures. PMID:25502015
High-order-harmonic generation driven by pulses with angular spatial chirp
NASA Astrophysics Data System (ADS)
Hernández-García, Carlos; Jaron-Becker, Agnieszka; Hickstein, Daniel D.; Becker, Andreas; Durfee, Charles G.
2016-02-01
We present and analyze a technique to drive high-order harmonics by laser pulses with an angular spatial chirp. Results of our numerical simulations show that each harmonic is emitted with an angular chirp which scales inversely with the harmonic order and leads to additional control of the spatial and temporal resolution of the spectrum. In particular, the use of angular chirp leads to separation of the harmonics in two dimensions where (i) high spectral resolution can be achieved and (ii) the temporal periodicity of the harmonic pulse trains can be controlled. We show that this technique does not require carrier-envelope-phase stabilization when using few-cycle laser pulses.
A high-order statistical tensor based algorithm for anomaly detection in hyperspectral imagery.
Geng, Xiurui; Sun, Kang; Ji, Luyan; Zhao, Yongchao
2014-01-01
Recently, high-order statistics have received more and more interest in the field of hyperspectral anomaly detection. However, most of the existing high-order statistics based anomaly detection methods require stepwise iterations since they are the direct applications of blind source separation. Moreover, these methods usually produce multiple detection maps rather than a single anomaly distribution image. In this study, we exploit the concept of coskewness tensor and propose a new anomaly detection method, which is called COSD (coskewness detector). COSD does not need iteration and can produce single detection map. The experiments based on both simulated and real hyperspectral data sets verify the effectiveness of our algorithm. PMID:25366706
NASA Astrophysics Data System (ADS)
Papanicolaou, N. C.; Aristotelous, A. C.
2015-10-01
In this work, we develop a High-Order Symmetric Interior Penalty (SIP) Discontinuous Galerkin (DG) Finite Element Method (FEM) to investigate convective flows in a rectangular cavity subject to both vertical and horizontal temperature gradients. The whole cavity is subject to gravity modulation (g-jitter), simulating a microgravity environment. The sensitivity of the bifurcation problem makes the use of a high-order accurate and efficient technique essential. Our method is validated by solving the plane-parallel flow problem and the results were found to be in good agreement with published results. The numerical method was designed to be easily extendable to even more complex flows.
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
NASA Technical Reports Server (NTRS)
Fisher, Travis C.; Carpenter, Mark H.
2013-01-01
Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.
Study of a high-order-mode gyrotron traveling-wave amplifier
Chiu, C. C.; Tsai, C. Y.; Kao, S. H.; Chu, K. R.; Barnett, L. R.; Luhmann, N. C. Jr.
2010-11-15
Physics and performance issues of a TE{sub 01}-mode gyrotron traveling-wave amplifier are studied in theory. For a high order mode, absolute instabilities on neighboring modes at the fundamental and higher cyclotron harmonic frequencies impose severe constraints to the device capability. Methods for their stabilization are outlined, on the basis of which the performance characteristics are examined in a multidimensional parameter space under the marginal stability criterion. The results demonstrate the viability of a high-order-mode traveling-wave amplifier and provide a roadmap for design tradeoffs among power, bandwidth, and efficiency. General trends are observed and illustrated with specific examples.
Neurodynamics-Based Robust Pole Assignment for High-Order Descriptor Systems.
Le, Xinyi; Wang, Jun
2015-11-01
In this paper, a neurodynamic optimization approach is proposed for synthesizing high-order descriptor linear systems with state feedback control via robust pole assignment. With a new robustness measure serving as the objective function, the robust eigenstructure assignment problem is formulated as a pseudoconvex optimization problem. A neurodynamic optimization approach is applied and shown to be capable of maximizing the robust stability margin for high-order singular systems with guaranteed optimality and exact pole assignment. Two numerical examples and vehicle vibration control application are discussed to substantiate the efficacy of the proposed approach. PMID:26357408
A perspective on high-order methods in computational fluid dynamics
NASA Astrophysics Data System (ADS)
Wang, ZhiJian
2016-01-01
There has been an intensive international effort to develop high-order Computational Fluid Dynamics (CFD) methods into design tools in aerospace engineering during the last one and half decades. These methods offer the potential to significantly improve solution accuracy and efficiency for vortex dominated turbulent flows. Enough progresses have been made in algorithm development, mesh generation and parallel computing that these methods are on the verge of being applied in a production design environment. Since many review papers have been written on the subject, I decide to offer a personal perspective on the state-of-the-art in high-order CFD methods and the challenges that must be overcome.
A high order accurate finite element algorithm for high Reynolds number flow prediction
NASA Technical Reports Server (NTRS)
Baker, A. J.
1978-01-01
A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.
Earthquake Rupture Dynamics using Adaptive Mesh Refinement and High-Order Accurate Numerical Methods
NASA Astrophysics Data System (ADS)
Kozdon, J. E.; Wilcox, L.
2013-12-01
Our goal is to develop scalable and adaptive (spatial and temporal) numerical methods for coupled, multiphysics problems using high-order accurate numerical methods. To do so, we are developing an opensource, parallel library known as bfam (available at http://bfam.in). The first application to be developed on top of bfam is an earthquake rupture dynamics solver using high-order discontinuous Galerkin methods and summation-by-parts finite difference methods. In earthquake rupture dynamics, wave propagation in the Earth's crust is coupled to frictional sliding on fault interfaces. This coupling is two-way, required the simultaneous simulation of both processes. The use of laboratory-measured friction parameters requires near-fault resolution that is 4-5 orders of magnitude higher than that needed to resolve the frequencies of interest in the volume. This, along with earlier simulations using a low-order, finite volume based adaptive mesh refinement framework, suggest that adaptive mesh refinement is ideally suited for this problem. The use of high-order methods is motivated by the high level of resolution required off the fault in earlier the low-order finite volume simulations; we believe this need for resolution is a result of the excessive numerical dissipation of low-order methods. In bfam spatial adaptivity is handled using the p4est library and temporal adaptivity will be accomplished through local time stepping. In this presentation we will present the guiding principles behind the library as well as verification of code against the Southern California Earthquake Center dynamic rupture code validation test problems.
NASA Astrophysics Data System (ADS)
Deng, Xiaogang; Mao, Meiliang; Tu, Guohua; Liu, Huayong; Zhang, Hanxin
2011-02-01
The geometric conservation law (GCL) includes the volume conservation law (VCL) and the surface conservation law (SCL). Though the VCL is widely discussed for time-depending grids, in the cases of stationary grids the SCL also works as a very important role for high-order accurate numerical simulations. The SCL is usually not satisfied on discretized grid meshes because of discretization errors, and the violation of the SCL can lead to numerical instabilities especially when high-order schemes are applied. In order to fulfill the SCL in high-order finite difference schemes, a conservative metric method (CMM) is presented. This method is achieved by computing grid metric derivatives through a conservative form with the same scheme applied for fluxes. The CMM is proven to be a sufficient condition for the SCL, and can ensure the SCL for interior schemes as well as boundary and near boundary schemes. Though the first-level difference operators δ3 have no effects on the SCL, no extra errors can be introduced as δ3 = δ2. The generally used high-order finite difference schemes are categorized as central schemes (CS) and upwind schemes (UPW) based on the difference operator δ1 which are used to solve the governing equations. The CMM can be applied to CS and is difficult to be satisfied by UPW. Thus, it is critical to select the difference operator δ1 to reduce the SCL-related errors. Numerical tests based on WCNS-E-5 show that the SCL plays a very important role in ensuring free-stream conservation, suppressing numerical oscillations, and enhancing the robustness of the high-order scheme in complex grids.
An almost symmetric Strang splitting scheme for the construction of high order composition methods.
Einkemmer, Lukas; Ostermann, Alexander
2014-12-01
In this paper we consider splitting methods for nonlinear ordinary differential equations in which one of the (partial) flows that results from the splitting procedure cannot be computed exactly. Instead, we insert a well-chosen state [Formula: see text] into the corresponding nonlinearity [Formula: see text], which results in a linear term [Formula: see text] whose exact flow can be determined efficiently. Therefore, in the spirit of splitting methods, it is still possible for the numerical simulation to satisfy certain properties of the exact flow. However, Strang splitting is no longer symmetric (even though it is still a second order method) and thus high order composition methods are not easily attainable. We will show that an iterated Strang splitting scheme can be constructed which yields a method that is symmetric up to a given order. This method can then be used to attain high order composition schemes. We will illustrate our theoretical results, up to order six, by conducting numerical experiments for a charged particle in an inhomogeneous electric field, a post-Newtonian computation in celestial mechanics, and a nonlinear population model and show that the methods constructed yield superior efficiency as compared to Strang splitting. For the first example we also perform a comparison with the standard fourth order Runge-Kutta methods and find significant gains in efficiency as well better conservation properties. PMID:25473146
An almost symmetric Strang splitting scheme for the construction of high order composition methods☆
Einkemmer, Lukas; Ostermann, Alexander
2014-01-01
In this paper we consider splitting methods for nonlinear ordinary differential equations in which one of the (partial) flows that results from the splitting procedure cannot be computed exactly. Instead, we insert a well-chosen state y⋆ into the corresponding nonlinearity B(y)y, which results in a linear term B(y⋆)y whose exact flow can be determined efficiently. Therefore, in the spirit of splitting methods, it is still possible for the numerical simulation to satisfy certain properties of the exact flow. However, Strang splitting is no longer symmetric (even though it is still a second order method) and thus high order composition methods are not easily attainable. We will show that an iterated Strang splitting scheme can be constructed which yields a method that is symmetric up to a given order. This method can then be used to attain high order composition schemes. We will illustrate our theoretical results, up to order six, by conducting numerical experiments for a charged particle in an inhomogeneous electric field, a post-Newtonian computation in celestial mechanics, and a nonlinear population model and show that the methods constructed yield superior efficiency as compared to Strang splitting. For the first example we also perform a comparison with the standard fourth order Runge–Kutta methods and find significant gains in efficiency as well better conservation properties. PMID:25473146
Double Double Cation Order in the High-Pressure Perovskites MnRMnSbO6.
Solana-Madruga, Elena; Arévalo-López, Ángel M; Dos Santos-García, Antonio J; Urones-Garrote, Esteban; Ávila-Brande, David; Sáez-Puche, Regino; Attfield, J Paul
2016-08-01
Cation ordering in ABO3 perovskites adds to their chemical variety and can lead to properties such as ferrimagnetism and magnetoresistance in Sr2 FeMoO6 . Through high-pressure and high-temperature synthesis, a new type of "double double perovskite" structure has been discovered in the family MnRMnSbO6 (R=La, Pr, Nd, Sm). This tetragonal structure has a 1:1 order of cations on both A and B sites, with A-site Mn(2+) and R(3+) cations ordered in columns and Mn(2+) and Sb(5+) having rock salt order on the B sites. The MnRMnSbO6 double double perovskites are ferrimagnetic at low temperatures with additional spin-reorientation transitions. The ordering direction of ferrimagnetic Mn spins in MnNdMnSbO6 changes from parallel to [001] below TC =76 K to perpendicular below the reorientation transition at 42 K at which Nd moments also order. Smaller rare earths lead to conventional monoclinic double perovskites (MnR)MnSbO6 for Eu and Gd. PMID:27312417
A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models
Guerra, Jorge E.; Ullrich, Paul A.
2016-06-01
Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δx) modes. Furthermore, high-order accuracy alsomore » eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Lastly, our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.« less
Unconventional charge order in a co-doped high-Tc superconductor.
Pelc, D; Vučković, M; Grafe, H-J; Baek, S-H; Požek, M
2016-01-01
Charge-stripe order has recently been established as an important aspect of cuprate high-Tc superconductors. However, owing to the complex interplay between competing phases and the influence of disorder, it is unclear how it emerges from the parent high-temperature state. Here we report on the discovery of an unconventional ordered phase between charge-stripe order and (pseudogapped) metal in the cuprate La1.8-xEu0.2SrxCuO4. We use three complementary experiments-nuclear quadrupole resonance, nonlinear conductivity and specific heat-to demonstrate that the order appears through a sharp phase transition and exists in a dome-shaped region of the phase diagram. Our results imply that the new phase is a state, which preserves translational symmetry: a charge nematic. We thus resolve the process of charge-stripe development in cuprates, show that this nematic phase is distinct from high-temperature pseudogap and establish a link with other strongly correlated electronic materials with prominent nematic order. PMID:27605152
A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models
NASA Astrophysics Data System (ADS)
Guerra, Jorge E.; Ullrich, Paul A.
2016-06-01
Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δx) modes. Furthermore, high-order accuracy also eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.
A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models
Guerra, Jorge E.; Ullrich, Paul A.
2016-06-01
Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δx) modes. Furthermore, high-order accuracy alsomore » eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.« less
Conservative high-order-accurate finite-difference methods for curvilinear grids
NASA Technical Reports Server (NTRS)
Rai, Man M.; Chakrvarthy, Sukumar
1993-01-01
Two fourth-order-accurate finite-difference methods for numerically solving hyperbolic systems of conservation equations on smooth curvilinear grids are presented. The first method uses the differential form of the conservation equations; the second method uses the integral form of the conservation equations. Modifications to these schemes, which are required near boundaries to maintain overall high-order accuracy, are discussed. An analysis that demonstrates the stability of the modified schemes is also provided. Modifications to one of the schemes to make it total variation diminishing (TVD) are also discussed. Results that demonstrate the high-order accuracy of both schemes are included in the paper. In particular, a Ringleb-flow computation demonstrates the high-order accuracy and the stability of the boundary and near-boundary procedures. A second computation of supersonic flow over a cylinder demonstrates the shock-capturing capability of the TVD methodology. An important contribution of this paper is the dear demonstration that higher order accuracy leads to increased computational efficiency.
Wang, Wei; Shu, Chi-Wang; Yee, H.C.; Sjögreen, Björn
2012-01-01
A new high order finite-difference method utilizing the idea of Harten ENO subcell resolution method is proposed for chemical reactive flows and combustion. In reaction problems, when the reaction time scale is very small, e.g., orders of magnitude smaller than the fluid dynamics time scales, the governing equations will become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present proposed method is a modified fractional step method which solves the convection step and reaction step separately. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with the computed flow variables in the shock region modified by the Harten subcell resolution idea. For numerical experiments, a fifth-order finite-difference WENO scheme and its anti-diffusion WENO variant are considered. A wide range of 1D and 2D scalar and Euler system test cases are investigated. Studies indicate that for the considered test cases, the new method maintains high order accuracy in space for smooth flows, and for stiff source terms with discontinuities, it can capture the correct propagation speed of discontinuities in very coarse meshes with reasonable CFL numbers.
High-order random Raman lasing in a PM fiber with ultimate efficiency and narrow bandwidth.
Babin, Sergey A; Zlobina, Ekaterina A; Kablukov, Sergey I; Podivilov, Evgeniy V
2016-01-01
Random Raman lasers attract now a great deal of attention as they operate in non-active turbid or transparent scattering media. In the last case, single mode fibers with feedback via Rayleigh backscattering generate a high-quality unidirectional laser beam. However, such fiber lasers have rather poor spectral and polarization properties, worsening with increasing power and Stokes order. Here we demonstrate a linearly-polarized cascaded random Raman lasing in a polarization-maintaining fiber. The quantum efficiency of converting the pump (1.05 μm) into the output radiation is almost independent of the Stokes order, amounting to 79%, 83%, and 77% for the 1(st) (1.11 μm), 2(nd) (1.17 μm) and 3(rd) (1.23 μm) order, respectively, at the polarization extinction ratio >22 dB for all orders. The laser bandwidth grows with increasing order, but it is almost independent of power in the 1-10 W range, amounting to ~1, ~2 and ~3 nm for orders 1-3, respectively. So, the random Raman laser exhibits no degradation of output characteristics with increasing Stokes order. A theory adequately describing the unique laser features has been developed. Thus, a full picture of the cascaded random Raman lasing in fibers is shown. PMID:26940082
High-order random Raman lasing in a PM fiber with ultimate efficiency and narrow bandwidth
Babin, Sergey A.; Zlobina, Ekaterina A.; Kablukov, Sergey I.; Podivilov, Evgeniy V.
2016-01-01
Random Raman lasers attract now a great deal of attention as they operate in non-active turbid or transparent scattering media. In the last case, single mode fibers with feedback via Rayleigh backscattering generate a high-quality unidirectional laser beam. However, such fiber lasers have rather poor spectral and polarization properties, worsening with increasing power and Stokes order. Here we demonstrate a linearly-polarized cascaded random Raman lasing in a polarization-maintaining fiber. The quantum efficiency of converting the pump (1.05 μm) into the output radiation is almost independent of the Stokes order, amounting to 79%, 83%, and 77% for the 1st (1.11 μm), 2nd (1.17 μm) and 3rd (1.23 μm) order, respectively, at the polarization extinction ratio >22 dB for all orders. The laser bandwidth grows with increasing order, but it is almost independent of power in the 1–10 W range, amounting to ~1, ~2 and ~3 nm for orders 1–3, respectively. So, the random Raman laser exhibits no degradation of output characteristics with increasing Stokes order. A theory adequately describing the unique laser features has been developed. Thus, a full picture of the cascaded random Raman lasing in fibers is shown. PMID:26940082
High-order terms in the renormalized perturbation theory for the Anderson impurity model
NASA Astrophysics Data System (ADS)
Pandis, Vassilis; Hewson, Alex C.
2015-09-01
We study the renormalized perturbation theory of the single-impurity Anderson model, particularly the high-order terms in the expansion of the self-energy in powers of the renormalized coupling U ˜. Though the presence of counterterms in the renormalized theory may appear to complicate the diagrammatics, we show how these can be seamlessly accommodated by carrying out the calculation order-by-order in terms of skeleton diagrams. We describe how the diagrams pertinent to the renormalized self-energy and four vertex can be automatically generated, translated into integrals, and numerically integrated. To maximize the efficiency of our approach we introduce a generalized k -particle/hole propagator, which is used to analytically simplify the resultant integrals and reduce the dimensionality of the integration. We present results for the self-energy and spectral density to fifth order in U ˜, for various values of the model asymmetry, and compare them to a numerical renormalization group calculation.
NASA Astrophysics Data System (ADS)
Wang, Guanghui; Zhang, Weifeng; Lu, Jiahui; Zhao, Huijun
2016-08-01
We analytically study dispersion properties and optical gradient forces of different-order transverse magnetic (TM) modes in two coupled hyperbolic metamaterial waveguides (HMMWs). According to Maxwell's equations, we obtain the dispersion relation of symmetric and antisymmetric modes, and calculate optical gradient forces of different-order modes by using Maxwell stress tensor. Numerical results show that the dispersion properties are dependent on the filling ratio, and the optical gradient forces of high-order TM modes are larger than the fundamental mode when the gap between two HMMWs is very narrow, but they weaken much faster than the case of low-order TM modes with the gap width increasing. In addition, the effects of the dielectric surrounding of waveguides on the coupling effect and optical gradient force are clarified. These properties offer an avenue for various optomechanical applications in optical sensors and actuators.
Performance optimization of high-order Lamb wave sensors based on silicon carbide substrates.
Chen, Zhe; Fan, Li; Zhang, Shu-yi; Zhang, Hui
2016-02-01
Silicon carbide (SiC), as a new type of material for substrates in micro-electromechanical system (MEMS), was given high consideration in virtue of the properties of high acoustic velocity, low loss, chemical resistance, and etc. In this work, five performance parameters, which are electromechanical coupling coefficients, mass sensitivities, conductivity sensitivities, insert losses and minimum detectable masses, are theoretically investigated in Lamb wave chemical sensors for gas sensing based on SiC substrates. It is presented that higher performance can be achieved based on high-order modes other than fundamental modes, and the abovementioned five parameters can be simultaneously optimized. Then, according to the optimized operating conditions, operating parameters of the SiC-based high-order Lamb wave sensors are designed, which can be easily realized in MEMS technology. Finally, it is demonstrates that the SiC-based sensor exhibits better performance than that of the sensor with a conventional silicon substrate. PMID:26474949
CgWind: A high-order accurate simulation tool for wind turbines and wind farms
Chand, K K; Henshaw, W D; Lundquist, K A; Singer, M A
2010-02-22
CgWind is a high-fidelity large eddy simulation (LES) tool designed to meet the modeling needs of wind turbine and wind park engineers. This tool combines several advanced computational technologies in order to model accurately the complex and dynamic nature of wind energy applications. The composite grid approach provides high-quality structured grids for the efficient implementation of high-order accurate discretizations of the incompressible Navier-Stokes equations. Composite grids also provide a natural mechanism for modeling bodies in relative motion and complex geometry. Advanced algorithms such as matrix-free multigrid, compact discretizations and approximate factorization will allow CgWind to perform highly resolved calculations efficiently on a wide class of computing resources. Also in development are nonlinear LES subgrid-scale models required to simulate the many interacting scales present in large wind turbine applications. This paper outlines our approach, the current status of CgWind and future development plans.
Numerical dissipation control in high order shock-capturing schemes for LES of low speed flows
NASA Astrophysics Data System (ADS)
Kotov, D. V.; Yee, H. C.; Wray, A. A.; Sjögreen, B.; Kritsuk, A. G.
2016-02-01
The Yee & Sjögreen adaptive numerical dissipation control in high order scheme (High Order Filter Methods for Wide Range of Compressible Flow Speeds, ICOSAHOM 09, 2009) is further improved for DNS and LES of shock-free turbulence and low speed turbulence with shocklets. There are vastly different requirements in the minimization of numerical dissipation for accurate turbulence simulations of different compressible flow types and flow speeds. Traditionally, the method of choice for shock-free turbulence and low speed turbulence are by spectral, high order central or high order compact schemes with high order linear filters. With a proper control of a local flow sensor, appropriate amount of numerical dissipation in high order shock-capturing schemes can have spectral-like accuracy for compressible low speed turbulent flows. The development of the method includes an adaptive flow sensor with automatic selection on the amount of numerical dissipation needed at each flow location for more accurate DNS and LES simulations with less tuning of parameters for flows with a wide range of flow speed regime during the time-accurate evolution, e.g., time varying random forcing. An automatic selection of the different flow sensors catered to the different flow types is constructed. A Mach curve and high-frequency oscillation indicators are used to reduce the tuning of parameters in controlling the amount of shock-capturing numerical dissipation to be employed for shock-free turbulence, low speed turbulence and turbulence with strong shocks. In Kotov et al. (High Order Numerical Methods for LES of Turbulent Flows with Shocks, ICCFD8, Chengdu, Sichuan, China, July 14-18, 2014) the LES of a turbulent flow with a strong shock by the Yee & Sjögreen scheme indicated a good agreement with the filtered DNS data. A work in progress for the application of the adaptive flow sensor for compressible turbulence with time-varying random forcing is forthcoming. The present study examines the
Influence of higher order modes on the beam stability in the high power superconducting proton linac
NASA Astrophysics Data System (ADS)
Schuh, Marcel; Gerigk, Frank; Tückmantel, Joachim; Welsch, Carsten P.
2011-05-01
Higher order modes (HOMs) can severely limit the operation of superconducting cavities in a linear accelerator with high beam current, high duty factor, and complex pulse structure. The full HOM spectrum has to be analyzed in order to identify potentially dangerous modes already during the design phase and to define their damping requirements. For this purpose a dedicated beam simulation code simulation of higher order mode dynamics (SMD) focused on beam-HOM interaction was developed, taking into account important effects like the HOM frequency spread, beam input jitter, different chopping patterns, as well as klystron and alignment errors. Here, SMD is used to investigate the influence of HOMs in detail in the superconducting proton linac at CERN and their potential to drive beam instabilities in the longitudinal and transverse plane.
A High-Order Finite-Volume Algorithm for Fokker-Planck Collisions in Magnetized Plasmas
Xiong, Z; Cohen, R H; Rognlien, T D; Xu, X Q
2007-04-18
A high-order finite volume algorithm is developed for the Fokker-Planck Operator (FPO) describing Coulomb collisions in strongly magnetized plasmas. The algorithm is based on a general fourth-order reconstruction scheme for an unstructured grid in the velocity space spanned by parallel velocity and magnetic moment. The method provides density conservation and high-order-accurate evaluation of the FPO independent of the choice of the velocity coordinates. As an example, a linearized FPO in constant-of-motion coordinates, i.e. the total energy and the magnetic moment, is developed using the present algorithm combined with a cut-cell merging procedure. Numerical tests include the Spitzer thermalization problem and the return to isotropy for distributions initialized with velocity space loss cones. Utilization of the method for a nonlinear FPO is straightforward but requires evaluation of the Rosenbluth potentials.
A high-order Legendre-WENO kernel density function method for modeling disperse flows
NASA Astrophysics Data System (ADS)
Smith, Timothy; Pantano, Carlos
2015-11-01
We present a high-order kernel density function (KDF) method for disperse flow. The numerical method used to solve the system of hyperbolic equations utilizes a Roe-like update for equations in non-conservation form. We will present the extension of the low-order method to high order using the Legendre-WENO method and demonstrate the improved capability of the method to predict statistics of disperse flows in an accurate, consistent and efficient manner. By construction, the KDF method already enforced many realizability conditions but others remain. The proposed method also considers these constraints and their performance will be discussed. This project was funded by NSF project NSF-DMS 1318161.
Preconditioned High-order WENO Scheme for Incompressible Viscous Flows Simulation
NASA Astrophysics Data System (ADS)
Qian, Z. S.; Zhang, J. B.; Li, C. X.
2011-09-01
A high-order accurate and highly-efficient finite difference algorithm for numerical simulation of the incompressible viscous flows has been developed. This algorithm is based on the pseudo-compressibility formulation, which combines the preconditioning technique for accelerating the time marching for stiff hyperbolic equations. Third-, fifth- and seventh-order accurate WENO schemes are used to discrete the inviscid fluxes and fourth- and sixth-order central schemes are employed for the viscous fluxes and metric terms. Implicit lower-upper symmetric Gauss-Seidel (LU-SGS) time marching procedure is performed for temporal discretization. The accuracy and the efficiency of the proposed method are demonstrated for several numerical test cases.
A high-order photon Monte Carlo method for radiative transfer in direct numerical simulation
Wu, Y.; Modest, M.F.; Haworth, D.C. . E-mail: dch12@psu.edu
2007-05-01
A high-order photon Monte Carlo method is developed to solve the radiative transfer equation. The statistical and discretization errors of the computed radiative heat flux and radiation source term are isolated and quantified. Up to sixth-order spatial accuracy is demonstrated for the radiative heat flux, and up to fourth-order accuracy for the radiation source term. This demonstrates the compatibility of the method with high-fidelity direct numerical simulation (DNS) for chemically reacting flows. The method is applied to address radiative heat transfer in a one-dimensional laminar premixed flame and a statistically one-dimensional turbulent premixed flame. Modifications of the flame structure with radiation are noted in both cases, and the effects of turbulence/radiation interactions on the local reaction zone structure are revealed for the turbulent flame. Computational issues in using a photon Monte Carlo method for DNS of turbulent reacting flows are discussed.
Higher-order modulation formats for spectral-efficient high-speed metro systems
NASA Astrophysics Data System (ADS)
Freund, R.; Nölle, M.; Seimetz, M.; Hilt, J.; Fischer, J.; Ludwig, R.; Schubert, C.; Bach, H.-G.; Velthaus, K.-O.; Schell, M.
2011-01-01
Worldwide, higher-order modulation formats are intensively investigated to further increase the spectral efficiency for building the next generation of high-speed metro systems. IQ-modulators, coherent receivers and electronic equalizers are hereby discussed as key devices. We report on system design issues as well as on HHI's latest achievements in developing InP based high-speed modulators and coherent receiver frontends.
Formation of highly ordered arrays of dimples on tantalum at the nanoscale.
El-Sayed, Hany; Singh, Sherdeep; Greiner, Mark T; Kruse, Peter
2006-12-01
We show that electropolishing of tantalum metal in a single step of about 5 min can reproducibly lead to dimples tens of nanometers in diameter, regular in shape, monodispersed in size, and arranged in highly ordered arrays which even transverse grain boundaries. Dimpled tantalum is ductile, high melting, and chemically inert, which makes it suitable for nanostructure synthesis even under extreme conditions, as demonstrated with a simple sputter coating and flame annealing procedure for gold nanoparticles. PMID:17163747
A high-order conservative collocation scheme and its application to global shallow-water equations
NASA Astrophysics Data System (ADS)
Chen, C.; Li, X.; Shen, X.; Xiao, F.
2015-02-01
In this paper, an efficient and conservative collocation method is proposed and used to develop a global shallow-water model. Being a nodal type high-order scheme, the present method solves the pointwise values of dependent variables as the unknowns within each control volume. The solution points are arranged as Gauss-Legendre points to achieve high-order accuracy. The time evolution equations to update the unknowns are derived under the flux reconstruction (FR) framework (Huynh, 2007). Constraint conditions used to build the spatial reconstruction for the flux function include the pointwise values of flux function at the solution points, which are computed directly from the dependent variables, as well as the numerical fluxes at the boundaries of the computational element, which are obtained as Riemann solutions between the adjacent elements. Given the reconstructed flux function, the time tendencies of the unknowns can be obtained directly from the governing equations of differential form. The resulting schemes have super convergence and rigorous numerical conservativeness. A three-point scheme of fifth-order accuracy is presented and analyzed in this paper. The proposed scheme is adopted to develop the global shallow-water model on the cubed-sphere grid, where the local high-order reconstruction is very beneficial for the data communications between adjacent patches. We have used the standard benchmark tests to verify the numerical model, which reveals its great potential as a candidate formulation for developing high-performance general circulation models.
Two-beam high-order harmonics from solids: Coupling mechanisms
Tarasevitch, A.; Wieczorek, J.; Kohn, R.; Bovensiepen, U.; Linde, D. von der
2010-11-15
The polarization of the two beam (driver-probe) high-order harmonic generation from solids is measured. The experiments, together with computer simulations, allow us to distinguish two different coupling mechanisms of the driver and the probe, resulting in different harmonic efficiencies and spectral slopes. We find that in the nonrelativistic regime the coupling is mostly due to the nonlinear plasma density modulation.
An Automated Approach to Very High Order Aeroacoustic Computations in Complex Geometries
NASA Technical Reports Server (NTRS)
Dyson, Rodger W.; Goodrich, John W.
2000-01-01
Computational aeroacoustics requires efficient, high-resolution simulation tools. And for smooth problems, this is best accomplished with very high order in space and time methods on small stencils. But 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-Kowalewslci recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that are located near wall boundaries. These procedures are used to automatically develop and 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.
Li, Xiaofan; Nie, Qing
2015-01-01
Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratures along with an extrapolation technique, leading to an arbitrarily high-order quadrature; in addition, a high-order (temporal) integration factor method, based on explicit representation of the mean curvature, is used to reduce the stability constraint on time-step. To apply this method to a periodic (in axial direction) and axi-symmetric elastically stressed cylinder, we also present a fast and accurate summation method for the periodic Green’s functions of isotropic elasticity. Using the high-order boundary integral method, we demonstrate that in absence of elasticity the cylinder surface pinches in finite time at the axis of the symmetry and the universal cone angle of the pinching is found to be consistent with the previous studies based on a self-similar assumption. In the presence of elastic stress, we show that a finite time, geometrical singularity occurs well before the cylindrical solid collapses onto the axis of symmetry, and the angle of the corner singularity on the cylinder surface is also estimated. PMID:26487788
High-order harmonics as a continuously tunable coherent femtosecond x-ray source
NASA Astrophysics Data System (ADS)
Nam, Chang Hee; Kim, Hyung Taek; Hong, Kyung-Han; Lee, Dong Gun; Kim, Jung-Hoon
2002-11-01
With the application of appropriately chirped laser pulses, harmonic chirp can be coherently controlled so that sharp harmonics be produced. Using the strong blueshift property and coherently controlling harmonic generation process, we demonstrated a continuously tunable high-order harmonic generation, without losing spectral sharpness.
ERIC Educational Resources Information Center
Roff, Jennifer
2010-01-01
Qualitative research has documented strategic behavior in response to child support policy. Parents of children on welfare have an incentive to avoid formal child support, since most states limit the amount of formal child support that women on welfare can receive (the "disregard") and have relatively high child support orders for low-income…
High Order Finite Difference Methods, Multidimensional Linear Problems and Curvilinear Coordinates
NASA Technical Reports Server (NTRS)
Nordstrom, Jan; Carpenter, Mark H.
1999-01-01
Boundary and interface conditions are derived for high order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.
A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.
1989-01-01
A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.
Maximally confined high-speed second-order silicon microdisk switches.
Young, Ralph Watson; Trotter, Douglas Chandler; Watts, Michael R.
2008-03-01
We demonstrate the first high-speed second-order silicon microdisk bandpass switch. The switch, constructed of a pair of 3 {micro}m radii active microdisks possesses {approx}40GHz flat-top passbands, a 4.2THz free-spectral-range, and a 2.4ns switching time.
High-order harmonic generation on atoms and ions with laser fields of relativistic intensities
Avetissian, H. K.; Markossian, A. G.; Mkrtchian, G. F.
2011-07-15
High-order harmonic generation (HHG) by hydrogenlike atoms or ions in the field of counterpropagating laser beams of standing-wave configuration, with linear polarizations and relativistic intensities, is studied. The relativistic quantum theory of HHG in such field configurations (homogeneous), at which the impeding factor of relativistic magnetic drift of superstrong laser fields can be eliminated, is presented.
Rotating-frame perspective on high-order-harmonic generation of circularly polarized light
NASA Astrophysics Data System (ADS)
Reich, Daniel M.; Madsen, Lars Bojer
2016-04-01
We employ a rotating frame of reference to elucidate high-order-harmonic generation of circularly polarized light by bicircular driving fields. In particular, we show how the experimentally observed circular components of the high-order-harmonic spectrum can be directly related to the corresponding quantities in the rotating frame. Supported by numerical simulations of the time-dependent Schrödinger equation, we deduce an optimal strategy for maximizing the cutoff in the high-order-harmonic plateau while keeping the two circular components of the emitted light spectrally distinct. Moreover, we show how the rotating-frame picture can be more generally employed for elliptical drivers. Finally, we point out how circular and elliptical driving fields show a near-duality to static electric and magnetic fields in a rotating-frame description. This demonstrates how high-order-harmonic generation of circularly polarized light under static electromagnetic fields can be emulated in practice even at static field strengths beyond current experimental capabilities.
Analysis of High Order Difference Methods for Multiscale Complex Compressible Flows
NASA Technical Reports Server (NTRS)
Sjoegreen, Bjoern; Yee, H. C.; Tang, Harry (Technical Monitor)
2002-01-01
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 with incremental studies was initiated. Here we further refine the analysis on, and improve the understanding of the adaptive numerical dissipation control strategy. Basically, the development of these schemes focuses on high order nondissipative schemes and takes advantage of the progress that has been made for the last 30 years in numerical methods for conservation laws, such as techniques for imposing boundary conditions, techniques for stability at shock waves, and techniques for stable and accurate long-time integration. We concentrate on high order centered spatial discretizations and a fourth-order Runge-Kutta temporal discretizations as the base scheme. Near the bound-aries, the base scheme has stable boundary difference operators. To further enhance stability, the split form of the inviscid flux derivatives is frequently used for smooth flow problems. To enhance nonlinear stability, linear high order numerical dissipations are employed away from discontinuities, and nonlinear filters are employed after each time step in order to suppress spurious oscillations near discontinuities to minimize the smearing of turbulent fluctuations. Although these schemes are built from many components, each of which is well-known, it is not entirely obvious how the different components be best connected. For example, the nonlinear filter could instead have been built into the spatial discretization, so that it would have been activated at each stage in the Runge-Kutta time stepping. We could think
High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows
NASA Astrophysics Data System (ADS)
Ivan, Lucian; Groth, Clinton P. T.
2014-01-01
A high-order, central, essentially non-oscillatory (CENO), finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of the Navier-Stokes equations on body-fitted multi-block mesh. In contrast to other ENO schemes which require reconstruction on multiple stencils, the proposed CENO method uses a hybrid reconstruction approach based on a fixed central stencil. This feature is crucial to avoiding the complexities associated with multiple stencils of ENO schemes, providing high-order accuracy at relatively lower computational cost as well as being very well suited for extension to unstructured meshes. The spatial discretization of the inviscid (hyperbolic) fluxes combines an unlimited high-order k-exact least-squares reconstruction technique following from the optimal central stencil with a monotonicity-preserving, limited, linear, reconstruction algorithm. This hybrid reconstruction procedure retains the unlimited high-order k-exact reconstruction for cells in which the solution is fully resolved and reverts to the limited lower-order counterpart for cells with under-resolved/discontinuous solution content. Switching in the hybrid procedure is determined by a smoothness indicator. The high-order viscous (elliptic) fluxes are computed to the same order of accuracy as the hyperbolic fluxes based on a k-order accurate cell interface gradient derived from the unlimited, cell-centred, reconstruction. A somewhat novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady mesh adaptation. The proposed numerical procedure is thoroughly analyzed for advection-diffusion problems characterized by the full range of Péclet numbers, and its predictive capabilities are also demonstrated for several inviscid and laminar flows. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non
Dissipative issue of high-order shock capturing schemes with non-convex equations of state
NASA Astrophysics Data System (ADS)
Heuzé, Olivier; Jaouen, Stéphane; Jourdren, Hervé
2009-02-01
It is well known that, closed with a non-convex equation of state (EOS), the Riemann problem for the Euler equations allows non-standard waves, such as split shocks, sonic isentropic compressions or rarefaction shocks, to occur. Loss of convexity then leads to non-uniqueness of entropic or Lax solutions, which can only be resolved via the Liu-Oleinik criterion (equivalent to the existence of viscous profiles for all admissible shock waves). This suggests that in order to capture the physical solution, a numerical scheme must provide an appropriate level of dissipation. A legitimate question then concerns the ability of high-order shock capturing schemes to naturally select such a solution. To investigate this question and evaluate modern as well as future high-order numerical schemes, there is therefore a crucial need for well-documented benchmarks. A thermodynamically consistent C∞ non-convex EOS that can be easily introduced in Eulerian as well as Lagrangian hydrocodes for test purposes is here proposed, along with a reference solution for an initial value problem exhibiting a complex composite wave pattern (the Bizarrium test problem). Two standard Lagrangian numerical approaches, both based on a finite volume method, are then reviewed (vNR and Godunov-type schemes) and evaluated on this Riemann problem. In particular, a complete description of several state-of-the-art high-order Godunov-type schemes applicable to general EOSs is provided. We show that this particular test problem reveals quite severe when working on high-order schemes, and recommend it as a benchmark for devising new limiters and/or next-generation highly accurate schemes.
Liu, Yong; Lan, Kun; Bagabas, Abdulaziz A; Zhang, Pengfei; Gao, Wenjun; Wang, Jingxiu; Sun, Zhenkun; Fan, Jianwei; Elzatahry, Ahmed A; Zhao, Dongyuan
2016-02-01
Well ordered, uniform 3D open macro/mesoporous TiO2 hollow microspheres with highly crystalline anatase thin shells have been successfully synthesized by a simple solvent evaporation-driven confined self-assembly method. The 3D open macro/mesoporous TiO2 hollow microspheres show high energy-conversion efficiency (up to 9.5%) and remarkable photocatalytic activity (with photodegradation of 100% for methylene blue in 12 min under UV light irradiation). PMID:26708310
Identification of interactions in fractional-order systems with high dimensions
Ji, Xiaoxi; Wu, Yu; Sheng, Wenbo; Lin, Wei
2014-06-15
This article proposes an approach to identify fractional-order systems with sparse interaction structures and high dimensions when observation data are supposed to be experimentally available. This approach includes two steps: first, it is to estimate the value of the fractional order by taking into account the solution properties of fractional-order systems; second, it is to identify the interaction coefficients among the system variables by employing the compressed sensing technique. An error analysis is provided analytically for this approach and a further improved approach is also proposed. Moreover, the applicability of the proposed approach is fully illustrated by two examples: one is to estimate the mutual interactions in a complex dynamical network described by fractional-order systems, and the other is to identify a high fractional-order and homogeneous sequential differential equation, which is frequently used to describe viscoelastic phenomena. All the results demonstrate the feasibility of figuring out the system mechanisms behind the data experimentally observed in physical or biological systems with viscoelastic evolution characters.
High-order moments of spin-orbit energy in a multielectron configuration.
Na, Xieyu; Poirier, M
2016-07-01
In order to analyze the energy-level distribution in complex ions such as those found in warm dense plasmas, this paper provides values for high-order moments of the spin-orbit energy in a multielectron configuration. Using second-quantization results and standard angular algebra or fully analytical expressions, explicit values are given for moments up to 10th order for the spin-orbit energy. Two analytical methods are proposed, using the uncoupled or coupled orbital and spin angular momenta. The case of multiple open subshells is considered with the help of cumulants. The proposed expressions for spin-orbit energy moments are compared to numerical computations from Cowan's code and agree with them. The convergence of the Gram-Charlier expansion involving these spin-orbit moments is analyzed. While a spectrum with infinitely thin components cannot be adequately represented by such an expansion, a suitable convolution procedure ensures the convergence of the Gram-Charlier series provided high-order terms are accounted for. A corrected analytical formula for the third-order moment involving both spin-orbit and electron-electron interactions turns out to be in fair agreement with Cowan's numerical computations. PMID:27575229
High-order moments of spin-orbit energy in a multielectron configuration
NASA Astrophysics Data System (ADS)
Na, Xieyu; Poirier, M.
2016-07-01
In order to analyze the energy-level distribution in complex ions such as those found in warm dense plasmas, this paper provides values for high-order moments of the spin-orbit energy in a multielectron configuration. Using second-quantization results and standard angular algebra or fully analytical expressions, explicit values are given for moments up to 10th order for the spin-orbit energy. Two analytical methods are proposed, using the uncoupled or coupled orbital and spin angular momenta. The case of multiple open subshells is considered with the help of cumulants. The proposed expressions for spin-orbit energy moments are compared to numerical computations from Cowan's code and agree with them. The convergence of the Gram-Charlier expansion involving these spin-orbit moments is analyzed. While a spectrum with infinitely thin components cannot be adequately represented by such an expansion, a suitable convolution procedure ensures the convergence of the Gram-Charlier series provided high-order terms are accounted for. A corrected analytical formula for the third-order moment involving both spin-orbit and electron-electron interactions turns out to be in fair agreement with Cowan's numerical computations.
Sun, J. P.; Matsuura, K.; Ye, G. Z.; Mizukami, Y.; Shimozawa, M.; Matsubayashi, K.; Yamashita, M.; Watashige, T.; Kasahara, S.; Matsuda, Y.; Yan, J. -Q.; Sales, B. C.; Uwatoko, Y.; Cheng, J. -G.; Shibauchi, T.
2016-01-01
The coexistence and competition between superconductivity and electronic orders, such as spin or charge density waves, have been a central issue in high transition-temperature (Tc) superconductors. Unlike other iron-based superconductors, FeSe exhibits nematic ordering without magnetism whose relationship with its superconductivity remains unclear. Moreover, a pressure-induced fourfold increase of Tc has been reported, which poses a profound mystery. Here we report high-pressure magnetotransport measurements in FeSe up to ∼15 GPa, which uncover the dome shape of magnetic phase superseding the nematic order. Above ∼6 GPa the sudden enhancement of superconductivity (Tc≤38.3 K) accompanies a suppression of magnetic order, demonstrating their competing nature with very similar energy scales. Above the magnetic dome, we find anomalous transport properties suggesting a possible pseudogap formation, whereas linear-in-temperature resistivity is observed in the normal states of the high-Tc phase above 6 GPa. The obtained phase diagram highlights unique features of FeSe among iron-based superconductors, but bears some resemblance to that of high-Tc cuprates. PMID:27431724
NASA Astrophysics Data System (ADS)
Sun, J. P.; Matsuura, K.; Ye, G. Z.; Mizukami, Y.; Shimozawa, M.; Matsubayashi, K.; Yamashita, M.; Watashige, T.; Kasahara, S.; Matsuda, Y.; Yan, J.-Q.; Sales, B. C.; Uwatoko, Y.; Cheng, J.-G.; Shibauchi, T.
2016-07-01
The coexistence and competition between superconductivity and electronic orders, such as spin or charge density waves, have been a central issue in high transition-temperature (Tc) superconductors. Unlike other iron-based superconductors, FeSe exhibits nematic ordering without magnetism whose relationship with its superconductivity remains unclear. Moreover, a pressure-induced fourfold increase of Tc has been reported, which poses a profound mystery. Here we report high-pressure magnetotransport measurements in FeSe up to ~15 GPa, which uncover the dome shape of magnetic phase superseding the nematic order. Above ~6 GPa the sudden enhancement of superconductivity (Tc<=38.3 K) accompanies a suppression of magnetic order, demonstrating their competing nature with very similar energy scales. Above the magnetic dome, we find anomalous transport properties suggesting a possible pseudogap formation, whereas linear-in-temperature resistivity is observed in the normal states of the high-Tc phase above 6 GPa. The obtained phase diagram highlights unique features of FeSe among iron-based superconductors, but bears some resemblance to that of high-Tc cuprates.
Sun, J P; Matsuura, K; Ye, G Z; Mizukami, Y; Shimozawa, M; Matsubayashi, K; Yamashita, M; Watashige, T; Kasahara, S; Matsuda, Y; Yan, J-Q; Sales, B C; Uwatoko, Y; Cheng, J-G; Shibauchi, T
2016-01-01
The coexistence and competition between superconductivity and electronic orders, such as spin or charge density waves, have been a central issue in high transition-temperature (Tc) superconductors. Unlike other iron-based superconductors, FeSe exhibits nematic ordering without magnetism whose relationship with its superconductivity remains unclear. Moreover, a pressure-induced fourfold increase of Tc has been reported, which poses a profound mystery. Here we report high-pressure magnetotransport measurements in FeSe up to ∼15 GPa, which uncover the dome shape of magnetic phase superseding the nematic order. Above ∼6 GPa the sudden enhancement of superconductivity (Tc≤38.3 K) accompanies a suppression of magnetic order, demonstrating their competing nature with very similar energy scales. Above the magnetic dome, we find anomalous transport properties suggesting a possible pseudogap formation, whereas linear-in-temperature resistivity is observed in the normal states of the high-Tc phase above 6 GPa. The obtained phase diagram highlights unique features of FeSe among iron-based superconductors, but bears some resemblance to that of high-Tc cuprates. PMID:27431724
Narrow-bandwidth high-order harmonics driven by long-duration hot spots
NASA Astrophysics Data System (ADS)
Kozlov, Maxim; Kfir, Ofer; Fleischer, Avner; Kaplan, Alex; Carmon, Tal; Schwefel, Harald G. L.; Bartal, Guy; Cohen, Oren
2012-06-01
We predict and investigate the emission of high-order harmonics by atoms that cross intense laser hot spots that last for a nanosecond or longer. An atom that moves through a nanometer-scale hot spot at characteristic thermal velocity can emit high-order harmonics in a similar fashion to an atom that is irradiated by a short-duration (picosecond-scale) laser pulse. We analyze the collective emission from a thermal gas and from a jet of atoms. In both cases, the line shape of a high-order harmonic exhibits a narrow spike with spectral width that is determined by the bandwidth of the driving laser. Finally, we discuss a scheme for producing long-duration laser hot spots with intensity in the range of the intensity threshold for high-harmonic generation. In the proposed scheme, the hot spot is produced by a long laser pulse that is consecutively coupled to a high-quality micro-resonator and a metallic nano-antenna. This system may be used for generating ultra-narrow bandwidth extreme-ultraviolet radiation through frequency up-conversion of a low-cost compact pump laser.
Structure/processing relationships of highly ordered lead salt nanocrystal superlattices.
Hanrath, Tobias; Choi, Joshua J; Smilgies, Detlef-M
2009-10-27
We investigated the influence of processing conditions, nanocrystal/substrate interactions and solvent evaporation rate on the ordering of strongly interacting nanocrystals by synergistically combining electron microscopy and synchrotron-based small-angle X-ray scattering analysis. Spin-cast PbSe nanocrystal films exhibited submicrometer-sized supracrystals with face-centered cubic symmetry and (001)(s) planes aligned parallel to the substrate. The ordering of drop-cast lead salt nanocrystal films was sensitive to the nature of the substrate and solvent evaporation dynamics. Nanocrystal films drop-cast on rough indium tin oxide substrates were polycrystalline with small grain size and low degree of orientation with respect to the substrate, whereas films drop-cast on flat Si substrates formed highly ordered face-centered cubic supracrystals with close-packed (111)(s) planes parallel to the substrate. The spatial coherence of nanocrystal films drop-cast in the presence of saturated solvent vapor was significantly improved compared to films drop-cast in a dry environment. Solvent vapor annealing was demonstrated as a postdeposition technique to modify the ordering of nanocrystals in the thin film. Octane vapor significantly improved the long-range order and degree of orientation of initially disordered or polycrystalline nanocrystal assemblies. Exposure to 1,2-ethanedithiol vapor caused partial displacement of surface bound oleic acid ligands and drastically degraded the degree of order in the nanocrystal assembly. PMID:19728701
High-order Harmonic Generation Driven by Sub-Cycle Shaped Laser Field
NASA Astrophysics Data System (ADS)
Zheng, Yinghui; Zeng, Zhinan; Wei, Pengfei; Miao, Jing; Li, Ruxin; Xu, Zhizhan
High-order harmonic generation can be described by the semiclassical three-step model, in which an electron is freed, accelerated away from an atom or molecule by a strong oscillating laser field, and then, upon reversal of the field, careened back into its parent ion. The shaped laser field has been proved to be an effective tool to control the three-step process and consequently to achieve the high intensity harmonic generation or an isolated attosecond pulse generation by changing the relative phase, intensity ratio, polarization, etc, between the pulses of shaped laser field. High-order harmonic and attosecond pulse generation driven by a shaped laser field synthesized with two or three laser pulses of controlled related phase are reviewed.
Different time scales in plasmonically enhanced high-order-harmonic generation
NASA Astrophysics Data System (ADS)
Zagoya, C.; Bonner, M.; Chomet, H.; Slade, E.; Figueira de Morisson Faria, C.
2016-05-01
We investigate high-order-harmonic generation in inhomogeneous media for reduced dimensionality models. We perform a phase-space analysis, in which we identify specific features caused by the field inhomogeneity. We compute high-order-harmonic spectra using the numerical solution of the time-dependent Schrödinger equation, and provide an interpretation in terms of classical electron trajectories. We show that the dynamics of the system can be described by the interplay of high-frequency and slow-frequency oscillations, which are given by Mathieu's equations. The latter oscillations lead to an increase in the cutoff energy, and, for small values of the inhomogeneity parameter, take place over many driving-field cycles. In this case, the two processes can be decoupled and the oscillations can be described analytically.
A generic mode selection strategy for high-order mode gyrotrons operating at multiple frequencies
NASA Astrophysics Data System (ADS)
Franck, Joachim; Avramidis, Konstantinos; Gantenbein, Gerd; Illy, Stefan; Jin, Jianbo; Thumm, Manfred; Jelonnek, John
2015-01-01
High-power, high-frequency gyrotrons for electron cyclotron resonance heating and current drive, such as proposed for the demonstration thermonuclear fusion reactor DEMO, require operating modes of very high order. As it is shown, the selection of the operating modes for such gyrotrons can be based on multi-frequency operability. A general selection strategy is derived, suitable for multi-purpose multi-frequency gyrotrons with quasi-optical mode converter and single-disc output window. Two examples, one of them relevant for future DEMO gyrotron designs, are discussed.
High-order local spatial context modeling by spatialized random forest.
Ni, Bingbing; Yan, Shuicheng; Wang, Meng; Kassim, Ashraf A; Tian, Qi
2013-02-01
In this paper, we propose a novel method for spatial context modeling toward boosting visual discriminating power. We are particularly interested in how to model high-order local spatial contexts instead of the intensively studied second-order spatial contexts, i.e., co-occurrence relations. Motivated by the recent success of random forest in learning discriminative visual codebook, we present a spatialized random forest (SRF) approach, which can encode an unlimited length of high-order local spatial contexts. By spatially random neighbor selection and random histogram-bin partition during the tree construction, the SRF can explore much more complicated and informative local spatial patterns in a randomized manner. Owing to the discriminative capability test for the random partition in each tree node's split process, a set of informative high-order local spatial patterns are derived, and new images are then encoded by counting the occurrences of such discriminative local spatial patterns. Extensive comparison experiments on face recognition and object/scene classification clearly demonstrate the superiority of the proposed spatial context modeling method over other state-of-the-art approaches for this purpose. PMID:23060330
High-order lattice Boltzmann models for wall-bounded flows at finite Knudsen numbers
NASA Astrophysics Data System (ADS)
Feuchter, C.; Schleifenbaum, W.
2016-07-01
We analyze a large number of high-order discrete velocity models for solving the Boltzmann-Bhatnagar-Gross-Krook equation for finite Knudsen number flows. Using the Chapman-Enskog formalism, we prove for isothermal flows a relation identifying the resolved flow regimes for low Mach numbers. Although high-order lattice Boltzmann models recover flow regimes beyond the Navier-Stokes level, we observe for several models significant deviations from reference results. We found this to be caused by their inability to recover the Maxwell boundary condition exactly. By using supplementary conditions for the gas-surface interaction it is shown how to systematically generate discrete velocity models of any order with the inherent ability to fulfill the diffuse Maxwell boundary condition accurately. Both high-order quadratures and an exact representation of the boundary condition turn out to be crucial for achieving reliable results. For Poiseuille flow, we can reproduce the mass flow and slip velocity up to the Knudsen number of 1. Moreover, for small Knudsen numbers, the Knudsen layer behavior is recovered.
Gold Nanopyramids Assembled into High-Order Stacks Exhibit Increased SERS Response
Stoerzinger, Kelsey A.; Hasan, Warefta; Lin, Julia Y.; Robles, Alex; Odom, Teri W.
2010-01-01
This Letter describes how gold pyramidal nanoshells (nanopyramids) can be assembled into low- and high-order structures by varying the rate of solvent evaporation and surface wettability. Single-particle and individual-cluster dark field scattering spectra on isolated, dimers and trimers of nanopyramids were compared. We found that the short wavelength resonances blue-shifted as the particles assembled; the magnitude of this shift was greater for high-order structures. To test which assembled architecture supported a larger Raman-active volume, we compared their surface enhanced Raman scattering (SERS) response of the resonant Raman molecule methylene blue (λex = 633 nm). We discovered that high-order structures exhibited more Raman scattering compared to low-order assemblies. Finite-difference time-domain modeling of nanopyramid assemblies revealed that the highest electromagnetic field intensities were localized between adjacent particle faces, a result that was consistent with the SERS observations. Thus, the local spatial arrangement of the same number of nanoparticles in assembled clusters is an important design parameter for optimizing nanoparticle-based SERS sensors. PMID:21666758
Spring-Pearson, Senanu M.; Stone, Joshua K.; Doyle, Adina; Allender, Christopher J.; Okinaka, Richard T.; Mayo, Mark; Broomall, Stacey M.; Hill, Jessica M.; Karavis, Mark A.; Hubbard, Kyle S.; Insalaco, Joseph M.; McNew, Lauren A.; Rosenzweig, C. Nicole; Gibbons, Henry S.; Currie, Bart J.; Wagner, David M.; Keim, Paul; Tuanyok, Apichai
2015-01-01
The pangenomic diversity in Burkholderia pseudomallei is high, with approximately 5.8% of the genome consisting of genomic islands. Genomic islands are known hotspots for recombination driven primarily by site-specific recombination associated with tRNAs. However, recombination rates in other portions of the genome are also high, a feature we expected to disrupt gene order. We analyzed the pangenome of 37 isolates of B. pseudomallei and demonstrate that the pangenome is ‘open’, with approximately 136 new genes identified with each new genome sequenced, and that the global core genome consists of 4568±16 homologs. Genes associated with metabolism were statistically overrepresented in the core genome, and genes associated with mobile elements, disease, and motility were primarily associated with accessory portions of the pangenome. The frequency distribution of genes present in between 1 and 37 of the genomes analyzed matches well with a model of genome evolution in which 96% of the genome has very low recombination rates but 4% of the genome recombines readily. Using homologous genes among pairs of genomes, we found that gene order was highly conserved among strains, despite the high recombination rates previously observed. High rates of gene transfer and recombination are incompatible with retaining gene order unless these processes are either highly localized to specific sites within the genome, or are characterized by symmetrical gene gain and loss. Our results demonstrate that both processes occur: localized recombination introduces many new genes at relatively few sites, and recombination throughout the genome generates the novel multi-locus sequence types previously observed while preserving gene order. PMID:26484663
Goyal, Amit , Kang; Sukill
2012-02-21
Novel articles and methods to fabricate same with self-assembled nanodots and/or nanorods of a single or multicomponent material within another single or multicomponent material for use in electrical, electronic, magnetic, electromagnetic and electrooptical devices is disclosed. Self-assembled nanodots and/or nanorods are ordered arrays wherein ordering occurs due to strain minimization during growth of the materials. A simple method to accomplish this when depositing in-situ films is also disclosed. Device applications of resulting materials are in areas of superconductivity, photovoltaics, ferroelectrics, magnetoresistance, high density storage, solid state lighting, non-volatile memory, photoluminescence, thermoelectrics and in quantum dot lasers.
Goyal, Amit
2013-09-17
Novel articles and methods to fabricate same with self-assembled nanodots and/or nanorods of a single or multicomponent material within another single or multicomponent material for use in electrical, electronic, magnetic, electromagnetic and electrooptical devices is disclosed. Self-assembled nanodots and/or nanorods are ordered arrays wherein ordering occurs due to strain minimization during growth of the materials. A simple method to accomplish this when depositing in-situ films is also disclosed. Device applications of resulting materials are in areas of superconductivity, photovoltaics, ferroelectrics, magnetoresistance, high density storage, solid state lighting, non-volatile memory, photoluminescence, thermoelectrics and in quantum dot lasers.
Nonlinear Comparison of High-Order and Optimized Finite-Difference Schemes
NASA Technical Reports Server (NTRS)
Hixon, R.
1998-01-01
The effect of reducing the formal order of accuracy of a finite-difference scheme in order to optimize its high-frequency performance is investigated using the I-D nonlinear unsteady inviscid Burgers'equation. It is found that the benefits of optimization do carry over into nonlinear applications. Both explicit and compact schemes are compared to Tam and Webb's explicit 7-point Dispersion Relation Preserving scheme as well as a Spectral-like compact scheme derived following Lele's work. Results are given for the absolute and L2 errors as a function of time.
Role of ionization in orientation dependence of molecular high-order harmonic generation
NASA Astrophysics Data System (ADS)
Chen, Y. J.; Hu, Bambi
2009-12-01
We investigate the orientation dependence of high-order harmonic generation (HHG) from O2 and CO2 molecules using the strong-field approximation (SFA). Our simulations reveal the important modulation of the ionization to the HHG orientation dependence, especially at larger orientation angles. By virtue of a simplified model arising from the SFA, we show that this modulation can be read from the harmonic order where the HHG spectra at different orientation angles intersect. These results give suggestions on probing the molecular structure and dynamics using HHG.
Reexamining the high-order harmonic generation of HD molecule in non-Born-Oppenheimer approximation
NASA Astrophysics Data System (ADS)
Du, Hongchuan; Yue, Shengjun; Wang, Huiqiao; Wu, Hongmei; Hu, Bitao
2016-03-01
The high-order harmonic generation of the HD molecule is studied in non-Born-Oppenheimer approximation. It is found that there are only the odd harmonics in the harmonic spectrum of the HD molecule though the generation of even harmonics is possible in principle. Theoretical analysis [T. Kreibich et al., Phys. Rev. Lett. 87, 103901 (2001)] reveals that the nuclear dipole moment can contribute to the generation of the even harmonics, but the acceleration of the nucleus is about three orders of magnitude less than that of the electron. Hence, the even harmonics cannot be observed in the harmonic spectrum of the HD molecule.
Small-displacement measurements using high-order Hermite-Gauss modes
Sun, Hengxin; Liu, Kui; Liu, Zunlong; Guo, Pengliang; Zhang, Junxiang; Gao, Jiangrui
2014-03-24
We present a scheme for small-displacement measurements using high-order Hermite-Gauss modes and balanced homodyne detection. We demonstrate its use with experimental results of displacement measurements using fundamental transverse mode TEM{sub 00} and first order transverse mode TEM{sub 10} as signal modes. The results show a factor of 1.41 improvement in measurement precision with the TEM{sub 10} mode compared with that with the TEM{sub 00} mode. This scheme has potential applications in precision metrology, atomic force microscopy, and optical imaging.
Application of organic compounds for high-order harmonic generation of ultrashort pulses
NASA Astrophysics Data System (ADS)
Ganeev, R. A.
2016-02-01
The studies of the high-order nonlinear optical properties of a few organic compounds (polyvinyl alcohol, polyethylene, sugar, coffee, and leaf) are reported. Harmonic generation in the laser-produced plasmas containing the molecules and large particles of above materials is demonstrated. These studies showed that the harmonic distributions and harmonic cutoffs from organic compound plasmas were similar to those from the graphite ablation. The characteristic feature of observed harmonic spectra was the presence of bluesided lobes near the lower-order harmonics.
Gkortsas, Vasileios-Marios; Bhardwaj, Siddharth; Lai, Chien-Jen; Hong, Kyung-Han; Falcao-Filho, Edilson L.; Kaertner, Franz X.
2011-07-15
High-order harmonic generation efficiency is theoretically modeled and compared with experiments using 400 and 800 nm driver pulses. It is shown that, for a short drive wavelength and a Keldysh parameter larger than 1, the Ammosov-Delone-Krainov (ADK) ionization model does not give a good agreement between theory and experiment. Since the ADK ionization model only accounts for tunnel ionization, it underestimates the yield of low-order harmonics from the wings of the driver pulse. In contrast, the Yudin-Ivanov ionization model [Phys. Rev. A 64, 013409 (2001)], which accounts for both tunnel and multiphoton ionization, gives much better agreement with the experimental results.
New high order iterative scheme in the solution of convection-diffusion equation
NASA Astrophysics Data System (ADS)
Ling, Sam Teek; Ali, Norhashidah Hj. Mohd.
2014-07-01
In this paper, a new fourth-order nine-point finite difference scheme based on the rotated grid combined with the traditional Successive Over Relaxation (SOR)-type iterative method is discussed in solving the two-dimensional convection-diffusion partial differential equation (pde) with variable coefficients. Numerical experiments are carried out to verify the high accuracy solution of the scheme. Comparisons with the exact solutions also show that the rotated scheme converges faster than the existing compact scheme of the same order.
Rapid, high-order accurate calculation of flows due to free source or vortex distributions
NASA Technical Reports Server (NTRS)
Halsey, D.
1981-01-01
Fast Fourier transform (FFT) techniques are applied to the problem of finding the flow due to source or vortex distributions in the field outside an airfoil or other two-dimensional body. Either the complex potential or the complex velocity may be obtained to a high order of accuracy, with computational effort similar to that required by second-order fast Poisson solvers. These techniques are applicable to general flow problems with compressibility and rotation. An example is given of their use for inviscid compressible flow.
High order asymptotic preserving nodal discontinuous Galerkin IMEX schemes for the BGK equation
NASA Astrophysics Data System (ADS)
Xiong, Tao; Jang, Juhi; Li, Fengyan; Qiu, Jing-Mei
2015-03-01
In this paper, we develop high-order asymptotic preserving (AP) schemes for the BGK equation in a hyperbolic scaling, which leads to the macroscopic models such as the Euler and compressible Navier-Stokes equations in the asymptotic limit. Our approaches are based on the so-called micro-macro formulation of the kinetic equation which involves a natural decomposition of the problem to the equilibrium and the non-equilibrium parts. The proposed methods are formulated for the BGK equation with constant or spatially variant Knudsen number. The new ingredients for the proposed methods to achieve high order accuracy are the following: we introduce discontinuous Galerkin (DG) discretization of arbitrary order of accuracy with nodal Lagrangian basis functions in space; we employ a high order globally stiffly accurate implicit-explicit (IMEX) Runge-Kutta (RK) scheme as time discretization. Two versions of the schemes are proposed: Scheme I is a direct formulation based on the micro-macro decomposition of the BGK equation, while Scheme II, motivated by the asymptotic analysis for the continuous problem, utilizes certain properties of the projection operator. Compared with Scheme I, Scheme II not only has better computational efficiency (the computational cost is reduced by half roughly), but also allows the establishment of a formal asymptotic analysis. Specifically, it is demonstrated that when 0 < ε ≪ 1, Scheme II, up to O (ε2), becomes a local DG discretization with an explicit RK method for the macroscopic compressible Navier-Stokes equations, a method in a similar spirit to the ones in Bassi and Rebay (1997) [3], Cockburn and Shu (1998) [16]. Numerical results are presented for a wide range of Knudsen number to illustrate the effectiveness and high order accuracy of the methods.
NASA Astrophysics Data System (ADS)
Schaal, Kevin; Bauer, Andreas; Chandrashekar, Praveen; Pakmor, Rüdiger; Klingenberg, Christian; Springel, Volker
2015-11-01
Solving the Euler equations of ideal hydrodynamics as accurately and efficiently as possible is a key requirement in many astrophysical simulations. It is therefore important to continuously advance the numerical methods implemented in current astrophysical codes, especially also in light of evolving computer technology, which favours certain computational approaches over others. Here we introduce the new adaptive mesh refinement (AMR) code TENET, which employs a high-order discontinuous Galerkin (DG) scheme for hydrodynamics. The Euler equations in this method are solved in a weak formulation with a polynomial basis by means of explicit Runge-Kutta time integration and Gauss-Legendre quadrature. This approach offers significant advantages over commonly employed second-order finite-volume (FV) solvers. In particular, the higher order capability renders it computationally more efficient, in the sense that the same precision can be obtained at significantly less computational cost. Also, the DG scheme inherently conserves angular momentum in regions where no limiting takes place, and it typically produces much smaller numerical diffusion and advection errors than an FV approach. A further advantage lies in a more natural handling of AMR refinement boundaries, where a fall-back to first order can be avoided. Finally, DG requires no wide stencils at high order, and offers an improved data locality and a focus on local computations, which is favourable for current and upcoming highly parallel supercomputers. We describe the formulation and implementation details of our new code, and demonstrate its performance and accuracy with a set of two- and three-dimensional test problems. The results confirm that DG schemes have a high potential for astrophysical applications.
High-Order Simulation of Non-Linear Oscillations and Shocks in the Solar Atmosphere
NASA Technical Reports Server (NTRS)
Bryson, S.; Kosovichev, A.; Levy, D.
2004-01-01
The solar atmosphere presents a rich source of highly non-linear magneto-hydrodynamic phenomena: strong gradients and forcing terms result in both large shocks and oscillations. The additional requirements of energy balance and initialization in hydrostatic equilibrium compound the challenge of this problem. A wealth of observational data allows us to check the results of our simulations. The problem of simulating the solar atmosphere provides, in addition to an interesting system in its own right, a challenging testbed for high-order shock-capturing methods. We discuss the challenge of simulating solar atmospheric phenomena, concentrating on various high-order central methods ranging from second to fourth order. Our method is based on the central-upwind scheme of Kurganov, Noelle and Petrova, which we extend to high order via various interpolants. We investigate various initial data for our simulations, corresponding to observed conditions in different regions of the solar surface: the normal quiet sun and sunspots. When non-oscillatory using second- and third-order methods, we are able to reproduce non-trivial observational results. In particular we find a correlation between initial data and both the shock speeds and particle oscillation spectra that match observations in the corresponding regions. When using fourth-order WENO interpolants, we find that while the individual shock profiles at any given time appear non-oscillatory, spurious oscillations appear in the fields after long time integrations. The issue of initialization in hydrostatic equilibrium raises difficult issues. Careful treatment of the gravitational source term can reduce violations of hydrostatic equilibrium, but difficulties remain, primarily due to discontinuities in the piecewise-polynomial reconstructions. In the case of the Euler equations in gravity, the use of high-order methods reduces the violation of hydrostatic equilibrium to a sufficiently low level for the above described results
Curvilinear finite-volume schemes using high-order compact interpolation
Fosso P, Arnaud Deniau, Hugues; Sicot, Frederic; Sagaut, Pierre
2010-07-01
During the last years, the need of high fidelity simulations on complex geometries for aeroacoustics predictions has grown. Most of high fidelity numerical schemes, in terms of low dissipative and low dispersive effects, lie on finite-difference (FD) approach. But for industrial applications, FD schemes are less robust compared to finite-volume (FV) ones. Thus the present study focuses on the development of a new compact FV scheme for two- and three-dimensional applications. The proposed schemes are formulated in the physical space and not in the computational space as it is the case in most of the known works. Therefore, they are more appropriate for general grids. They are based on compact interpolation to approximate interface-averaged field values using known cell-averaged values. For each interface, the interpolation coefficients are determined by matching Taylor series expansions around the interface center. Two types of schemes can be distinguished. The first one uses only the curvilinear abscissa along a mesh line to derive a sixth-order compact interpolation formulae while the second, more general, uses coordinates in a spatial three-dimensional frame well chosen. This latter is formally sixth-order accurate in a preferred direction almost orthogonal to the interface and at most fourth-order accurate in transversal directions. For non-linear problems, different approaches can be used to keep the high-order scheme. However, in the present paper, a MUSCL-like formulation was sufficient to address the presented test cases. All schemes have been modified to treat multiblock and periodic interfaces in such a way that high-order accuracy, stability, good spectral resolution, conservativeness and low computational costs are guaranteed. This is a first step to insure good scalability of the schemes although parallel performances issues are not addressed. As high frequency waves, badly resolved, could be amplified and then destabilize the scheme, compact filtering
Valley in the efficiency of the high-order harmonic yield at ultra-high laser intensities.
Pérez-Hernández, J A; Roso, L; Zaïr, A; Plaja, L
2011-09-26
We study the process of high-order harmonic generation using laser pulses with non-adiabatic turn-on and intensities well above saturation. As a main point, we report the existence of a valley structure in the efficiency of single-atom high-order harmonic generation with increasing laser intensities. Consequently, after an initial decrease, the high-frequency radiation yield is shown to increase for higher intensities, returning to a level similar to the case below saturation. Such behavior contradicts the general belief of a progressive degradation of the harmonic emission at ultrahigh intensities, based on the experience with pulses with smoother turn-on. We shall show that this behavior corresponds to the emergence of a new pathway for high-order harmonic generation, which takes place during the pulse turn-on. Our study combines trajectory analysis, wavelet techniques and the numerical integration of 3-Dimensional Time Dependent Schrödinger Equation. The increase in efficiency raises the possibility of employing ultrahigh intensities to generate high-frequency radiation beyond the water window. PMID:21996884
Constructing Higher-Order DNA Nanoarchitectures with Highly Purified DNA Nanocages.
Xing, Shu; Jiang, Dawei; Li, Fan; Li, Jiang; Li, Qian; Huang, Qing; Guo, Linjie; Xia, Jiaoyun; Shi, Jiye; Fan, Chunhai; Zhang, Lan; Wang, Lihua
2015-06-24
DNA nanostructures have attracted great attention due to their precisely controllable geometry and great potential in various areas including bottom-up self-assembly. However, construction of higher-order DNA nanoarchitectures with individual DNA nanostructures is often hampered with the purity and quantity of these "bricks". Here, we introduced size exclusion chromatography (SEC) to prepare highly purified tetrahedral DNA nanocages in large scale and demonstrated that precise quantification of DNA nanocages was the key to the formation of higher-order DNA nanoarchitectures. We successfully purified a series of DNA nanocages with different sizes, including seven DNA tetrahedra with different edge lengths (7, 10, 13, 17, 20, 26, 30 bp) and one trigonal bipyramid with a 20-bp edge. These highly purified and aggregation-free DNA nanocages could be self-assembled into higher-order DNA nanoarchitectures with extraordinarily high yields (98% for dimer and 95% for trimer). As a comparison, unpurified DNA nanocages resulted in low yield of 14% for dimer and 12% for trimer, respectively. AFM images cleraly presented the characteristic structure of monomer, dimer and trimer, impling the purified DNA nanocages well-formed the designed nanoarchitectures. Therefore, we have demonstrated that highly purified DNA nanocages are excellent "bricks" for DNA nanotechnology and show great potential in various applications of DNA nanomaterials. PMID:25345465
Non-leachable highly luminescent ordered mesoporous SiO2 spherical particles
NASA Astrophysics Data System (ADS)
Rocha, L. A.; Caiut, J. M. A.; Messaddeq, Y.; Ribeiro, S. J. L.; Martines, M. A. U.; Freiria, J. do C.; Dexpert-Ghys, J.; Verelst, M.
2010-04-01
Ordered mesoporous highly luminescent SiO2 particles have been synthesized by spray pyrolysis from solutions containing tetraethylorthosilicate (TEOS) and either cetyltrimethylammonium bromide (CTAB) or the block copolymer Pluronic F-68 as structure-directing agents. Rhodamine B (RhB)-containing samples were prepared by using a simple wet impregnation method followed by the growing of a second silica shell in order to prevent leaching of the dye. The obtained materials were characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM), powder x-ray diffraction (XRD), ultraviolet-visible spectroscopy (UV-vis) and photoluminescence (PL). Powders with polydisperse spherical grains were obtained displaying an ordered hexagonal array of mesochannels. Luminescence results reveal that RhB molecules have been successfully encapsulated into the channels of mesoporous particles as monomeric species and that a well-defined silica coating hindered dye leaching.
Role of multiphoton bunching in high-order ghost imaging with thermal light sources
Liu Qian; Chen Xihao; Luo Kaihong; Wu Lingan; Wu Wei
2009-05-15
The intrinsic higher-order correlation of intensities which gives a measure of 'pure' correlations among photons (corresponding to multiphoton bunching) is investigated with regard to ghost imaging with thermal light. The synchronous detection of the same light field by all reference detectors, which is a necessary condition for achieving an Nth-order ghost image based on N-photon bunching, is discussed. Furthermore, it is found that the enhanced high visibility of Nth-order ghost imaging is a consequence of the contribution of N-photon bunching, which is not a small value but is equal to the sum of all contributions from (N-1)-photon bunching. These results differ from those obtained by certain other groups.
Wang, Jie; Zong, Qun; Su, Rui; Tian, Bailing
2014-05-01
This paper investigates the problem of tracking control with uncertainties for a flexible air-breathing hypersonic vehicle (FAHV). In order to overcome the analytical intractability of this model, an Input-Output linearization model is constructed for the purpose of feedback control design. Then, the continuous finite time convergence high order sliding mode controller is designed for the Input-Output linearization model without uncertainties. In addition, a nonlinear disturbance observer is applied to estimate the uncertainties in order to compensate the controller and disturbance suppression, where disturbance observer and controller synthesis design is obtained. Finally, the synthesis of controller and disturbance observer is used to achieve the tracking for the velocity and altitude of the FAHV and simulations are presented to illustrate the effectiveness of the control strategies. PMID:24534328
High order surface aberration contributions from phase space analysis of differential rays.
Chen, Bo; Herkommer, Alois M
2016-03-21
Phase space methods are very popular for illumination systems or paraxial system analysis. In this paper it will be shown that it is also a promising tool to visualize and quantify surface aberration contributions, including all orders. The method is based on the calculation and propagation of a differential ray pair. In order to validate the method we compare to Aldis calculus, an exact method to determine high order aberrations in rotational symmetric systems. A triplet lens is used as an example to visualize the results. The analysis indicates that the phase space method is a very good approximation to Aldis calculus and moreover it is not limited to any symmetry assumptions. PMID:27136789
Research on high-order approximation of radiative transfer equation for image reconstruction
NASA Astrophysics Data System (ADS)
Ma, Wenjuan; Gao, Feng; Wu, Linhui; Yi, Xi; Zhu, Pingping; Zhao, Huijuan
2011-03-01
In this article, we derive the two-dimensional spherical harmonics equations to three-order (P3) of Radiative Transfer Equation for anisotropic scattering. We also solved this equations using Galerkin finite element method and compared the solutions with the first-order diffusion equation and Monte Carlo simulation. the benchmark problems are tested, and we found that the developed three-order model with high absorb coefficient is able to significantly improve the diffusion solution in circle geometry, and the radiance distribution close to light source is more accurate. It is significant for accurate modeling of light propagation in small tissue geometries in small animal imaging. Then, the inverse model for the simultaneous reconstruction of the absorption images is proposed based on P3 equations, and the feasibility and effectiveness of this method are proved by the simulation.
High-order cyclo-difference techniques: An alternative to finite differences
NASA Technical Reports Server (NTRS)
Carpenter, Mark H.; Otto, John C.
1993-01-01
The summation-by-parts energy norm is used to establish a new class of high-order finite-difference techniques referred to here as 'cyclo-difference' techniques. These techniques are constructed cyclically from stable subelements, and require no numerical boundary conditions; when coupled with the simultaneous approximation term (SAT) boundary treatment, they are time asymptotically stable for an arbitrary hyperbolic system. These techniques are similar to spectral element techniques and are ideally suited for parallel implementation, but do not require special collocation points or orthogonal basis functions. The principal focus is on methods of sixth-order formal accuracy or less; however, these methods could be extended in principle to any arbitrary order of accuracy.
Coaxial higher-order mode damper employing a high-pass filter
Kang, Y.W.; Jiang, X.
1997-08-01
Two different types of coaxial higher-order mode (HOM) dampers have been investigated for the Advanced Photon Source (APS) storage ring cavities: e-probe dampers and h-loop dampers. Realization of the h-loop dampers has been difficult because the loop antenna couples not only to the HOMs but also to the accelerating mode and results in loss of Q at the fundamental frequency. Previously, a first-order fundamental rejection filter was tested with unsatisfactory rejection characteristics. This problem can be overcome by using a higher-order high-pass filter between the loop and the matched load. Prototype dampers have been fabricated and tested in a storage ring single-cell cavity and the damping characteristic was analyzed.
NASA Astrophysics Data System (ADS)
Xue, Zheng-wei; Guo, Ya-ding; Chen, Zhong-zheng; Li, Shuai; Xu, Yi-ting; Xu, Jian; Wang, Bao-shan; Gong, Ke-ling; Gao, Hong-wei; Bo, Yong; Peng, Qin-jun; Cui, Da-fu; Xu, Zu-yan
2015-12-01
We present a compact refractive shaping system for actively compensating low order aberrations of high power slab lasers. The shaping system includes three spherical lenses and two cylindrical lenses. Both theoretical and experimental investigations were performed to evaluate the compensation capability of the refractive shaping system. For a typical input beam with large low order aberrations of peak-to-valley (PV)=66.10λ and root-mean-square (RMS)=16.05λ, adjusting the distance between lenses, the wavefront aberrations are reduced to PV=0.48λ, RMS=0.10λ for the theoretical simulation and PV=0.50λ, RMS=0.11λ for the experimental result, respectively. It indicates that the main low order aberrations of defocus and 0° astigmatism can be significantly compensated by actively adjusting the distance between lenses and the experimental result agree well with the theoretical simulation.
A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions
NASA Technical Reports Server (NTRS)
Sun, Xian-He; Zhuang, Yu
1997-01-01
In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.
Wilcox, Lucas C.; Stadler, Georg; Burstedde, Carsten; Ghattas, Omar
2010-12-10
We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic-acoustic media. A velocity-strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic-acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic-acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case. Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.
NASA Astrophysics Data System (ADS)
Wilcox, Lucas C.; Stadler, Georg; Burstedde, Carsten; Ghattas, Omar
2010-12-01
We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic-acoustic media. A velocity-strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic-acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic-acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case. Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.
NASA Technical Reports Server (NTRS)
Shu, Chi-Wang
2004-01-01
This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier
Giraldo, Francis X. . E-mail: giraldo@nrlmry.navy.mil
2006-05-20
High-order triangle-based discontinuous Galerkin (DG) methods for hyperbolic equations on a rotating sphere are presented. The DG method can be characterized as the fusion of finite elements with finite volumes. This DG formulation uses high-order Lagrange polynomials on the triangle using nodal sets up to 15th order. The finite element-type area integrals are evaluated using order 2N Gauss cubature rules. This leads to a full mass matrix which, unlike for continuous Galerkin (CG) methods such as the spectral element (SE) method presented in Giraldo and Warburton [A nodal triangle-based spectral element method for the shallow water equations on the sphere, J. Comput. Phys. 207 (2005) 129-150], is small, local and efficient to invert. Two types of finite volume-type flux integrals are studied: a set based on Gauss-Lobatto quadrature points (order 2N - 1) and a set based on Gauss quadrature points (order 2N). Furthermore, we explore conservation and advection forms as well as strong and weak forms. Seven test cases are used to compare the different methods including some with scale contractions and shock waves. All three strong forms performed extremely well with the strong conservation form with 2N integration being the most accurate of the four DG methods studied. The strong advection form with 2N integration performed extremely well even for flows with shock waves. The strong conservation form with 2N - 1 integration yielded results almost as good as those with 2N while being less expensive. All the DG methods performed better than the SE method for almost all the test cases, especially for those with strong discontinuities. Finally, the DG methods required less computing time than the SE method due to the local nature of the mass matrix.
A Framework for Efficient Structured Max-Margin Learning of High-Order MRF Models.
Komodakis, Nikos; Xiang, Bo; Paragios, Nikos
2015-07-01
We present a very general algorithm for structured prediction learning that is able to efficiently handle discrete MRFs/CRFs (including both pairwise and higher-order models) so long as they can admit a decomposition into tractable subproblems. At its core, it relies on a dual decomposition principle that has been recently employed in the task of MRF optimization. By properly combining such an approach with a max-margin learning method, the proposed framework manages to reduce the training of a complex high-order MRF to the parallel training of a series of simple slave MRFs that are much easier to handle. This leads to a very efficient and general learning scheme that relies on solid mathematical principles. We thoroughly analyze its theoretical properties, and also show that it can yield learning algorithms of increasing accuracy since it naturally allows a hierarchy of convex relaxations to be used for loss-augmented MAP-MRF inference within a max-margin learning approach. Furthermore, it can be easily adapted to take advantage of the special structure that may be present in a given class of MRFs. We demonstrate the generality and flexibility of our approach by testing it on a variety of scenarios, including training of pairwise and higher-order MRFs, training by using different types of regularizers and/or different types of dissimilarity loss functions, as well as by learning of appropriate models for a variety of vision tasks (including high-order models for compact pose-invariant shape priors, knowledge-based segmentation, image denoising, stereo matching as well as high-order Potts MRFs). PMID:26352450
On controlling nonlinear dissipation in high order filter methods for ideal and non-ideal MHD
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sjogreen, B.
2004-01-01
The newly developed adaptive numerical dissipation control in spatially high order filter schemes for the compressible Euler and Navier-Stokes equations has been recently extended to the ideal and non-ideal magnetohydrodynamics (MHD) equations. These filter schemes are applicable to complex unsteady MHD high-speed shock/shear/turbulence problems. They also provide a natural and efficient way for the minimization of Div(B) numerical error. The adaptive numerical dissipation mechanism 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 from numerical dissipation contamination. The numerical dissipation considered consists of high order linear dissipation for the suppression of high frequency oscillation and the nonlinear dissipative portion of high-resolution shock-capturing methods for discontinuity capturing. The applicable nonlinear dissipative portion of high-resolution shock-capturing methods is very general. The objective of this paper is to investigate the performance of three commonly used types of nonlinear numerical dissipation for both the ideal and non-ideal MHD.
High Order Finite Volume Nonlinear Schemes for the Boltzmann Transport Equation
Bihari, B L; Brown, P N
2005-03-29
The authors apply the nonlinear WENO (Weighted Essentially Nonoscillatory) scheme to the spatial discretization of the Boltzmann Transport Equation modeling linear particle transport. The method is a finite volume scheme which ensures not only conservation, but also provides for a more natural handling of boundary conditions, material properties and source terms, as well as an easier parallel implementation and post processing. It is nonlinear in the sense that the stencil depends on the solution at each time step or iteration level. By biasing the gradient calculation towards the stencil with smaller derivatives, the scheme eliminates the Gibb's phenomenon with oscillations of size O(1) and reduces them to O(h{sup r}), where h is the mesh size and r is the order of accuracy. The current implementation is three-dimensional, generalized for unequally spaced meshes, fully parallelized, and up to fifth order accurate (WENO5) in space. For unsteady problems, the resulting nonlinear spatial discretization yields a set of ODE's in time, which in turn is solved via high order implicit time-stepping with error control. For the steady-state case, they need to solve the non-linear system, typically by Newton-Krylov iterations. There are several numerical examples presented to demonstrate the accuracy, non-oscillatory nature and efficiency of these high order methods, in comparison with other fixed-stencil schemes.
Highly Ordered Organic Molecular Thin Films on Silicon Studied by STM and LEED
NASA Astrophysics Data System (ADS)
Wagner, Sean; Zhang, Pengpeng
2014-03-01
Achieving growth of long-range ordered organic molecular thin films on inorganic substrates continues to be a significant challenge for organic electronics applications. Here, we report the growth of highly ordered zinc phthalocyanine (ZnPc) thin films both in-plane and out-of-plane on the deactivated Si(111) surface by scanning tunneling microscopy (STM) and low energy electron diffraction (LEED). By adjusting the substrate temperature during deposition, the anisotropic step-flow growth mode can be accessed causing a reduction in the substrate symmetry which allows for the long-range in-plane ordering as well as the decrease of grain boundary density. Additionally, the ZnPc molecules are able to maintain a highly ordered configuration in multi-layers despite a gradual decrease in the molecule-substrate interaction, which is attributed to the strong interlayer π- π interaction. We appreciate the fruitful discussion with Prof. Richard Lunt. This research is funded by the DOE Office of Science Early Career Research Program (Grant number DE-SC0006400) through the Office of Basic Energy Sciences.
High-energy amplitudes in N = 4 SYM in the next-to-leading order
Chirilli, Giovanni; Balitsky, Ian
2010-03-16
In this study, the high-energy behavior of the N = 4 SYM amplitudes in the Regge limit can be calculated order by order in perturbation theory using the high-energy operator expansion in Wilson lines. At large $N_c$, a typical four-point amplitude is determined by a single BFKL pomeron. The conformal structure of the four-point amplitude is fixed in terms of two functions: pomeron intercept and the coefficient function in front of the pomeron (the product of two residues). The pomeron intercept is universal while the coefficient function depends on the correlator in question. The intercept is known in the firstmore » two orders in coupling constant: BFKL intercept and NLO BFKL intercept calculated in Ref. 1. As an example of using the Wilson-line OPE, we calculate the coefficient function in front of the pomeron for the correlator of four $Z^2$ currents in the first two orders in perturbation theory.« less
Toward a consistent framework for high order mesh refinement schemes in numerical relativity
NASA Astrophysics Data System (ADS)
Mongwane, Bishop
2015-05-01
It has now become customary in the field of numerical relativity to couple high order finite difference schemes to mesh refinement algorithms. To this end, different modifications to the standard Berger-Oliger adaptive mesh refinement algorithm have been proposed. In this work we present a fourth order stable mesh refinement scheme with sub-cycling in time for numerical relativity. We do not use buffer zones to deal with refinement boundaries but explicitly specify boundary data for refined grids. We argue that the incompatibility of the standard mesh refinement algorithm with higher order Runge Kutta methods is a manifestation of order reduction phenomena, caused by inconsistent application of boundary data in the refined grids. Our scheme also addresses the problem of spurious reflections that are generated when propagating waves cross mesh refinement boundaries. We introduce a transition zone on refined levels within which the phase velocity of propagating modes is allowed to decelerate in order to smoothly match the phase velocity of coarser grids. We apply the method to test problems involving propagating waves and show a significant reduction in spurious reflections.
Capturing non-equilibrium phenomena in rarefied polyatomic gases: A high-order macroscopic model
NASA Astrophysics Data System (ADS)
Rahimi, Behnam; Struchtrup, Henning
2014-05-01
A high-order macroscopic model for the accurate description of rarefied polyatomic gas flows is introduced based on a kinetic equation of Bhatnagar-Gross-Krook (BGK)-type, where the different energy exchange processes are accounted for by two collision terms. The order of magnitude method is applied to the primary moment equations to acquire the optimized moment definitions and the final scaled set of Grad's 36 moment equations for polyatomic gases. The two Knudsen numbers of the system are used for model reduction in terms of their powers, which yields a wide range of different reduced systems, a total of 13 different orders. These include, at lower order, a modification of the Navier-Stokes-Fourier (NSF) equations which shows considerable extended range of validity in comparison to the classical NSF equations. The highest order of accuracy considered gives a set of 18 regularized partial differential equations (PDEs) (R18). Attenuation and speed of linear waves are studied as the first application of the many sets of equations. For frequencies where the internal degrees of freedom are effectively frozen, the equations reproduce the behavior of monatomic gases.
Numerical pricing of options using high-order compact finite difference schemes
NASA Astrophysics Data System (ADS)
Tangman, D. Y.; Gopaul, A.; Bhuruth, M.
2008-09-01
We consider high-order compact (HOC) schemes for quasilinear parabolic partial differential equations to discretise the Black-Scholes PDE for the numerical pricing of European and American options. We show that for the heat equation with smooth initial conditions, the HOC schemes attain clear fourth-order convergence but fail if non-smooth payoff conditions are used. To restore the fourth-order convergence, we use a grid stretching that concentrates grid nodes at the strike price for European options. For an American option, an efficient procedure is also described to compute the option price, Greeks and the optimal exercise curve. Comparisons with a fourth-order non-compact scheme are also done. However, fourth-order convergence is not experienced with this strategy. To improve the convergence rate for American options, we discuss the use of a front-fixing transformation with the HOC scheme. We also show that the HOC scheme with grid stretching along the asset price dimension gives accurate numerical solutions for European options under stochastic volatility.
Modelling stock order flows with non-homogeneous intensities from high-frequency data
NASA Astrophysics Data System (ADS)
Gorshenin, Andrey K.; Korolev, Victor Yu.; Zeifman, Alexander I.; Shorgin, Sergey Ya.; Chertok, Andrey V.; Evstafyev, Artem I.; Korchagin, Alexander Yu.
2013-10-01
A micro-scale model is proposed for the evolution of such information system as the limit order book in financial markets. Within this model, the flows of orders (claims) are described by doubly stochastic Poisson processes taking account of the stochastic character of intensities of buy and sell orders that determine the price discovery mechanism. The proposed multiplicative model of stochastic intensities makes it possible to analyze the characteristics of the order flows as well as the instantaneous proportion of the forces of buyers and sellers, that is, the imbalance process, without modelling the external information background. The proposed model gives the opportunity to link the micro-scale (high-frequency) dynamics of the limit order book with the macro-scale models of stock price processes of the form of subordinated Wiener processes by means of limit theorems of probability theory and hence, to use the normal variance-mean mixture models of the corresponding heavy-tailed distributions. The approach can be useful in different areas with similar properties (e.g., in plasma physics).
Wong, M. C. H.; Brichta, J.-P.; Bhardwaj, V. R.
2010-06-15
We report detailed measurements of high-order harmonic generation in chloromethane molecules (CCl{sub 4}, CHCl{sub 3}, and CH{sub 2}Cl{sub 2}) to show that fingerprints of symmetry and electronic structure can be decoded from high-order harmonic generation even in complex randomly oriented molecules. In our measurements, orbital symmetries of these molecules are manifested as both extended harmonic cutoffs and a local minimum in the ellipticity dependence of the cut-off harmonics, suggesting the occurrence of quantum interferences during ionization. The harmonic spectra exhibit distinct interference minima at {approx}42 and {approx}60 eV. We attribute the former to the Cooper minimum in the photoionization cross section and the latter to intramolecular interference during the recombination process.
High-order harmonic generation from C{sub 60}-rich plasma
Ganeev, R. A.; Elouga Bom, L. B.; Ozaki, T.; Wong, M. C. H.; Brichta, J.-P.; Bhardwaj, V. R.; Redkin, P. V.
2009-10-15
We performed systematic investigation of high-order harmonic generation from fullerene-rich laser-produced plasmas. We studied harmonic generation by varying several experimental parameters, such as the delay between the ablation and driving pulses, and divergence and polarization of the pump laser. Enhancement of harmonic yield is observed near 20 eV, which is attributed to the influence of a broadband plasmon resonance of C{sub 60} on the nonlinear optical response of fullerene-rich plasma. This increase in the harmonic intensity occurs despite the increased absorption by C{sub 60} at these wavelengths. Using simulations based on time-dependent density-functional theory, we confirm that this effect is due to the influence of collective excitations. We compare harmonic generation from fullerenes using lasers with 793 nm and 396 nm wavelengths, which show the influence of plasmon resonance on the conversion efficiency of high-order harmonics for different laser wavelengths.
Role of long quantum orbits in high-order harmonic generation
Milosevic, D.B.; Becker, W.
2002-12-01
Single-atom high-order harmonic generation is considered in the strong-field approximation, as formulated in the Lewenstein model, and analyzed in terms of quantum orbits. Orbits are classified according to the solutions of the saddle-point equations. The results of a numerical integration are compared with the saddle-point approximation and the uniform approximation. Approximate analytical solutions for long orbits are presented. The formalism developed is used to analyze the enhancement of high-order harmonic generation near channel closings. The enhancements exactly at the channel closings are extremely narrow and built up by the constructive interference of a very large number of quantum orbits. Additional broader enhancements occur slightly below channel closings. They are generated by the interplay of a medium number of orbits.
Real Gas Computation Using an Energy Relaxation Method and High-Order WENO Schemes
NASA Technical Reports Server (NTRS)
Montarnal, Philippe; Shu, Chi-Wang
1998-01-01
In this paper, we use a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition into two parts: one part is associated with a simpler pressure law and the other part (the nonlinear deviation) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the first part. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.
A third-order-accurate upwind scheme for Navier-Stokes solutions at high Reynolds numbers
NASA Astrophysics Data System (ADS)
Agarwal, R. K.
1981-01-01
A third-order-accurate upwind scheme is presented for solution of the steady two-dimensional Navier-Stokes equations in stream-function/vorticity form. The scheme is found to be accurate and stable at high Reynolds numbers. A series of test computations is performed on flows with large recirculating regions. In particular, highly accurate solutions are obtained for flow in a driven square cavity up to Reynolds numbers of 10,000. These computations are used to critically evaluate the accuracy of other existing first- and second-order-accurate upwind schemes. In addition, computations are carried out for flow in a channel with symmetric sudden expansion, flow in a channel with a symmetrically placed blunt base, and the flowfield of an impinging jet. Good agreement is obtained with the computations of other investigators as well as with the available experimental data.
NASA Astrophysics Data System (ADS)
Qu, Fengyu; Lin, Huiming; Wu, Xiang; Li, Xiaofeng; Qiu, Shilun; Zhu, Guangshan
2010-05-01
The bimodal porous structured silica materials consisting of macropores with the diameter of 5-20 μm and framework-like mesopores with the diameter of 4.7-6.0 nm were prepared using natural Manchurian ash and mango linin as macropored hard templates and P123 as mesopore soft templates, respectively. The macroporous structures of Manchurian ash and mango linin were replicated with the walls containing highly ordered mesoporous silica as well. As-synthesized dual porous silica was characterized by scanning electron microscope (SEM), powder X-ray diffraction (XRD), transmission electron microscope (TEM) and nitrogen adsorption/desorption, fourier transform IR (FTIR) spectroscopy, and thermo-gravimetric analyzer (TGA). Ibuprofen (Ibu) was employed as a model drug and the release profiles showed that the dual porous material had a sustained drug delivery capability. And such highly ordered dual pore silica materials may have potential applications for bimolecular adsorption/separation and tissue repairing.
Psychological support for junior high school students: sibling order and sex.
Terada, Tomonori; Kasai, Makiko; Asano, Koji
2006-08-01
This study is a re-analysis of published data on psychological support for 609 junior high school students (317 boys, 292 girls, mean age = 14.1, SD = 0.8) based on the self-report, Psychological Support Scale, to evaluate sibling order as eldest or youngest and sex. In an earlier study, the questionnaire had been modified to be applicable to junior high school students. The study re-examined the data by extracting samples for categories of eldest and youngest siblings, for re-analysis of self-reported psychological support by sibling order and sex. Eldest children reported receiving more psychological support from both mother and father than youngest. Also, eldest boys received significantly greater psychological support from both the parents than the youngest boys or girls. PMID:17037465
High-order sampling schemes for path integrals and Gaussian chain simulations of polymers
Müser, Martin H.; Müller, Marcus
2015-05-07
In this work, we demonstrate that path-integral schemes, derived in the context of many-body quantum systems, benefit the simulation of Gaussian chains representing polymers. Specifically, we show how to decrease discretization corrections with little extra computation from the usual O(1/P{sup 2}) to O(1/P{sup 4}), where P is the number of beads representing the chains. As a consequence, high-order integrators necessitate much smaller P than those commonly used. Particular emphasis is placed on the questions of how to maintain this rate of convergence for open polymers and for polymers confined by a hard wall as well as how to ensure efficient sampling. The advantages of the high-order sampling schemes are illustrated by studying the surface tension of a polymer melt and the interface tension in a binary homopolymers blend.
On high-order denoising models and fast algorithms for vector-valued images.
Brito-Loeza, Carlos; Chen, Ke
2010-06-01
Variational techniques for gray-scale image denoising have been deeply investigated for many years; however, little research has been done for the vector-valued denoising case and the very few existent works are all based on total-variation regularization. It is known that total-variation models for denoising gray-scaled images suffer from staircasing effect and there is no reason to suggest this effect is not transported into the vector-valued models. High-order models, on the contrary, do not present staircasing. In this paper, we introduce three high-order and curvature-based denoising models for vector-valued images. Their properties are analyzed and a fast multigrid algorithm for the numerical solution is provided. AMS subject classifications: 68U10, 65F10, 65K10. PMID:20172828
A high-order fast method for computing convolution integral with smooth kernel
Qiang, Ji
2009-09-28
In this paper we report on a high-order fast method to numerically calculate convolution integral with smooth non-periodic kernel. This method is based on the Newton-Cotes quadrature rule for the integral approximation and an FFT method for discrete summation. The method can have an arbitrarily high-order accuracy in principle depending on the number of points used in the integral approximation and a computational cost of O(Nlog(N)), where N is the number of grid points. For a three-point Simpson rule approximation, the method has an accuracy of O(h{sup 4}), where h is the size of the computational grid. Applications of the Simpson rule based algorithm to the calculation of a one-dimensional continuous Gauss transform and to the calculation of a two-dimensional electric field from a charged beam are also presented.
A Simple Route to Highly Oriented and Ordered Nanoporous Block Copolymer Templates
Park,S.; Wang, J.; Kim, B.; Xu, J.; Russell, T.
2008-01-01
Controlling the orientation and lateral ordering of the block copolymer microdomains is essential to their use as templates and scaffolds for the fabrication of nanostructured materials. In addition, a process must be robust, simple to implement, and rapid, and should not introduce disruptive processing steps that would impede their use. Here, we describe thin films of poly(styrene-b-4-vinylpyridine) (PS-b-P4VP) diblock copolymers, spin-coated from mixed solvents that show highly oriented, cylindrical microdomains with a high degree of order on a wide range of substrates, including silicon oxide, polystyrene, germanium, polyimide, and poly(butylene terephthalate). In addition, the preferential solvation of the P4VP block with an alcohol caused a surface reconstruction that resulted in the formation of a nanoporous film upon drying. The evaporation of gold onto the reconstructed films produced thermally stable and reactive ion etching resistant films.
Zolotarev, V V; Leshko, A Yu; Pikhtin, N A; Lyutetskiy, A V; Slipchenko, S O; Bakhvalov, K V; Lubyanskiy, Ya V; Rastegaeva, M G; Tarasov, I S
2014-10-31
We have studied the spectral characteristics of multimode semiconductor lasers with high-order surface diffraction gratings based on asymmetric separate-confinement heterostructures grown by metalorganic vapour phase epitaxy (λ = 1070 nm). Experimental data demonstrate that, in the temperature range ±50 °C, the laser emission spectrum is ∼5 Å in width and contains a fine structure of longitudinal and transverse modes. A high-order (m = 15) surface diffraction grating is shown to ensure a temperature stability of the lasing spectrum dλ/dT = 0.9 Å K{sup -1} in this temperature range. From analysis of the fine structure of the lasing spectrum, we have evaluated the mode spacing and, thus, experimentally determined the effective length of the Bragg diffraction grating, which was ∼400 μm in our samples. (lasers)
Multi-input partial eigenvalue assignment for high order control systems with time delay
NASA Astrophysics Data System (ADS)
Zhang, Lei
2016-05-01
In this paper, we consider the partial eigenvalue assignment problem for high order control systems with time delay. Ram et al. (2011) [1] have shown that a hybrid method can be used to solve partial quadratic eigenvalue assignment problem of single-input vibratory system. Based on this theory, a rather simple algorithm for solving multi-input partial eigenvalue assignment for high order control systems with time delay is proposed. Our method can assign the expected eigenvalues and keep the no spillover property. The solution can be implemented with only partial information of the eigenvalues and the corresponding eigenvectors of the matrix polynomial. Numerical examples are given to illustrate the efficiency of our approach.
Two-center interference in high-order harmonic generation from heteronuclear diatomic molecules.
Zhu, Xiaosong; Zhang, Qingbin; Hong, Weiyi; Lan, Pengfei; Lu, Peixiang
2011-01-17
Two-center interference for heteronuclear diatomic molecules (HeDM) is investigated. The minimum in the high-order harmonic spectrum, as a consequence of the destructive interference, is shifted to lower harmonic orders compared with that in a homonuclear case. This phenomenon is explained by performing phase analysis. It is found that, for an HeDM, the high harmonic spectrum contains information not only on the internuclear separation but also on the properties of the two separate centers, which implies the potential application of estimating the asymmetry of molecules and judging the linear combination of atomic orbitals (LCAO) for the highest occupied molecular orbital (HOMO). Moreover, the possibility to monitor the evolution of HOMO itself in molecular dynamics is also promised. PMID:21263583
A Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin for Diffusion
NASA Technical Reports Server (NTRS)
Huynh, H. T.
2009-01-01
We introduce a new approach to high-order accuracy for the numerical solution of diffusion problems by solving the equations in differential form using a reconstruction technique. The approach has the advantages of simplicity and economy. It results in several new high-order methods including a simplified version of discontinuous Galerkin (DG). It also leads to new definitions of common value and common gradient quantities at each interface shared by the two adjacent cells. In addition, the new approach clarifies the relations among the various choices of new and existing common quantities. Fourier stability and accuracy analyses are carried out for the resulting schemes. Extensions to the case of quadrilateral meshes are obtained via tensor products. For the two-point boundary value problem (steady state), it is shown that these schemes, which include most popular DG methods, yield exact common interface quantities as well as exact cell average solutions for nearly all cases.
Persistence of magnetic order in a highly excited Cu2+ state in CuO
NASA Astrophysics Data System (ADS)
Staub, U.; de Souza, R. A.; Beaud, P.; Möhr-Vorobeva, E.; Ingold, G.; Caviezel, A.; Scagnoli, V.; Delley, B.; Turner, J. J.; Krupin, O.; Lee, W.-S.; Chuang, Y.-D.; Patthey, L.; Moore, R. G.; Lu, D.; Yi, M.; Kirchmann, P. S.; Trigo, M.; Denes, P.; Doering, D.; Hussain, Z.; Shen, Z. X.; Prabhakaran, D.; Boothroyd, A. T.; Johnson, S. L.
2014-06-01
We use ultrafast resonant x-ray diffraction to study the magnetic order in CuO under conditions of high electronic excitation. By measuring changes in the spectral shape of the Cu2+ magnetic (1/2 0 -1/2) reflection we investigate how an intense optical pump pulse perturbs the electronic and magnetic states. We observe an energy shift in the magnetic resonance at short times after the pump pulse. This shift is compared with expectations from band structure calculations at different electronic temperatures. This spectral line shift indicates that although the electrons are heated to effective electron temperatures far above TN on a time scale faster than the experimental resolution, magnetic order persists in this highly excited state for several hundred femtoseconds.
Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation
NASA Technical Reports Server (NTRS)
Kouatchou, Jules; Halem, Milton (Technical Monitor)
2000-01-01
We combine a high order compact finite difference approximation and collocation techniques to numerically solve the two dimensional heat equation. The resulting method is implicit arid can be parallelized with a strategy that allows parallelization across both time and space. We compare the parallel implementation of the new method with a classical implicit method, namely the Crank-Nicolson method, where the parallelization is done across space only. Numerical experiments are carried out on the SGI Origin 2000.
Finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems
NASA Astrophysics Data System (ADS)
Xie, Xue-Jun; Zhang, Xing-Hui; Zhang, Kemei
2016-07-01
This paper studies the finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems. Based on the stochastic Lyapunov theorem on finite-time stability, by using the homogeneous domination method, the adding one power integrator and sign function method, constructing a ? Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed-loop system finite-time stable in probability.
The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Carbone, Ludovico; Fulda, Paul; Bond, Charlotte; Brueckner, Frank; Brown, Daniel; Wang, Mengyao; Lodhia, Deepali; Palmer, Rebecca; Freise, Andreas
2013-01-01
Thermal noise in high-reflectivity mirrors is a major impediment for several types of high-precision interferometric experiments that aim to reach the standard quantum limit or to cool mechanical systems to their quantum ground state. This is for example the case of future gravitational wave observatories, whose sensitivity to gravitational wave signals is expected to be limited in the most sensitive frequency band, by atomic vibration of their mirror masses. One promising approach being pursued to overcome this limitation is to employ higher-order Laguerre-Gauss (LG) optical beams in place of the conventionally used fundamental mode. Owing to their more homogeneous light intensity distribution these beams average more effectively over the thermally driven fluctuations of the mirror surface, which in turn reduces the uncertainty in the mirror position sensed by the laser light. We demonstrate a promising method to generate higher-order LG beams by shaping a fundamental Gaussian beam with the help of diffractive optical elements. We show that with conventional sensing and control techniques that are known for stabilizing fundamental laser beams, higher-order LG modes can be purified and stabilized just as well at a comparably high level. A set of diagnostic tools allows us to control and tailor the properties of generated LG beams. This enabled us to produce an LG beam with the highest purity reported to date. The demonstrated compatibility of higher-order LG modes with standard interferometry techniques and with the use of standard spherical optics makes them an ideal candidate for application in a future generation of high-precision interferometry. PMID:23962813
New multiple-soliton (kink) solutions for the high-order Boussinesq-Burgers equation
NASA Astrophysics Data System (ADS)
Guo, Peng; Wu, Xiang; Wang, Liangbi
2016-07-01
The homogeneous balance method is extended to find more new solutions of nonlinear evolution equations. As illustrative examples, many new multiple-soliton (kink) solutions of the high-order Boussinesq-Burgers equation are constructed. It is shown that the homogeneous balance method may provide us with a straightforward and effective mathematic tool for generating new multiple-soliton (kink) solutions of nonlinear evolution equations.
High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains
NASA Astrophysics Data System (ADS)
Fisher, Travis C.; Carpenter, Mark H.
2013-11-01
Nonlinear entropy stability is used to derive provably stable high-order finite difference operators including boundary closure stencils, for the compressible Navier-Stokes equations. A comparison technique is used to derive a new Entropy Stable Weighted Essentially Non-Oscillatory (SSWENO) finite difference method, appropriate for simulations of problems with shocks. Viscous terms are approximated using conservative, entropy stable, narrow-stencil finite difference operators. The efficacy of the new discrete operators is demonstrated using both smooth and discontinuous test cases.
NASA Astrophysics Data System (ADS)
Tarasevitch, A. P.; Kohn, R.; von der Linde, D.
2009-07-01
The advantages of using two beam high order harmonic generation (HOHG) from solids are discussed. The two-pulse technique allows additional control of the parameters essential for the attosecond pulse generation. We show that spectral filtering is not necessary for the generation of attosecond pulses. The simple oscillating mirror model is in qualitative agreement with the computer simulations. We present the results of first experiments using two beams for HOHG.
Modulated phase matching and high-order harmonic enhancement mediated by the carrier-envelope phase
Faccio, Daniele; Serrat, Carles; Cela, Jose M.; Farres, Albert; Di Trapani, Paolo; Biegert, Jens
2010-01-15
The process of high-order harmonic generation in gases is numerically investigated in the presence of a few-cycle pulsed-Bessel-beam pump, featuring a periodic modulation in the peak intensity due to large carrier-envelope-phase mismatch. A two-decade enhancement in the conversion efficiency is observed and interpreted as the consequence of a mechanism known as a nonlinearly induced modulation in the phase mismatch.
High-order-harmonic generation in gas with a flat-top laser beam
Boutu, W.; Auguste, T.; Binazon, L.; Gobert, O.; Carre, B.; Boyko, O.; Valentin, C.; Balcou, Ph.; Merdji, H.
2011-12-15
We present experimental and numerical results on high-order-harmonic generation with a flat-top laser beam. We show that a simple binary tunable phase plate, made of two concentric glass plates, can produce a flat-top profile at the focus of a Gaussian infrared beam. Both experiments and numerical calculations show that there is a scaling law between the harmonic generation efficiency and the increase of the generation volume.
Tunable high-order sideband spectra generation using a photonic molecule optomechanical system
Cao, Cong; Mi, Si-Chen; Gao, Yong-Pan; He, Ling-Yan; Yang, Daquan; Wang, Tie-Jun; Zhang, Ru; Wang, Chuan
2016-01-01
A tunable high-order sideband spectra generation scheme is presented by using a photonic molecule optomechanical system coupled to a waveguide beyond the perturbation regime. The system is coherently driven by a two-tone laser consisting of a continuous-wave control field and a pulsed driving field which propagates through the waveguide. The frequency spectral feature of the output field is analyzed via numerical simulations, and we confirm that under the condition of intense and nanosecond pulse driving, the output spectrum exhibits the properties of high-order sideband frequency spectra. In the experimentally available parameter range, the output spectrum can be efficiently tuned by the system parameters, including the power of the driving pulse and the coupling rate between the cavities. In addition, analysis of the carrier-envelop phase-dependent effect of high-order sideband generation indicates that the system may present dependence upon the phase of the pulse. This may provide a further insight of the properties of cavity optomechanics in the nonlinear and non-perturbative regime, and may have potential applications in optical frequency comb and communication based on the optomechanical platform. PMID:26960430
Tunable high-order sideband spectra generation using a photonic molecule optomechanical system.
Cao, Cong; Mi, Si-Chen; Gao, Yong-Pan; He, Ling-Yan; Yang, Daquan; Wang, Tie-Jun; Zhang, Ru; Wang, Chuan
2016-01-01
A tunable high-order sideband spectra generation scheme is presented by using a photonic molecule optomechanical system coupled to a waveguide beyond the perturbation regime. The system is coherently driven by a two-tone laser consisting of a continuous-wave control field and a pulsed driving field which propagates through the waveguide. The frequency spectral feature of the output field is analyzed via numerical simulations, and we confirm that under the condition of intense and nanosecond pulse driving, the output spectrum exhibits the properties of high-order sideband frequency spectra. In the experimentally available parameter range, the output spectrum can be efficiently tuned by the system parameters, including the power of the driving pulse and the coupling rate between the cavities. In addition, analysis of the carrier-envelop phase-dependent effect of high-order sideband generation indicates that the system may present dependence upon the phase of the pulse. This may provide a further insight of the properties of cavity optomechanics in the nonlinear and non-perturbative regime, and may have potential applications in optical frequency comb and communication based on the optomechanical platform. PMID:26960430
A high-order element-based Galerkin Method for the global shallow water equations.
Nair, Ramachandran D.; Tufo, Henry M.; Levy, Michael Nathan
2010-08-01
The shallow water equations are used as a test for many atmospheric models because the solution mimics the horizontal aspects of atmospheric dynamics while the simplicity of the equations make them useful for numerical experiments. This study describes a high-order element-based Galerkin method for the global shallow water equations using absolute vorticity, divergence, and fluid depth (atmospheric thickness) as the prognostic variables, while the wind field is a diagnostic variable that can be calculated from the stream function and velocity potential (the Laplacians of which are the vorticity and divergence, respectively). The numerical method employed to solve the shallow water system is based on the discontinuous Galerkin and spectral element methods. The discontinuous Galerkin method, which is inherently conservative, is used to solve the equations governing two conservative variables - absolute vorticity and atmospheric thickness (mass). The spectral element method is used to solve the divergence equation and the Poisson equations for the velocity potential and the stream function. Time integration is done with an explicit strong stability-preserving second-order Runge-Kutta scheme and the wind field is updated directly from the vorticity and divergence at each stage, and the computational domain is the cubed sphere. A stable steady-state test is run and convergence results are provided, showing that the method is high-order accurate. Additionally, two tests without analytic solutions are run with comparable results to previous high-resolution runs found in the literature.
Sericin removal from raw Bombyx mori silk scaffolds of high hierarchical order.
Teuschl, Andreas Herbert; van Griensven, Martijn; Redl, Heinz
2014-05-01
Silk fibroin has previously been described as a promising candidate for ligament tissue engineering (TE) approaches. For biocompatibility reasons, silkworm silk requires removal of sericin, which can elicit adverse immune responses in the human body. One disadvantage of the required degumming process is the alteration of the silk fiber structural properties, which can hinder textile engineering of high order hierarchical structures. Therefore, the aim of this study was to find a way to remove sericin from a compact and highly ordered raw silk fiber matrix. The wire rope design of the test model scaffold comprises several levels of geometric hierarchy. Commonly used degumming solutions fail in removing sericin in this wire rope design. Weight loss measurements, picric acid and carmine staining as well as scanning electron microscopy demonstrated that the removal of sericin from the model scaffold of a wire rope design can be achieved through a borate buffer-based system. Furthermore, the borate buffer degummed silks were shown to be nontoxic and did not alter cell proliferation behavior. The possibility to remove sericin after the textile engineering process has taken place eases the production of highly ordered scaffold structures and may expand the use of silk as scaffold material in further TE and regenerative medicine applications. PMID:24066942
NASA Astrophysics Data System (ADS)
Jiang, Zhen-Hua; Yan, Chao; Yu, Jian
2013-08-01
Two types of implicit algorithms have been improved for high order discontinuous Galerkin (DG) method to solve compressible Navier-Stokes (NS) equations on triangular grids. A block lower-upper symmetric Gauss-Seidel (BLU-SGS) approach is implemented as a nonlinear iterative scheme. And a modified LU-SGS (LLU-SGS) approach is suggested to reduce the memory requirements while retain the good convergence performance of the original LU-SGS approach. Both implicit schemes have the significant advantage that only the diagonal block matrix is stored. The resulting implicit high-order DG methods are applied, in combination with Hermite weighted essentially non-oscillatory (HWENO) limiters, to solve viscous flow problems. Numerical results demonstrate that the present implicit methods are able to achieve significant efficiency improvements over explicit counterparts and for viscous flows with shocks, and the HWENO limiters can be used to achieve the desired essentially non-oscillatory shock transition and the designed high-order accuracy simultaneously.
Hierarchically ordered mesoporous Co3O4 materials for high performance Li-ion batteries
Sun, Shijiao; Zhao, Xiangyu; Yang, Meng; Wu, Linlin; Wen, Zhaoyin; Shen, Xiaodong
2016-01-01
Highly ordered mesoporous Co3O4 materials have been prepared via a nanocasting route with three-dimensional KIT-6 and two-dimensional SBA-15 ordered mesoporous silicas as templates and Co(NO3)2 · 6H2O as precursor. Through changing the hydrothermal treating temperature of the silica template, ordered mesoporous Co3O4 materials with hierarchical structures have been developed. The larger pores around 10 nm provide an efficient transport for Li ions, while the smaller pores between 3–5 nm offer large electrochemically active areas. Electrochemical impedance analysis proves that the hierarchical structure contributes to a lower charge transfer resistance in the mesoporous Co3O4 electrode than the mono-sized structure. High reversible capacities around 1141 mAh g−1 of the hierarchically mesoporous Co3O4 materials are obtained, implying their potential applications for high performance Li-ion batteries. PMID:26781265
photon-plasma: A modern high-order particle-in-cell code
Haugbølle, Troels; Frederiksen, Jacob Trier; Nordlund, Åke
2013-06-15
We present the photon-plasma code, a modern high order charge conserving particle-in-cell code for simulating relativistic plasmas. The code is using a high order implicit field solver and a novel high order charge conserving interpolation scheme for particle-to-cell interpolation and charge deposition. It includes powerful diagnostics tools with on-the-fly particle tracking, synthetic spectra integration, 2D volume slicing, and a new method to correctly account for radiative cooling in the simulations. A robust technique for imposing (time-dependent) particle and field fluxes on the boundaries is also presented. Using a hybrid OpenMP and MPI approach, the code scales efficiently from 8 to more than 250.000 cores with almost linear weak scaling on a range of architectures. The code is tested with the classical benchmarks particle heating, cold beam instability, and two-stream instability. We also present particle-in-cell simulations of the Kelvin-Helmholtz instability, and new results on radiative collisionless shocks.
Surface contribution to high-order aberrations using the Aldis therem and Andersen's algorithms
NASA Astrophysics Data System (ADS)
Ortiz-Estardante, A.; Cornejo-Rodriguez, Alejandro
1990-07-01
Formulae and computer programs were developed for surface contributions to high order aberrations coefficients using the Aldis theorem and Andersen algor ithms for a symmetr ical optical system. 2. THEORY Using the algorithms developed by T. B. Andersent which allow to calculate the high order aberrations coefficients of an optical system. We were able to obtain a set of equations for the contributions of each surface of a centered optical system to such aberration coefficiets by using the equations of Andersen and the so called Aldis theorem 3. COMPUTER PROGRAMS AND EXAMPLES. The study for the case of an object at infinite has been completed and more recently the object to finite distance case has been also finished . The equations have been properly programed for the two above mentioned situations . Some typical designs of optical systems will be presented and some advantages and disadvantages of the developed formulae and method will be discussed. 4. CONCLUSIONS The algorithm developed by Anderson has a compact notation and structure which is suitable for computers. Using those results obtained by Anderson together with the Aldis theorem a set of equations were derived and programmed for the surface contributions of a centered optical system to high order aberrations. 5. REFERENCES 1. T . B. Andersen App 1. Opt. 3800 (1980) 2. A. Cox A system of Optical Design Focal Press 1964 18 / SPIE
Direct isosurface visualization of hex-based high-order geometry and attribute representations.
Martin, Tobias; Cohen, Elaine; Kirby, Robert M
2012-05-01
In this paper, we present a novel isosurface visualization technique that guarantees the accurate visualization of isosurfaces with complex attribute data defined on (un)structured (curvi)linear hexahedral grids. Isosurfaces of high-order hexahedral-based finite element solutions on both uniform grids (including MRI and CT scans) and more complex geometry representing a domain of interest that can be rendered using our algorithm. Additionally, our technique can be used to directly visualize solutions and attributes in isogeometric analysis, an area based on trivariate high-order NURBS (Non-Uniform Rational B-splines) geometry and attribute representations for the analysis. Furthermore, our technique can be used to visualize isosurfaces of algebraic functions. Our approach combines subdivision and numerical root finding to form a robust and efficient isosurface visualization algorithm that does not miss surface features, while finding all intersections between a view frustum and desired isosurfaces. This allows the use of view-independent transparency in the rendering process. We demonstrate our technique through a straightforward CPU implementation on both complex-structured and complex-unstructured geometries with high-order simulation solutions, isosurfaces of medical data sets, and isosurfaces of algebraic functions. PMID:22442127
Orbiting binary black hole evolutions with a multipatch high order finite-difference approach
Pazos, Enrique; Tiglio, Manuel; Duez, Matthew D.; Kidder, Lawrence E.; Teukolsky, Saul A.
2009-07-15
We present numerical simulations of orbiting black holes for around 12 cycles, using a high order multipatch approach. Unlike some other approaches, the computational speed scales almost perfectly for thousands of processors. Multipatch methods are an alternative to adaptive mesh refinement, with benefits of simplicity and better scaling for improving the resolution in the wave zone. The results presented here pave the way for multipatch evolutions of black hole-neutron star and neutron star-neutron star binaries, where high resolution grids are needed to resolve details of the matter flow.
High-order exact solutions for pseudo-plane ideal flows
NASA Astrophysics Data System (ADS)
Sun, Che
2016-08-01
A steady pseudo-plane ideal flow (PIF) model is derived from the 3D Euler equations under Boussinesq approximation. The model is solved analytically to yield high-degree polynomial exact solutions. Unlike quadratic flows, the cubic and quartic solutions display reduced geometry in the form of straightline jet, circular vortex, and multipolar strain field. The high-order circular-vortex solutions are vertically aligned and even the non-aligned multipolar strain-field solutions display vertical concentricity. Such geometry reduction is explained by an analytical theorem stating that only straightline jet and circular vortex have functional solutions to the PIF model.
Phase properties of laser high-order harmonics generated on plasma mirrors.
Quéré, F; Thaury, C; Geindre, J-P; Bonnaud, G; Monot, P; Martin, Ph
2008-03-01
As a high-intensity laser-pulse reflects on a plasma mirror, high-order harmonics of the incident frequency can be generated in the reflected beam. We present a numerical study of the phase properties of these individual harmonics, and demonstrate experimentally that they can be coherently controlled through the phase of the driving laser field. The harmonic intrinsic phase, resulting from the generation process, is directly related to the coherent sub-laser-cycle dynamics of plasma electrons, and thus constitutes a new experimental probe of these dynamics. PMID:18352718
Phase Properties of Laser High-Order Harmonics Generated on Plasma Mirrors
Quere, F.; Thaury, C.; Bonnaud, G.; Monot, P.; Martin, Ph.
2008-03-07
As a high-intensity laser-pulse reflects on a plasma mirror, high-order harmonics of the incident frequency can be generated in the reflected beam. We present a numerical study of the phase properties of these individual harmonics, and demonstrate experimentally that they can be coherently controlled through the phase of the driving laser field. The harmonic intrinsic phase, resulting from the generation process, is directly related to the coherent sub-laser-cycle dynamics of plasma electrons, and thus constitutes a new experimental probe of these dynamics.
High-order ENO schemes applied to two- and three-dimensional compressible flow
NASA Technical Reports Server (NTRS)
Shu, Chi-Wang; Erlebacher, Gordon; Zang, Thomas A.; Whitaker, David; Osher, Stanley
1991-01-01
High order essentially non-oscillatory (ENO) finite difference schemes are applied to the 2-D and 3-D compressible Euler and Navier-Stokes equations. Practical issues, such as vectorization, efficiency of coding, cost comparison with other numerical methods, and accuracy degeneracy effects, are discussed. Numerical examples are provided which are representative of computational problems of current interest in transition and turbulence physics. These require both nonoscillatory shock capturing and high resolution for detailed structures in the smooth regions and demonstrate the advantage of ENO schemes.
Yoshii, Kazumichi; Miyaji, Godai; Miyazaki, Kenzo
2009-06-01
We apply high-order harmonic generation to sensitive measurements of the molecular rotational temperature in a thin supersonic gas beam. The method uses nonresonant pump and probe femtosecond laser pulses to generate harmonic radiation from coherently rotating molecules. The rotational temperature of molecules can be derived accurately with high spatial and temporal resolutions from the Fourier spectrum of time-dependent signals. The validity of this method was tested for an expanding flow of an N(2) beam with a rapid temperature decrease. The results show the versatile applicability of this method. PMID:19488137
NASA Astrophysics Data System (ADS)
Denker, Carsten; Mascarinas, Dulce; Xu, Yan; Cao, Wenda; Yang, Guo; Wang, Haimin; Goode, Philip R.; Rimmele, Thomas
2005-04-01
We present, for the first time, high-spatial-resolution observations combining high-order adaptive optics (AO), frame selection, and post-facto image correction via speckle masking. The data analysis is based on observations of solar active region NOAA 10486 taken with the Dunn Solar Telescope (DST) at the Sacramento Peak Observatory (SPO) of the National Solar Observatory (NSO) on 29 October 2003. The high Strehl ratio encountered in AO corrected short-exposure images provides highly improved signal-to-noise ratios leading to a superior recovery of the object’s Fourier phases. This allows reliable detection of small-scale solar features near the diffraction limit of the telescope. Speckle masking imaging provides access to high-order wavefront aberrations, which predominantly originate at high atmospheric layers and are only partially corrected by the AO system. In addition, the observations provided qualitative measures of the image correction away from the lock point of the AO system. We further present a brief inspection of the underlying imaging theory discussing the limitations and prospects of this multi-faceted image reconstruction approach in terms of the recovery of spatial information, photometric accuracy, and spectroscopic applications.
Scattering of high order guided wave modes around a through-thickness circular hole
NASA Astrophysics Data System (ADS)
Travaglini, Christophe; Bescond, Christophe; França, Demartonne Ramos; Kruger, Silvio E.; Viens, Martin; Bélanger, Pierre
2016-02-01
Ultrasonic guided waves have the ability to propagate long distances with minimal attenuation, which makes them particularly interesting in structural health monitoring (SHM) applications. Using the baseline subtraction approach, the signal from a defect-free structure is compared with the actual monitoring signal to detect and locate defects. There are many scientific publications on low-frequency guided waves for SHM purposes, and the interaction between guided wave fundamental modes and defects is also well documented. There is however a very limited number of studies on high order modes. High-frequency guided waves may enable the detection of smaller cracks related to conventional low-frequency guided wave SHM. The main difficulty at high frequency is the existence of several modes with different velocities. This study investigates the scattering of high order guided wave modes around a through-thickness hole with a view to developing a highly sensitive SHM method. A 3D finite element model of a 305 mm × 305 mm × 1.6 mm aluminium plate was used to determine the scattering of cracks on the circumference of a through-thickness hole in the middle of the plate. Crack properties such as orientation, length and depth were studied. A subset of the finite element simulations were validated against experimental results. The experimental setup comprised a film type PZT actuator bonded on the side of the plate and a laser interferometer detector. An input signal centered at 4 MHz was used in all simulations and experiments.
NASA Astrophysics Data System (ADS)
Liu, Dan; Zeng, Chao; Qu, Deyu; Tang, Haolin; Li, Yu; Su, Bao-Lian; Qu, Deyang
2016-07-01
Nitrogen-doped ordered mesoporous carbons (OMCs) have been synthesized via aqueous cooperative assembly route in the presence of basic amino acids as either polymerization catalysts or nitrogen dopants. This method allows the large-scale production of nitrogen-doped OMCs with tunable composition, structure and morphology while maintaining highly ordered mesostructures. For instances, the nitrogen content can be varied from ∼1 wt% to ∼6.3 wt% and the mesophase can be either 3-D body-centered cubic or 2-D hexagonal. The specific surface area for typical OMCs is around 600 m2 g-1, and further KOH activation can significantly enhance the surface area to 1866 m2 g-1 without destroying the ordered mesostructures. Benefiting from hierarchically ordered porous structure, nitrogen-doping effect and large-scale production availability, the synthesized OMCs show a great potential towards supercapacitor application. When measured in a symmetrical two-electrode configuration with an areal mass loading of ∼3 mg cm-2, the activated OMC exhibits high capacitance (186 F g-1 at 0.25 A g-1) and good rate capability (75% capacity retention at 20 A g-1) in ionic liquid electrolyte. Even as the mass loading is up to ∼12 mg cm-2, the OMC electrode still yields a specific capacitance of 126 F g-1 at 20 A g-1.
High-Order Accurate Solutions to the Helmholtz Equation in the Presence of Boundary Singularities
NASA Astrophysics Data System (ADS)
Britt, Darrell Steven, Jr.
Problems of time-harmonic wave propagation arise in important fields of study such as geological surveying, radar detection/evasion, and aircraft design. These often involve highfrequency waves, which demand high-order methods to mitigate the dispersion error. We propose a high-order method for computing solutions to the variable-coefficient inhomogeneous Helmholtz equation in two dimensions on domains bounded by piecewise smooth curves of arbitrary shape with a finite number of boundary singularities at known locations. We utilize compact finite difference (FD) schemes on regular structured grids to achieve highorder accuracy due to their efficiency and simplicity, as well as the capability to approximate variable-coefficient differential operators. In this work, a 4th-order compact FD scheme for the variable-coefficient Helmholtz equation on a Cartesian grid in 2D is derived and tested. The well known limitation of finite differences is that they lose accuracy when the boundary curve does not coincide with the discretization grid, which is a severe restriction on the geometry of the computational domain. Therefore, the algorithm presented in this work combines high-order FD schemes with the method of difference potentials (DP), which retains the efficiency of FD while allowing for boundary shapes that are not aligned with the grid without sacrificing the accuracy of the FD scheme. Additionally, the theory of DP allows for the universal treatment of the boundary conditions. One of the significant contributions of this work is the development of an implementation that accommodates general boundary conditions (BCs). In particular, Robin BCs with discontinuous coefficients are studied, for which we introduce a piecewise parameterization of the boundary curve. Problems with discontinuities in the boundary data itself are also studied. We observe that the design convergence rate suffers whenever the solution loses regularity due to the boundary conditions. This is
Leng, Wei; Ju, Lili; Gunzburger, Max; Price, Stephen; Ringler, Todd
2012-01-01
The numerical modeling of glacier and ice sheet evolution is a subject of growing interest, in part because of the potential for models to inform estimates of global sea level change. This paper focuses on the development of a numerical model that determines the velocity and pressure fields within an ice sheet. Our numerical model features a high-fidelity mathematical model involving the nonlinear Stokes system and combinations of no-sliding and sliding basal boundary conditions, high-order accurate finite element discretizations based on variable resolution grids, and highly scalable parallel solution strategies, all of which contribute to a numerical model that can achieve accurate velocity and pressure approximations in a highly efficient manner. We demonstrate the accuracy and efficiency of our model by analytical solution tests, established ice sheet benchmark experiments, and comparisons with other well-established ice sheet models.
High-pressure phase transitions in ordered and disordered Bi2Te2Se.
Nielsen, M B; Parisiades, P; Madsen, S R; Bremholm, M
2015-08-21
We report studies of pressure-induced phase transitions of ordered and disordered ternary tetradymite-like Bi2Te2Se by synchrotron powder X-ray diffraction (PXRD) in diamond anvil cells (DACs) for pressures up to 59 and 49 GPa, respectively. The first sample (SB) was prepared from a single crystal with ordered Se/Te sites while the second sample (Q) was prepared from a quenched melt resulting in disordered Se/Te. This allows for an investigation of the effect of disorder on the phase transitions and the equation of states (EoS) of the tetradymite-like α phase. Fitting of a third order Birch-Murnaghan EoS to the α phases yielded bulk moduli K0 of 34.5(10) and 38.3(17) GPa and K' of 6.2(3) and 5.0(5) for the SB and Q samples, respectively. An electronic topological transition (ETT) was identified in both samples at pressures of 4.4 and 3.1 GPa, respectively. This was followed by a transition near 11 GPa to a phase that is isostructural with the β phase of Bi2Te3. The Se/Te ordering only affects the transition pressure to a small extent. A cubic phase that resembles the δ phase observed in high-pressure studies of Bi2Te3 appears at 17-20 GPa, but the ternary composition leads to a more complex structure. The presence of a low angle diffraction peak in the δ phase demonstrates that the true structure is not simply body-centred cubic. In this way the samples resemble Bi2Se3 where Bi and Se show a high degree of ordering, but the proposed structure of δ-Bi2Se3 also does not fully describe the data for δ-Bi2Te2Se. PMID:26169469
NASA Technical Reports Server (NTRS)
Crivellini, A.; Golubev, V.; Mankbadi, R.; Scott, J. R.; Hixon, R.; Povinelli, L.; Kiraly, L. James (Technical Monitor)
2002-01-01
The nonlinear response of symmetric and loaded airfoils to an impinging vortical gust is investigated in the parametric space of gust dimension, intensity, and frequency. The study, which was designed to investigate the validity limits for a linear analysis, is implemented by applying a nonlinear high-order prefactored compact code and comparing results with linear solutions from the GUST3D frequency-domain solver. Both the unsteady aerodynamic and acoustic gust responses are examined.
High-order implicit time-marching methods for unsteady fluid flow simulation
NASA Astrophysics Data System (ADS)
Boom, Pieter David
Unsteady computational fluid dynamics (CFD) is increasingly becoming a critical tool in the development of emerging technologies and modern aircraft. In spite of rapid mathematical and technological advancement, these simulations remain computationally intensive and time consuming. More efficient temporal integration will promote a wider use of unsteady analysis and extend its range of applicability. This thesis presents an investigation of efficient high-order implicit time-marching methods for application in unsteady compressible CFD. A generalisation of time-marching methods based on summation-by-parts (SBP) operators is described which reduces the number of stages required to obtain a prescribed order of accuracy, thus improving their efficiency. The classical accuracy and stability theory is formally extended for these generalised SBP (GSBP) methods, including superconvergence and nonlinear stability. Dual-consistent SBP and GSBP time-marching methods are shown to form a subclass of implicit Runge-Kutta methods, which enables extensions of nonlinear accuracy and stability results. A novel family of fully-implicit GSBP Runge-Kutta schemes based on Gauss quadrature are derived which are both algebraically stable and L-stable with order 2s - 1, where s is the number of stages. In addition, a numerical tool is developed for the construction and optimisation of general linear time-marching methods. The tool is applied to the development of several low-stage-order L-stable diagonally-implicit methods, including a diagonally-implicit GSBP Runge-Kutta scheme. The most notable and efficient method developed is a six-stage fifth-order L-stable stiffly-accurate explicit-first-stage singly-diagonally-implicit Runge-Kutta (ESDIRK5) method with stage order two. The theoretical results developed in this thesis are supported by numerical simulations, and the predicted relative efficiency of the schemes is realised.
High-Order Implicit-Explicit Multi-Block Time-stepping Method for Hyperbolic PDEs
NASA Technical Reports Server (NTRS)
Nielsen, Tanner B.; Carpenter, Mark H.; Fisher, Travis C.; Frankel, Steven H.
2014-01-01
This work seeks to explore and improve the current time-stepping schemes used in computational fluid dynamics (CFD) in order to reduce overall computational time. A high-order scheme has been developed using a combination of implicit and explicit (IMEX) time-stepping Runge-Kutta (RK) schemes which increases numerical stability with respect to the time step size, resulting in decreased computational time. The IMEX scheme alone does not yield the desired increase in numerical stability, but when used in conjunction with an overlapping partitioned (multi-block) domain significant increase in stability is observed. To show this, the Overlapping-Partition IMEX (OP IMEX) scheme is applied to both one-dimensional (1D) and two-dimensional (2D) problems, the nonlinear viscous Burger's equation and 2D advection equation, respectively. The method uses two different summation by parts (SBP) derivative approximations, second-order and fourth-order accurate. The Dirichlet boundary conditions are imposed using the Simultaneous Approximation Term (SAT) penalty method. The 6-stage additive Runge-Kutta IMEX time integration schemes are fourth-order accurate in time. An increase in numerical stability 65 times greater than the fully explicit scheme is demonstrated to be achievable with the OP IMEX method applied to 1D Burger's equation. Results from the 2D, purely convective, advection equation show stability increases on the order of 10 times the explicit scheme using the OP IMEX method. Also, the domain partitioning method in this work shows potential for breaking the computational domain into manageable sizes such that implicit solutions for full three-dimensional CFD simulations can be computed using direct solving methods rather than the standard iterative methods currently used.
Liu, Xiaolin; Lauer, Kathryn K.; Ward, Barney D.; Rao, Stephen M.; Li, Shi-Jiang; Hudetz, Anthony G.
2011-01-01
Current theories suggest that disrupting cortical information integration may account for the mechanism of general anesthesia in suppressing consciousness. Human cognitive operations take place in hierarchically structured neural organizations in the brain. The process of low-order neural representation of sensory stimuli becoming integrated in high-order cortices is also known as cognitive binding. Combining neuroimaging, cognitive neuroscience, and anesthetic manipulation, we examined how cognitive networks involved in auditory verbal memory are maintained in wakefulness, disrupted in propofol-induced deep sedation, and re-established in recovery. Inspired by the notion of cognitive binding, an fMRI-guided connectivity analysis was utilized to assess the integrity of functional interactions within and between different levels of the task-defined brain regions. Task-related responses persisted in the primary auditory cortex (PAC), but vanished in the inferior frontal gyrus (IFG) and premotor areas in deep sedation. For connectivity analysis, seed regions representing sensory and high-order processing of the memory task were identified in the PAC and IFG. Propofol disrupted connections from the PAC seed to the frontal regions and thalamus, but not the connections from the IFG seed to a set of widely distributed brain regions in the temporal, frontal, and parietal lobes (with exception of the PAC). These later regions have been implicated in mediating verbal comprehension and memory. These results suggest that propofol disrupts cognition by blocking the projection of sensory information to high-order processing networks and thus preventing information integration. Such findings contribute to our understanding of anesthetic mechanisms as related to information and integration in the brain. PMID:21932265
Anilkumar, P; Jayakannan, M
2006-06-20
We demonstrate here, for the first time, a unique strategy for conducting polyaniline nanofibers based on renewable resources. Naturally available cardanol, which is an industrial waste and main pollutant from the cashew nut industry, is utilized for producing well-defined polyaniline nanofibers. A new amphiphilic molecule is designed and developed from cardanol, which forms a stable emulsion with aniline for a wide composition range in water (1:1 to 1:100 dopant/aniline mole ratio) to produce polyaniline nanofibers. The scanning electron microscopy and transmission electron microscopy analysis of the nanofibers reveals that the dopant/aniline ratio plays a major role in determining the shape and size of polyaniline nanofibers. The nanofiber length increases with the increase in the dopant/aniline ratio, and perfectly linear, well-defined nanofibers of lengths as long as 7-8 muM were produced. The amphiphilic dopant has a built-in head-to-tail geometry and effectively penetrates into the polyaniline chains to form highly organized nanofibers. Wide-angle X-ray diffraction (WXRD) spectra of the nanofibers showed a new peak at 2theta = 6.3 (d spacing = 13.9 A) corresponding to the three-dimensional solid-state ordering of polyaniline-dopant chains, and this peak intensity increases with increase in the nanofiber length. The comparison of morphology and WXRD reveals that high ordering in polyaniline chains results in the formation of long, well-defined nanofibers, and this direct correlation for the polyaniline nanofibers with solid-state ordering has been established. The conductivity of the polyaniline nanofibers also increases with increase in the solid-state ordering rather than increasing with the extent of doping. The polyaniline nanofibers are freely soluble in water and possess high environmental and thermal stability up to 300 degrees C for various applications. PMID:16768535
Monot, Pascal; Doumy, Gilles; Dobosz, Sundrine; Perdrix, Michel; D'Oliveira, Pascal; Quéré, Fabion; Réau, Fabrice; Martin, Philippe; Audebert, Patrick; Gauthier, Jean-Claude; Geindre, Jean-Paul
2004-04-15
We demonstrate the use of a plasma mirror to obtain 60-fs 10-TW laser pulses with a temporal contrast of 10(8) on a nanosecond time scale and 10(6) on a picosecond time scale, and we use these high-contrast pulses to generate high harmonics by nonlinear reflection on a plasma with a steep electronic density gradient. Well-collimated harmonics up to 20th order are observed for a laser intensity of approximately equal to 3 x 10(17) W/cm2, whereas no harmonics are obtained without the plasma mirror. PMID:15119413
NASA Astrophysics Data System (ADS)
Wang, Xiaorui; Yang, Yanfu; Liu, Meng; Yao, Yong
2016-07-01
Fundamental and harmonic self-pulse generation was experimentally observed on both first order and higher order Stokes components. The generated pulses with the same order harmonic repetition rate are obtained on multiple Stokes components simultaneously. The pulse generation on first order Stokes component can be attributed to periodic pump depletion in Brillouin gain medium. The pulse generation of high order Stokes component can be considered as pulse oscillation pumped by the former order Stokes. With high Erbium pump power, by setting the proper attenuation between Brillouin medium and Faraday rotation mirror, the harmonic pulse generations up to fifth order have been achieved.
Three-Dimensional High-Order Spectral Finite Volume Method for Unstructured Grids
NASA Technical Reports Server (NTRS)
Liu, Yen; Vinokur, Marcel; Wang, Z. J.; Kwak, Dochan (Technical Monitor)
2002-01-01
Many areas require a very high-order accurate numerical solution of conservation laws for complex shapes. This paper deals with the extension to three dimensions of the Spectral Finite Volume (SV) method for unstructured grids, which was developed to solve such problems. We first summarize the limitations of traditional methods such as finite-difference, and finite-volume for both structured and unstructured grids. We then describe the basic formulation of the spectral finite volume method. What distinguishes the SV method from conventional high-order finite-volume methods for unstructured triangular or tetrahedral grids is the data reconstruction. Instead of using a large stencil of neighboring cells to perform a high-order reconstruction, the stencil is constructed by partitioning each grid cell, called a spectral volume (SV), into 'structured' sub-cells, called control volumes (CVs). One can show that if all the SV cells are partitioned into polygonal or polyhedral CV sub-cells in a geometrically similar manner, the reconstructions for all the SVs become universal, irrespective of their shapes, sizes, orientations, or locations. It follows that the reconstruction is reduced to a weighted sum of unknowns involving just a few simple adds and multiplies, and those weights are universal and can be pre-determined once for all. The method is thus very efficient, accurate, and yet geometrically flexible. The most critical part of the SV method is the partitioning of the SV into CVs. In this paper we present the partitioning of a tetrahedral SV into polyhedral CVs with one free parameter for polynomial reconstructions up to degree of precision five. (Note that the order of accuracy of the method is one order higher than the reconstruction degree of precision.) The free parameter will be determined by minimizing the Lebesgue constant of the reconstruction matrix or similar criteria to obtain optimized partitions. The details of an efficient, parallelizable code to solve
Tan, B. S.; Harrison, N.; Zhu, Z.; Balakirev, F.; Ramshaw, B. J.; Srivastava, A.; Sabok-Sayr, S. A.; Dabrowski, B.; Lonzarich, G. G.; Sebastian, Suchitra E.
2015-01-01
The normal state in the hole underdoped copper oxide superconductors has proven to be a source of mystery for decades. The measurement of a small Fermi surface by quantum oscillations on suppression of superconductivity by high applied magnetic fields, together with complementary spectroscopic measurements in the hole underdoped copper oxide superconductors, point to a nodal electron pocket from charge order in YBa2Cu3O6+δ. Here, we report quantum oscillation measurements in the closely related stoichiometric material YBa2Cu4O8, which reveals similar Fermi surface properties to YBa2Cu3O6+δ, despite the nonobservation of charge order signatures in the same spectroscopic techniques, such as X-ray diffraction, that revealed signatures of charge order in YBa2Cu3O6+δ. Fermi surface reconstruction in YBa2Cu4O8 is suggested to occur from magnetic field enhancement of charge order that is rendered fragile in zero magnetic fields because of its potential unconventional nature and/or its occurrence as a subsidiary to more robust underlying electronic correlations. PMID:26199413
Tan, B S; Harrison, N; Zhu, Z; Balakirev, F; Ramshaw, B J; Srivastava, A; Sabok-Sayr, S A; Sabok, S A; Dabrowski, B; Lonzarich, G G; Sebastian, Suchitra E
2015-08-01
The normal state in the hole underdoped copper oxide superconductors has proven to be a source of mystery for decades. The measurement of a small Fermi surface by quantum oscillations on suppression of superconductivity by high applied magnetic fields, together with complementary spectroscopic measurements in the hole underdoped copper oxide superconductors, point to a nodal electron pocket from charge order in YBa2Cu3(6+δ). Here, we report quantum oscillation measurements in the closely related stoichiometric material YBa2Cu4O8, which reveals similar Fermi surface properties to YBa2Cu3(6+δ), despite the nonobservation of charge order signatures in the same spectroscopic techniques, such as X-ray diffraction, that revealed signatures of charge order in YBa2Cu3(6+δ). Fermi surface reconstruction in YBa2Cu4O8 is suggested to occur from magnetic field enhancement of charge order that is rendered fragile in zero magnetic fields because of its potential unconventional nature and/or its occurrence as a subsidiary to more robust underlying electronic correlations. PMID:26199413
Atomic ordering in cubic bismuth telluride alloy phases at high pressure
NASA Astrophysics Data System (ADS)
Loa, I.; Bos, J.-W. G.; Downie, R. A.; Syassen, K.
2016-06-01
Pressure-induced transitions from ordered intermetallic phases to substitutional alloys to semi-ordered phases were studied in a series of bismuth tellurides. By using angle-dispersive x-ray diffraction, the compounds Bi4Te5 , BiTe, and Bi2Te were observed to form alloys with the disordered body-centered cubic (bcc) crystal structure upon compression to above 14-19 GPa at room temperature. The BiTe and Bi2Te alloys and the previously discovered high-pressure alloys of Bi2Te3 and Bi4Te3 were all found to show atomic ordering after gentle annealing at very moderate temperatures of ˜100 ∘C . Upon annealing, BiTe transforms from bcc to the B2 (CsCl) crystal-structure type, and the other phases adopt semi-disordered variants thereof, featuring substitutional disorder on one of the two crystallographic sites. The transition pressures and atomic volumes of the alloy phases show systematic variations across the BimTen series including the end members Bi and Te. First-principles calculations were performed to characterize the electronic structure and chemical bonding properties of B2-type BiTe and to identify the driving forces of the ordering transition. The calculated Fermi surface of B2-type BiTe has an intricate structure and is predicted to undergo three topological changes between 20 and 60 GPa.
Performance of Low Dissipative High Order Shock-Capturing Schemes for Shock-Turbulence Interactions
NASA Technical Reports Server (NTRS)
Sandham, N. D.; Yee, H. C.
1998-01-01
Accurate and efficient direct numerical simulation of turbulence in the presence of shock waves represents a significant challenge for numerical methods. The objective of this paper is to evaluate the performance of high order compact and non-compact central spatial differencing employing total variation diminishing (TVD) shock-capturing dissipations as characteristic based filters for two model problems combining shock wave and shear layer phenomena. A vortex pairing model evaluates the ability of the schemes to cope with shear layer instability and eddy shock waves, while a shock wave impingement on a spatially-evolving mixing layer model studies the accuracy of computation of vortices passing through a sequence of shock and expansion waves. A drastic increase in accuracy is observed if a suitable artificial compression formulation is applied to the TVD dissipations. With this modification to the filter step the fourth-order non-compact scheme shows improved results in comparison to second-order methods, while retaining the good shock resolution of the basic TVD scheme. For this characteristic based filter approach, however, the benefits of compact schemes or schemes with higher than fourth order are not sufficient to justify the higher complexity near the boundary and/or the additional computational cost.
NASA Technical Reports Server (NTRS)
Shu, Chi-Wang
2000-01-01
This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the
Adaptive Numerical Dissipation Control in High Order Schemes for Multi-D Non-Ideal MHD
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sjoegreen, B.
2005-01-01
The required type and amount of numerical dissipation/filter to accurately resolve all relevant multiscales of complex MHD unsteady high-speed shock/shear/turbulence/combustion problems are not only physical problem dependent, but also vary from one flow region to another. In addition, proper and efficient control of the divergence of the magnetic field (Div(B)) numerical error for high order shock-capturing methods poses extra requirements for the considered type of CPU intensive computations. 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 from 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 multiresolution wavelets (WAV) (for the above types of flow feature). These filters also provide a natural and efficient way for the minimization of Div(B) numerical error.
Kan, Kan; Wang, Lei; Yu, Peng; Jiang, Baojiang; Shi, Keying; Fu, Honggang
2016-05-21
Two-dimensional (2D) quasi-ordered nitrogen-enriched porous carbon (QNPC) nanohybrids, with the characteristics of an ultrathin graphite nanosheet framework and thick quasi-ordered nitrogen-doped carbon cladding with a porous texture, have been synthesized via an in situ polymerization assembly method. In the synthesis, the expandable graphite (EG) is enlarged by an intermittent microwave method, and then aniline monomers are intercalated into the interlayers of the expanded EG with the assistance of a vacuum. Subsequently, the intercalated aniline monomers could assemble on the interlayer surface of the expanded EG, accompanied by the in situ polymerization from aniline monomers to polyaniline. Meanwhile, the expanded EG could be exfoliated to graphite nanosheets. By subsequent pyrolysis and activation processes, the QNPC nanohybrids could be prepared. As supercapacitor electrodes, a typical QNPC12-700 sample derived from the precursor containing an EG content of 12%, with a high level of nitrogen doping of 5.22 at%, offers a high specific capacitance of 305.7 F g(-1) (1 A g(-1)), excellent rate-capability and long-term stability. Notably, an extremely high energy density of 95.7 Wh kg(-1) at a power density of 449.7 W kg(-1) in an ionic liquid electrolyte can be achieved. The unique structural features and moderate heteroatom doping of the QNPC nanohybrids combines electrochemical double layer and faradaic capacitance contributions, which make these nanohybrids ideal candidates as electrode materials for high-performance energy storage devices. PMID:27122446
Control of high-order harmonics for attoscience using a static-electric-field pattern
Serrat, Carles
2011-12-15
Quantum control in high-order-harmonic generation is considered theoretically by using a spatial distribution of static electric fields along the propagation direction of the driving field. It is shown that the trajectories of the electrons during its acceleration by the laser field in the high-harmonics-generation process can be controlled by periodically distributed static electric fields, which conveniently shape the driving laser field during propagation. Applying this mechanism, a quasi-phase-matching scheme that leads to filtered enhanced high harmonics is achieved. The harmonics in the plateau region are enhanced due to periodical phase variations in the long quantum trajectories as a consequence of the faster change experienced by the intensity-dependent phase along the longer electron trajectories. This effect should be observed in all quasi-phase-matching schemes based on perturbation of the microscopic quantum phase. The richness of adding a static-electric-field spatial pattern in the interaction region suggests a general scheme for feedback loop control in high-order-harmonic generation.
NASA Astrophysics Data System (ADS)
Dimov, Ivailo; Goswami, Pallab; Jia, Xun; Chakravarty, Sudip
2008-10-01
We consider incommensurate order parameters for electrons on a square lattice which reduce to d -density wave order when the ordering wave vector Q is close to Q0=(π/a,π/a) , a being the lattice spacing and describe the associated charge and current distributions within a single-harmonic approximation that conserves current to lowest order. Such incommensurate orders can arise at the mean-field level in extended Hubbard models, but the main goal here is to explore thoroughly the consequences within a Hartree-Fock approximation. We find that Fermi surface reconstruction in the underdoped regime can correctly capture the phenomenology of the recent quantum oscillation experiments that suggest incommensurate order, in particular the de Haas-van Alphen oscillations of the magnetization in high fields and very low temperatures in presumably the mixed state of these superconductors. For 10% hole doping in YBa2Cu3O6+δ , we find in addition to the main frequency around 530 T arising from the electron pocket and a hole frequency at around 1650 T, a new low frequency from a smaller hole pocket at 250 T for which there are some indications that require further investigations. The oscillation corresponding to the electron pocket will be further split due to bilayer coupling, but the splitting is sufficiently small to require more refined measurements. The truly incommensurate d -density wave breaks both time reversal and inversion, but the product of these two symmetry operations is preserved. The resulting Fermi surface splits into spin-up and spin-down sectors that are inversion conjugates. Each of the spin sectors results in a band structure that violates reflection symmetry, which can be determined in spin and angle-resolved photoemission spectroscopies. For those experiments such as the current photoemission experiments or the quantum oscillation measurements that cannot resolve the spin components, the bands will appear to be symmetric because of the equal mixture of
A unified approach for a posteriori high-order curved mesh generation using solid mechanics
NASA Astrophysics Data System (ADS)
Poya, Roman; Sevilla, Ruben; Gil, Antonio J.
2016-06-01
The paper presents a unified approach for the a posteriori generation of arbitrary high-order curvilinear meshes via a solid mechanics analogy. The approach encompasses a variety of methodologies, ranging from the popular incremental linear elastic approach to very sophisticated non-linear elasticity. In addition, an intermediate consistent incrementally linearised approach is also presented and applied for the first time in this context. Utilising a consistent derivation from energy principles, a theoretical comparison of the various approaches is presented which enables a detailed discussion regarding the material characterisation (calibration) employed for the different solid mechanics formulations. Five independent quality measures are proposed and their relations with existing quality indicators, used in the context of a posteriori mesh generation, are discussed. Finally, a comprehensive range of numerical examples, both in two and three dimensions, including challenging geometries of interest to the solids, fluids and electromagnetics communities, are shown in order to illustrate and thoroughly compare the performance of the different methodologies. This comparison considers the influence of material parameters and number of load increments on the quality of the generated high-order mesh, overall computational cost and, crucially, the approximation properties of the resulting mesh when considering an isoparametric finite element formulation.
Axicons for mode conversion in high peak power, higher-order mode, fiber amplifiers.
Nicholson, J W; DeSantolo, A; Westbrook, P S; Windeler, R S; Kremp, T; Headley, C; DiGiovanni, D J
2015-12-28
Higher-order mode fiber amplifiers have demonstrated effective areas as large as 6000 μm2, allowing for high pulse energy and peak power amplification. Long-period gratings are used to convert the fundamental mode to the higher-order mode at the entrance to the amplifier, and reconvert back to the fundamental at the exit, to achieve a diffraction limited beam. However, long period gratings are susceptible to nonlinearity at high peak power. In this work, we propose and demonstrate axicons for linear bulk-optic mode conversion at the output of higher order mode amplifiers. We achieve an M2 of less than 1.25 for 80% mode conversion efficiency. Experiments with pulsed amplifiers confirm that the mode conversion is free from nonlinearity. Furthermore, chirp pulse amplifier experiments confirm that HOM amplifiers plus axicon mode convertors provide energy scalability in femtosecond pulses, compared to smaller effective area, fundamental mode fiber amplifiers. We also propose and demonstrate a route towards fiber integration of the axicon mode convertor by fabricating axicons directly on the tip of the fiber amplifier end-cap. PMID:26832045
A unified approach for a posteriori high-order curved mesh generation using solid mechanics
NASA Astrophysics Data System (ADS)
Poya, Roman; Sevilla, Ruben; Gil, Antonio J.
2016-09-01
The paper presents a unified approach for the a posteriori generation of arbitrary high-order curvilinear meshes via a solid mechanics analogy. The approach encompasses a variety of methodologies, ranging from the popular incremental linear elastic approach to very sophisticated non-linear elasticity. In addition, an intermediate consistent incrementally linearised approach is also presented and applied for the first time in this context. Utilising a consistent derivation from energy principles, a theoretical comparison of the various approaches is presented which enables a detailed discussion regarding the material characterisation (calibration) employed for the different solid mechanics formulations. Five independent quality measures are proposed and their relations with existing quality indicators, used in the context of a posteriori mesh generation, are discussed. Finally, a comprehensive range of numerical examples, both in two and three dimensions, including challenging geometries of interest to the solids, fluids and electromagnetics communities, are shown in order to illustrate and thoroughly compare the performance of the different methodologies. This comparison considers the influence of material parameters and number of load increments on the quality of the generated high-order mesh, overall computational cost and, crucially, the approximation properties of the resulting mesh when considering an isoparametric finite element formulation.
Effect of high pressure on the formation of ordered phases in Ta-C systems
Markhasev, B.I.; Dzhamarov, S.S.; Geshko, E.I.; Klyugvant, V.V.; Pilipovskii, Y.L.; Shamatov, Y.M.
1985-03-01
This paper considers the effect of pressure on the completion of the transformations TaC /SUB x/ Ta/sub 4/C/sub 3/ and TaC /SUB x/ Ta/sub 2/C. The data show that in the samples with C/Ta = 0.68 and 0.71, the applied pressure substantially increases the diffraction peak heights of the ordered phases, Ta/sub 4/C/sub 3/ and Ta/sub 2/C. In samples with C/Ta = 0.76, high pressure does not generally increase the intensities of the diffracted peaks of Ta/sub 4/C/sub 3/ and Ta/sub 2/C, however the equilibrium between them is displaced to the side of increased Ta/sub 2/C content. In one of the samples a complete disappearance of the disordered TaC /SUB x/ is not observed. It is concluded that high pressure ( about7GPa) promotes the transition of nonstoichiometric TaC /SUB x/ into ordered Ta/sub 4/C/sub 3/ and Ta/sub 2/C as well as broadens the existence region of the latter. A complete transformation of TaC /SUB x/ into the ordered phase does not occur even at pressures up to about 9 GPa.
Adaptation strategies for high order discontinuous Galerkin methods based on Tau-estimation
NASA Astrophysics Data System (ADS)
Kompenhans, Moritz; Rubio, Gonzalo; Ferrer, Esteban; Valero, Eusebio
2016-02-01
In this paper three p-adaptation strategies based on the minimization of the truncation error are presented for high order discontinuous Galerkin methods. The truncation error is approximated by means of a τ-estimation procedure and enables the identification of mesh regions that require adaptation. Three adaptation strategies are developed and termed a posteriori, quasi-a priori and quasi-a priori corrected. All strategies require fine solutions, which are obtained by enriching the polynomial order, but while the former needs time converged solutions, the last two rely on non-converged solutions, which lead to faster computations. In addition, the high order method permits the spatial decoupling for the estimated errors and enables anisotropic p-adaptation. These strategies are verified and compared in terms of accuracy and computational cost for the Euler and the compressible Navier-Stokes equations. It is shown that the two quasi-a priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment. Namely, for a viscous boundary layer flow, we obtain a speedup of 6.6 and 7.6 for the quasi-a priori and quasi-a priori corrected approaches, respectively.
Frequency dependence of quantum path interference in non-collinear high-order harmonic generation
NASA Astrophysics Data System (ADS)
Shi-Yang, Zhong; Xin-Kui, He; Hao, Teng; Peng, Ye; Li-Feng, Wang; Peng, He; Zhi-Yi, Wei
2016-02-01
High-order harmonic generation (HHG) driven by two non-collinear beams including a fundamental and its weak second harmonic is numerically studied. The interference of harmonics from adjacent electron quantum paths is found to be dependent on the relative delay of the driving pulse, and the dependences are different for different harmonic orders. This frequency dependence of the interference is attributed to the spatial frequency chirp in the HHG beam resulting from the harmonic dipole phase, which in turn provides a potential way to gain an insight into the generation of high-order harmonics. As an example, the intensity dependent dipole phase coefficient α is retrieved from the interference fringe. Project supported by the National Key Basic Research Program of China (Grant Nos. 2013CB922401 and 2013CB922402), the National Key Scientific Instrument and Equipment Development Projects, China (Grant No. 2012YQ12004704), the National Natural Science Foundation of China (Grant No. 11374356), and the International Joint Research Program of National Natural Science Foundation of China (Grant No. 61210017).
High-order central Hermite WENO schemes: Dimension-by-dimension moment-based reconstructions
NASA Astrophysics Data System (ADS)
Tao, Zhanjing; Li, Fengyan; Qiu, Jianxian
2016-08-01
In this paper, a class of high-order central finite volume schemes is proposed for solving one- and two-dimensional hyperbolic conservation laws. Formulated on staggered meshes, the methods involve Hermite WENO (HWENO) spatial reconstructions, and Lax-Wendroff type discretizations or the natural continuous extension of Runge-Kutta methods in time. Differently from the central Hermite WENO methods we developed previously in Tao et al. (2015) [34], the spatial reconstructions, a core ingredient of the methods, are based on the zeroth-order and the first-order moments of the solution, and are implemented through a dimension-by-dimension strategy when the spatial dimension is higher than one. This leads to much simpler implementation of the methods in higher dimension and better cost efficiency. Meanwhile, the proposed methods have the attractive features of the general central Hermite WENO methods such as being compact in reconstruction and requiring neither flux splitting nor numerical fluxes, while being accurate and essentially non-oscillatory. A collection of one- and two-dimensional numerical examples is presented to demonstrate high resolution and robustness of the methods in capturing smooth and non-smooth solutions.
A general approach for high order absorbing boundary conditions for the Helmholtz equation
NASA Astrophysics Data System (ADS)
Zarmi, Asaf; Turkel, Eli
2013-06-01
When solving a scattering problem in an unbounded space, one needs to implement the Sommerfeld condition as a boundary condition at infinity, to ensure no energy penetrates the system. In practice, solving a scattering problem involves truncating the region and implementing a boundary condition on an artificial outer boundary. Bayliss, Gunzburger and Turkel (BGT) suggested an Absorbing Boundary Condition (ABC) as a sequence of operators aimed at annihilating elements from the solution's series representation. Their method was practical only up to a second order condition. Later, Hagstrom and Hariharan (HH) suggested a method which used auxiliary functions and enabled implementation of higher order conditions. We compare various absorbing boundary conditions (ABCs) and introduce a new method to construct high order ABCs, generalizing the HH method. We then derive from this general method ABCs based on different series representations of the solution to the Helmholtz equation - in polar, elliptical and spherical coordinates. Some of these ABCs are generalizations of previously constructed ABCs and some are new. These new ABCs produce accurate solutions to the Helmholtz equation, which are much less dependent on the various parameters of the problem, such as the value of k, or the eccentricity of the ellipse. In addition to constructing new ABCs, our general method sheds light on the connection between various ABCs. Computations are presented to verify the high accuracy of these new ABCs.
High order numerical simulations of the Richtmyer- Meshkov instability in a relativistic fluid
NASA Astrophysics Data System (ADS)
Zanotti, O.; Dumbser, M.
2015-07-01
We study the Richtmyer-Meshkov (RM) instability of a relativistic perfect fluid by means of high order numerical simulations with adaptive mesh refinement (AMR). The numerical scheme combines a finite volume reconstruction in space, a local space-time discontinuous Galerkin predictor method, a high order one-step time update scheme, and a "cell-by-cell" space-time AMR strategy with time-accurate local time stepping. In this way, third order accurate (both in space and in time) numerical simulations of the RM instability are performed, spanning a wide parameter space. We present results both for the case in which a light fluid penetrates into a higher density one (Atwood number A > 0) and for the case in which a heavy fluid penetrates into a lower density one (Atwood number A < 0). We find that for large Lorentz factors γs of the incident shock wave, the relativistic RM instability is substantially weakened and ultimately suppressed. More specifically, the growth rate of the RM instability in the linear phase has a local maximum which occurs at a critical value of γs ≈ [1.2, 2]. Moreover, we have also revealed a genuinely relativistic effect, absent in Newtonian hydrodynamics, which arises in three dimensional configurations with a non-zero velocity component tangent to the incident shock front. In particular, in A > 0 models, the tangential velocity has a net magnification effect, while in A < 0 models, the tangential velocity has a net suppression effect.
High-order state estimation for space-plane with several antennas
NASA Astrophysics Data System (ADS)
Ono, Shuji
The real-time flight control and safety system on the ground for a launch rocket or a return spacecraft has ofter required a new tool, in order to evaluate the functioning of the on-board flight control system. This needs estimation of the high-order state vector of attitude angle, angular rate, thrust, its offset, and dynamic parameters, beyond the ordinary estimation of position and velocity. This paper presents new algorithms for both stochastic and deterministic estimation of the high-order state vectors of a space-plane equipped with several antennas, so as to distinguish the outer information (range & range rate, etc.) from each antenna. The simulation for a powered flight of return-to-Earth phase shows that the estimation has remarkably higher precision as the body scale becomes bigger. This paper would give one of fundamental guidelines both for the construction of the ground control system separate from telemeter data, and for the design of the on-board flight control system with the true robustness by two independent on-board logics, for future space-plane.
NASA Technical Reports Server (NTRS)
Liu, Yen; Vinokur, Marcel; Wang, Z. J.
2004-01-01
A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of
NASA Astrophysics Data System (ADS)
Del Zanna, L.; Zanotti, O.; Bucciantini, N.; Londrillo, P.
2007-10-01
Aims:We present a new numerical code, ECHO, based on a Eulerian conservative high-order scheme for time dependent three-dimensional general relativistic magnetohydrodynamics (GRMHD) and magnetodynamics (GRMD). ECHO is aimed at providing a shock-capturing conservative method able to work at an arbitrary level of formal accuracy (for smooth flows), where the other existing GRMHD and GRMD schemes yield an overall second order at most. Moreover, our goal is to present a general framework based on the 3+1 Eulerian formalism, allowing for different sets of equations and different algorithms and working in a generic space-time metric, so that ECHO may be easily coupled to any solver for Einstein's equations. Methods: Our finite-difference conservative scheme previously developed for special relativistic hydrodynamics and MHD is extended here to the general relativistic case. Various high-order reconstruction methods are implemented and a two-wave approximate Riemann solver is used. The induction equation is treated by adopting the upwind constrained transport (UCT) procedures, appropriate to preserving the divergence-free condition of the magnetic field in shock-capturing methods. The limiting case of magnetodynamics (also known as force-free degenerate electrodynamics) is implemented by simply replacing the fluid velocity with the electromagnetic drift velocity and by neglecting the contribution of matter to the stress tensor. Results: ECHO is particularly accurate, efficient, versatile, and robust. It has been tested against several astrophysical applications, like magnetized accretion onto black holes and constant angular momentum thick disks threaded by toroidal fields. A novel test of the propagation of large-amplitude, circularly polarized Alfvén waves is proposed, and this allows us to prove the spatial and temporal high-order properties of ECHO very accurately. In particular, we show that reconstruction based on a monotonicity-preserving (MP) filter applied to a
Pump-probe study of atoms and small molecules with laser driven high order harmonics
NASA Astrophysics Data System (ADS)
Cao, Wei
A commercially available modern laser can emit over 1015 photons within a time window of a few tens of femtoseconds (10-15second), which can be focused into a spot size of about 10 mum, resulting in a peak intensity above 1014W/cm2. This paves the way for table-top strong field physics studies such as above threshold ionization (ATI), non-sequential double ionization (NSDI), high order harmonic generation (HHG), etc.. Among these strong laser-matter interactions, high order harmonic generation, which combines many photons of the fundamental laser field into a single photon, offers a unique way to generate light sources in the vacuum ultraviolet (VUV) or extreme ultraviolet (EUV) region. High order harmonic photons are emitted within a short time window from a few tens of femtoseconds down to a few hundreds of attoseconds (10 -18second). This highly coherent nature of HHG allows it to be synchronized with an infrared (IR) laser pulse, and the pump-probe technique can be adopted to study ultrafast dynamic processes in a quantum system. The major work of this thesis is to develop a table-top VUV(EUV) light source based on HHG, and use it to study dynamic processes in atoms and small molecules with the VUV(EUV)-pump IR-probe method. A Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) apparatus is used for momentum imaging of the interaction products. Two types of high harmonic pump pulses are generated and applied for pump-probe studies. The first one consists of several harmonics forming a short attosecond pulse train (APT) in the EUV regime (around 40 eV). We demonstrate that, (1) the auto-ionization process triggered by the EUV in cation carbon-monoxide and oxygen molecules can be modified by scanning the EUV-IR delay, (2) the phase information of quantum trajectories in bifurcated high harmonics can be extracted by performing an EUV-IR cross-correlation experiment, thus disclosing the macroscopic quantum control in HHG. The second type of high harmonic source
High-order harmonic generation with Rydberg atoms by using an intense few-cycle pulse
NASA Astrophysics Data System (ADS)
Zhai, Zhen; Zhu, Qiren; Chen, Jing; Yan, Zong-Chao; Fu, Panming; Wang, Bingbing
2011-04-01
We demonstrate that high-order harmonic generation (HHG) with both high cutoff frequency and high conversion efficiency can be realized by using a Rydberg atom in a few-cycle laser pulse. This is because a Rydberg state has a large electron orbital radius and small binding energy; therefore an electron in the Rydberg state can be ionized easily and accelerated directly toward the core under the interaction of a few-cycle laser pulse, leading to emission of harmonic photons. In this case, the tunneling process of the electron is not involved and, hence, the conversion efficiency and the cutoff frequency of harmonic generation can be higher than that predicted by the conventional three-step model.
Ferré, A.; Boguslavskiy, A. E.; Dagan, M.; Blanchet, V.; Bruner, B. D.; Burgy, F.; Camper, A.; Descamps, D.; Fabre, B.; Fedorov, N.; Gaudin, J.; Geoffroy, G.; Mikosch, J.; Patchkovskii, S.; Petit, S.; Ruchon, T.; Soifer, H.; Staedter, D.; Wilkinson, I.; Stolow, A.; Dudovich, N.; Mairesse, Y.
2015-01-01
High-order harmonic generation in polyatomic molecules generally involves multiple channels of ionization. Their relative contribution can be strongly influenced by the presence of resonances, whose assignment remains a major challenge for high-harmonic spectroscopy. Here we present a multi-modal approach for the investigation of unaligned polyatomic molecules, using SF6 as an example. We combine methods from extreme-ultraviolet spectroscopy, above-threshold ionization and attosecond metrology. Fragment-resolved above-threshold ionization measurements reveal that strong-field ionization opens at least three channels. A shape resonance in one of them is found to dominate the signal in the 20–26 eV range. This resonance induces a phase jump in the harmonic emission, a switch in the polarization state and different dynamical responses to molecular vibrations. This study demonstrates a method for extending high-harmonic spectroscopy to polyatomic molecules, where complex attosecond dynamics are expected. PMID:25608712
Highly ordered Pb(Zr₀.₅₂ Ti₀.₄₈)O₃ piezoelectric nanorod arrays.
Yang, Su Chul; Sanghadasa, Mohan; Priya, Shashank
2013-06-01
One-dimensional (1D) piezoelectric nanostructures have attracted significant attention for a broad range of applications including optoelectronics, thermoelectrics, electrochemical and electromechanical converters. We demonstrate the synthesis of 1D nanostructures based upon Pb(Zr0.52Ti0.48)O3 (PZT) on conductive substrates via sol-gel template synthesis. The vertically aligned PZT nanostructures with heights around one micron were synthesized by vacuum infiltration of sol-gel precursors into highly ordered cylindrical pores of anodized aluminum oxide templates. The 1D nanostructures were developed on large scale platinized silicon wafers and exhibited dense rod-like structure with a uniform diameter of 90 nm and an aspect ratio of 10. Scanning probe microscopy conducted on individual nanorods demonstrated good electromechanical properties with a high piezoelectric magnitude of 41 pm V(-1). We believe that this study opens the possibility of developing high performance nanoscale piezoelectric sensors and transducers. PMID:23637024
High-order harmonic generation from laser plasma produced by pulses of different duration
Ganeev, R. A.; Suzuki, M.; Baba, M.; Kuroda, H.
2007-08-15
The high-order harmonic generation was analyzed by interaction of the femtosecond pulses with the laser plasma produced on the surfaces of various targets. The plasma formation was accomplished by the interaction of the prepulse radiation of different pulse duration (160 fs, 1.5 ps, 210 ps, and 20 ns) with the low-Z (lithium, boron, carbon), medium-Z (manganese, zinc, nickel), and high-Z (silver, barium) targets. We showed that plasma formation conditions play a crucial role in harmonic generation and the optimization of this process mostly depends on the energy of prepulse rather than its intensity at the target surface. These studies also demonstrated that the delay between the prepulse and femtosecond pulse is another important parameter, which distinguishes harmonic generation in the cases of the low- and high-Z targets.
Ferré, A; Boguslavskiy, A E; Dagan, M; Blanchet, V; Bruner, B D; Burgy, F; Camper, A; Descamps, D; Fabre, B; Fedorov, N; Gaudin, J; Geoffroy, G; Mikosch, J; Patchkovskii, S; Petit, S; Ruchon, T; Soifer, H; Staedter, D; Wilkinson, I; Stolow, A; Dudovich, N; Mairesse, Y
2015-01-01
High-order harmonic generation in polyatomic molecules generally involves multiple channels of ionization. Their relative contribution can be strongly influenced by the presence of resonances, whose assignment remains a major challenge for high-harmonic spectroscopy. Here we present a multi-modal approach for the investigation of unaligned polyatomic molecules, using SF6 as an example. We combine methods from extreme-ultraviolet spectroscopy, above-threshold ionization and attosecond metrology. Fragment-resolved above-threshold ionization measurements reveal that strong-field ionization opens at least three channels. A shape resonance in one of them is found to dominate the signal in the 20-26 eV range. This resonance induces a phase jump in the harmonic emission, a switch in the polarization state and different dynamical responses to molecular vibrations. This study demonstrates a method for extending high-harmonic spectroscopy to polyatomic molecules, where complex attosecond dynamics are expected. PMID:25608712
Coherent diffractive imaging microscope with a high-order harmonic source.
Dinh, Khuong Ba; Le, Hoang Vu; Hannaford, Peter; Dao, Lap Van
2015-06-10
We report the generation of highly coherent extreme ultraviolet sources with wavelengths around 30 and 10 nm by phase-matched high-order harmonic generation (HHG) in a gas cell filled with argon and helium, respectively. We then perform coherent diffractive imaging (CDI) by using a focused narrow-bandwidth HHG source with wavelength around 30 nm as an illumination beam for two kinds of samples. The first is a transmission sample and the second is a absorption sample. In addition, we report the successful reconstruction of a complex absorption sample using a tabletop high-harmonic source. This will open the path to the realization of a compact soft x-ray microscope to investigate biological samples such as membrane proteins. PMID:26192827
NASA Astrophysics Data System (ADS)
Mohan, Ranjini R.; Varma, Sreekanth J.; Sankaran, Jayalekshmi
2016-04-01
The present work highlights the remarkably high shielding effectiveness of about 68 dB, exhibited by highly ordered and doped polyaniline films, in the microwave frequency range 4-12 GHz, obtained by self-stabilized dispersion polymerization as the synthesis route. The observed shielding effectiveness is found to depend quite sensitively on the electrical conducting properties, which are predominantly controlled by the nature and concentration of the dopants. The structural and morphological characterization of the films using XRD and TEM techniques reveals surprisingly high extent of crystallinity, which contributes significantly towards enhancing the electrical conductivity of the films. Most of the available reports on the microwave response of conducting polymer film samples deal with much thicker films, compared to the micrometer thick films of the present studies. The shielding effectiveness of acid doped, micrometer thick polyaniline films reported in the present work far exceeds most of the previously reported values and meets the commercial requirements.
An Investigation of High-Order Shock-Capturing Methods for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Casper, Jay; Baysal, Oktay
1997-01-01
This project is motivated by the desire to develop numerical methods that will be useful in the study of compressible flows that exhibit aeroacoustic phenomena. Solutions to linear problems have been investigated through the development of a computer code based on the recent dispersion-relation-preserving (DRP) methodology. In regard to nonlinear problems, the class of essentially nonoscillatory (ENO) schemes have been considered as the primary candidates for solving aeroacoustic problems in which discontinuities are involved. Discontinuities in the solution itself (e.g. shocks) as well as in the geometry on which the problem is defined have been studied. Two-dimensional nonlinear problems were considered in order to determine if the one-dimensional results obtained in the first phase of this project were extendable to more realistic problems. Conclusions have been drawn in regard to the ability to numerically predict solutions of nonlinear problems with shocks to high-order accuracy.
Optimal control of attosecond pulse synthesis from high-order harmonic generation
Ben Haj Yedder, A.; Le Bris, C.; Atabek, O.; Chelkowski, S.; Bandrauk, A. D.
2004-04-01
Numerical solutions of the time-dependent Schroedinger equation for a three-dimensional H atom and an efficient genetic algorithm are used to optimize short intense excitation laser pulses in order to generate high-order harmonics from which we synthesize single attosecond pulses. It is shown that chirping of excitation pulses at intensities {approx}10{sup 14} W/cm{sup 2} and duration of up to {approx}16 fs can lead to synthesis of single attosecond pulses. The optimal excitation pulses and the phases of the generated harmonics are compared with the nonoptimized ones, showing thus the usefulness of genetic algorithm schemes in the search of optimal conditions for synthesizing single attosecond pulses.
Probe of Multielectron Dynamics in Xenon by Caustics in High-Order Harmonic Generation.
Faccialà, D; Pabst, S; Bruner, B D; Ciriolo, A G; De Silvestri, S; Devetta, M; Negro, M; Soifer, H; Stagira, S; Dudovich, N; Vozzi, C
2016-08-26
We investigated the giant resonance in xenon by high-order harmonic generation spectroscopy driven by a two-color field. The addition of a nonperturbative second harmonic component parallel to the driving field breaks the symmetry between neighboring subcycles resulting in the appearance of spectral caustics at two distinct cutoff energies. By controlling the phase delay between the two color components it is possible to tailor the harmonic emission in order to amplify and isolate the spectral feature of interest. In this Letter we demonstrate how this control scheme can be used to investigate the role of electron correlations that give birth to the giant resonance in xenon. The collective excitations of the giant dipole resonance in xenon combined with the spectral manipulation associated with the two-color driving field allow us to see features that are normally not accessible and to obtain a good agreement between the experimental results and the theoretical predictions. PMID:27610855
Intelligent Tracking Control for a Class of Uncertain High-Order Nonlinear Systems.
Zhao, Xudong; Shi, Peng; Zheng, Xiaolong; Zhang, Jianhua
2016-09-01
This brief is concerned with the problem of intelligent tracking control for a class of high-order nonlinear systems with completely unknown nonlinearities. An intelligent adaptive control algorithm is presented by combining the adaptive backstepping technique with the neural networks' approximation ability. It is shown that the practical output tracking performance of the system is achieved using the proposed state-feedback controller under two mild assumptions. In particular, by introducing a parameter in the derivations, the tracking error between the time-varying target signal and the output can be reduced via tuning the controller design parameters. Moreover, in order to solve the problem of overparameterization, which is a common issue in adaptive control design, a controller with one adaptive law is also designed. Finally, simulation results are given to show the effectiveness of the theoretical approaches and the potential of the proposed new design techniques. PMID:26277002
High-order micro-ring resonator with perfect transmission using symmetrical Fibonacci structures.
Tsao, C W; Cheng, Y H; Hsueh, W J
2015-09-15
A symmetrical Fibonacci micro-ring resonator (SFMR) has been presented to avoid the coupled resonator optical waveguide (CROW) bottle, which is a bottle-shaped distribution for high orders in transmission spectra. The SFMR features three advantages that improve filtering quality compared to that provided by traditional periodic micro-ring resonators. First, sharper resonances are obtained by eliminating the CROW bottle from the mini gaps that appear in the major-band region. Second, peaks with perfect transmission are always obtained without a radius and coupling modulation in the mini-band regions and major-band regions. Third, the full width at half-maximum of the band-edge peak decreases with the increasing generation order. PMID:26371905
Efficient simulation of cardiac electrical propagation using high order finite elements
NASA Astrophysics Data System (ADS)
Arthurs, Christopher J.; Bishop, Martin J.; Kay, David
2012-05-01
We present an application of high order hierarchical finite elements for the efficient approximation of solutions to the cardiac monodomain problem. We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component. We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time. Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.
Thierry, Agnès; Khanna, Varun; Créno, Sophie; Lafontaine, Ingrid; Ma, Laurence; Bouchier, Christiane; Dujon, Bernard
2015-01-01
Copy number variation of chromosomal segments is now recognized as a major source of genetic polymorphism within natural populations of eukaryotes, as well as a possible cause of genetic diseases in humans, including cancer, but its molecular bases remain incompletely understood. In the baker’s yeast Saccharomyces cerevisiae, a variety of low-order amplifications (segmental duplications) were observed after adaptation to limiting environmental conditions or recovery from gene dosage imbalance, and interpreted in terms of replication-based mechanisms associated or not with homologous recombination. Here we show the emergence of novel high-order amplification structures, with corresponding overexpression of embedded genes, during evolution under favourable growth conditions of severely unfit yeast cells bearing genetically disabled genomes. Such events form massively extended chromosomes, which we propose to call macrotene, whose characteristics suggest the products of intrachromosomal rolling-circle type of replication structures, probably initiated by increased accidental template switches under important cellular stress conditions. PMID:25635677
Montarnal, Damien; Delbosc, Nicolas; Chamignon, Cécile; Virolleaud, Marie-Alice; Luo, Yingdong; Hawker, Craig J; Drockenmuller, Eric; Bernard, Julien
2015-09-14
We designed efficient precursors that combine complementary associative groups with exceptional binding affinities and thiocarbonylthio moieties enabling precise RAFT polymerization. Well defined PS and PMMA supramolecular polymers with molecular weights up to 30 kg mol(-1) are synthesized and shown to form highly stable supramolecular diblock copolymers (BCPs) when mixed, in non-polar solvents or in the bulk. Hierarchical self-assembly of such supramolecular BCPs by thermal annealing affords morphologies with excellent lateral order, comparable to features expected from covalent diblock copolymer analogues. Simple washing of the resulting materials with protic solvents disrupts the supramolecular association and selectively dissolves one polymer, affording a straightforward process for preparing well-ordered nanoporous materials without resorting to crosslinking or invasive chemical degradations. PMID:26234749
NASA Technical Reports Server (NTRS)
Fatemi, Emad; Jerome, Joseph; Osher, Stanley
1989-01-01
A micron n+ - n - n+ silicon diode is simulated via the hydrodynamic model for carrier transport. The numerical algorithms employed are for the non-steady case, and a limiting process is used to reach steady state. The simulation employs shock capturing algorithms, and indeed shocks, or very rapid transition regimes, are observed in the transient case for the coupled system, consisting of the potential equation and the conservation equations describing charge, momentum, and energy transfer for the electron carriers. These algorithms, termed essentially non-oscillatory, were successfully applied in other contexts to model the flow in gas dynamics, magnetohydrodynamics, and other physical situations involving the conservation laws in fluid mechanics. The method here is first order in time, but the use of small time steps allows for good accuracy. Runge-Kutta methods allow one to achieve higher accuracy in time if desired. The spatial accuracy is of high order in regions of smoothness.
Microgravity Isolation Control System Design Via High-Order Sliding Mode Control
NASA Technical Reports Server (NTRS)
Shkolnikov, Ilya; Shtessel, Yuri; Whorton, Mark S.; Jackson, Mark
2000-01-01
Vibration isolation control system design for a microgravity experiment mount is considered. The controller design based on dynamic sliding manifold (DSM) technique is proposed to attenuate the accelerations transmitted to an isolated experiment mount either from a vibrating base or directly generated by the experiment, as well as to stabilize the internal dynamics of this nonminimum phase plant. An auxiliary DSM is employed to maintain the high-order sliding mode on the primary sliding manifold in the presence of uncertain actuator dynamics of second order. The primary DSM is designed for the closed-loop system in sliding mode to be a filter with given characteristics with respect to the input external disturbances.
Multi-dimensional high-order numerical schemes for Lagrangian hydrodynamics
Dai, William W; Woodward, Paul R
2009-01-01
An approximate solver for multi-dimensional Riemann problems at grid points of unstructured meshes, and a numerical scheme for multi-dimensional hydrodynamics have been developed in this paper. The solver is simple, and is developed only for the use in numerical schemes for hydrodynamics. The scheme is truely multi-dimensional, is second order accurate in both space and time, and satisfies conservation laws exactly for mass, momentum, and total energy. The scheme has been tested through numerical examples involving strong shocks. It has been shown that the scheme offers the principle advantages of high-order Codunov schemes; robust operation in the presence of very strong shocks and thin shock fronts.
NASA Astrophysics Data System (ADS)
Zhang, Qian; Zhu, Jinwei; Wang, Ying; Feng, Jiangtao; Yan, Wei; Xu, Hao
2014-07-01
To explore the kinetics of photoelectrocatalytic degradation of salicylic acid, one of the important PPCPs, highly ordered TiO2 nanotube arrays (NTs) were prepared by the electrochemical anodization and characterized with scanning electron microscopy and X-ray diffraction techniques. The effect of TiO2 NTs properties, bias potential, initial salicylic acid concentration and solution pH on the degradation efficiency was studied and carefully analyzed. The results revealed that the salicylic acid degradation follows quasi-first order kinetics in the photoelectrocatalytic process, and the fastest decay kinetics was achieved in acidic environment (pH 2). The result was further interpreted through the electrochemical impedance spectroscopy. It is confirmed that the electrochemical assisted photocatalysis is a synergetic approach to combat stable organic substances with improved efficiency.
Steering and focusing effects in TESLA cavity due to high order mode and input couplers
Piot, P.; Dohlus, M.; Flottmann, K.; Marx, M.; Wipf, S.G.; /DESY
2005-05-01
Many state-of-art electron accelerator proposals incorporate TESLA-type superconducting radio-frequency (rf) cavities [1]. These standing wave rf cavities include rf input couplers and a pair of high order mode (HOM) couplers to absorb the energy associated to HOM field excited as the bunch passes through the cavity. In the present paper we investigate, using numerical simulations, the impact of the input and HOM couplers on the beam dynamics to zeroth and first order in initial position, and present parametric studies of the strength of these effects for various incoming beam energies. We finally study the impact of this asymmetric field on the beam dynamics, taking as an example the low energy section of the X-ray FEL injector.
Effect of nuclear motion on spectral broadening of high-order harmonic generation.
Yuan, Xiaolong; Wei, Pengfei; Liu, Candong; Ge, Xiaochun; Zheng, Yinghui; Zeng, Zhinan; Li, Ruxin
2016-04-18
High-order harmonic generation (HHG) in molecular targets is experimentally investigated in order to reveal the role of the nuclear motion played in the harmonic generation process. An obvious broadening in the harmonic spectrum from the H_{2} molecule is observed in comparison with the harmonic spectrum generated from other molecules with relatively heavy nuclei. We also find that the harmonic yield from the H_{2} molecule is much weaker than the yield from those gas targets with the similar ionization potentials, such as Ar atom and N_{2} molecule. The yield suppression and the spectrum broadening of HHG can be attributed to the vibrational motion of nuclear induced by the driving laser pulse. Moreover, the one-dimensional (1D) time-dependent Schrödinger equation (TDSE) with the non-Born-Oppenheimer (NBO) treatment is numerically solved to provide a theoretical support to our explanation. PMID:27137258
Relaxation approximations to second-order traffic flow models by high-resolution schemes
Nikolos, I.K.; Delis, A.I.; Papageorgiou, M.
2015-03-10
A relaxation-type approximation of second-order non-equilibrium traffic models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms with the attractive feature that neither Riemann solvers nor characteristic decompositions are in need. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. To discretize the resulting relaxation system, high-resolution reconstructions in space are considered. Emphasis is given on a fifth-order WENO scheme and its performance. The computations reported demonstrate the simplicity and versatility of relaxation schemes as numerical solvers.
Nonlinear Fourier-transform spectroscopy of D{sub 2} using high-order harmonic radiation
Furukawa, Yusuke; Nabekawa, Yasuo; Saugout, Sebastien; Midorikawa, Katsumi; Okino, Tomoya; Yamanouchi, Kaoru
2010-07-15
We have determined the multiphoton ionization and dissociation pathways of D{sub 2} with the simultaneous irradiation of the high-order harmonic fields and the low-order harmonic fields of Ti:sapphire laser pulses in the visible-vacuum ultraviolet region with the aid of a nonlinear Fourier-transform spectroscopy. By analyzing the interferometric autocorrelation signal of the measured velocity map images of D{sup +}, we were able to decompose the measured momentum distribution into three momentum distribution images representing the three distinct dissociation pathways, which are sequentially two-photon absorption processes of D{sub 2} via the electronic ground state (X {sup 2{Sigma}}{sub g}{sup +}) of D{sub 2}{sup +} to the first excited state (A {sup 2{Sigma}}{sub u}{sup +}), leading to the dissociation into D{sup +} + D.
A high-order harmonic generation apparatus for time- and angle-resolved photoelectron spectroscopy
Frietsch, B.; Gahl, C.; Teichmann, M.; Weinelt, M.; Carley, R.; Döbrich, K.; Schwarzkopf, O.; Wernet, Ph.
2013-07-15
We present a table top setup for time- and angle-resolved photoelectron spectroscopy to investigate band structure dynamics of correlated materials driven far from equilibrium by femtosecond laser pulse excitation. With the electron-phonon equilibration time being in the order of 1–2 ps it is necessary to achieve sub-picosecond time resolution. Few techniques provide both the necessary time and energy resolution to map non-equilibrium states of the band structure. Laser-driven high-order harmonic generation is such a technique. In our experiment, a grating monochromator delivers tunable photon energies up to 40 eV. A photon energy bandwidth of 150 meV and a pulse duration of 100 fs FWHM allow us to cover the k-space necessary to map valence bands at different k{sub z} and detect outer core states.
Selective suppression of high order axial modes of the gyrotron backward-wave oscillator
Pao, K. F.; Fan, C. T.; Chang, T. H.; Chiu, C. C.; Chu, K. R.
2007-09-15
Selective suppression of high order axial modes of the gyrotron backward-wave oscillator (gyro-BWO) is investigated in theory and in experiment. The gyro-BWO interaction is much more efficient in a down-tapered interaction structure, while it is also more susceptible to the problem of axial mode competition in such a structure. Because higher order axial modes (at a higher oscillation frequency) penetrate deeper into the interaction structure, application of distributed wall loss at the downstream end of the interaction structure is shown to be effective for selective suppression of these modes with minor effects on the efficiency of the desired fundamental axial mode. A stable gyro-BWO operating in a single mode throughout the entire beam pulse is demonstrated on the basis of this principle. Theoretical and experimental results are found to be in good agreement.
Ganmor, Elad; Segev, Ronen; Schneidman, Elad
2011-01-01
Information is carried in the brain by the joint activity patterns of large groups of neurons. Understanding the structure and function of population neural codes is challenging because of the exponential number of possible activity patterns and dependencies among neurons. We report here that for groups of ~100 retinal neurons responding to natural stimuli, pairwise-based models, which were highly accurate for small networks, are no longer sufficient. We show that because of the sparse nature of the neural code, the higher-order interactions can be easily learned using a novel model and that a very sparse low-order interaction network underlies the code of large populations of neurons. Additionally, we show that the interaction network is organized in a hierarchical and modular manner, which hints at scalability. Our results suggest that learnability may be a key feature of the neural code. PMID:21602497
The a(4) Scheme-A High Order Neutrally Stable CESE Solver
NASA Technical Reports Server (NTRS)
Chang, Sin-Chung
2009-01-01
The CESE development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a nondissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To provide a solid foundation for a systematic CESE development of high order schemes, in this paper we describe a new high order (4-5th order) and neutrally stable CESE solver of a 1D advection equation with a constant advection speed a. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and two points at the lower time level. Because it is associated with four independent mesh variables (the numerical analogues of the dependent variable and its first, second, and third-order spatial derivatives) and four equations per mesh point, the new scheme is referred to as the a(4) scheme. As in the case of other similar CESE neutrally stable solvers, the a(4) scheme enforces conservation laws in space-time locally and globally, and it has the basic, forward marching, and backward marching forms. Except for a singular case, these forms are equivalent and satisfy a space-time inversion (STI) invariant property which is shared by the advection equation. Based on the concept of STI invariance, a set of algebraic relations is developed and used to prove the a(4) scheme must be neutrally stable when it is stable. Numerically, it has been established that the scheme is stable if the value of the Courant number is less than 1/3
Role of high-order dispersion on strong-field laser-molecule interactions
NASA Astrophysics Data System (ADS)
Dantus, Marcos; Nairat, Muath
2016-05-01
Strong-field (1012- 1016 W/ cm2) laser-matter interactions are characterized by the extent of fragmentation and charge of the resulting ions as a function of peak intensity and pulse duration. Interactions are influenced by high-order dispersion, which is difficult to characterize and compress. Fourth-order dispersion (FOD) causes a time-symmetric pedestal, while third-order dispersion (TOD) causes a leading (negative) or following (positive) pedestal. Here, we report on strong-field interactions with pentane and toluene molecules, tracking the molecular ion and the doubly charged carbon ion C2+ yields as a function of TOD and FOD for otherwise transform-limited (TL) 35fs pulses. We find TL pulses enhance molecular ion yield and suppress C2+ yield, while FOD reverses this trend. Interestingly, the leading pedestal in negative TOD enhances C2+ yield compared to positive TOD. Pulse pedestals are of particular importance in strong-field science because target ionization or alignment can be induced well before the main pulse arrives. A pedestal following an intense laser pulse can cause sequential ionization or accelerate electrons causing cascaded ionization. Control of high-order dispersion allows us to provide strong-field measurements that can help address the mechanisms responsible for different product ions in the presence and absence of pedestals. Financial support of this work comes from the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy, DOE SISGR (DE-SC0002325)
NASA Astrophysics Data System (ADS)
Gao, Junhui
2013-05-01
Overlap grid is usually used in numerical simulation of flow with complex geometry by high order finite difference scheme. It is difficult to generate overlap grid and the connectivity information between adjacent blocks, especially when interpolation is required for non-coincident overlap grids. In this study, an interface flux reconstruction (IFR) method is proposed for numerical simulation using high order finite difference scheme with multi-block structured grids. In this method the neighboring blocks share a common face, and the fluxes on each block are matched to set the boundary conditions for each interior block. Therefore this method has the promise of allowing discontinuous grids on either side of an interior block interface. The proposed method is proven to be stable for 7-point central DRP scheme coupled with 4-point and 5-point boundary closure schemes, as well as the 4th order compact scheme coupled with 3rd order boundary closure scheme. Four problems are numerically solved with the developed code to validate the interface flux reconstruction method in this study. The IFR method coupled with the 4th order DRP scheme or compact scheme is validated to be 4th order accuracy with one and two dimensional waves propagation problems. Two dimensional pulse propagation in mean flow is computed with wavy mesh to demonstrate the ability of the proposed method for non-uniform grid. To demonstrate the ability of the proposed method for complex geometry, sound scattering by two cylinders is simulated and the numerical results are compared with the analytical data. It is shown that the numerical results agree well with the analytical data. Finally the IFR method is applied to simulate viscous flow pass a cylinder at Reynolds number 150 to show its capability for viscous problem. The computed pressure coefficient on the cylinder surface, the frequency of vortex shedding, the lift and drag coefficients are presented. The numerical results are compared with the data
A High-order Eulerian-Lagrangian Finite Element Method for Coupled Electro-mechanical Systems
NASA Astrophysics Data System (ADS)
Brandstetter, Gerd
The main focus of this work is on the development of a high-order Eulerian-Lagrangian finite element method for the simulation of electro-mechanical systems. The coupled problem is solved by a staggered scheme, where the mechanical motion is discretized by standard Lagrangian finite elements, and the electrical field is solved on a fixed Eulerian grid with embedded boundary conditions. Traditional Lagrangian-Lagrangian or arbitrary Lagrangian-Eulerian (ALE) methods encounter deficiencies, for example, when dealing with mesh distortion due to large deformations, or topology changes due to contacting bodies. The presented Eulerian-Lagrangian approach addresses these issues in a natural way. Within this context we develop a high-order immersed boundary discontinuous-Galerkin (IB-DG) method, which is shown to be necessary for (i) the accurate representation of the electrical gradient along nonlinear boundary features such as singular corners, and (ii) to achieve full convergence during the iterative global solution. We develop an implicit scheme based on the mid-point rule, as well as an explicit scheme based on the centered-difference method, with the incorporation of energy conserving, frictionless contact algorithms for an elastic-to-rigid-surface contact. The performance of the proposed method is assessed for several benchmark tests: the electro-static force vector around a singular corner, the quasi-static pull-in of an electro-mechanically actuated switch, the excitation of a carbon nanotube at resonance, and the cyclic impact simulation of a micro-electro-mechanical resonant-switch. We report improved accuracy for the high-order method as compared to low-order methods, and linear convergence in the iterative solution of the staggered scheme. Additionally, we investigate a Newton-Krylov shooting scheme in order to directly find cyclic steady states of electro-mechanical devices excited at resonance-- as opposed to a naive time-stepping from zero initial
Th unnatural order of things: A history of the high school science sequence
NASA Astrophysics Data System (ADS)
Robbins, Dennis M.
Historical studies of US high school science education are rare. This study examines the historical origins of a unique characteristic of the secondary science curriculum, the Biology-Chemistry-Physics (B-C-P) order of courses. Statements from scientists, educators and the media claim that B-C-P has been the traditional curriculum sequence for over a century and can be traced back to the influential educational commission known as the Committee of Ten (CoT) of 1893. This study examines the history of the ordering of high school science subjects over the last 150 years. The reports and primary documents of important national educational commissions, such as the CoT, were searched for their recommendations on secondary science, particularly on course ordering. These recommendations were then compared to national, state and local statistical data on subject offerings and student enrollments to measure the effect of these national commissions on school policy. This study concludes that the Committee of Ten did not create B-P-C. The CoT made six recommendations, five placed Chemistry before Physics (P-C). One recommendation for C-P met with strong disagreement because it was thought an illogical order. Biology as a "uniform" course did not exist at this time and so the CoT made no recommendations for its grade placement. Statistical data shows that B-C-P evolved over many decades. From 1860 up to 1920 most schools used a P-C curriculum believing Physics was a foundational prerequisite of Chemistry. Biology was introduced in the early 1900s and it assumed a position before the physical sciences. Through the 1920s Chemistry and Physics were placed equally likely in 11th or 12 th grades and Biology was in the 10th grade. After World War II, B-C-P became the dominant pattern, exhibited in over 90% of schools. But up to this point in time no educational body or national commission had recommended B-C-P. The Biology-Chemistry-Physics order of courses is a product of many
A third-order mode high frequency biosensor with atomic resolution.
Cai, Hua-Lin; Yang, Yi; Chen, Xiao; Mohammad, Mohammad Ali; Ye, Tian-Xiang; Guo, Cang-Ran; Yi, Li-Ting; Zhou, Chang-Jian; Liu, Jing; Ren, Tian-Ling
2015-09-15
An atomic resolution ultra-high sensitivity surface acoustic wave (SAW) biosensor for DNA sequences and cells detection is proposed. Interdigitated transducers (IDTs) fabricated on LiNbO3 substrate achieve a high quality factor (Q) of over 4000 at a frequency of 6.4 GHz (third-order harmonic mode) using an optimized design and process. The biosensor shows excellent linear responses to target DNA in the range from 1 μg/ml to 1 ng/ml with a high sensitivity of 6.7 × 10(-16)g/cm(2)/Hz, hence the difference of a single hybridized DNA base can also be distinguished. With such a high mass resolution, the biosensor is capable of quantitative detection of living cancer cells. The frequency responses of single mouse mammary adenocarcinoma (EMT6) cell and mouse fibroblast (3T3) cell are studied. The interferences in the experiments show insignificant influence on the frequency shift, which verifies the high selectivity of the biosensor. The biosensor is also able to repeat the sensing ability after rough cleaning, therefore cost reduction is achieved from the recycling process in practical applications. The detection limit is defined from the noise analysis of the device, atomic resolution is realized according to the calculation, thereby initiating a potential tool for high-precision medical diagnoses and phenomena observation at the atomic-level. PMID:25913447
A high-order time formulation of the RBC schemes for unsteady compressible Euler equations
NASA Astrophysics Data System (ADS)
Lerat, A.
2015-12-01
Residual-Based Compact (RBC) schemes can approximate the compressible Euler equations with a high space-accuracy on a very compact stencil. For instance on a 2-D Cartesian mesh, the 5th- and 7th-order accuracy can be reached on a 5 × 5-point stencil. The time integration of the RBC schemes uses a fully implicit method of 2nd-order accuracy (Gear method) usually solved by a dual-time approach. This method is efficient for computing compressible flows in slow unsteady regimes, but for quick unsteady flows, it may be costly and not accurate enough. A new time-formulation is proposed in the present paper. Unusually, in a RBC scheme the time derivative occurs, through linear discrete operators due to compactness, not only in the main residual but also in the other two residuals (in 2-D) involved in the numerical dissipation. To extract the time derivative, a space-factorization method which preserves the high accuracy in space is developed for reducing the algebra to the direct solution of simple linear systems on the mesh lines. Then a time-integration of high accuracy is selected for the RBC schemes by comparing the efficiency of four classes of explicit methods. The new time-formulation is validated for the diagonal advection of a Gaussian shape, the rotation of a hump, the advection of a vortex for a long time and the interaction of a vortex with a shock.
NASA Astrophysics Data System (ADS)
Wang, Junfeng; Liang, Chunlei; Miesch, Mark S.
2015-06-01
We present a novel and powerful Compressible High-ORder Unstructured Spectral-difference (CHORUS) code for simulating thermal convection and related fluid dynamics in the interiors of stars and planets. The computational geometries are treated as rotating spherical shells filled with stratified gas. The hydrodynamic equations are discretized by a robust and efficient high-order Spectral Difference Method (SDM) on unstructured meshes. The computational stencil of the spectral difference method is compact and advantageous for parallel processing. CHORUS demonstrates excellent parallel performance for all test cases reported in this paper, scaling up to 12 000 cores on the Yellowstone High-Performance Computing cluster at NCAR. The code is verified by defining two benchmark cases for global convection in Jupiter and the Sun. CHORUS results are compared with results from the ASH code and good agreement is found. The CHORUS code creates new opportunities for simulating such varied phenomena as multi-scale solar convection, core convection, and convection in rapidly-rotating, oblate stars.
Word sense disambiguation via high order of learning in complex networks
NASA Astrophysics Data System (ADS)
Silva, Thiago C.; Amancio, Diego R.
2012-06-01
Complex networks have been employed to model many real systems and as a modeling tool in a myriad of applications. In this paper, we use the framework of complex networks to the problem of supervised classification in the word disambiguation task, which consists in deriving a function from the supervised (or labeled) training data of ambiguous words. Traditional supervised data classification takes into account only topological or physical features of the input data. On the other hand, the human (animal) brain performs both low- and high-level orders of learning and it has facility to identify patterns according to the semantic meaning of the input data. In this paper, we apply a hybrid technique which encompasses both types of learning in the field of word sense disambiguation and show that the high-level order of learning can really improve the accuracy rate of the model. This evidence serves to demonstrate that the internal structures formed by the words do present patterns that, generally, cannot be correctly unveiled by only traditional techniques. Finally, we exhibit the behavior of the model for different weights of the low- and high-level classifiers by plotting decision boundaries. This study helps one to better understand the effectiveness of the model.
NASA Astrophysics Data System (ADS)
Xue, Yaru; Yang, Jing; Ma, Jitao; Chen, Yangkang
2016-06-01
The Radon transform is widely used for multiple elimination. Since the Radon transform is not an orthogonal transform, it cannot preserve the amplitude of primary reflections well. The prediction and adaptive subtraction method is another widely used approach for multiple attenuation, which demands that the primaries are orthogonal with the multiples. However, the orthogonality assumption is not true for non-stationary field seismic data. In this paper, the high-order sparse Radon transform (HOSRT) method is introduced to protect the amplitude variation with offset information during the multiple subtraction procedures. The HOSRT incorporates the high-resolution Radon transform with the orthogonal polynomial transform. Because the Radon transform contains the trajectory information of seismic events and the orthogonal polynomial transform contains the amplitude variation information of seismic events, their combination constructs an overcomplete transform and obtains the benefits of both the high-resolution property of the Radon transform and the amplitude preservation of the orthogonal polynomial transform. A fast nonlinear filter is adopted in the adaptive subtraction step in order to avoid the orthogonality assumption that is used in traditional adaptive subtraction methods. The application of the proposed approach to synthetic and field data examples shows that the proposed method can improve the separation performance by preserving more useful energy.
Jia, Lichao; Lawrence, Geoffrey; Balasubramanian, V V; Choi, Goeun; Choy, Jin-Ho; Abdullah, Aboubakr M; Elzatahry, Ahmed; Ariga, Katsuhiko; Vinu, Ajayan
2015-01-01
Ordered porous carbon films with tunable pore diameters, immobilized with glucose oxidase (GOD) have been fabricated and employed for the construction of a biosensor for glucose molecules. The as-prepared porous films have large specific surface areas and highly ordered porous structure with uniform pore sizes, which are critical for the immobilization of large amounts of GOD and support the promotion of heterogeneous electron transfer. The developed biosensors give enough room for the encapsulation of a high amount of GOD molecules and show excellent biosensing performance with a linear response to glucose concentration ranging from 0.5 to 9 mM and a detection limit of 1.5 μM. It is also demonstrated that the sensitivity of the biosensor can be easily tuned by modulating the pore size of carbon film as it dictates the amount of immobilization of GOD in the porous channels. The fabricated carbon-film-based biosensor has a good stability and a high reproducibility, which opens the gateway for the commercialization of this excellent technology. PMID:25394330
The effects of molecular vibration on the yield of high-order harmonic generation.
NASA Astrophysics Data System (ADS)
Xia, Jiangfan
2005-05-01
It is well-accepted that the high-order harmonic spectrum is the results of interference between many attosecond pulses. Each of the attosecond pulse is produced by a three-step process taking place within one laser cycle. For light molecules such as H2, the first step is the ionization of one electron. When the freed electron returns to the H2^+, the internuclear distance is changed. This may cause the electron to miss the ion during its revisit, thus reducing its probability to recombine with the parent ion. As a result, the high harmonic generation yield is lower for H2 than D2, since D2 has a longer vibration period (˜21 fs) than that of H2 (˜15 fs). Here we report, to the best of our knowledge, the first experimental observation of the effects of vibration on the yield of HHG in molecules. We compared the high-order harmonic spectra of H2, HD and D2. The shortest pulses were ˜8 fs, which is almost the same as one half of the vibration period of H2. Using such short pulses assures that the internuclear distances of all three types of molecules are in the increasing phase of a cycle when the harmonics are generated. From the HHG spectra it is evident that the yield of D2 is a factor of two higher than that of H2, while that of HD is in between. This is consistent with the theoretical predictions.
Extension of Low Dissipative High Order Hydrodynamics Schemes for MHD Equations
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sjoegreen, Bjoern; Mansour, Nagi (Technical Monitor)
2002-01-01
The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD (magnetohydrodynamic) 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 curvi-linear grids. The three features of the present MHD scheme over existing schemes in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion magnetized flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike existing schemes for the conservative MHD equations which suffer from ill-conditioned eigen-decompositions, the present scheme makes use of a well-conditioned eigen-decomposition to solve the conservative form of the MHD equations. This is due to, partly. the fact that the divergence of the magnetic field condition is a different type of constraint from its incompressible Navier-Stokes cousin. Third, a new approach to minimize the numerical error of the divergence free magnetic condition for high order scheme is introduced.
Towards high-order modulation using complex modulation of semiconductor lasers.
Che, Di; Yuan, Feng; Shieh, William
2016-03-21
Optical communication using high-speed on-off-keying signal by directly modulated semiconductor lasers (DML) was one of the most significant breakthroughs for telecommunication in 1960s. The wide deployment of 2.5-Gb/s per-channel transoceanic optical fiber links in 1990s drove the internet as a global phenomenon. However, the detrimental frequency chirp of DML prevents its application to the subsequent internet capacity evolution. Today, the state-of-the-art long-haul optical transponder uses external modulators to support high-order complex modulation. In contrast, this paper shows that the "detrimental" chirp effect can be exploited to generate complex modulation with a single DML, which achieves dramatic sensitivity gain of signal-to-noise-ratio compared to the conventional intensity modulation of DML. By using large chirp parameters, complex-modulated DML paves an attractive pathway towards high-order pulse-amplitude modulation with an ultra-low transmitter cost, which has great potential in future medium reach optical communications. PMID:27136852