High order well-balanced schemes
Noelle, Sebastian; Xing, Yulong; Shu, Chi-wang
2010-01-01
In this paper the authors review some recent work on high-order well-balanced schemes. A characteristic feature of hyperbolic systems of balance laws is the existence of non-trivial equilibrium solutions, where the effects of convective fluxes and source terms cancel each other. Well-balanced schemes satisfy a discrete analogue of this balance and are therefore able to maintain an equilibrium state. They discuss two classes of schemes, one based on high-order accurate, non-oscillatory finite difference operators which are well-balanced for a general class of equilibria, and the other one based on well-balanced quadratures, which can - in principle - be applied to all equilibria. Applications include equilibria at rest, where the flow velocity vanishes, and also the more challenging moving flow equilibria. Numerical experiments show excellent resolution of unperturbed as well as slightly perturbed equilibria.
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.
Tsunami wave propagation using a high-order well-balanced finite volume scheme
NASA Astrophysics Data System (ADS)
Castro, Cristóbal E.
2010-05-01
In this work we present a new numerical tool suitable for tsunami wave propagation simulations. We developed a finite volume high-order well-balanced numerical method on unstructured meshes based on the ADER-FV scheme [1]. We use the ADER-FV[2,3] scheme to solve with arbitrary accuracy in space and time the shallow water equation with non-constant bathymetry. In order to properly simulate a tsunami wave propagation we introduce the well-balanced or C-property[4] in the high-order numerical solution. In this presentation we address two important issues that appear when one tries to solve a tsunami propagation problem. First, when small gravity waves are propagated for hundred of wave-lengths, the accuracy in space and time of the numerical method is fundamental to preserve the amplitude. In this presentation we study the propagation of small perturbations over long distances, relating the order of accuracy, the mesh dimension and the wave amplitude. Second, as we deal with high-order schemes we can naturally use polynomial representation of the bathymetry. Here we try to understand the influence of the bathymetry representation in the final solution. [1] C. E. Castro et al. "ADER scheme on unstructured meshes for shallow water: simulation of tsunami waves", submitted [2] E. F. Toro et al. "Towards very high order godunov schemes". In E. F. Toro, editor, Godunov methods; Theory and applications, pages 907--940, Oxford, 2001. Kluwer Academic Plenum Publishers. [3] E. F. Toro and V. A. Titarev. "Solution of the generalized Riemann problem for advection-reaction equations". Proc. Roy. Soc. London, pages 271--281, 2002. [4] A. Bermúdez and M. E. Vázquez. "Upwind methods for hyperbolic conservation laws with source terms". Computer and Fluids, 23(8):1049--1071, 1994.
Construction of low dissipative high-order well-balanced filter schemes for non-equilibrium flows
Wang Wei; Yee, H.C.; Sjoegreen, Bjoern; Magin, Thierry; Shu, Chi-Wang
2011-05-20
The goal of this paper is to generalize the well-balanced approach for non-equilibrium flow studied by Wang et al. (2009) to a class of low dissipative high-order shock-capturing filter schemes and to explore more advantages of well-balanced schemes in reacting flows. More general 1D and 2D reacting flow models and new examples of shock turbulence interactions are provided to demonstrate the advantage of well-balanced schemes. The class of filter schemes developed by Yee et al. (1999) , Sjoegreen and Yee (2004) and Yee and Sjoegreen (2007) consist of two steps, a full time step of spatially high-order non-dissipative base scheme and an adaptive non-linear 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 accuracy). 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; and 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.
Xing, Yulong; Zhang, Xiangxiong; Shu, Chi-wang
2010-01-01
Shallow water equations with a non-flat bottom topography have been widely used to model flows in rivers and coastal areas. An important difficulty arising in these simulations is the appearance of dry areas where no water is present, as standard numerical methods may fail in the presence of these areas. These equations also have still water steady state solutions in which the flux gradients are nonzero but exactly balanced by the source term. In this paper we propose a high order discontinuous Galerkin method which can maintain the still water steady state exactly, and at the same time can preserve the non-negativity of the water height without loss of mass conservation. A simple positivity-preserving limiter, valid under suitable CFL condition, will be introduced in one dimension and then extended to two dimensions with rectangular meshes. Numerical tests are performed to verify the positivity-preserving property, well-balanced property, high order accuracy, and good resolution for smooth and discontinuous solutions.
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.
NASA Astrophysics Data System (ADS)
Canestrelli, Alberto; Dumbser, Michael; Siviglia, Annunziato; Toro, Eleuterio F.
2010-03-01
In this paper, we study the numerical approximation of the two-dimensional morphodynamic model governed by the shallow water equations and bed-load transport following a coupled solution strategy. The resulting system of governing equations contains non-conservative products and it is solved simultaneously within each time step. The numerical solution is obtained using a new high-order accurate centered scheme of the finite volume type on unstructured meshes, which is an extension of the one-dimensional PRICE-C scheme recently proposed in Canestrelli et al. (2009) [5]. The resulting first-order accurate centered method is then extended to high order of accuracy in space via a high order WENO reconstruction technique and in time via a local continuous space-time Galerkin predictor method. The scheme is applied to the shallow water equations and the well-balanced properties of the method are investigated. Finally, we apply the new scheme to different test cases with both fixed and movable bed. An attractive future of the proposed method is that it is particularly suitable for engineering applications since it allows practitioners to adopt the most suitable sediment transport formula which better fits the field data.
2011-01-19
waves in the outer solar ( chromosphere and corona) and other stellar atmospheres. The waves are simulated by using a high-resolution, well-balanced...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. 1. Introduction Waves and oscillations are a significant means for the transport and
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.
Xing Yulong . E-mail: xing@dam.brown.edu; Shu Chiwang . E-mail: shu@dam.brown.edu
2006-05-20
Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source term. In our earlier work [J. Comput. Phys. 208 (2005) 206-227; J. Sci. Comput., accepted], we designed a well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme, which at the same time maintains genuine high order accuracy for general solutions, to a class of hyperbolic systems with separable source terms including the shallow water equations, the elastic wave equation, the hyperbolic model for a chemosensitive movement, the nozzle flow and a two phase flow model. In this paper, we generalize high order finite volume WENO schemes and Runge-Kutta discontinuous Galerkin (RKDG) finite element methods to the same class of hyperbolic systems to maintain a well-balanced property. Finite volume and discontinuous Galerkin finite element schemes are more flexible than finite difference schemes to treat complicated geometry and adaptivity. However, because of a different computational framework, the maintenance of the well-balanced property requires different technical approaches. After the description of our well-balanced high order finite volume WENO and RKDG schemes, we perform extensive one and two dimensional simulations to verify the properties of these schemes such as the exact preservation of the balance laws for certain steady state solutions, the non-oscillatory property for general solutions with discontinuities, and the genuine high order accuracy in smooth regions.
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.
Sheng, Lizhi; Jiang, Lili; Wei, Tong; Fan, Zhuangjun
2016-10-01
The well-matched electrochemical parameters of positive and negative electrodes, such as specific capacitance, rate performance, and cycling stability, are important for obtaining high-performance asymmetric supercapacitors. Herein, a facile and cost-effective strategy is demonstrated for the fabrication of 3D densely stacked graphene (DSG) and graphene-MnO2 (G-MnO2 ) architectures as the electrode materials for asymmetric supercapacitors (ASCs) by using MnO2 -intercalated graphite oxide (GO-MnO2 ) as the precursor. DSG has a stacked graphene structure with continuous ion transport network in-between the sheets, resulting in a high volumetric capacitance of 366 F cm(-3) , almost 2.5 times than that of reduced graphene oxide, as well as long cycle life (93% capacitance retention after 10 000 cycles). More importantly, almost similar electrochemical properties, such as specific capacitance, rate performance, and cycling stability, are obtained for DSG as the negative electrode and G-MnO2 as the positive electrode. As a result, the assembled ASC delivers both ultrahigh gravimetric and volumetric energy densities of 62.4 Wh kg(-1) and 54.4 Wh L(-1) (based on total volume of two electrodes) in 1 m Na2 SO4 aqueous electrolyte, respectively, much higher than most of previously reported ASCs in aqueous electrolytes.
A well-balanced numerical scheme for shallow water simulation on adaptive grids
NASA Astrophysics Data System (ADS)
Zhang, H. J.; Zhou, J. Z.; Bi, S.; Li, Q. Q.; Fan, Y.
2014-04-01
The efficiency of solving two-dimensional shallow-water equations (SWEs) is vital for simulation of large-scale flood inundation. For flood flows over real topography, local high-resolution method, which uses adaptable grids, is required in order to prevent the loss of accuracy of the flow pattern while saving computational cost. This paper introduces an adaptive grid model, which uses an adaptive criterion calculated on the basis of the water lever. The grid adaption is performed by manipulating subdivision levels of the computation grids. As the flow feature varies during the shallow wave propagation, the local grid density changes adaptively and the stored information of neighbor relationship updates correspondingly, achieving a balance between the model accuracy and running efficiency. In this work, a well-balanced (WB) scheme for solving SWEs is introduced. In reconstructions of Riemann state, the definition of the unique bottom elevation on grid interfaces is modified, and the numerical scheme is pre-balanced automatically. By the validation against two idealist test cases, the proposed model is applied to simulate flood inundation due to a dam-break of Zhanghe Reservoir, Hubei province, China. The results show that the presented model is robust and well-balanced, has nice computational efficiency and numerical stability, and thus has bright application prospects.
A well-balanced scheme for the shallow-water equations with topography or Manning friction
NASA Astrophysics Data System (ADS)
Michel-Dansac, Victor; Berthon, Christophe; Clain, Stéphane; Foucher, Françoise
2017-04-01
We consider the shallow-water equations with Manning friction or topography, as well as a combination of both these source terms. The main purpose of this work concerns the derivation of a non-negativity preserving and well-balanced scheme that approximates solutions of the system and preserves the associated steady states, including the moving ones. In addition, the scheme has to deal with vanishing water heights and transitions between wet and dry areas. To address such issues, a particular attention is paid to the study of the steady states related to the friction source term. Then, a Godunov-type scheme is obtained by using a relevant average of the source terms in order to enforce the required well-balance property. An implicit treatment of both topography and friction source terms is also exhibited to improve the scheme while dealing with vanishing water heights. A second-order well-balanced MUSCL extension is designed, as well as an extension for the two-dimensional case. Numerical experiments are performed in order to highlight the properties of the scheme.
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.
High order discontinuous Galerkin discretizations with discontinuity resolution within the cell
NASA Astrophysics Data System (ADS)
Ekaterinaris, John; Panourgias, Konstantinos
2016-11-01
The nonlinear filter of Yee et al. and used for low dissipative well-balanced high order accurate finite-difference schemes is adapted to the finite element context of discontinuous Galerkin (DG) discretizations. The performance of the proposed nonlinear filter for DG discretizations is demonstrated for different orders of expansions for one- and multi-dimensional problems with exact solutions. It is shown that for higher order discretizations discontinuity resolution within the cell is achieved and the design order of accuracy is preserved. The filter is applied for inviscid and viscous flow test problems including strong shocks interactions to demonstrate that the proposed dissipative mechanism for DG discretizations yields superior results compared to the results obtained with the TVB limiter and high-order hierarchical limiting. The proposed approach is suitable for p-adaptivity in order to locally enhance resolution of three-dimensional flow simulations.
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.
Multiscale high-order/low-order (HOLO) algorithms and applications
NASA Astrophysics Data System (ADS)
Chacón, L.; Chen, G.; Knoll, D. A.; Newman, C.; Park, H.; Taitano, W.; Willert, J. A.; Womeldorff, G.
2017-02-01
We review the state of the art in the formulation, implementation, and performance of so-called high-order/low-order (HOLO) algorithms for challenging multiscale problems. HOLO algorithms attempt to couple one or several high-complexity physical models (the high-order model, HO) with low-complexity ones (the low-order model, LO). The primary goal of HOLO algorithms is to achieve nonlinear convergence between HO and LO components while minimizing memory footprint and managing the computational complexity in a practical manner. Key to the HOLO approach is the use of the LO representations to address temporal stiffness, effectively accelerating the convergence of the HO/LO coupled system. The HOLO approach is broadly underpinned by the concept of nonlinear elimination, which enables segregation of the HO and LO components in ways that can effectively use heterogeneous architectures. The accuracy and efficiency benefits of HOLO algorithms are demonstrated with specific applications to radiation transport, gas dynamics, plasmas (both Eulerian and Lagrangian formulations), and ocean modeling. Across this broad application spectrum, HOLO algorithms achieve significant accuracy improvements at a fraction of the cost compared to conventional approaches. It follows that HOLO algorithms hold significant potential for high-fidelity system scale multiscale simulations leveraging exascale computing.
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 Methods For Wave Propagation
2008-01-01
typically combined with high-order explicit time-integration methods such as the multi-stage Runge - Kutta procedure. In addition to the spatial and temporal... methods include both an explicit Runge - Kutta fourth- order temporally accurate scheme as well as an implicit, approximately factored Beam-Warming scheme of...12]. 3.2.3 Time Integration The equations are integrated in time with the classical fourth-order four-stage Runge - Kutta method . With R denoting the
A well-balanced unified gas-kinetic scheme for multiscale flow transport under gravitational field
NASA Astrophysics Data System (ADS)
Xiao, Tianbai; Cai, Qingdong; Xu, Kun
2017-03-01
The gas dynamics under gravitational field is usually associated with multiple scale nature due to large density variation and a wide variation of local Knudsen number. It is challenging to construct a reliable numerical algorithm to accurately capture the non-equilibrium physical effect in different regimes. In this paper, a well-balanced unified gas-kinetic scheme (UGKS) for all flow regimes under gravitational field will be developed, which can be used for the study of non-equilibrium gravitational gas system. The well-balanced scheme here is defined as a method to evolve an isolated gravitational system under any initial condition to a hydrostatic equilibrium state and to keep such a solution. To preserve such a property is important for a numerical scheme, which can be used for the study of slowly evolving gravitational system, such as the formation of star and galaxy. Based on the Boltzmann model with external forcing term, the UGKS uses an analytic time-dependent (or scale-dependent) solution in the construction of the discretized fluid dynamic equations in the cell size and time step scales, i.e., the so-called direct modeling method. As a result, with the variation of the ratio between the numerical time step and local particle collision time, the UGKS is able to recover flow physics in different regimes and provides a continuous spectrum of gas dynamics. For the first time, the flow physics of a gravitational system in the transition regime can be studied using the UGKS, and the non-equilibrium phenomena in such a gravitational system can be clearly identified. Many numerical examples will be used to validate the scheme. New physical observation, such as the correlation between the gravitational field and the heat flux in the transition regime, will be presented. The current method provides an indispensable tool for the study of non-equilibrium gravitational system.
A Class of High Order Nonlocal Operators
NASA Astrophysics Data System (ADS)
Tian, Xiaochuan; Du, Qiang
2016-12-01
We study a class of nonlocal operators that may be seen as high order generalizations of the well known nonlocal diffusion operators. We present properties of the associated nonlocal functionals and nonlocal function spaces including nonlocal versions of Sobolev inequalities such as the nonlocal Poincaré and nonlocal Gagliardo-Nirenberg inequalities. Nonlocal characterizations of high order Sobolev spaces in the spirit of Bourgain-Brezis-Mironescu are provided. Applications of nonlocal calculus of variations to the well-posedness of linear nonlocal models of elastic beams and plates are also considered.
Management of high-order multiple gestation.
Elliott, John P
2005-06-01
High-order multiple gestation presents unique challenges to the clinician to obtain the best possible outcome. An aggressive proactive approach works best compared with a wait-and-treat strategy when complications occur. Frequent ultrasound evaluations, fetal fibronectin testing, and contraction monitoring are important diagnostic tools. Aggressive weight gain, bed rest, and relaxation techniques are important interventions. Tocolytic drugs are used to prevent preterm labor, and aggressive dosing of MgSO4, terbutaline pumps, and oral agents are advocated to treat preterm labor. Outcome is generally good with high-order multiple gestation with this management protocol.
Arbitrarily high order nodal and characteristic methods
Azmy, Y.Y.
1994-09-01
The quest for higher computational efficiency initially led researchers in the neutron transport area to develop and implement high-order approximations for solving the linear Boltzmann equational. This drive aimed at achieving higher accuracy on coarse meshes, thereby resulting in a net savings of computational resources represented by execution time and memory. Many endeavors succeeded in reaching this goal, producing a variety of elegent, albeit complicated, formalisms, that proved extremely accurate and efficient in solving test, as well as practical applications, problems. The two main classes of high order transport methods that recieved the most attention are the Nodal and Characteristic methods. A de facto linear order standard for the spatial approximation (even though Quadratic Nodal Methods were also considered) was dictated by the algebraic complexity of the derivation of the discrete variable equations, the programming complexity of implementing and verifying them in codes, and limitations on computational resources available to run such codes. The significant advances in computational resources in terms of hardware capacity and speed, as well as architectural innovations such as vector and parallel processing, all but eliminated the third (above) obstacle towards the development and implementation of even higher order methods. The algebraic and programming complexities, on the other hand, were alleviated to some extent by the development of Arbitrarily High Order Transport methods of the Nodal and the Characteristic types, which are discussed in this report.
A 2D well-balanced shallow flow model for unstructured grids with novel slope source term treatment
NASA Astrophysics Data System (ADS)
Hou, Jingming; Liang, Qiuhua; Simons, Franz; Hinkelmann, Reinhard
2013-02-01
Within the framework of the Godunov-type cell-centered finite volume (CCFV) scheme, this paper proposes a 2D well-balanced shallow water model for unstructured grids. In this model, the face-based van Albada limiting scheme is employed in conjunction with a directional correction to reconstruct second order spatial values at the midpoint of the considered face. The Harten, Lax and van Leer approximate Riemann solver with the Contact wave restored (HLLC) is applied to compute the fluxes of mass and momentum, while the splitting implicit method is utilized to solve the friction source terms. The novel aspects of the model include the new limited directional correction with which the new local extrema caused by the unlimited correction are prevented efficiently, the simplified non-negative water depth reconstruction used to get rid of numerical instabilities and in turn to preserve mass conservation at wet-dry interfaces and the novel slope source term treatment which suits complex unstructured grids well by transforming the slope source of a cell into fluxes at its faces. This model is able to preserve the C-property and mass conservation, to achieve good convergence to steady state, to capture discontinuous flows and to handle complex flows involving wetting and drying over uneven beds on unstructured grids with poor connectivity in an accurate, efficient and robust way. These capabilities are verified against analytical solutions, numerical results of alternative models and experimental and field data.
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.
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
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
2015-01-01
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.
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 harmonic generation in alkanes
Altucci, C.; Velotta, R.; Heesel, E.; Springate, E.; Marangos, J. P.; Vozzi, C.; Benedetti, E.; Calegari, F.; Sansone, G.; Stagira, S.; Nisoli, M.; Tosa, V.
2006-04-15
We have investigated the process of high-order harmonic generation in light alkanes by using femtosecond laser pulses. We show the experimental results cannot be matched by a model that assumes a single active electron only in a hydrogenic s orbital. Clear evidences are shown of the important role played by the p-like character originating from the covalent C-H bond. By constructing a suitable mixture of s-type and p-type atomic wave functions, an excellent agreement between measurements in methane and simulations is found, thus confirming the validity of the developed method as a general tool for the analysis of high-order harmonic generation in complex molecules.
NASA Astrophysics Data System (ADS)
Panourgias, Konstantinos T.; Ekaterinaris, John A.
2016-12-01
The nonlinear filter introduced by Yee et al. (1999) [27] and extensively used in the development of low dissipative well-balanced high order accurate finite-difference schemes is adapted to the finite element context of discontinuous Galerkin (DG) discretizations. The filter operator is constructed in the canonical computational domain for the standard cubical element where it is applied to the computed conservative variables in a direction per direction basis. Filtering becomes possible for all element types in unstructured meshes using collapsed coordinate transformations. The performance of the proposed nonlinear filter for DG discretizations is demonstrated and evaluated for different orders of expansions for one-dimensional and multidimensional problems with exact solutions. It is shown that for higher order discretizations discontinuity resolution within the cell is achieved and the design order of accuracy is preserved. The filter is applied for a number of standard inviscid flow test problems including strong shocks interactions to demonstrate that the proposed dissipative mechanism for DG discretizations yields superior results compared to the results obtained with the total variation bounded (TVB) limiter and high-order hierarchical limiting. The proposed approach is suitable for p-adaptivity in order to locally enhance resolution of three-dimensional flow simulations that include discontinuities and complex flow features.
High order path integrals made easy
NASA Astrophysics Data System (ADS)
Kapil, Venkat; Behler, Jörg; Ceriotti, Michele
2016-12-01
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the system. Many approaches have been suggested to reduce the required number of replicas. Among these, high-order factorizations of the Boltzmann operator are particularly attractive for high-precision and low-temperature scenarios. Unfortunately, to date, several technical challenges have prevented a widespread use of these approaches to study the nuclear quantum effects in condensed-phase systems. Here we introduce an inexpensive molecular dynamics scheme that overcomes these limitations, thus making it possible to exploit the improved convergence of high-order path integrals without having to sacrifice the stability, convenience, and flexibility of conventional second-order techniques. The capabilities of the method are demonstrated by simulations of liquid water and ice, as described by a neural-network potential fitted to the dispersion-corrected hybrid density functional theory calculations.
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.
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 Methods for Computational Physics
1999-03-01
the finite element space Vh such that Vj= 1,...,N: Rh( p )(xj,t) - p (Xýj,t) = 0, £ = 0,..., k, (2.34) where the points xj,t are the Gauss- Radau ...element refinement (h- p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the com- putation of...work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementa- tion of the h- p finite element
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).
Novel highly ordered core–shell nanoparticles
Dey, Sonal; Hossain, Mohammad D.; Mayanovic, Robert A.; Wirth, Richard; Gordon, Robert A.
2016-10-26
Core–shell nanoparticles have potential for a wide range of applications due to the tunability of their magnetic, catalytic, electronic, optical, and other physicochemical properties. A frequent drawback in the design of core–shell nanoparticles and nanocrystals is the lack of control over an extensive, disordered, and compositionally distinct interface that occurs due to the dissimilarity of structural and compositional phases of the core and shell. In this work, we demonstrate a new hydrothermal nanophase epitaxy (HNE) technique to synthesize highly structurally ordered α-Cr_{2}O_{3}@α-Co_{0.38}Cr_{1.62}O_{2.92} inverted core–shell nanoparticles (CSNs) with evidence for the nanoscale growth of corundum structure beginning from the core and extending completely into the shell of the CSNs with minimal defects at the interface. The high-resolution TEM results show a sharp interface exhibiting epitaxial atomic registry of shell atoms over highly ordered core atoms. The XPS and Co K-edge XANES analyses indicate the +2 oxidation state of cobalt is incorporated in the shell of the CSNs. Our XPS and EXAFS results are consistent with oxygen vacancy formation in order to maintain charge neutrality upon substitution of the Co^{2+} ion for the Cr^{3+} ion in the α-Co_{0.38}Cr_{1.62}O_{2.92} shell. Furthermore, the CSNs exhibit the magnetic exchange bias effect, which is attributed to the exchange anisotropy at the interface made possible by the nanophase epitaxial growth of the α-Co_{0.38}Cr_{1.62}O_{2.92} shell on the α-Cr_{2}O_{3} core of the nanoparticles. The combination of a well-structured, sharp interface and novel nanophase characteristics is highly desirable for nanostructures having enhanced magnetic properties.
Polarization-fan high-order harmonics
NASA Astrophysics Data System (ADS)
Fleischer, Avner; Bordo, Eliyahu; Kfir, Ofer; Sidorenko, Pavel; Cohen, Oren
2017-02-01
We predict high-order harmonics in which the polarization within the spectral bandwidth of each harmonic varies with frequency continuously and significantly. For example, the interaction of counter-rotating circularly-polarized bichromatic drivers having close central frequencies with isotropic gas leads to the emission of polarization-fan harmonics where each harmonic in the spectrum has the following property: it is nearly circularly-polarized in one tail of the harmonic peak, linear in the center of the peak and nearly circular with the opposite helicity in the opposite tail. Also, we show that polarization-fan high harmonics with modulated ellipticity are obtained when elliptical drivers are used. Polarization-fan harmonics are obtained as a result of multiple (at least two) head-on recollisions of electrons with their parent ions occurring from different angles in a two-dimensional plane. The use of bichromatic drivers with close central frequencies largely preserves the single-cycle, single-atom and macroscopic physics of ‘ordinary’ high harmonic generation, where both the driver and high harmonics are linearly polarized. Thus, it should offer several attracting features, including (i) a direct route for extending the maximal photon energy of observed helical high harmonics to keV by using bichromatic drivers only in the mid-IR region and (ii) utilizing phase matching methods that were developed for ‘ordinary’ high harmonic generation driven by quasi-monochromatic pulses (e.g. pressure tuning phase matching). These polarization-fan harmonics may be utilized for exploring non-repetitive ultrafast chiral phenomena, e.g. dynamics of magnetic domains, in a single shot.
NASA Astrophysics Data System (ADS)
Gao, Fangzheng; Wu, Yuqiang; Yu, Xin
2016-12-01
In this paper, the problem of global stabilisation by state feedback is investigated for a class of stochastic high-order nonlinear systems with both high-order and low-order nonlinearities, to which the existing control methods are inapplicable. Based on the generalised stochastic Lyapunov theorem, and by skillfully using the method of adding a power integrator, a continuous state feedback controller is successfully constructed, which can guarantee the global asymptotic stability in probability of the resulting closed-loop system in the sense of weak solution, and also is able to lead to an interesting result of finite-time stabilisation under appropriate conditions. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approach.
Moyal, Dominique
2012-06-01
Skin exposure to sunlight can cause many adverse effects. It is now recognized that both Ultraviolet A (UVA) and UVB wavelengths are responsible for the detrimental effects of solar radiation on skin. With our increasing knowledge on the harmful effects of UVA, the need for effective, well-balanced photoprotection has become more crucial. Numerous clinical studies showed that well-balanced sunscreen, with a SPF/UVAPF ratio ≤ 3, provide the most effective protection against pigmentation (especially on dark skin), DNA damage, UV-induced skin immunosuppression and photodermatoses. The calculation of UVA protection required in Asia revealed its particular importance in India, and gives clear evidence that the SPF value alone is not sufficient to evaluate the efficacy of a sunscreen.
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, Kimberly Susan
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 ~10^{13}-10^{14} W/cm^{2}) is focused into a dense (~10^{17} particles/cm^{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 "source". 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 Energy Stable WENO Schemes
NASA Technical Reports Server (NTRS)
Yamaleev, Nail K.; Carpenter, Mark H.
2009-01-01
A third-order Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite difference scheme developed by Yamaleev and Carpenter was proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, a systematic approach is presented that enables 'energy stable' modifications for existing WENO schemes of any order. The technique is demonstrated by developing a one-parameter family of fifth-order upwind-biased ESWENO schemes; ESWENO schemes up to eighth order are presented in the appendix. New weight functions are also developed that provide (1) formal consistency, (2) much faster convergence for smooth solutions with an arbitrary number of vanishing derivatives, and (3) improved resolution near strong discontinuities.
High order 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 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 tail in Schwarzschild spacetime
NASA Astrophysics Data System (ADS)
Casals, Marc; Ottewill, Adrian
2015-12-01
We present an analysis of the behavior at late times of linear field perturbations of a Schwarzschild black hole spacetime. In particular, we give explicit analytic expressions for the field perturbations (for a specific ℓ-multipole) of general spin up to the first four orders at late times. These expressions are valid at arbitrary radius and include, apart from the well-known power-law tail decay at leading order (˜t-2 ℓ-3), a new logarithmic behavior at third leading order (˜t-2 ℓ-5ln t ). We obtain these late-time results by developing an analytical formalism initially formulated by Mano, Suzuki and Takasugi (MST) [Prog. Theor. Phys. 95, 1079 (1996); 96, 549 (1996)] formalism and by expanding the various MST Fourier-mode quantities for small frequency. While we give explicit expansions up to the first four leading orders (for small frequency for the Fourier modes, for late time for the field perturbation), we give a prescription for obtaining expressions to arbitrary order within a "perturbative regime."
A high performance totally ordered multicast protocol
NASA Technical Reports Server (NTRS)
Montgomery, Todd; Whetten, Brian; Kaplan, Simon
1995-01-01
This paper presents the Reliable Multicast Protocol (RMP). RMP provides a totally ordered, reliable, atomic multicast service on top of an unreliable multicast datagram service such as IP Multicasting. RMP is fully and symmetrically distributed so that no site bears un undue portion of the communication load. RMP provides a wide range of guarantees, from unreliable delivery to totally ordered delivery, to K-resilient, majority resilient, and totally resilient atomic delivery. These QoS guarantees are selectable on a per packet basis. RMP provides many communication options, including virtual synchrony, a publisher/subscriber model of message delivery, an implicit naming service, mutually exclusive handlers for messages, and mutually exclusive locks. It has commonly been held that a large performance penalty must be paid in order to implement total ordering -- RMP discounts this. On SparcStation 10's on a 1250 KB/sec Ethernet, RMP provides totally ordered packet delivery to one destination at 842 KB/sec throughput and with 3.1 ms packet latency. The performance stays roughly constant independent of the number of destinations. For two or more destinations on a LAN, RMP provides higher throughput than any protocol that does not use multicast or broadcast.
Periodicity of high-order neural functions
NASA Technical Reports Server (NTRS)
Kellaway, P.; Borda, R. P.; Frost, J. D.; Carrie, J. R. G.; Coats, A. C.
1973-01-01
The results of recent studies on higher order, integrative processes in the central nervous system are reported. Attempts were made to determine whether these processes exhibit any ongoing rhythmicity which might manifest itself in alterations of attention and alertness. Experiments were also designed to determine if a periodicity approximating that of the REM could be detected in various parameters of brain electrical activity.
NASA Astrophysics Data System (ADS)
Naing, Soe; Yamada, Takanobu; Nakanishi, Kimio
According to the third conference of parties (COP3), Japan has set a target of reducing greenhouse gas emissions by 6% by the year 2010. Cogeneration system is a recently potent method which its environmental benefits, through the highly efficient utilization of fuel that is related to reduction emissions. The particular purpose of this paper is to support the selection of cogeneration technologies by acquiring the optimal useful thermal energy and electrical power from system with well-efficiency balance method and fuel saving approaching method. When a micro gas turbine (MGT) is operated under ambient condition, the discharged hot gases from the MGT may be expanded at its exhaust stage and cooled by an exhaust heat exchanger which composes with a single stage absorption heat exchanger. The performance and annual total fuel saving amount of cogeneration plant will be investigated and compared with separated production of heat and power system. Eventually, this cogeneration plant will be reduced the fuel consumption rate in operation that will be also reduced the emissions and fuel cost when the system will gain highly efficiency of thermal energy and electrical power.
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.
Frances, Oriane; Fatemi, Fataneh; Pompon, Denis; Guittet, Eric; Sizun, Christina; Pérez, Javier; Lescop, Ewen; Truan, Gilles
2015-03-24
Diflavin reductases are bidomain electron transfer proteins in which structural reorientation is necessary to account for the various intramolecular and intermolecular electron transfer steps. Using small-angle x-ray scattering and nuclear magnetic resonance data, we describe the conformational free-energy landscape of the NADPH-cytochrome P450 reductase (CPR), a typical bidomain redox enzyme composed of two covalently-bound flavin domains, under various experimental conditions. The CPR enzyme exists in a salt- and pH-dependent rapid equilibrium between a previously described rigid, locked state and a newly characterized, highly flexible, unlocked state. We further establish that maximal electron flux through CPR is conditioned by adjustable stability of the locked-state domain interface under resting conditions. This is rationalized by a kinetic scheme coupling rapid conformational sampling and slow chemical reaction rates. Regulated domain interface stability associated with fast stochastic domain contacts during the catalytic cycle thus provides, to our knowledge, a new paradigm for improving our understanding of multidomain enzyme function.
First-order high- Tc SQUID gradiometer
NASA Astrophysics Data System (ADS)
Kong, X. Y.; Nakatani, Y.; Yutani, A.; Maki, T.; Itozaki, H.
2008-09-01
SQUID gradiometers are attractive for magnetic field measurements in noisy environments. A first-order planar gradiometer has been designed and fabricated. The layout of the planar gradiometer used to have two symmetric pickup coils; however, our design adopted one compensation loop with the same size as the SQUID loop at the symmetric position to reduce the imbalance caused by the SQUID. The gradient field resolution is up to 2.2 pT cm -1 Hz -1/2 (white noise) and 30 pT cm -1 Hz -1/2 at 1 Hz.
High-Order CESE Methods for the Euler Equations
2010-11-01
Technical Paper 3. DATES COVERED (From - To) 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER High-Order CESE Methods for the Euler Equations 5b. GRANT NUMBER...of high-order CESE methods for solving nonlinear hyperbolic partial differential equations. A series of high-order algorithms have been developed...based on a systematic, recursive formulation that achieves fourth-, sixth-, and eighth-order accuracy. The new high-order CESE method shares many
High order dark wavefront sensing simulations
NASA Astrophysics Data System (ADS)
Ragazzoni, Roberto; Arcidiacono, Carmelo; Farinato, Jacopo; Viotto, Valentina; Bergomi, Maria; Dima, Marco; Magrin, Demetrio; Marafatto, Luca; Greggio, Davide; Carolo, Elena; Vassallo, Daniele
2016-07-01
Dark wavefront sensing takes shape following quantum mechanics concepts in which one is able to "see" an object in one path of a two-arm interferometer using an as low as desired amount of light actually "hitting" the occulting object. A theoretical way to achieve such a goal, but in the realm of wavefront sensing, is represented by a combination of two unequal beams interferometer sharing the same incoming light, and whose difference in path length is continuously adjusted in order to show different signals for different signs of the incoming perturbation. Furthermore, in order to obtain this in white light, the path difference should be properly adjusted vs the wavelength used. While we incidentally describe how this could be achieved in a true optomechanical setup, we focus our attention to the simulation of a hypothetical "perfect" dark wavefront sensor of this kind in which white light compensation is accomplished in a perfect manner and the gain is selectable in a numerical fashion. Although this would represent a sort of idealized dark wavefront sensor that would probably be hard to match in the real glass and metal, it would also give a firm indication of the maximum achievable gain or, in other words, of the prize for achieving such device. Details of how the simulation code works and first numerical results are outlined along with the perspective for an in-depth analysis of the performances and its extension to more realistic situations, including various sources of additional noise.
Perturbative approach for non local and high order derivative theories
Avilez, Ana A.; Vergara, J. David
2009-04-20
We propose a reduction method of classical phase space of high order derivative theories in singular and non singular cases. The mechanism is to reduce the high order phase space by imposing suplementary constraints, such that the evolution takes place in a submanifold where high order degrees of freedom are absent. The reduced theory is ordinary and is cured of the usual high order theories diseases, it approaches well low energy dynamics.
NASA Astrophysics Data System (ADS)
Zhang, Xing-Hui; Xie, Xue-Jun
2014-03-01
This paper studies the state feedback control problem for a class of nonlinear systems with high-order and low-order nonlinearities. The introduction of the sign function together with the method of adding a power integrator and Lyapunov stability theorem makes the closed-loop system globally asymptotically stable. Exploiting the idea of how to deal with growth nonlinearities with both high order and low order being relaxed to some intervals is the focus of this work.
High-Order CESE Methods for Solving Hyperbolic PDEs (Preprint)
2011-05-03
DATES COVERED (From - To) 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER High-Order CESE Methods for Solving Hyperbolic PDEs (Preprint) 5b. GRANT NUMBER...continuous mesh refinement. The new high-order CESE method shares many favorable attributes of the original second-order CESE method, including: (i...Fluid Dynamics CESE ˙4th International Journal of Computational Fluid Dynamics Vol. 00, No. 00, Month 2009, 1–19 RESEARCH ARTICLE High-Order CESE
A high-order accurate embedded boundary method for first order hyperbolic equations
NASA Astrophysics Data System (ADS)
Mattsson, Ken; Almquist, Martin
2017-04-01
A stable and high-order accurate embedded boundary method for first order hyperbolic equations is derived. Where the grid-boundaries and the physical boundaries do not coincide, high order interpolation is used. The boundary stencils are based on a summation-by-parts framework, and the boundary conditions are imposed by the SAT penalty method, which guarantees linear stability for one-dimensional problems. Second-, fourth-, and sixth-order finite difference schemes are considered. The resulting schemes are fully explicit. Accuracy and numerical stability of the proposed schemes are demonstrated for both linear and nonlinear hyperbolic systems in one and two spatial dimensions.
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.
High diffraction order grating interferometer for pitch measurement
NASA Astrophysics Data System (ADS)
Apostol, Dan; Udrea, Cristian; Garoi, Florin; Vasile, Tiberius; Logofătu, Petre Cătălin
2011-10-01
A grating interferometer that uses the high diffraction orders in conjunction with a Twyman-Green commercial interferometer is used for the measurement of in plane movement of gratings. The high diffraction orders ensures the amplification of the measurement precision with a factor equal to the diffraction order of the measurement in principle, because no imaging of features marking the beginning and the end of the measured length feature is necessary, and therefore the resolution limits associated with microscope imaging are eliminated.
A High-Order Multiscale Global Atmospheric Model
NASA Astrophysics Data System (ADS)
Nair, R. D.
2015-12-01
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 for HOMAM 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.
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.
Zhang, Lanqiang; Guo, Youming; Rao, Changhui
2017-02-20
Multi-conjugate adaptive optics (MCAO) is the most promising technique currently developed to enlarge the corrected field of view of adaptive optics for astronomy. In this paper, we propose a new configuration of solar MCAO based on high order ground layer adaptive optics and low order high altitude correction, which result in a homogeneous correction effect in the whole field of view. An individual high order multiple direction Shack-Hartmann wavefront sensor is employed in the configuration to detect the ground layer turbulence for low altitude correction. Furthermore, the other low order multiple direction Shack-Hartmann wavefront sensor supplies the wavefront information caused by high layers' turbulence through atmospheric tomography for high altitude correction. Simulation results based on the system design at the 1-meter New Vacuum Solar Telescope show that the correction uniform of the new scheme is obviously improved compared to conventional solar MCAO configuration.
A stable 1D multigroup high-order low-order method
Yee, Ben Chung; Wollaber, Allan Benton; Haut, Terry Scot; ...
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
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.) 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.
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.
Uniformly high order accurate essentially non-oscillatory schemes 3
NASA Technical Reports Server (NTRS)
Harten, A.; Engquist, B.; Osher, S.; Chakravarthy, S. R.
1986-01-01
In this paper (a third in a series) the construction and the analysis of essentially non-oscillatory shock capturing methods for the approximation of hyperbolic conservation laws are presented. Also presented is a hierarchy of high order accurate schemes which generalizes Godunov's scheme and its second order accurate MUSCL extension to arbitrary order of accuracy. The design involves an essentially non-oscillatory piecewise polynomial 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. The reconstruction algorithm is derived from a new interpolation technique that when applied to piecewise smooth data gives high-order accuracy whenever the function is smooth but avoids a Gibbs phenomenon at discontinuities. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and consequently the resulting schemes are highly nonlinear.
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.
Role of Excited States In High-order Harmonic Generation.
Beaulieu, S; Camp, S; Descamps, D; Comby, A; Wanie, V; Petit, S; Légaré, F; Schafer, K J; Gaarde, M B; Catoire, F; Mairesse, Y
2016-11-11
We investigate the role of excited states in high-order harmonic generation by studying the spectral, spatial, and temporal characteristics of the radiation produced near the ionization threshold of argon by few-cycle laser pulses. We show that the population of excited states can lead either to direct extreme ultraviolet emission through free induction decay or to the generation of high-order harmonics through ionization from these states and recombination to the ground state. By using the attosecond lighthouse technique, we demonstrate that the high-harmonic emission from excited states is temporally delayed by a few femtoseconds compared to the usual harmonics, leading to a strong nonadiabatic spectral redshift.
Role of Excited States In High-order Harmonic Generation
NASA Astrophysics Data System (ADS)
Beaulieu, S.; Camp, S.; Descamps, D.; Comby, A.; Wanie, V.; Petit, S.; Légaré, F.; Schafer, K. J.; Gaarde, M. B.; Catoire, F.; Mairesse, Y.
2016-11-01
We investigate the role of excited states in high-order harmonic generation by studying the spectral, spatial, and temporal characteristics of the radiation produced near the ionization threshold of argon by few-cycle laser pulses. We show that the population of excited states can lead either to direct extreme ultraviolet emission through free induction decay or to the generation of high-order harmonics through ionization from these states and recombination to the ground state. By using the attosecond lighthouse technique, we demonstrate that the high-harmonic emission from excited states is temporally delayed by a few femtoseconds compared to the usual harmonics, leading to a strong nonadiabatic spectral redshift.
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.
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
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 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.
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
Separation of high order harmonics with fluoride windows.
Allison, T K; van Tilborg, J; Wright, T W; Hertlein, M P; Falcone, R W; Belkacem, A
2009-05-25
The ensemble of lower orders produced in high order harmonic generation can be efficiently temporally separated 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 use this simple and inexpensive technique in a pump/probe experiment to resolve femtosecond dynamics in the ethylene molecule.
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.
Pulse stabilization by high-order dispersion management
NASA Astrophysics Data System (ADS)
Moeser, J.; Gabitov, I.; Jones, C. K. R. T.
2002-12-01
The stabilizing effects of dispersion management (DM) at second and third order are studied for both single-channel and wavelength-division multiplexed (WDM) systems. We first derive a model for the slow evolution of a pulse in an optical fiber with high-order dispersion management (HODM). For single-channel systems, in contrast with conventional DM with constant third-order dispersion, this equation possesses a stable solution, the ground state for its associated Hamiltonian, which propagates nearly periodically under direct numerical simulation. Improved performance for WDM systems is also observed, as complicated pulse interactions, which can lead to undesirable effects such as frequency shift, are prevented by HODM.
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 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.
Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows
NASA Technical Reports Server (NTRS)
Sjoegreen, Bjoern; Yee, Helen C.; Mansour, Nagi (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 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
Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.
2012-09-20
The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered
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.
A high order theory for uniform and laminated plates
NASA Technical Reports Server (NTRS)
Lo, K. H.; Christensen, R. M.; Wu, E. M.
1976-01-01
A theory of plate deformation is derived which accounts for the effects of transverse shear deformation, transverse normal strain, and a nonlinear distribution of the in-plane displacements with respect to the thickness coordinate. The theory is compared with lower order plate theories through application to a particular problem involving a plate acted upon by a sinusoidal surface pressure. Comparison is also made with exact elasticity solution of this problem. It is found that when the ratio of the characteristic length of the load pattern to the plate thickness is of the order of unity, lower order theories are inadequate and the present high order theory is required to give meaningful results. Results are given for the bending of symmetric cross-ply and angle-ply laminates. Comparison with exact elasticity solutions indicates that the present plate theory is sufficiently accurate for predicting the behavior of thick laminates.
Improving the Accuracy of High-Order Nodal Transport Methods
Azmy, Y.Y.; Buscaglia, G.C.; Zamonsky, O.M.
1999-09-27
This paper outlines some recent advances towards improving the accuracy of neutron calculations using the Arbitrarily High Order Transport-Nodal (AHOT-N) Method. These transport advances consist of several contributions: (a) A formula for the spatial weights that allows for the polynomial order to be raised arbitrarily high without suffering from pollution from round-off, error; (b) A reconstruction technique for the angular flux, based upon a recursive formula, that reduces the pointwise error by one order; (c) An a posterior error indicator that estimates the true error and its distribution throughout the domain, so that it can be used for adaptively reftig the approximation. Present results are mainly for ID, extension to 2D-3D is in progress.
NASA Astrophysics Data System (ADS)
Bao, Lei; Nair, Ramachandran D.; Tufo, Henry M.
2014-08-01
A well-balanced discontinuous Galerkin (DG) flux-form shallow-water (SW) model on the sphere is developed and compared with a nodal DG SW model cast in the vector-invariant form for accuracy and conservation properties. A second-order diffusion scheme based on the local discontinuous Galerkin (LDG) method is added to the viscous version of the SW model and tested for conservation behaviors. The inviscid flux-form SW model is found to have better conservation of total energy and zonal angular momentum while the vector-invariant form provides better ability of conserving potential enstrophy. The inviscid flux-form tends to generate spurious vorticity but the LDG scheme combined with a well-balanced treatment can effectively eliminate the small-scale noise and generate smooth and accurate results.
Glucose level regulation via integral high-order sliding modes.
Dorel, Lela
2011-04-01
Diabetes is a condition in which the body either does not produce enough insulin, or does not properly respond to it. This causes the glucose level in blood to increase. An algorithm based on Integral High-Order Sliding Mode technique is proposed, which keeps the normal blood glucose level automatically releasing insulin into the blood. The system is highly insensitive to inevitable parametric and model uncertainties, measurement noises and small delays.
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.}
Local dynamics for high-order semilinear hyperbolic equations
NASA Astrophysics Data System (ADS)
Volevich, L. R.; Shirikyan, A. R.
2000-06-01
This paper is devoted to studying high-order semilinear hyperbolic equations. It is assumed that the equation is a small perturbation of an equation with real constant coefficients and that the roots of the full symbol of the unperturbed equation with respect to the variable \\tau dual to time are either separated from the imaginary axis or lie outside the domain \
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.
On Convergence of High Order Shock Capturing Difference Schemes
NASA Astrophysics Data System (ADS)
Ostapenko, V.
2010-11-01
A convergence of high order shock capturing difference schemes is analyzed. Notions of weak finite difference approximations which conserve a sense on discontinuous solutions are introduced. Necessary and sufficient conditions of these approximations are obtained. It is shown that among the explicit two-layer in time conservative difference schemes there are no schemes which can have high order of weak approximation. A compact scheme of the same third order of classical and weak approximations is constructed. There is demonstrated an advantage of this scheme in comparison to TVD scheme at shock-capturing computations. A difference approximation of ɛ Rankine-Hugoniot (RH) conditions is investigated. It is shown that TVD type schemes (in contrast to non-TVD schemes, whose numerical fluxes are smooth enough) can approximate ɛ RH-conditions at most with the first order. Given examples show that non-TVD schemes (in contrast to TVD schemes) can have the second order of integral convergence through the smearing shocks and as a result can conserve a higher accuracy in the post shock regions.
High-order Finite Element Analysis of Boundary Layer Flows
NASA Astrophysics Data System (ADS)
Zhang, Alvin; Sahni, Onkar
2014-11-01
Numerical analysis of boundary layer flows requires careful approximations, specifically the use of a mesh with layered and graded elements near the (viscous) walls. This is referred to as a boundary layer mesh, which for complex geometries is composed of triangular elements on the walls that are inflated or extruded into the volume along the wall-normal direction up to a desired height while the rest of the domain is filled with unstructured tetrahedral elements. Linear elements with C0 inter-element continuity are employed and in some situations higher order C0 elements are also used. However, these elements only enforce continuity whereas high-order smoothness is not attained as will be the case with C1 inter-element continuity and higher. As a result, C0 elements result in a poor approximation of the high-order boundary layer behavior. To achieve greater inter-element continuity in boundary layer region, we employ B-spline basis functions along the wall-normal direction (i.e., only in the layered portion of the mesh). In the rest of the fully unstructured mesh, linear or higher order C0 elements are used as appropriate. In this study we demonstrate the benefits of finite-element analysis based on such higher order and continuity basis functions for boundary layer flows.
High-order perturbations of a spherical collapsing star
Brizuela, David; Martin-Garcia, Jose M.; Sperhake, Ulrich; Kokkotas, Kostas D.
2010-11-15
A formalism to deal with high-order perturbations of a general spherical background was developed in earlier work [D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 74, 044039 (2006); D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 76, 024004 (2007)]. In this paper, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the energy-momentum tensor at any order in terms of the perturbed fluid's pressure, density, and velocity. In general, these expressions are not linear and have sources depending on lower-order perturbations. For the second-order case we make the explicit decomposition of these sources in tensor spherical harmonics. Then, a general procedure is given to evolve the perturbative equations of motions of the perfect fluid for any value of the harmonic label. Finally, with the problem of a spherical collapsing star in mind, we discuss the high-order perturbative matching conditions across a timelike surface, in particular, the surface separating the perfect fluid interior from the exterior vacuum.
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.
High-order perturbations of a spherical collapsing star
NASA Astrophysics Data System (ADS)
Brizuela, David; Martín-García, José M.; Sperhake, Ulrich; Kokkotas, Kostas D.
2010-11-01
A formalism to deal with high-order perturbations of a general spherical background was developed in earlier work [D. Brizuela, J. M. Martín-García, and G. A. Mena Marugán, Phys. Rev. DPRVDAQ1550-7998 74, 044039 (2006);10.1103/PhysRevD.74.044039 D. Brizuela, J. M. Martín-García, and G. A. Mena Marugán, Phys. Rev. DPRVDAQ1550-7998 76, 024004 (2007)10.1103/PhysRevD.76.024004]. In this paper, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the energy-momentum tensor at any order in terms of the perturbed fluid’s pressure, density, and velocity. In general, these expressions are not linear and have sources depending on lower-order perturbations. For the second-order case we make the explicit decomposition of these sources in tensor spherical harmonics. Then, a general procedure is given to evolve the perturbative equations of motions of the perfect fluid for any value of the harmonic label. Finally, with the problem of a spherical collapsing star in mind, we discuss the high-order perturbative matching conditions across a timelike surface, in particular, the surface separating the perfect fluid interior from the exterior vacuum.
High-order dispersion effects in two-photon interference
NASA Astrophysics Data System (ADS)
Mazzotta, Zeudi; Cialdi, Simone; Cipriani, Daniele; Olivares, Stefano; Paris, Matteo G. A.
2016-12-01
Two-photon interference and Hong-Ou-Mandel (HOM) effect are relevant tools for quantum metrology and quantum information processing. In optical coherence tomography, the HOM effect is exploited to achieve high-resolution measurements with the width of the HOM dip being the main parameter. On the other hand, applications like dense coding require high-visibility performance. Here we address high-order dispersion effects in two-photon interference and study, theoretically and experimentally, the dependence of the visibility and the width of the HOM dip on both the pump spectrum and the downconverted photon spectrum. In particular, a spatial light modulator is exploited to experimentally introduce and manipulate a custom phase function to simulate the high-order dispersion effects. Overall, we show that it is possible to effectively introduce high-order dispersion effects on the propagation of photons and also to compensate for such effect. Our results clarify the role of the different dispersion phenomena and pave the way for optimization procedures in quantum technological applications involving PDC photons and optical fibers.
Development of high-order segmented MEMS deformable mirrors
NASA Astrophysics Data System (ADS)
Helmbrecht, Michael A.; He, Min; Kempf, Carl J.
2012-03-01
The areas of biological microscopy, ophthalmic research, and atmospheric turbulence correction require high-order DMs to obtain diffraction-limited images. Iris AO has been developing high-order MEMS DMs to address these requirements. Recent development has resulted in fully functional 489-actuator DMs capable of 9.5 µm stroke. For laser applications, the DMs were modified to make them compatible with high-reflectance dielectric coatings. Experimental results for the 489-actuator DMs with dielectric coatings shows they can be made with superb optical quality λ/93.3 rms (11.4 nm rms) and λ/75.9 rms (20.3 nm rms) for 1064 nm and 1540 nm coatings. Laser testing has demonstrated 300 W/cm2 power handling with off-the-shelf packaging. Power handling of 2800 W/cm2 is projected when incorporating packaging optimized for heat transfer.
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.
On high-order perturbative calculations at finite density
NASA Astrophysics Data System (ADS)
Ghişoiu, Ioan; Gorda, Tyler; Kurkela, Aleksi; Romatschke, Paul; Säppi, Matias; Vuorinen, Aleksi
2017-02-01
We discuss the prospects of performing high-order perturbative calculations in systems characterized by a vanishing temperature but finite density. In particular, we show that the determination of generic Feynman integrals containing fermionic chemical potentials can be reduced to the evaluation of three-dimensional phase space integrals over vacuum on-shell amplitudes - a result reminiscent of a previously proposed "naive real-time formalism" for vacuum diagrams. Applications of these rules are discussed in the context of the thermodynamics of cold and dense QCD, where it is argued that they facilitate an extension of the Equation of State of cold quark matter to higher perturbative orders.
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.
High order accurate finite difference schemes based on symmetry preservation
NASA Astrophysics Data System (ADS)
Ozbenli, Ersin; Vedula, Prakash
2016-11-01
A new algorithm for development of high order accurate finite difference schemes for numerical solution of partial differential equations using Lie symmetries is presented. Considering applicable symmetry groups (such as those relevant to space/time translations, Galilean transformation, scaling, rotation and projection) of a partial differential equation, invariant numerical schemes are constructed based on the notions of moving frames and modified equations. Several strategies for construction of invariant numerical schemes with a desired order of accuracy are analyzed. Performance of the proposed algorithm is demonstrated using analysis of one-dimensional partial differential equations, such as linear advection diffusion equations inviscid Burgers equation and viscous Burgers equation, as our test cases. Through numerical simulations based on these examples, the expected improvement in accuracy of invariant numerical schemes (up to fourth order) is demonstrated. Advantages due to implementation and enhanced computational efficiency inherent in our proposed algorithm are presented. Extension of the basic framework to multidimensional partial differential equations is also discussed.
Coronagraphy with the AEOS High Order Adaptive Optics System
NASA Astrophysics Data System (ADS)
Lloyd, J. P.; Graham, J. R.; Kalas, P.; Oppenheimer, B. R.; Sivaramakrishnan, A.; Makidon, R. B.; Macintosh, B. A.; Max, C. E.; Baudoz, P.; Kuhn, J. R.; Potter, D.
2001-05-01
Adaptive Optics has recently become a widely used technique to acquire sensitive, diffraction limited images in the near infrared with large ground based telescopes. Most astronomical targets are faint; driving astronomical AO systems towards large subapertures; resulting in a compromise between guide star brightness, observing wavelength, resolution and Strehl ratio. Space surveilance systems have recently been developed that exploit high order adaptive optics systems to take diffraction limited images in visible light on 4 meter class telescopes on bright (V<8) targets. There is, however, a particular niche that can be exploited by turning these visible light space surveillance systems to astronomical use at infrared wavelengths. At the longer wavelengths, the strehl ratio rises dramatically, thus placing more light into the diffracted Airy pattern at the expense of the atmospheric halo. A coronagraph can be used to suppress the diffracted light, and observe faint companions and debris disks around nearby, bright stars. Observations of these very high contrast objects benefit greatly from much higher order adaptive optics systems than are presently available to the astronomical commnunity. The National Science Foundation and Air Force Office of Scientific Research is sponsoring a program to conduct astronomical observations at the AEOS facility. We are presently developing an astronomical coronagraph to be deployed at the Air Force AEOS facility. We describe the coronagraph, and discuss the advantages and limitations of ground based high order AO for high contrast imaging.
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
High-order synchronization of hair cell bundles
NASA Astrophysics Data System (ADS)
Levy, Michael; Molzon, Adrian; Lee, Jae-Hyun; Kim, Ji-Wook; Cheon, Jinwoo; Bozovic, Dolores
2016-12-01
Auditory and vestibular hair cell bundles exhibit active mechanical oscillations at natural frequencies that are typically lower than the detection range of the corresponding end organs. We explore how these noisy nonlinear oscillators mode-lock to frequencies higher than their internal clocks. A nanomagnetic technique is used to stimulate the bundles without an imposed mechanical load. The evoked response shows regimes of high-order mode-locking. Exploring a broad range of stimulus frequencies and intensities, we observe regions of high-order synchronization, analogous to Arnold Tongues in dynamical systems literature. Significant areas of overlap occur between synchronization regimes, with the bundle intermittently flickering between different winding numbers. We demonstrate how an ensemble of these noisy spontaneous oscillators could be entrained to efficiently detect signals significantly above the characteristic frequencies of the individual cells.
High-order synchronization of hair cell bundles
Levy, Michael; Molzon, Adrian; Lee, Jae-Hyun; Kim, Ji-wook; Cheon, Jinwoo; Bozovic, Dolores
2016-01-01
Auditory and vestibular hair cell bundles exhibit active mechanical oscillations at natural frequencies that are typically lower than the detection range of the corresponding end organs. We explore how these noisy nonlinear oscillators mode-lock to frequencies higher than their internal clocks. A nanomagnetic technique is used to stimulate the bundles without an imposed mechanical load. The evoked response shows regimes of high-order mode-locking. Exploring a broad range of stimulus frequencies and intensities, we observe regions of high-order synchronization, analogous to Arnold Tongues in dynamical systems literature. Significant areas of overlap occur between synchronization regimes, with the bundle intermittently flickering between different winding numbers. We demonstrate how an ensemble of these noisy spontaneous oscillators could be entrained to efficiently detect signals significantly above the characteristic frequencies of the individual cells. PMID:27974743
Directed liquid phase assembly of highly ordered metallic nanoparticle arrays
Wu, Yueying; Dong, Nanyi; Fu, Shaofang; ...
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
Improving the Accuracy of High-Order Nodal Transport Methods
Azmy, Y.Y.; Buscaglia, G.C.; Zamonsky, O.M.
1999-09-27
This paper outlines some recent advances towards improving the accuracy of neutron transport calculations using the Arbitrarily High Order Transport-Nodal (AHOT-N) Method. These advances consist of several contributions: (a) A formula for the spatial weights that allows for the polynomial order to be raised arbitrarily high without suffering adverse effects from round-off error; (b) A reconstruction technique for the angular flux, based upon a recursive formula, that reduces the pointwise error by one ordeq (c) An a posterior error indicator that estimates the true error and its distribution throughout the domain, so that it can be used for adaptively refining the approximation. Present results are mainly for ID, extension to 2D-3D is in progress.
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.
Range Image Flow using High-Order Polynomial Expansion
2013-09-01
give a special thanks to Dr. Steve Hobbs for his help with the high-order tensor calculations. MATLAB ® is a registered...that using multiple spatial scales and past information improve the final flow estimation, as we would expect. Also, we will port the MATLAB R...taken column- wise and diagonalized, and f is the range image data, taken column-wise. The values of these weights for a Velodyne R© and Odetic lidar
Inductive monopole detector employing planar high order superconducting gradiometer coils
Tesche, C.D.; Chi, C.C.; Tsuei, C.C.; Chaudhari, P.
1983-08-15
The characteristics and performance of a family of high-order planar gradiometer detectors for inductive detection of magnetic monopoles are discussed. Conventional superconducting magnetometers used for monopole detection must be operated in an extremely stable, low field environment. This places a severe restriction on the cross-sectional area of such detectors. However, planar gradiometer detectors permit the use of relatively large area detectors in coincidence without requiring a corresponding increase in the stability of the ambient field.
Visualization of High-Order Finite Element Methods
2013-03-27
Peters , Valerio Pascucci, Robert M. Kirby and Claudio T. Silva, "Topology Verification for Isosurface Extraction", IEEE Transactions on Visualization...Visualization of High-Order Methods Professor Robert M. Kirby , Mr. Robert Haimes University of Utah Office of Sponsored Programs University of Utah Salt Lake...ORGANIZATION REPORT NUMBER 19a. NAME OF RESPONSIBLE PERSON 19b. TELEPHONE NUMBER Robert Kirby 801-585-3421 3. DATES COVERED (From - To) 26-Sep-2008
Astronomical coronagraphy with high-order adaptive optics systems
NASA Astrophysics Data System (ADS)
Lloyd, James P.; Graham, James R.; Kalas, Paul; Oppenheimer, Ben R.; Sivaramakrishnan, Anand; Makidon, Russell B.; Macintosh, Bruce A.; Max, Claire E.; Baudoz, Pierre; Kuhn, Jeff R.; Potter, Dan
2001-12-01
Space surveillance systems have recently been developed that exploit high order adaptive optics systems to take diffraction limited images in visible light on 4 meter class telescopes. Most astronomical targets are faint, thus driving astronomical AO systems towards larger subapertures, and thus longer observing wavelengths for diffraction limited imaging at moderate Strehl ratio. There is, however, a particular niche that can be exploited by turning these visible light space surveillance systems to astronomical use at infrared wavelengths. At the longer wavelengths, the Strehl ratio rises dramatically, thus placing more light into the diffracted Airy pattern compared to the atmospheric halo. A Lyot coronagraph can be used to suppress the diffracted light from an on axis star, and observe faint companions and debris disks around nearby, bright stars. These very high contrast objects can only be observed with much higher order adaptive optics systems than are presently available to the astronomical community. We describe simulations of high order adaptive optics coronagraphs, and outline a project to deploy an astronomical coronagraph at the Air Force AEOS facility at the Maui Space Surveillance System.
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.
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.
Integrated high-order surface diffraction gratings for diode lasers
Zolotarev, V V; Leshko, A Yu; Pikhtin, N A; Slipchenko, S O; Sokolova, Z N; Lubyanskiy, Ya V; Voronkova, N V; Tarasov, I S
2015-12-31
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. (lasers)
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.
Multigroup Radiation-Hydrodynamics with a High-Order, Low-Order Method
Wollaber, Allan Benton; Park, HyeongKae; Lowrie, Robert Byron; ...
2016-12-09
Recent efforts at Los Alamos National Laboratory to develop a moment-based, scale-bridging [or high-order (HO)–low-order (LO)] algorithm for solving large varieties of the transport (kinetic) systems have shown promising results. A part of our ongoing effort is incorporating this methodology into the framework of the Eulerian Applications Project to achieve algorithmic acceleration of radiationhydrodynamics simulations in production software. By starting from the thermal radiative transfer equations with a simple material-motion correction, we derive a discretely consistent energy balance equation (LO equation). We demonstrate that the corresponding LO system for the Monte Carlo HO solver is closely related to the originalmore » LO system without material-motion corrections. We test the implementation on a radiative shock problem and show consistency between the energy densities and temperatures in the HO and LO solutions as well as agreement with the semianalytic solution. We also test the approach on a more challenging two-dimensional problem and demonstrate accuracy enhancements and algorithmic speedups. This paper extends a recent conference paper by including multigroup effects.« less
Multigroup Radiation-Hydrodynamics with a High-Order, Low-Order Method
Wollaber, Allan Benton; Park, HyeongKae; Lowrie, Robert Byron; Rauenzahn, Rick M.; Cleveland, Mathew Allen
2016-12-09
Recent efforts at Los Alamos National Laboratory to develop a moment-based, scale-bridging [or high-order (HO)–low-order (LO)] algorithm for solving large varieties of the transport (kinetic) systems have shown promising results. A part of our ongoing effort is incorporating this methodology into the framework of the Eulerian Applications Project to achieve algorithmic acceleration of radiationhydrodynamics simulations in production software. By starting from the thermal radiative transfer equations with a simple material-motion correction, we derive a discretely consistent energy balance equation (LO equation). We demonstrate that the corresponding LO system for the Monte Carlo HO solver is closely related to the original LO system without material-motion corrections. We test the implementation on a radiative shock problem and show consistency between the energy densities and temperatures in the HO and LO solutions as well as agreement with the semianalytic solution. We also test the approach on a more challenging two-dimensional problem and demonstrate accuracy enhancements and algorithmic speedups. This paper extends a recent conference paper by including multigroup effects.
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.
Diffusion-Weighted Images Superresolution Using High-Order SVD.
Wu, Xi; Yang, Zhipeng; Hu, Jinrong; Peng, Jing; He, Peiyu; Zhou, Jiliu
2016-01-01
The spatial resolution of diffusion-weighted imaging (DWI) is limited by several physical and clinical considerations, such as practical scanning times. Interpolation methods, which are widely used to enhance resolution, often result in blurred edges. Advanced superresolution scanning acquires images with specific protocols and long acquisition times. In this paper, we propose a novel single image superresolution (SR) method which introduces high-order SVD (HOSVD) to regularize the patch-based SR framework on DWI datasets. The proposed method was implemented on an adaptive basis which ensured a more accurate reconstruction of high-resolution DWI datasets. Meanwhile, the intrinsic dimensional decreasing property of HOSVD is also beneficial for reducing the computational burden. Experimental results from both synthetic and real DWI datasets demonstrate that the proposed method enhances the details in reconstructed high-resolution DWI datasets and outperforms conventional techniques such as interpolation methods and nonlocal upsampling.
Diffusion-Weighted Images Superresolution Using High-Order SVD
Yang, Zhipeng; Hu, Jinrong; Peng, Jing; He, Peiyu
2016-01-01
The spatial resolution of diffusion-weighted imaging (DWI) is limited by several physical and clinical considerations, such as practical scanning times. Interpolation methods, which are widely used to enhance resolution, often result in blurred edges. Advanced superresolution scanning acquires images with specific protocols and long acquisition times. In this paper, we propose a novel single image superresolution (SR) method which introduces high-order SVD (HOSVD) to regularize the patch-based SR framework on DWI datasets. The proposed method was implemented on an adaptive basis which ensured a more accurate reconstruction of high-resolution DWI datasets. Meanwhile, the intrinsic dimensional decreasing property of HOSVD is also beneficial for reducing the computational burden. Experimental results from both synthetic and real DWI datasets demonstrate that the proposed method enhances the details in reconstructed high-resolution DWI datasets and outperforms conventional techniques such as interpolation methods and nonlocal upsampling. PMID:27635150
High-order total variation minimization for interior SPECT
NASA Astrophysics Data System (ADS)
Yang, Jiansheng; Yu, Hengyong; Jiang, Ming; Wang, Ge
2012-01-01
Recently, we developed an approach for solving the computed tomography (CT) interior problem based on the high-order TV (HOT) minimization, assuming that a region-of-interest (ROI) is piecewise polynomial. In this paper, we generalize this finding from the CT field to the single-photon emission computed tomography (SPECT) field, and prove that if an ROI is piecewise polynomial, then the ROI can be uniquely reconstructed from the SPECT projection data associated with the ROI through the HOT minimization. Also, we propose a new formulation of HOT, which has an explicit formula for any n-order piecewise polynomial function, while the original formulation has no explicit formula for n ⩾ 2. Finally, we verify our theoretical results in numerical simulation, and discuss relevant issues.
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-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.
NASA Astrophysics Data System (ADS)
De Basabe, Jonás D.; Sen, Mrinal K.
2010-04-01
We investigate the stability of some high-order finite element methods, namely the spectral element method and the interior-penalty discontinuous Galerkin method (IP-DGM), for acoustic or elastic wave propagation that have become increasingly popular in the recent past. We consider the Lax-Wendroff method (LWM) for time stepping and show that it allows for a larger time step than the classical leap-frog finite difference method, with higher-order accuracy. In particular the fourth-order LWM allows for a time step 73 per cent larger than that of the leap-frog method; the computational cost is approximately double per time step, but the larger time step partially compensates for this additional cost. Necessary, but not sufficient, stability conditions are given for the mentioned methods for orders up to 10 in space and time. The stability conditions for IP-DGM are approximately 20 and 60 per cent more restrictive than those for SEM in the acoustic and elastic cases, respectively.
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
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.
Discrimination of Epoxy Curing by High Lamb Modes Order
NASA Astrophysics Data System (ADS)
Gauthier, Camille; Leduc, Damien; Galy, Jocelyne; Elkettani, Mounsif Echherif; Izbicki, Jean-Louis
This work is a contribution to the non destructive testing of structural adhesive bonding by ultrasonic methods. The aim of this paper is to link acoustic behaviors of epoxy bulk samples to their level of cure, quantified by a partial or a total epoxy conversion. The bulk longitudinal and shear waves velocities are measured for each sample. They are used to determine the theoretical dispersion curves of Lamb waves. Theoretical results predict a high sensitivity of some high order Lamb modes to the cure level by the variation of their wavenumber, for a given mode and for the same frequency range. In parallel, an experimental study is conducted to determine the experimental dispersion curves. The experimental results and the predicted ones are in a good agreement.
Convergence Properties of High-order Boltzmann Machines.
Lozano, J Antonio; Graña, Manuel; d'Anjou, Alicia; Albizuri, F Xabier
1996-12-01
The high-order Boltzmann machine (HOBM) approximates probability distributions defined on a set of binary variables, through a learning algorithm that uses Monte Carlo methods. The approximation distribution is a normalized exponential of a consensus function formed by high-degree terms and the structure of the HOBM is given by the set of weighted connections. We prove the convexity of the Kullback-Leibler divergence between the distribution to learn and the approximation distribution of the HOBM. We prove the convergence of the learning algorithm to the strict global minimum of the divergence, which corresponds to the maximum likelihood estimate of the connection weights, establishing the uniqueness of the solution. These theoretical results do not hold in the conventional Boltzmann machine, where the consensus function has first and second-degree terms and hidden units are used. Copyright 1996 Elsevier Science Ltd.
Nullomers and High Order Nullomers in Genomic Sequences
Vergni, Davide; Santoni, Daniele
2016-01-01
A nullomer is an oligomer that does not occur as a subsequence in a given DNA sequence, i.e. it is an absent word of that sequence. The importance of nullomers in several applications, from drug discovery to forensic practice, is now debated in the literature. Here, we investigated the nature of nullomers, whether their absence in genomes has just a statistical explanation or it is a peculiar feature of genomic sequences. We introduced an extension of the notion of nullomer, namely high order nullomers, which are nullomers whose mutated sequences are still nullomers. We studied different aspects of them: comparison with nullomers of random sequences, CpG distribution and mean helical rise. In agreement with previous results we found that the number of nullomers in the human genome is much larger than expected by chance. Nevertheless antithetical results were found when considering a random DNA sequence preserving dinucleotide frequencies. The analysis of CpG frequencies in nullomers and high order nullomers revealed, as expected, a high CpG content but it also highlighted a strong dependence of CpG frequencies on the dinucleotide position, suggesting that nullomers have their own peculiar structure and are not simply sequences whose CpG frequency is biased. Furthermore, phylogenetic trees were built on eleven species based on both the similarities between the dinucleotide frequencies and the number of nullomers two species share, showing that nullomers are fairly conserved among close species. Finally the study of mean helical rise of nullomers sequences revealed significantly high mean rise values, reinforcing the hypothesis that those sequences have some peculiar structural features. The obtained results show that nullomers are the consequence of the peculiar structure of DNA (also including biased CpG frequency and CpGs islands), so that the hypermutability model, also taking into account CpG islands, seems to be not sufficient to explain nullomer phenomenon
Multilevel perspective on high-order harmonic generation in solids
NASA Astrophysics Data System (ADS)
Wu, Mengxi; Browne, Dana A.; Schafer, Kenneth J.; Gaarde, Mette B.
2016-12-01
We investigate high-order harmonic generation in a solid, modeled as a multilevel system dressed by a strong infrared laser field. We show that the cutoff energies and the relative strengths of the multiple plateaus that emerge in the harmonic spectrum can be understood both qualitatively and quantitatively by considering a combination of adiabatic and diabatic processes driven by the strong field. Such a model was recently used to interpret the multiple plateaus exhibited in harmonic spectra generated by solid argon and krypton [G. Ndabashimiye et al., Nature 534, 520 (2016), 10.1038/nature17660]. We also show that when the multilevel system originates from the Bloch state at the Γ point of the band structure, the laser-dressed states are equivalent to the Houston states [J. B. Krieger and G. J. Iafrate, Phys. Rev. B 33, 5494 (1986), 10.1103/PhysRevB.33.5494] and will therefore map out the band structure away from the Γ point as the laser field increases. This leads to a semiclassical three-step picture in momentum space that describes the high-order harmonic generation process in a solid.
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.
Large eddy simulation using high-resolution and high-order methods.
Drikakis, D; Hahn, M; Mosedale, A; Thornber, B
2009-07-28
Restrictions on computing power make direct numerical simulation too expensive for complex flows; thus, the development of accurate large eddy simulation (LES) methods, which are industrially applicable and efficient, is required. This paper reviews recent findings about the leading order dissipation rate associated with high-resolution methods and improvements to the standard schemes for use in highly turbulent flows. Results from implicit LES are presented for a broad range of flows and numerical schemes, ranging from the second-order monotone upstream-centered schemes for conservation laws to very high-order (up to ninth-order) weighted essentially non-oscillatory schemes.
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
Plasma undulator excited by high-order mode lasers
NASA Astrophysics Data System (ADS)
Wang, Jingwei; Rykovanov, Sergey
2016-10-01
A laser-created plasma undulator together with a laser-plasma accelerator makes it possible to construct an economical and extremely compact XFEL. However, the spectrum spread of the radiation from the current plasma undulators is too large for XFELs, because of the different values of strength parameters. The phase slippage between the electrons and the wakefield also limits the number of the electron oscillation cycles, thus reduces the performance of XFEL. Here we proposed a phase-locked plasma undulator created by high-order mode lasers. The modulating field is uniform along the transverse direction by choosing appropriate laser intensities of the modes, which enables all the electrons oscillate with the same strength parameter. The plasma density is tapered to lock the phase between the electrons and the wakefield, which signally increases the oscillation cycles. As a result, X-ray radiation with high brightness and narrow bandwidth is generated by injecting a high-energy electron beam into the novel plasma undulator. The beam loading limit indicates that the current of the electron beam could be hundreds of Ampere. These properties imply that such a plasma undulator may have great potential in compact XFELs. This work was supported by the Helmholtz Association (Young Investigator's Group No. VH-NG-1037).
High-order Harmonic Generation in Ultra Thin Plasma Foil
NASA Astrophysics Data System (ADS)
Shuai, Bin; Shen, Baifei; Li, Ruxin; Xu, Zhizhan
Via l-D Particle In Cell (PIC) simulations, we investigated the high-order harmonic emission from flim plasma foils irradiated by two circular- polarized, counter-propagating laser pulses with their electrical vectors rotating in different directions. More than 200 harmonics can be generated with a laser intensity of 1021 W/cm2. When the duration of laser gets shorter, the frequencies of harmonics were severely modulated due to the Doppler shift caused by the movement of the plasma boundary when the foil is being compressed. The Doppler shift can be estimated by the simulation results, and this effect can also be reduced or modified by introducing frequency chirping to the pump pulse.
Switching-surge characteristics of high-phase-order lines
1982-03-01
High phase order (HPO) is the use of more than the conventional three phases for electric power transmission. A previous study evaluated the general feasibility of the HPO concept and defined the need for design information in specific areas, including the need for switching surge data. This study was undertaken to obtain switching surge characteristics applicable to a broad spectrum of utility system applications, thereby supplying data for practical HPO design, and to obtain detailed data on switching surges to define test parameters for HPO testing and insulation system design. Both objectives were met, and voltage magnitude data for 6- and 12-phase systems are presented and compared with 3-0 systems. (LCL)
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.
Coherent selection of invisible high-order electromagnetic excitations
NASA Astrophysics Data System (ADS)
Tseng, Ming Lun; Fang, Xu; Savinov, Vassili; Wu, Pin Chieh; Ou, Jun-Yu; Zheludev, Nikolay I.; Tsai, Din Ping
2017-03-01
Far-field spectroscopy and mapping of electromagnetic near-field distribution are the two dominant tools for analysis and characterization of the electromagnetic response in nanophotonics. Despite the widespread use, these methods can fail at identifying weak electromagnetic excitations masked by stronger neighboring excitations. This is particularly problematic in ultrafast nanophotonics, including optical sensing, nonlinear optics and nanolasers, where the broad resonant modes can overlap to a significant degree. Here, using plasmonic metamaterials, we demonstrate that coherent spectroscopy can conveniently isolate and detect such hidden high-order photonic excitations. Our results establish that the coherent spectroscopy is a powerful new tool. It complements the conventional methods for analysis of the electromagnetic response, and provides a new route to designing and characterizing novel photonic devices and materials.
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 hydrodynamic algorithms for exascale computing
Morgan, Nathaniel Ray
2016-02-05
Hydrodynamic algorithms are at the core of many laboratory missions ranging from simulating ICF implosions to climate modeling. The hydrodynamic algorithms commonly employed at the laboratory and in industry (1) typically lack requisite accuracy for complex multi- material vortical flows and (2) are not well suited for exascale computing due to poor data locality and poor FLOP/memory ratios. Exascale computing requires advances in both computer science and numerical algorithms. We propose to research the second requirement and create a new high-order hydrodynamic algorithm that has superior accuracy, excellent data locality, and excellent FLOP/memory ratios. This proposal will impact a broad range of research areas including numerical theory, discrete mathematics, vorticity evolution, gas dynamics, interface instability evolution, turbulent flows, fluid dynamics and shock driven flows. If successful, the proposed research has the potential to radically transform simulation capabilities and help position the laboratory for computing at the exascale.
Coherent selection of invisible high-order electromagnetic excitations
Tseng, Ming Lun; Fang, Xu; Savinov, Vassili; Wu, Pin Chieh; Ou, Jun-Yu; Zheludev, Nikolay I.; Tsai, Din Ping
2017-01-01
Far-field spectroscopy and mapping of electromagnetic near-field distribution are the two dominant tools for analysis and characterization of the electromagnetic response in nanophotonics. Despite the widespread use, these methods can fail at identifying weak electromagnetic excitations masked by stronger neighboring excitations. This is particularly problematic in ultrafast nanophotonics, including optical sensing, nonlinear optics and nanolasers, where the broad resonant modes can overlap to a significant degree. Here, using plasmonic metamaterials, we demonstrate that coherent spectroscopy can conveniently isolate and detect such hidden high-order photonic excitations. Our results establish that the coherent spectroscopy is a powerful new tool. It complements the conventional methods for analysis of the electromagnetic response, and provides a new route to designing and characterizing novel photonic devices and materials. PMID:28295021
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
Lu, Guo-Wei; Sakamoto, Takahide; Kawanishi, Tetsuya
2013-03-11
In order to adapt to the dynamics in the future optical networks, we propose a flexible high-order QAM transmitter using a tandem in-phase/quadrature (IQ) modulators to synthesize different high-order quadrature amplitude modulation (QAM) formats, such as 16QAM, 32 or 36QAM and 64QAM. To generate high-order QAMs, an offset-QAM is firstly generated using an IQ modulator driven by electronics with reduced modulation-level, and then mapped to other quadrants through another following IQ modulator configured as a standard quadrature phase-shift keying (QPSK) modulator. All of the embedded sub-Mach-Zehnder modulators are operated in push-pull configurations to avoid introducing excess phase chirp. In contrast with the schemes based on a single IQ modulator driven by multilevel electronics or a highly-integrated parallel modulator, by deploying commercially-available optical modulators and driving electronics with reduced modulation-level, the transmitter complexity in optics and electronics is well-balanced. In the case of generating optical 64QAM, different from another tandem scheme deploying dual-drive IQ modulator driven by independent four binary streams, less phase chirp is observed in our proposed scheme, and comparable implementation penalty is obtained even without applying additional specific compensation algorithm in the coherent receiver. Moreover, thanks to the tandem structure and the deployment of QPSK modulator, the obtained high-order QAM is naturally differentially coded, which is helpful to solve the phase ambiguity at coherent receiver. We experimentally demonstrate the generations of these high-order QAMs including 16QAM, 32/36QAM and 64QAM, and confirm the error-free operations with comparable BER performance to the "electrical" approach based on a single IQ modulator.
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
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.
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.
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.
High order total variation method for interior tomography
NASA Astrophysics Data System (ADS)
Yang, Jiansheng; Yu, Hengyong; Cong, Wenxiang; Jiang, Ming; Wang, Ge
2012-10-01
While classic CT theory targets exact reconstruction of a whole cross-section or an entire object, practical applications often focus on a region of interest (ROI). The long-standing interior problem is well known that an internal ROI cannot be exactly reconstruct only from truncated projection data associated with x-rays through the ROI. Although lambda tomography was developed to target gradient-like features of an internal ROI for the interior problem, it has not been well accepted in the biomedical community. On the other hand, approximate local reconstruction methods are subject to biases and artifacts. Recently, the interior problem is re-visited with appropriate prior knowledge, delivering practical results. First, the interior problem can be exactly and stably solved if a sub-region in an ROI is known. Thereafter, the sub-region knowledge can be replaced by certain rather weak constraints. For local reconstruction, a candidate image can be represented as the sum of the truth and an ambiguity component. Very surprisingly, the ROI image is prove to be the unique minimizer of the total variation (TV) or high order total variation (HOT) functional subject to the measurement, if the ROI is piece-wise constant or polynomial. Interior tomography algorithms based on HOT minimization have been developed for x-ray CT, and then extended for interior SPECT and interior differential phasecontrast tomography, respectively. In this paper, we will summarize the main theoretical and algorithmic results.
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.
Complex structure of spatially resolved high-order-harmonic spectra
NASA Astrophysics Data System (ADS)
Catoire, F.; Ferré, A.; Hort, O.; Dubrouil, A.; Quintard, L.; Descamps, D.; Petit, S.; Burgy, F.; Mével, E.; Mairesse, Y.; Constant, E.
2016-12-01
We investigate the spatiospectral coupling appearing in the spatially resolved high-order-harmonic spectra generated in gases. When ionization is weak, harmonic generation in the far field often exhibits rings surrounding a central spot centered on each odd harmonics in the spatiospectral domain. The nature of these structures is debated. They could stem from interferences between the emission of short and long trajectories, or could be the signature of the temporal and spatial dependence of the longitudinal phase matching of long trajectories (Maker fringes). We conducted spectrally and spatially resolved measurements of the harmonic spectra as a function of pressure, intensity, and ellipticity. In addition, we performed calculations where only a single emission plane is included (i.e., omitting deliberately the longitudinal phase matching), reproducing the features experimentally observed. This study has been completed by the spatiospectral coupling when strong ionization occurs leading to complex patterns which have been compared to calculations using the same model and also show good agreement. We conclude that many spatiospectral structures of the harmonic spectrum can be interpreted in terms of spatial and temporal transverse coherence of the emitting medium without resorting to longitudinal phase matching or quantum phase interference between short and long trajectories.
Knocking down highly-ordered large-scale nanowire arrays.
Pevzner, Alexander; Engel, Yoni; Elnathan, Roey; Ducobni, Tamir; Ben-Ishai, Moshit; Reddy, Koteeswara; Shpaisman, Nava; Tsukernik, Alexander; Oksman, Mark; Patolsky, Fernando
2010-04-14
The large-scale assembly of nanowire elements with controlled and uniform orientation and density at spatially well-defined locations on solid substrates presents one of the most significant challenges facing their integration in real-world electronic applications. Here, we present the universal "knocking-down" approach, based on the controlled in-place planarization of nanowire elements, for the formation of large-scale ordered nanowire arrays. The controlled planarization of the nanowires is achieved by the use of an appropriate elastomer-covered rigid-roller device. After being knocked down, each nanowire in the array can be easily addressed electrically, by a simple single photolithographic step, to yield a large number of nanoelectrical devices with an unprecedented high-fidelity rate. The approach allows controlling, in only two simple steps, all possible array parameters, that is, nanowire dimensions, chemical composition, orientation, and density. The resulting knocked-down arrays can be further used for the creation of massive nanoelectronic-device arrays. More than million devices were already fabricated with yields over 98% on substrate areas of up, but not limited to, to 10 cm(2).
Highly ordered carbon nanotubes based on porous aluminum oxide.
Pan, H; Gao, H; Lim, S H; Feng, Y P; Lin, J
2004-11-01
Highly ordered carbon nanotubes (CNTs) are widely pursued due to their unique properties. Anodic aluminum oxide (AAO) exhibits great possibility for this purpose. Here, CNTs based on AAO templates were produced using acetylene or ethylene as the hydrocarbon sources with or without the presence of Co catalysts. CNTs grown on the Co-embedded AAO samples were normally confined within the nanopores of the AAO template. It was found that C2H4 normally requires 100 degrees C higher pyrolysis temperature than C2H2 under otherwise identical conditions. The pyrolysis temperature is greatly reduced with the presence of Co catalysts. CNTs can grow out of the nanopores if Co particles are present at the bottom of the nanopores, and if the nanopores are short in length or large in diameter. The graphitization of AAO-template grown CNTs was studied by Raman spectroscopy. CNTs produced from ethylene are generally better in graphitization than those from acetylene, and CNTs grown with the presence of Co catalysts deposited at the bottom of nanopores are better than those without Co catalysts or with Co catalysts coated on the entire inner wall of nanopores. The growth temperature is found not to play a critical role in graphitization.
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 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.
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.
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.
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.
High order discretization schemes for the CIR process
NASA Astrophysics Data System (ADS)
Alfonsi, Aurelien
2010-01-01
This paper presents weak second and third order schemes for the Cox-Ingersoll-Ross (CIR) process, without any restriction on its parameters. At the same time, it gives a general recursive construction method for getting weak second order schemes that extend the one introduced by Ninomiya and Victoir. Combine both these results, this allows us to propose a second order scheme for more general affine diffusions. Simulation examples are given to illustrate the convergence of these schemes on CIR and Heston models.
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.
The extended high-order sandwich panel theory
NASA Astrophysics Data System (ADS)
Phan, Catherine N.
The contribution of this thesis is an extended high-order sandwich panel theory (EHSAPT) for sandwich beams/wide panels, in which the axial stresses are taken into account as well as the shear and transverse normal stresses in the core, and its validation. The general nonlinear formulation of EHSAPT is given in Chapter 2. Validation of the present theory is made by comparison with elasticity solutions and experimental data. The accuracy of EHSAPT is assessed for the standard class of structural analysis problems which include: static loading, static instability (global buckling and wrinkling), free vibrations, and dynamic loading. In Chapter 3 the static response to a half-sine distributed load applied to the top face sheet of a simply supported sandwich beam/wide panel is solved. Validation is made with elasticity, and Euler-Bernoulli beam, first order shear deformation theory, and HSAPT were also included for comparison. In Chapter 4 the static global buckling critical load is determined for a simply supported sandwich beam/wide panel under edgewise loading. Validation is made with elasticity, and Allen's formula and HSAPT are included for comparison. In Chapter 5 the static wrinkling critical load of a simply supported sandwich beam/wide panel is investigated. Validation includes comparison with elasticity, experimental results reported in literature, and recently acquired experimental results. Results using Hoff-Mautner's wrinkling formula and HSAPT are also shown. In Chapter 6 the free vibrations of a simply supported sandwich beam/wide panel are explored, and the predicted antisymmetric and symmetric natural frequencies are compared to experimental results found in the literature and with elasticity. The last validation of EHSAPT is made for the dynamic response to a half-sine distributed load with an exponential time decay applied to the top face sheet of a simply supported sandwich beam. Results are compared with elasticity. The response from using HSAPT is
High-order-harmonic generation in atomic and molecular systems
NASA Astrophysics Data System (ADS)
Suárez, Noslen; Chacón, Alexis; Pérez-Hernández, Jose A.; Biegert, Jens; Lewenstein, Maciej; Ciappina, Marcelo F.
2017-03-01
High-order-harmonic generation (HHG) results from the interaction of ultrashort laser pulses with matter. It configures an invaluable tool to produce attosecond pulses, moreover, to extract electron structural and dynamical information of the target, i.e., atoms, molecules, and solids. In this contribution, we introduce an analytical description of atomic and molecular HHG, that extends the well-established theoretical strong-field approximation (SFA). Our approach involves two innovative aspects: (i) First, the bound-continuum and rescattering matrix elements can be analytically computed for both atomic and multicenter molecular systems, using a nonlocal short range model, but separable, potential. When compared with the standard models, these analytical derivations make possible to directly examine how the HHG spectra depend on the driven media and laser-pulse features. Furthermore, we can turn on and off contributions having distinct physical origins or corresponding to different mechanisms. This allows us to quantify their importance in the various regions of the HHG spectra. (ii) Second, as reported recently [N. Suárez et al., Phys. Rev. A 94, 043423 (2016), 10.1103/PhysRevA.94.043423], the multicenter matrix elements in our theory are free from nonphysical gauge- and coordinate-system-dependent terms; this is accomplished by adapting the coordinate system to the center from which the corresponding time-dependent wave function originates. Our SFA results are contrasted, when possible, with the direct numerical integration of the time-dependent Schrödinger equation in reduced and full dimensionality. Very good agreement is found for single and multielectronic atomic systems, modeled under the single active electron approximation, and for simple diatomic molecular systems. Interference features, ubiquitously present in every strong-field phenomenon involving a multicenter target, are also captured by our model.
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 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.
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.
Transport properties of stripe-ordered high Tc cuprates
NASA Astrophysics Data System (ADS)
Jie, Qing; Han, Su Jung; Dimitrov, Ivo; Tranquada, J. M.; Li, Qiang
2012-11-01
Transport measurements provide important characterizations of the nature of stripe order in the cuprates. Initial studies of systems such as La1.6-xNd0.4SrxCuO4 demonstrated the strong anisotropy between in-plane and c-axis resistivities, but also suggested that stripe order results in a tendency towards insulating behavior within the planes at low temperature. More recent work on La2-xBaxCuO4 with x = 1/8 has revealed the occurrence of quasi-two-dimensional superconductivity that onsets with spin-stripe order. The suppression of three-dimensional superconductivity indicates a frustration of the interlayer Josephson coupling, motivating a proposal that superconductivity and stripe order are intertwined in a pair-density-wave state. Complementary characterizations of the low-energy states near the Fermi level are provided by measurements of the Hall and Nernst effects, each revealing intriguing signatures of stripe correlations and ordering. We review and discuss this work.
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 T{sub c} superconducting second-order gradiometer
Kittel, A.; Kouznetsov, K.A.; McDermott, R.; Oh, B.; Clarke, J. |
1998-10-01
A planar, second-order gradiometer was fabricated from single-layer YBa{sub 2}Cu{sub 3}O{sub 7{minus}x} films. The gradiometer consists of a symmetric flux transformer with an overall length of 80 mm inductively coupled to a directly coupled magnetometer, and has a baseline of 31 mm. The mutual inductance between the flux transformer and the magnetometer is adjusted mechanically to reduce the response to a uniform magnetic field applied perpendicularly to the plane of the gradiometer to typically 50 ppm. From an independent measurement, the residual first-order gradient response was determined to be at most 1.4{percent} relative to the second-order gradient response. {copyright} {ital 1998 American Institute of Physics.}
High-order numerical solutions using cubic splines
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1975-01-01
The cubic spline collocation procedure for the numerical solution of partial differential equations was reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a nonuniform mesh and overall fourth-order accuracy for a uniform mesh. Application of the technique was made to the Burger's equation, to the flow around a linear corner, to the potential flow over a circular cylinder, and to boundary layer problems. The results confirmed the higher-order accuracy of the spline method and suggest that accurate solutions for more practical flow problems can be obtained with relatively coarse nonuniform meshes.
Compact high order schemes for the Euler equations
NASA Technical Reports Server (NTRS)
Abarbanel, Saul; Kumar, Ajay
1988-01-01
An implicit approximate factorization (AF) algorithm is constructed which has the following 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.
Performance of Several High Order Numerical Methods for Supersonic Combustion
NASA Technical Reports Server (NTRS)
Sjoegreen, Bjoern; Yee, H. C.; Don, Wai Sun; Mansour, Nagi N. (Technical Monitor)
2001-01-01
The performance of two recently developed numerical methods by Yee et al. and Sjoegreen and Yee using postprocessing nonlinear filters is examined for a 2-D multiscale viscous supersonic react-live flow. These nonlinear filters can improve nonlinear instabilities and at the same time can capture shock/shear waves accurately. They do not, belong to the class of TVD, ENO or WENO schemes. Nevertheless, they combine stable behavior at discontinuities and detonation without smearing the smooth parts of the flow field. For the present study, we employ a fourth-order Runge-Kutta in time and a sixth-order non-dissipative spatial base scheme for the convection and viscous terms. We denote the resulting nonlinear filter schemes ACM466-RK4 and WAV66-RK4.
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.
Nonlinear diffraction from high-order Hermite-Gauss beams.
Kalinowski, Ksawery; Shapira, Asia; Libster-Hershko, Ana; Arie, Ady
2015-01-01
We investigate experimentally and theoretically the nonlinearly diffracted second harmonic light from the first-order Hermite-Gauss beam. We investigate the cases of loosely and tightly focused beams in a periodically poled lithium niobate crystal in the temperature range near the birefringent phase matching. Unlike the case of fundamental Gaussian beam, the nonlinear diffracted beam is spatially structured. Its shape depends on the focusing conditions and on the crystal temperature. Furthermore, for the case of tight focusing, the diffracted beam structure depends on the beam's position with respect to the domain wall.
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.
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.
High-order variational perturbation theory for the free energy.
Weissbach, Florian; Pelster, Axel; Hamprecht, Bodo
2002-09-01
In this paper we introduce a generalization to the algebraic Bender-Wu recursion relation for the eigenvalues and the eigenfunctions of the anharmonic oscillator. We extend this well known formalism to the time-dependent quantum statistical Schrödinger equation, thus obtaining the imaginary-time evolution amplitude by solving a recursive set of ordinary differential equations. This approach enables us to evaluate global and local quantum statistical quantities of the anharmonic oscillator to much higher orders than by evaluating Feynman diagrams. We probe our perturbative results by deriving a perturbative expression for the free energy, which is then subject to variational perturbation theory as developed by Kleinert, yielding convergent results for the free energy for all values of the coupling strength.
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.
High resolution study of magnetic ordering at absolute zero.
Lee, M; Husmann, A; Rosenbaum, T F; Aeppli, G
2004-05-07
High resolution pressure measurements in the zero-temperature limit provide a unique opportunity to study the behavior of strongly interacting, itinerant electrons with coupled spin and charge degrees of freedom. Approaching the precision that has become the hallmark of experiments on classical critical phenomena, we characterize the quantum critical behavior of the model, elemental antiferromagnet chromium, lightly doped with vanadium. We resolve the sharp doubling of the Hall coefficient at the quantum critical point and trace the dominating effects of quantum fluctuations up to surprisingly high temperatures.
Generation of high-order harmonics in a high-intensity laser radiation field
Platonenko, Viktor T; Strelkov, V V
1998-07-31
An analysis is made of the generation of high-order harmonics by atoms and ions in high-intensity laser beams. A brief description is given of the main experimental relationships governing such generation, of methods for numerical solution of the Schrodinger equation for an atom in a strong field, and of some approximate models which make it possible to understand the mechanism of the effect (in particular, the 'semiclassical' model). A detailed discussion is made of an analytic quantum-mechanical theory of high-order harmonic generation in a one-electron system with the Coulomb, delta-like, and other potentials. Expressions are provided for the complex amplitudes of harmonics generated by monochromatic and bichromatic excitation. The results of simulation of high-order harmonic generation in an extended medium are given. This simulation takes into account the phases of the harmonics and their dependences on the amplitude of the fundamental-frequency field. The phase-matching problem and ways of solving it, the problem of the spectrum and duration of a pulse of a single harmonic and of the feasibility of controlling them, the problem of the total harmonic field, and other topics are considered. (review)
Aspects of Skill in Understanding High-Order Semantic Relations.
1985-07-25
EXPRESSING A CAUSAL RELATION High Constraint During 1984, six advances in research on tooth decay and its treatment were reported, so public health...officials are predicting the end of tooth decay by the year 2000. During 1984, six advances in research on tooth decay and its treatment were reported...leading public health officials to predict the end of tooth decay by the year 2000. *Low Constraint Illegal sports gambling is no longer the target of
Preparation of electrochemically active silicon nanotubes in highly ordered arrays.
Grünzel, Tobias; Lee, Young Joo; Kuepper, Karsten; Bachmann, Julien
2013-01-01
Silicon as the negative electrode material of lithium ion batteries has a very large capacity, the exploitation of which is impeded by the volume changes taking place upon electrochemical cycling. A Si electrode displaying a controlled porosity could circumvent the difficulty. In this perspective, we present a preparative method that yields ordered arrays of electrochemically competent silicon nanotubes. The method is based on the atomic layer deposition of silicon dioxide onto the pore walls of an anodic alumina template, followed by a thermal reduction with lithium vapor. This thermal reduction is quantitative, homogeneous over macroscopic samples, and it yields amorphous silicon and lithium oxide, at the exclusion of any lithium silicides. The reaction is characterized by spectroscopic ellipsometry for thin silica films, and by nuclear magnetic resonance and X-ray photoelectron spectroscopy for nanoporous samples. After removal of the lithium oxide byproduct, the silicon nanotubes can be contacted electrically. In a lithium ion electrolyte, they then display the electrochemical waves also observed for other bulk or nanostructured silicon systems. The method established here paves the way for systematic investigations of how the electrochemical properties (capacity, charge/discharge rates, cyclability) of nanoporous silicon negative lithium ion battery electrode materials depend on the geometry.
Detection of Doppler Microembolic Signals Using High Order Statistics
Geryes, Maroun; Hassan, Walid; Mcheick, Ali
2016-01-01
Robust detection of the smallest circulating cerebral microemboli is an efficient way of preventing strokes, which is second cause of mortality worldwide. Transcranial Doppler ultrasound is widely considered the most convenient system for the detection of microemboli. The most common standard detection is achieved through the Doppler energy signal and depends on an empirically set constant threshold. On the other hand, in the past few years, higher order statistics have been an extensive field of research as they represent descriptive statistics that can be used to detect signal outliers. In this study, we propose new types of microembolic detectors based on the windowed calculation of the third moment skewness and fourth moment kurtosis of the energy signal. During energy embolus-free periods the distribution of the energy is not altered and the skewness and kurtosis signals do not exhibit any peak values. In the presence of emboli, the energy distribution is distorted and the skewness and kurtosis signals exhibit peaks, corresponding to the latter emboli. Applied on real signals, the detection of microemboli through the skewness and kurtosis signals outperformed the detection through standard methods. The sensitivities and specificities reached 78% and 91% and 80% and 90% for the skewness and kurtosis detectors, respectively. PMID:28096889
NASA Astrophysics Data System (ADS)
Schubert, Thomas; Schneck, Emanuel; Tanaka, Motomu
2011-08-01
Molecular dynamics simulations with atomistic detail of the gel phase and melting transitions of dipalmitoyl phosphatidylcholine bilayers in water reveal the dependency of many thermodynamic and structural parameters on the initial system ordering. We quantitatively compare different methods to create a gel phase system and we observe that a very high ordering of the gel phase starting system is necessary to observe behavior which reproduces experimental data. We performed heating scans with speeds down to 0.5 K/ns and could observe sharp first order phase transitions. Also, we investigated the transition enthalpy as the natural intrinsic parameter of first order phase transitions, and obtained a quantitative match with experimental values. Furthermore, we performed systematic investigations of the statistical distribution and heating rate dependency of the microscopic phase transition temperature.
NASA Astrophysics Data System (ADS)
Hu, Zhicheng; Li, Ruo; Qiao, Zhonghua
2016-12-01
We study the acceleration of steady-state computation for microflow, which is modeled by the high-order moment models derived recently from the steady-state Boltzmann equation with BGK-type collision term. By using the lower-order model correction, a novel nonlinear multi-level moment solver is developed. Numerical examples verify that the resulting solver improves the convergence significantly thus is able to accelerate the steady-state computation greatly. The behavior of the solver is also numerically investigated. It is shown that the convergence rate increases, indicating the solver would be more efficient, as the total levels increases. Three order reduction strategies of the solver are considered. Numerical results show that the most efficient order reduction strategy would be ml-1 = ⌈ml / 2 ⌉.
Schubert, Thomas; Schneck, Emanuel; Tanaka, Motomu
2011-08-07
Molecular dynamics simulations with atomistic detail of the gel phase and melting transitions of dipalmitoyl phosphatidylcholine bilayers in water reveal the dependency of many thermodynamic and structural parameters on the initial system ordering. We quantitatively compare different methods to create a gel phase system and we observe that a very high ordering of the gel phase starting system is necessary to observe behavior which reproduces experimental data. We performed heating scans with speeds down to 0.5 K/ns and could observe sharp first order phase transitions. Also, we investigated the transition enthalpy as the natural intrinsic parameter of first order phase transitions, and obtained a quantitative match with experimental values. Furthermore, we performed systematic investigations of the statistical distribution and heating rate dependency of the microscopic phase transition temperature.
High-order finite element methods for seismic wave propagation
NASA Astrophysics Data System (ADS)
de Basabe Delgado, Jonas De Dios
Purely numerical methods based on the Finite Element Method (FEM) are becoming increasingly popular in seismic modeling for the propagation of acoustic and elastic waves in geophysical models. These methods offer a better control on the accuracy and more geometrical flexibility than the Finite Difference methods that have been traditionally used for the generation of synthetic seismograms. However, the success of these methods has outpaced their analytic validation. The accuracy of the FEMs used for seismic wave propagation is unknown in most cases and therefore the simulation parameters in numerical experiments are determined by empirical rules. I focus on two methods that are particularly suited for seismic modeling: the Spectral Element Method (SEM) and the Interior-Penalty Discontinuous Galerkin Method (IP-DGM). The goals of this research are to investigate the grid dispersion and stability of SEM and IP-DGM, to implement these methods and to apply them to subsurface models to obtain synthetic seismograms. In order to analyze the grid dispersion and stability, I use the von Neumann method (plane wave analysis) to obtain a generalized eigenvalue problem. I show that the eigenvalues are related to the grid dispersion and that, with certain assumptions, the size of the eigenvalue problem can be reduced from the total number of degrees of freedom to one proportional to the number of degrees of freedom inside one element. The grid dispersion results indicate that SEM of degree greater than 4 is isotropic and has a very low dispersion. Similar dispersion properties are observed for the symmetric formulation of IP-DGM of degree greater than 4 using nodal basis functions. The low dispersion of these methods allows for a sampling ratio of 4 nodes per wavelength to be used. On the other hand, the stability analysis shows that, in the elastic case, the size of the time step required in IP-DGM is approximately 6 times smaller than that of SEM. The results from the analysis
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.
High-order harmonics in light curves of Kepler planets
NASA Astrophysics Data System (ADS)
Armstrong, Caden; Rein, Hanno
2015-10-01
The Kepler mission was launched in 2009 and has discovered thousands of planet candidates. In a recent paper, Esteves et al. found a periodic signal in the light curves of KOI-13 and HAT-P-7, with a frequency triple the orbital frequency of a transiting planet. We found similar harmonics in many systems with a high occurrence rate. At this time, the origins of the signal are not entirely certain. We look carefully at the possibility of errors being introduced through our data processing routines but conclude that the signal is real. The harmonics on multiples of the orbital frequency are a result of non-sinusoidal periodic signals. We speculate on their origin and generally caution that these harmonics could lead to wrong estimates of planet albedos, beaming mass estimates, and ellipsoidal variations.
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
High order multi-grid methods to solve the Poisson equation
NASA Technical Reports Server (NTRS)
Schaffer, S.
1981-01-01
High order multigrid methods based on finite difference discretization of the model problem are examined. The following methods are described: (1) a fixed high order FMG-FAS multigrid algorithm; (2) the high order methods; and (3) results are presented on four problems using each method with the same underlying fixed FMG-FAS algorithm.
NASA Astrophysics Data System (ADS)
Huang, F.-T.; Gloter, A.; Chu, M.-W.; Chou, F. C.; Shu, G. J.; Liu, L.-K.; Chen, C. H.; Colliex, C.
2010-09-01
A new scanning transmission electron microscopy (STEM) imaging technique using high-order Laue zones (named HOLZ-STEM), a diffraction contrast which has been strenuously avoided or minimized in traditional STEM imaging, can be used to obtain the additional 1D periodic information along the electron propagation axis without sacrificing atomic resolution in the lateral (2D) dimension. HOLZ-STEM has been demonstrated to resolve the 3D long-range Na ordering of Na0.71CoO2. Direct evidence of spiral-like Na-trimer chains twisting along the c axis is unambiguously established in real space.
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)
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-order shock-fitted detonation propagation in high explosives
NASA Astrophysics Data System (ADS)
Romick, Christopher M.; Aslam, Tariq D.
2017-03-01
A highly accurate numerical shock and material interface fitting scheme composed of fifth-order spatial and third- or fifth-order temporal discretizations is applied to the two-dimensional reactive Euler equations in both slab and axisymmetric geometries. High rates of convergence are not typically possible with shock-capturing methods as the Taylor series analysis breaks down in the vicinity of discontinuities. Furthermore, for typical high explosive (HE) simulations, the effects of material interfaces at the charge boundary can also cause significant computational errors. Fitting a computational boundary to both the shock front and material interface (i.e. streamline) alleviates the computational errors associated with captured shocks and thus opens up the possibility of high rates of convergence for multi-dimensional shock and detonation flows. Several verification tests, including a Sedov blast wave, a Zel'dovich-von Neumann-Döring (ZND) detonation wave, and Taylor-Maccoll supersonic flow over a cone, are utilized to demonstrate high rates of convergence to nontrivial shock and reaction flows. Comparisons to previously published shock-capturing multi-dimensional detonations in a polytropic fluid with a constant adiabatic exponent (PF-CAE) are made, demonstrating significantly lower computational error for the present shock and material interface fitting method. For an error on the order of 10 m /s, which is similar to that observed in experiments, shock-fitting offers a computational savings on the order of 1000. In addition, the behavior of the detonation phase speed is examined for several slab widths to evaluate the detonation performance of PBX 9501 while utilizing the Wescott-Stewart-Davis (WSD) model, which is commonly used in HE modeling. It is found that the thickness effect curve resulting from this equation of state and reaction model using published values is dramatically more steep than observed in recent experiments. Utilizing the present fitting
Bolding, Simon R.; Cleveland, Mathew Allen; Morel, Jim E.
2016-10-21
In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S_{2} equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used to compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.
Bolding, Simon R.; Cleveland, Mathew Allen; Morel, Jim E.
2016-10-21
In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used to computemore » consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.« less
A high-order immersed boundary method for high-fidelity turbulent combustion simulations
NASA Astrophysics Data System (ADS)
Minamoto, Yuki; Aoki, Kozo; Osawa, Kosuke; Shi, Tuo; Prodan, Alexandru; Tanahashi, Mamoru
2016-11-01
Direct numerical simulations (DNS) have played important roles in the research of turbulent combustion. With the recent advancement in high-performance computing, DNS of slightly complicated configurations such as V-, various jet and swirl flames have been performed, and such DNS will further our understanding on the physics of turbulent combustion. Since these configurations include walls that do not necessarily conform with the preferred mesh coordinates for combustion DNS, most of these simulations use presumed profiles for inflow/near-wall flows as boundary conditions. A high-order immersed boundary method suited for parallel computation is one way to improve these simulations. The present research implements such a boundary technique in a combustion DNS code, and simulations are performed to confirm its accuracy and performance. This work was partly supported by Council for Science, Technology and Innovation, Cross-ministerial Strategic Innovation Promotion Program (SIP), "Innovative Combustion Technology" (Funding agency: JST).
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.
Federal Register 2010, 2011, 2012, 2013, 2014
2012-06-21
... International Trade Administration High Pressure Steel Cylinders From the People's Republic of China... duty order on high pressure steel cylinders (``steel cylinders'') from the People's Republic of China.... See High Pressure Steel Cylinders From the People's Republic of China: Final...
NASA Astrophysics Data System (ADS)
Nasilowski, Tomasz; Skorupski, Krzysztof; Makara, Mariusz; Statkiewicz-Barabach, Gabriela; Mergo, Pawel; Marc, Pawel; Jaroszewicz, Leszek
2011-05-01
Microstructured fibres (MSF) or photonic crystal fibres (PCF) possess a number of unique properties enabling a wide range of novel applications either in the telecommunication or in the sensing domain. In this paper we show that highly birefringent (HB) MSF with a dedicated design that allows inscribing fibre Bragg gratings in the MSF core can serve as pressure or stress transducers with extremely large sensitivity of second order mode, while exhibiting a low sensitivity to temperature drifts. Therefore, Bragg gratings inscribed in such MSF may offer a viable alternative to traditional optical fibre sensors of much lower stress sensitivity that require temperature compensation mechanisms and that are not intrinsically capable of distinguishing stress and temperature.
A finite-volume high-order ENO scheme for two-dimensional hyperbolic systems
NASA Technical Reports Server (NTRS)
Casper, Jay; Atkins, H. L.
1993-01-01
The finite-volume approach is presently used to obtain a 2D, high-order accurate and basically nonoscillatory shock-capture method whose high-order spatial accuracy is obtained by means of a piecewise polynomial approximation of the solution from cell averages. Attention is given to a high-order spatial operator that is able to both retain high-order accuracy in smooth regions and avoid the oscillations that are associated with interpolations across steep gradients. The operator is extended to hyperbolic systems of equations and curvilinear meshes.
High-Order Harmonic Spectral Filter with the Double Fourier Series on a Sphere
NASA Astrophysics Data System (ADS)
Cheong, Hyeong-Bin; Kwon, In-Hyuk; Goo, Tae-Young; Lee, Myeong-Joo
2002-04-01
A high-order harmonic spectral filter (HSF) is implemented to smooth out a field variable defined on a spherical surface using the double Fourier series (DFS) as orthogonal basis functions. The filter consists of the solution of the high-order harmonic diffusion equation with the implicit method, where the high-order harmonic operator is split into second- or lower-order harmonic operators. The second-order harmonic operator is replaced by a pentadiagonal matrix whose elements are the spectral coefficients. First, a biharmonic spectral filter (BiHSF), the prototype of the high-order HSF, is developed where only the second-order harmonic operator is included. It is found that the computational error for the inversion of a pentadiagonal matrix remains in the order of machine rounding. Compared to the mixed-order HSF with DFS used in the previous study, which contains the second- and third-order harmonic operators, the BiHSF can provide a sharper cutoff of high wavenumbers as well as improved computational efficiency. These advantages come from the fact that for each set of spectral coefficients the BiHSF needs only a single inversion of the pentadiagonal matrix whereas the mixed-order HSF requires triple inversions and an auxiliary operation of the tridiagonal matrix. Based on the BiHSF, the high-order HSF up to the sixth order, which is composed of a multiple inversion of tri- or pentadiagonal matrices, is designed. Tests with the rotated Gaussian fields revealed that the HSF with DFS is isotropic. Application to various problems, including a time-dependent strongly nonlinear case and the observed flow, indicates that the high-order HSF is well capable of smoothing out selectively high-wavenumber components without significantly affecting the conserved quantity, such as total (kinetic) energy.
High-order ionospheric effects on electron density estimation from Fengyun-3C GPS radio occultation
NASA Astrophysics Data System (ADS)
Li, Junhai; Jin, Shuanggen
2017-03-01
GPS radio occultation can estimate ionospheric electron density and total electron content (TEC) with high spatial resolution, e.g., China's recent Fengyun-3C GPS radio occultation. However, high-order ionospheric delays are normally ignored. In this paper, the high-order ionospheric effects on electron density estimation from the Fengyun-3C GPS radio occultation data are estimated and investigated using the NeQuick2 ionosphere model and the IGRF12 (International Geomagnetic Reference Field, 12th generation) geomagnetic model. Results show that the high-order ionospheric delays have large effects on electron density estimation with up to 800 el cm-3, which should be corrected in high-precision ionospheric density estimation and applications. The second-order ionospheric effects are more significant, particularly at 250-300 km, while third-order ionospheric effects are much smaller. Furthermore, the high-order ionospheric effects are related to the location, the local time, the radio occultation azimuth and the solar activity. The large high-order ionospheric effects are found in the low-latitude area and in the daytime as well as during strong solar activities. The second-order ionospheric effects have a maximum positive value when the radio occultation azimuth is around 0-20°, and a maximum negative value when the radio occultation azimuth is around -180 to -160°. Moreover, the geomagnetic storm also affects the high-order ionospheric delay, which should be carefully corrected.
High-Performance High-Order Simulation of Wave and Plasma Phenomena
NASA Astrophysics Data System (ADS)
Klockner, Andreas
This thesis presents results aiming to enhance and broaden the applicability of the discontinuous Galerkin ("DG") method in a variety of ways. DG was chosen as a foundation for this work because it yields high-order finite element discretizations with very favorable numerical properties for the treatment of hyperbolic conservation laws. In a first part, I examine progress that can be made on implementation aspects of DG. In adapting the method to mass-market massively parallel computation hardware in the form of graphics processors ("GPUs"), I obtain an increase in computation performance per unit of cost by more than an order of magnitude over conventional processor architectures. Key to this advance is a recipe that adapts DG to a variety of hardware through automated self-tuning. I discuss new parallel programming tools supporting GPU run-time code generation which are instrumental in the DG self-tuning process and contribute to its reaching application floating point throughput greater than 200 GFlops/s on a single GPU and greater than 3 TFlops/s on a 16-GPU cluster in simulations of electromagnetics problems in three dimensions. I further briefly discuss the solver infrastructure that makes this possible. In the second part of the thesis, I introduce a number of new numerical methods whose motivation is partly rooted in the opportunity created by GPU-DG: First, I construct and examine a novel GPU-capable shock detector, which, when used to control an artificial viscosity, helps stabilize DG computations in gas dynamics and a number of other fields. Second, I describe my pursuit of a method that allows the simulation of rarefied plasmas using a DG discretization of the electromagnetic field. Finally, I introduce new explicit multi-rate time integrators for ordinary differential equations with multiple time scales, with a focus on applicability to DG discretizations of time-dependent problems.
GPU-based volume visualization from high-order finite element fields.
Nelson, Blake; Kirby, Robert M; Haimes, Robert
2014-01-01
This paper describes a new volume rendering system for spectral/hp finite-element methods that has as its goal to be both accurate and interactive. Even though high-order finite element methods are commonly used by scientists and engineers, there are few visualization methods designed to display this data directly. Consequently, visualizations of high-order data are generally created by first sampling the high-order field onto a regular grid and then generating the visualization via traditional methods based on linear interpolation. This approach, however, introduces error into the visualization pipeline and requires the user to balance image quality, interactivity, and resource consumption. We first show that evaluation of the volume rendering integral, when applied to the composition of piecewise-smooth transfer functions with the high-order scalar field, typically exhibits second-order convergence for a wide range of high-order quadrature schemes, and has worst case first-order convergence. This result provides bounds on the ability to achieve high-order convergence to the volume rendering integral. We then develop an algorithm for optimized evaluation of the volume rendering integral, based on the categorization of each ray according to the local behavior of the field and transfer function. We demonstrate the effectiveness of our system by running performance benchmarks on several high-order fluid-flow simulations.
Abd-Elhameed, W. M.
2014-01-01
This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Chebyshev polynomials are deduced as special cases. Some new reduction formulae for summing some terminating hypergeometric functions of unit argument are also deduced. As an application, and with the aid of the new introduced derivatives formulae, an algorithm for solving special sixth-order boundary value problems are implemented with the aid of applying Galerkin method. A numerical example is presented hoping to ascertain the validity and the applicability of the proposed algorithms. PMID:25386599
Quantum and quasi-classical analyses of high order emission processes
Schafer, K.J.; Kulander, K.C.
1993-06-01
High-order harmonic generation from atoms and ions cuts off in accord with the simple rule: E{sub c} {approximately} I{sub p} + 3U{sub p}. This cutoff rule as well as the lack of a cutoff in high- order electron energy spectra can be understood via a simple extension of existing two step quasi-classical models.
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.
High-order numerical simulations of the flow around wings at moderately high Reynolds number
NASA Astrophysics Data System (ADS)
Vinuesa, Ricardo; Negi, Prabal; Hosseini, Seyed M.; Hanifi, Ardeshir; Henningson, Dan S.; Schlatter, Philipp
2016-11-01
The results of a DNS of the flow around a wing section represented by a NACA4412 profile, with Rec = 400 , 000 and 5° angle of attack, are presented in this study. The high-order spectral-element code Nek5000 was used for the computations. The Clauser pressure-gradient parameter β ranges from = 0 to 85 on the suction side, and the maximum Reθ and Reτ values are around 2 , 800 and 373, respectively. The adversre pressure gradient (APG) on the suction side of the wing leads to a progressively increasing value of the inner peak in the tangential velocity fluctuations, as well as the development of an outer peak, which is also observed in the other components of the Reynolds-stress tensor. Close to the trailing edge, i.e., at x / c = 0 . 9 , the outer peak in the inner-scaled tangential velocity profile is larger than the inner peak. These effects are connected to the fact that the large-scale motions of the flow become energized due to the APG, as apparent from spanwise-premultiplied power spectral density plots. Preliminary comparisons between DNS and well-resolved LES data, based on a relaxation-term filtering approach, are also presented with the aim of further extending the Reynolds number to Rec = 1 , 000 , 000 . Funded by the Swedish Research Council (VR) and the Knut and Alice Wallenberg Foundation.
NASA Astrophysics Data System (ADS)
Zhang, Y. Q.; Pang, M.; Chen, W. Q.
2015-02-01
Implementing the high-order surface stress model into the Bernoulli-Euler beam theory, the transverse vibration of an axially compressed nanowire embedded in elastic medium is investigated. Closed-form expression is obtained for the natural frequency of a simply supported nanowire. The influences of compressive axial load, high-order surface stress and surrounding elastic medium on the natural frequency are discussed. Additionally, the analytical solution of axial buckling load for the simply supported nanowire is derived, which takes into account the effects of high-order surface stress and surrounding elastic medium. It is concluded from numerical results that the natural frequency of transverse vibration of the nanowire is dependent upon axial load, surrounding elastic medium, and high-order surface stress. Similarly, the dependences of the buckling load on surrounding elastic medium and high-order surface stress are significant.
High-order fractional partial differential equation transform for molecular surface construction
Hu, Langhua; Chen, Duan; Wei, Guo-Wei
2013-01-01
Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model
High-order fractional partial differential equation transform for molecular surface construction.
Hu, Langhua; Chen, Duan; Wei, Guo-Wei
2013-01-01
Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model
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.
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.
Detecting High-Order Epistasis in Nonlinear Genotype-Phenotype Maps
Sailer, Zachary R.; Harms, Michael J.
2017-01-01
High-order epistasis has been observed in many genotype-phenotype maps. These multi-way interactions between mutations may be useful for dissecting complex traits and could have profound implications for evolution. Alternatively, they could be a statistical artifact. High-order epistasis models assume the effects of mutations should add, when they could in fact multiply or combine in some other nonlinear way. A mismatch in the “scale” of the epistasis model and the scale of the underlying map would lead to spurious epistasis. In this article, we develop an approach to estimate the nonlinear scales of arbitrary genotype-phenotype maps. We can then linearize these maps and extract high-order epistasis. We investigated seven experimental genotype-phenotype maps for which high-order epistasis had been reported previously. We find that five of the seven maps exhibited nonlinear scales. Interestingly, even after accounting for nonlinearity, we found statistically significant high-order epistasis in all seven maps. The contributions of high-order epistasis to the total variation ranged from 2.2 to 31.0%, with an average across maps of 12.7%. Our results provide strong evidence for extensive high-order epistasis, even after nonlinear scale is taken into account. Further, we describe a simple method to estimate and account for nonlinearity in genotype-phenotype maps. PMID:28100592
Detecting High-Order Epistasis in Nonlinear Genotype-Phenotype Maps.
Sailer, Zachary R; Harms, Michael J
2017-03-01
High-order epistasis has been observed in many genotype-phenotype maps. These multi-way interactions between mutations may be useful for dissecting complex traits and could have profound implications for evolution. Alternatively, they could be a statistical artifact. High-order epistasis models assume the effects of mutations should add, when they could in fact multiply or combine in some other nonlinear way. A mismatch in the "scale" of the epistasis model and the scale of the underlying map would lead to spurious epistasis. In this article, we develop an approach to estimate the nonlinear scales of arbitrary genotype-phenotype maps. We can then linearize these maps and extract high-order epistasis. We investigated seven experimental genotype-phenotype maps for which high-order epistasis had been reported previously. We find that five of the seven maps exhibited nonlinear scales. Interestingly, even after accounting for nonlinearity, we found statistically significant high-order epistasis in all seven maps. The contributions of high-order epistasis to the total variation ranged from 2.2 to 31.0%, with an average across maps of 12.7%. Our results provide strong evidence for extensive high-order epistasis, even after nonlinear scale is taken into account. Further, we describe a simple method to estimate and account for nonlinearity in genotype-phenotype maps.
High-order positivity-satisfying scheme for multi-component flows
NASA Astrophysics Data System (ADS)
Shahbazi, Khosro
2016-11-01
A high-order maximum-principle-satisfying scheme for the multi-component flow computations featuring jumps and discontinuities due to shock waves and phase interfaces is presented. The scheme is based on high-order weighted-essentially non-oscillatory (WENO) finite volume schemes and high-order limiters to ensure the maximum principle or positivity of the various field variables including the density, pressure, and order parameters identifying each phase. The two-component flow model considered besides the Euler equation of gas dynamics consists of advection of two parameters of the stiffened gas equation, characterizing each phase. The design of the high-order limiter is based on limiting the quadrature values of the density, pressure and order parameters reconstructed using a high-order WENO scheme. The convergence and the order of accuracy of the scheme is illustrated using the smooth isentropic vortex problem with very small density and pressure. The effectiveness and robustness of the scheme in computing the challenging problem of shock wave interaction with a cloud of bubbles tightly clustered and placed in a body of liquid is also demonstrated.
Information content and complexity in the high-order organization of DNA.
Minsky, Abraham
2004-01-01
Nucleic acids are characterized by a vast structural variability. Secondary structural conformations include the main polymorphs A, B, and Z, cruciforms, intrinsic curvature, and multistranded motifs. DNA secondary motifs are stabilized and regulated by the primary base sequence, contextual effects, environmental factors, as well as by high-order DNA packaging modes. The high-order modes are, in turn, affected by secondary structures and by the environment. This review is concerned with the flow of structural information among the hierarchical structural levels of DNA molecules, the intricate interplay between the various factors that affect these levels, and the regulation and physiological significance of DNA high-order structures.
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.
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.
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 optimal control of space trajectories with uncertain boundary conditions
NASA Astrophysics Data System (ADS)
Di Lizia, P.; Armellin, R.; Bernelli-Zazzera, F.; Berz, M.
2014-01-01
A high order optimal control strategy is proposed in this work, based on the use of differential algebraic techniques. In the frame of orbital mechanics, differential algebra allows to represent, by high order Taylor polynomials, the dependency of the spacecraft state on initial conditions and environmental parameters. The resulting polynomials can be manipulated to obtain the high order expansion of the solution of two-point boundary value problems. Since the optimal control problem can be reduced to a two-point boundary value problem, differential algebra is used to compute the high order expansion of the solution of the optimal control problem about a reference trajectory. Whenever perturbations in the nominal conditions occur, new optimal control laws for perturbed initial and final states are obtained by the mere evaluation of polynomials. The performances of the method are assessed on lunar landing, rendezvous maneuvers, and a low-thrust Earth-Mars transfer.
Nonadiabatic spectral redshift of high-order harmonics with the help of a VUV pulse
NASA Astrophysics Data System (ADS)
Du, Hongchuan; Xue, Shan; Wang, Huiqiao; Zhang, Zhilei; Hu, Bitao
2015-06-01
We theoretically investigate the nonadiabatic spectral redshift of high-order harmonics with the help of a VUV pulse. It is found that the nonadiabatic spectral redshift of high-order harmonics can be observed when a weak VUV pulse is properly added in the falling part of the fundamental laser due to the nonadiabatic response of the dipole to rapid change of laser intensity. Further time-frequency analysis shows that the high-order harmonics are mainly generated in the falling part of the fundamental pulse. This is because the VUV pulse enhances the ionization in the falling part of the fundamental pulse by the 1s-2p transition of He+ . In addition, this scheme is also used to observe the nonadiabatic spectral blueshift of high-order harmonics by changing the time delay between the fundamental laser and the VUV pulse.
Nonresonant high-order nonlinear optical properties of silver nanoparticles in aqueous solution.
Rativa, Diego; de Araujo, R E; Gomes, A S L
2008-11-10
In this work we determine the third, fifth- and seventh-order nonresonant nonlinear optical properties of silver nanoparticles (9 nm average diameter) colloids in aqueous solution under high intensity excitation. The nonlinear optical response and its dependence with the nanoparticles filling factor was measured and theoretically described. We show that for low inclusion concentration, the third order nonlinearity of the colloid can be described by the generalized Maxwell-Garnett model. With the increase of the nanoparticle concentration, changes in the medium nonlinearities was observed leading to high order effects. The fifth- and seventh- order susceptibilities were obtained for highly concentrated silver nanoparticle colloid and the data was supported by a theoretical model. The conventional Z-scan technique was employed, using 80 f s laser pulses at 800 nm, in a regime of high pulse energy (microJ) and low repetition rate (1 kHz).
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.
High Order Accurate Algorithms for Shocks, Rapidly Changing Solutions and Multiscale Problems
2014-11-13
for front propagation with obstacles, and homotopy method for steady states. Applications include high order simulations for 3D gaseous detonations ...obstacles, and homotopy method for steady states. Applications include high order simulations for 3D gaseous detonations , sound generation study via... detonation waves, Combustion and Flame, (02 2013): 0. doi: 10.1016/j.combustflame.2012.10.002 Yang Yang, Ishani Roy, Chi-Wang Shu, Li-Zhi Fang. THE
Ros-Yanez, Tanya; Ruiz, Daniel; Lopez, Diego; Hilgert, Tom; Dupre, Luc; Vandenberghe, Robert E.; Houbaert, Yvan
2005-05-15
The present work attempts to assess the influence of order phenomena on the magnetostriction of high Fe-Si alloys for electrical applications. The magnetostriction of high silicon electrical steels in the range of 4 to 6 wt. % Si was studied regarding the effect of processing and thermal treatment. In addition, power losses and saturation magnetization measurements were performed and {sup 57}Fe Moessbauer spectroscopy was used to evaluate and quantify the degree of order.
Simultaneous Object Classification and Segmentation with High-Order Multiple Shape Models
2009-05-01
SIMULTANEOUS OBJECT CLASSIFICATION AND SEGMENTATION WITH HIGH-ORDER MULTIPLE SHAPE MODELS By Federico Lecumberry Álvaro Pardo and Guillermo Sapiro...Simultaneous Object Classification and Segmentation with High-Order Multiple Shape Models Federico Lecumberry , Student Member, IEEE, Álvaro Pardo, Member...weighted linear F. Lecumberry is with the Instituto de Ingenierı́a Eléctrica, Facultad de Ingenierı́a, Universidad de la República, Montevideo
A Technique for Removing an Important Class of Trojan Horses from High-Order Languages
1988-01-01
A Technique for Removing an Important Class of Trojan Horses from High Order Languages∗ John McDermott Center for Secure Information Technology...Ken Thompson described a sophisticated Trojan horse attack on a compiler, one that is undetectable by any search of the compiler source code. The...object of the compiler Trojan horse is to modify the semantics of the high order language in a way that breaks the security of a trusted system generated
Fushitani, Mizuho; Hishikawa, Akiyoshi
2016-01-01
We present applications of extreme ultraviolet (XUV) single-order laser harmonics to gas-phase ultrafast photoelectron spectroscopy. Ultrashort XUV pulses at 80 nm are obtained as the 5th order harmonics of the fundamental laser at 400 nm by using Xe or Kr as the nonlinear medium and separated from other harmonic orders by using an indium foil. The single-order laser harmonics is applied for real-time probing of vibrational wavepacket dynamics of I2 molecules in the bound and dissociating low-lying electronic states and electronic-vibrational wavepacket dynamics of highly excited Rydberg N2 molecules. PMID:27795976
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.
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
NASA Astrophysics Data System (ADS)
Christlieb, Andrew J.; Liu, Yuan; Tang, Qi; Xu, Zhengfu
2015-01-01
In this paper, we generalize the maximum-principle-preserving (MPP) flux limiting technique developed by Xu (2013) [20] to a class of high order finite volume weighted essentially non-oscillatory (WENO) schemes for scalar conservation laws and the compressible Euler system on unstructured meshes in one and two dimensions. The key idea of this parameterized limiting technique is to limit the high order numerical flux with a first order flux which preserves the MPP or positivity-preserving (PP) property. The main purpose of this paper is to investigate the flux limiting approach with high order finite volume method on unstructured meshes which are often needed for solving some important problems on irregular domains. Truncation error analysis based on one-dimensional nonuniform meshes is presented to justify that the proposed MPP schemes can maintain third order accuracy in space and time. We also demonstrate through smooth test problems that the proposed third order MPP/PP WENO schemes coupled with a third order Runge-Kutta (RK) method attain the desired order of accuracy. Several test problems containing strong shocks and complex domain geometries are also presented to assess the performance of the schemes.
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.
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.
Convergence of high order perturbative expansions in open system quantum dynamics
NASA Astrophysics Data System (ADS)
Xu, Meng; Song, Linze; Song, Kai; Shi, Qiang
2017-02-01
We propose a new method to directly calculate high order perturbative expansion terms in open system quantum dynamics. They are first written explicitly in path integral expressions. A set of differential equations are then derived by extending the hierarchical equation of motion (HEOM) approach. As two typical examples for the bosonic and fermionic baths, specific forms of the extended HEOM are obtained for the spin-boson model and the Anderson impurity model. Numerical results are then presented for these two models. General trends of the high order perturbation terms as well as the necessary orders for the perturbative expansions to converge are analyzed.
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.
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.
Fast Simulating High Order Models Application to Micro Electro-Mechanical Systems (MEMS)
Yacine, Z.; Benfdila, A.; Djennoune, S.
2009-03-05
The approximation of high order systems by low order models is one of the important problems in system theory. The use of a reduced order model makes it easier to implement analysis, simulations and control system designs. Numerous methods are available in the literature for order reduction of linear continuous systems in time domain as well as in frequency domain. But, this is not the case for non linear systems. The well known Trajectory Piece-Wise Linear approach (TPWL) elaborated to nonlinear model order reduction guarantees a simplification and an accurate representation of the behaviour of strongly non linear systems handling local and global approximation. The present attempt is towards evolving an improvement for the TPWL order reduction technique, which ensures a good quality of approximation combining the advantages of the Krylov subspaces method and the local linearization. We illustrate the technique on a MEMS circuit (Micro Electro-Mechanical System)
Fast Simulating High Order Models Application to Micro Electro-Mechanical Systems (MEMS)
NASA Astrophysics Data System (ADS)
Yacine, Z.; Djennoune, S.; Benfdila, A.
2009-03-01
The approximation of high order systems by low order models is one of the important problems in system theory. The use of a reduced order model makes it easier to implement analysis, simulations and control system designs. Numerous methods are available in the literature for order reduction of linear continuous systems in time domain as well as in frequency domain. But, this is not the case for non linear systems. The well known Trajectory Piece-Wise Linear approach (TPWL) elaborated to nonlinear model order reduction guarantees a simplification and an accurate representation of the behaviour of strongly non linear systems handling local and global approximation. The present attempt is towards evolving an improvement for the TPWL order reduction technique, which ensures a good quality of approximation combining the advantages of the Krylov subspaces method and the local linearization. We illustrate the technique on a MEMS circuit (Micro Electro-Mechanical System).
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)
Lind, S. J.; Stansby, P. K.
2016-12-01
The incompressible Smoothed Particle Hydrodynamics (ISPH) method is derived in Eulerian form with high-order smoothing kernels to provide increased accuracy for a range of steady and transient internal flows. Periodic transient flows, in particular, demonstrate high-order convergence and accuracies approaching, for example, spectral mesh-based methods. The improved accuracies are achieved through new high-order Gaussian kernels applied over regular particle distributions with time stepping formally up to 2nd order for transient flows. The Eulerian approach can be easily extended to model free surface flows by merging from Eulerian to Lagrangian regions in an Arbitrary-Lagrangian-Eulerian (ALE) fashion, and a demonstration with periodic wave propagation is presented. In the long term, it is envisaged that the method will greatly increase the accuracy and efficiency of SPH methods, while retaining the flexibility of SPH in modelling free surface and multiphase flows.
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
Two-dimensional gratings of hexagonal holes for high order diffraction suppression.
Liu, Ziwei; Shi, Lina; Pu, Tanchao; Li, Hailiang; Niu, Jiebin; Wang, Guanya; Xie, Changqing
2017-01-23
We propose two-dimensional gratings comprised of a large number of identical and similarly oriented hexagonal holes for the high order diffraction suppression. An analytical study of the diffraction property for such gratings, based on both square and triangle arrays, is described. The dependence of the high order diffraction property on the hole shape and size is investigated. Notably, theoretical calculation reveals that the 2nd, 3rd and 4th order diffractions adjacent to the 1st order diffraction can be completely suppressed, and the 5th order diffraction efficiency is as low as 0.01%, which will be submerged in the background noise for most practical applications. The 1st order diffraction intensity efficiency 6.93% can be achieved as the hexagonal holes along y-axis connect with each other. For the case of b=P_{y}/3, the 1st order diffraction intensity efficiency is 3.08%. The experimental results are also presented, confirming the theoretical predictions. Especially, our two-dimensional gratings have the ability to form free-standing structures which are highly desired for the x-ray region. Comparing with the grating of the square array, the grating of the triangle array is easy to be fabricated by silicon planar process due to the large spacing between any two adjacent holes. Our results should be of great interest in a wide spectrum unscrambling from the infrared to the x-ray region.
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.
78 FR 65744 - High End Ventures, Inc., Order of Suspension of Trading
Federal Register 2010, 2011, 2012, 2013, 2014
2013-11-01
... From the Federal Register Online via the Government Publishing Office SECURITIES AND EXCHANGE COMMISSION High End Ventures, Inc., Order of Suspension of Trading October 21, 2013. It appears to the... securities of High End Ventures, Inc. because it has not filed any periodic reports since the period...
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.
On shifted Jacobi spectral method for high-order multi-point boundary value problems
NASA Astrophysics Data System (ADS)
Doha, E. H.; Bhrawy, A. H.; Hafez, R. M.
2012-10-01
This paper reports a spectral tau method for numerically solving multi-point boundary value problems (BVPs) of linear high-order ordinary differential equations. The construction of the shifted Jacobi tau approximation is based on conventional differentiation. This use of differentiation allows the imposition of the governing equation at the whole set of grid points and the straight forward implementation of multiple boundary conditions. Extension of the tau method for high-order multi-point BVPs with variable coefficients is treated using the shifted Jacobi Gauss-Lobatto quadrature. Shifted Jacobi collocation method is developed for solving nonlinear high-order multi-point BVPs. The performance of the proposed methods is investigated by considering several examples. Accurate results and high convergence rates are achieved.
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
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.
Rieben, Robert N.
2004-01-01
The goal of this dissertation is two-fold. 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.
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.
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.
NASA Astrophysics Data System (ADS)
Rieben, Robert N.
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.
High-order aberration control during exposure for leading-edge lithography projection optics
NASA Astrophysics Data System (ADS)
Ohmura, Yasuhiro; Tsuge, Yosuke; Hirayama, Toru; Ikezawa, Hironori; Inoue, Daisuke; Kitamura, Yasuhiro; Koizumi, Yukio; Hasegawa, Keisuke; Ishiyama, Satoshi; Nakashima, Toshiharu; Kikuchi, Takahisa; Onda, Minoru; Takase, Yohei; Nagahiro, Akimasa; Isago, Susumu; Kawahara, Hidetaka
2016-03-01
High throughput with high resolution imaging has been key to the development of leading-edge microlithography. However, management of thermal aberrations due to lens heating during exposure has become critical for simultaneous achievement of high throughput and high resolution. Thermal aberrations cause CD drift and overlay error, and these errors lead directly to edge placement errors (EPE). Management and control of high order thermal aberrations is a critical requirement. In this paper, we will show practical performance of the lens heating with dipole and other typical illumination conditions for finer patterning. We confirm that our new control system can reduce the high-order aberrations and enable critical-dimension uniformity CDU during the exposure.
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 aberrations calculation of a hexapole corrector using a differential algebra method
NASA Astrophysics Data System (ADS)
Kang, Yongfeng; Liu, Xing; Zhao, Jingyi; Tang, Tiantong
2017-02-01
A differential algebraic (DA) method is proved as an unusual and effective tool in numerical analysis. It implements conveniently differentiation up to arbitrary high order, based on the nonstandard analysis. In this paper, the differential algebra (DA) method has been employed to compute the high order aberrations up to the fifth order of a practical hexapole corrector including round lenses and hexapole lenses. The program has been developed and tested as well. The electro-magnetic fields of arbitrary point are obtained by local analytic expressions, then field potentials are transformed into new forms which can be operated in the DA calculation. In this paper, the geometric and chromatic aberrations up to fifth order of a practical hexapole corrector system are calculated by the developed program.
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.
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.
Highly ordered self-assembled nanoscale periodic faceting in GaAs(631) homoepitaxial growth
NASA Astrophysics Data System (ADS)
Cruz-Hernández, E.; Shimomura, S.; Méndez-García, V. H.
2012-08-01
We report on the self-assembly of large-order-correlated nanoscale faceting on GaAs(631)A substrates grown by molecular beam epitaxy. The surface morphology of the grown samples as a function of the growth temperature and the As-beam equivalent pressure was studied using atomic force microscopy. A two-dimensional autocorrelation function analysis was performed in order to quantitatively determine the uniformity of the surface corrugation. By optimizing the growth conditions, correlated faceted areas as large as 1.7 × 1.7 μm2 are obtained. The highly ordered surface corrugation discussed here provides useful insights to prepare highly ordered facet planes for the self organized growth of quantum wires.
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.
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 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.
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.
Improved design of high order superconducting gradiometer coils for magnetic monopole detection
Donaldson, G.B.; Bain, R.J.P.
1984-11-01
A family of planar superconducting magnetic gradiometers for use as magnetic monopole detectors has recently been proposed. We describe an alternative system which reduces the number of loop crossovers for a two-dimensional Nth order gradiometer from approximately 2/sup 2N/ to N/sup 2/. This system permits much higher order gradiometers to be used, for a given detector area and superconducting quantum interference device input inductance, resulting in improved signal to noise performance. The simplification of design should also minimize the practical difficulties of fabricating high order gradiometers.
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.
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.
Development of a three-dimensional high-order strand-grids approach
NASA Astrophysics Data System (ADS)
Tong, Oisin
Development of a novel high-order flux correction method on strand grids is presented. The method uses a combination of flux correction in the unstructured plane and summation-by-parts operators in the strand direction to achieve high-fidelity solutions. Low-order truncation errors are cancelled with accurate flux and solution gradients in the flux correction method, thereby achieving a formal order of accuracy of 3, although higher orders are often obtained, especially for highly viscous flows. In this work, the scheme is extended to high-Reynolds number computations in both two and three dimensions. Turbulence closure is achieved with a robust version of the Spalart-Allmaras turbulence model that accommodates negative values of the turbulence working variable, and the Menter SST turbulence model, which blends the k-epsilon and k-o turbulence models for better accuracy. A major advantage of this high-order formulation is the ability to implement traditional finite volume-like limiters to cleanly capture shocked and discontinuous flows. In this work, this approach is explored via a symmetric limited positive (SLIP) limiter. Extensive verification and validation is conducted in two and three dimensions to determine the accuracy and fidelity of the scheme for a number of different cases. Verification studies show that the scheme achieves better than third order accuracy for low and high-Reynolds number flows. Cost studies show that in three-dimensions, the third-order flux correction scheme requires only 30% more walltime than a traditional second-order scheme on strand grids to achieve the same level of convergence. In order to overcome meshing issues at sharp corners and other small-scale features, a unique approach to traditional geometry, coined "asymptotic geometry," is explored. Asymptotic geometry is achieved by filtering out small-scale features in a level set domain through min/max flow. This approach is combined with a curvature based strand shortening
On the dynamics of a high-order Lorenz-Stenflo system
NASA Astrophysics Data System (ADS)
Rech, Paulo C.
2016-12-01
Results presented in a recent paper in this journal concerning a continuous-time dynamical system, namely that involving high-order Lorenz-Stenflo equations, are extended in this paper. More specifically, the present paper reports on nonlinear dynamics of a six-variable, four-parameter high-order Lorenz-Stenflo system. Six cross-sections of a four-dimensional parameter-space are considered. By using Lyapunov exponents spectra to characterize the dynamical behavior at each point of each of these plots, it is shown that different regions are allowed, from equilibrium point to chaos regions. It is also shown that hyperchaos is not an allowed behavior in a high-order Lorenz-Stenflo system. In addition, new results reported here are compared with those obtained for the original Lorenz-Stenflo system.
Polarization control of high order harmonics in the EUV photon energy range.
Vodungbo, Boris; Barszczak Sardinha, Anna; Gautier, Julien; Lambert, Guillaume; Valentin, Constance; Lozano, Magali; Iaquaniello, Grégory; Delmotte, Franck; Sebban, Stéphane; Lüning, Jan; Zeitoun, Philippe
2011-02-28
We report the generation of circularly polarized high order harmonics in the extreme ultraviolet range (18-27 nm) from a linearly polarized infrared laser (40 fs, 0.25 TW) focused into a neon filled gas cell. To circularly polarize the initially linearly polarized harmonics we have implemented a four-reflector phase-shifter. Fully circularly polarized radiation has been obtained with an efficiency of a few percents, thus being significantly more efficient than currently demonstrated direct generation of elliptically polarized harmonics. This demonstration opens up new experimental capabilities based on high order harmonics, for example, in biology and materials science. The inherent femtosecond time resolution of high order harmonic generating table top laser sources renders these an ideal tool for the investigation of ultrafast magnetization dynamics now that the magnetic circular dichroism at the absorption M-edges of transition metals can be exploited.
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.
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.
NASA Astrophysics Data System (ADS)
Zhang, Xiangxiong
2017-01-01
We construct a local Lax-Friedrichs type positivity-preserving flux for compressible Navier-Stokes equations, which can be easily extended to multiple dimensions for generic forms of equations of state, shear stress tensor and heat flux. With this positivity-preserving flux, any finite volume type schemes including discontinuous Galerkin (DG) schemes with strong stability preserving Runge-Kutta time discretizations satisfy a weak positivity property. With a simple and efficient positivity-preserving limiter, high order explicit Runge-Kutta DG schemes are rendered preserving the positivity of density and internal energy without losing local conservation or high order accuracy. Numerical tests suggest that the positivity-preserving flux and the positivity-preserving limiter do not induce excessive artificial viscosity, and the high order positivity-preserving DG schemes without other limiters can produce satisfying non-oscillatory solutions when the nonlinear diffusion in compressible Navier-Stokes equations is accurately resolved.
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.
Overlay control methodology comparison: field-by-field and high-order methods
NASA Astrophysics Data System (ADS)
Huang, Chun-Yen; Chiu, Chui-Fu; Wu, Wen-Bin; Shih, Chiang-Lin; Huang, Chin-Chou Kevin; Huang, Healthy; Choi, DongSub; Pierson, Bill; Robinson, John C.
2012-03-01
Overlay control in advanced integrated circuit (IC) manufacturing is becoming one of the leading lithographic challenges in the 3x and 2x nm process nodes. Production overlay control can no longer meet the stringent emerging requirements based on linear composite wafer and field models with sampling of 10 to 20 fields and 4 to 5 sites per field, which was the industry standard for many years. Methods that have emerged include overlay metrology in many or all fields, including the high order field model method called high order control (HOC), and field by field control (FxFc) methods also called correction per exposure. The HOC and FxFc methods were initially introduced as relatively infrequent scanner qualification activities meant to supplement linear production schemes. More recently, however, it is clear that production control is also requiring intense sampling, similar high order and FxFc methods. The added control benefits of high order and FxFc overlay methods need to be balanced with the increased metrology requirements, however, without putting material at risk. Of critical importance is the proper control of edge fields, which requires intensive sampling in order to minimize signatures. In this study we compare various methods of overlay control including the performance levels that can be achieved.
The costs of ignoring high-order correlations in populations of model neurons.
Michel, Melchi M; Jacobs, Robert A
2006-03-01
Investigators debate the extent to which neural populations use pair-wise and higher-order statistical dependencies among neural responses to represent information about a visual stimulus. To study this issue, three statistical decoders were used to extract the information in the responses of model neurons about the binocular disparities present in simulated pairs of left-eye and right-eye images: (1) the full joint probability decoder considered all possible statistical relations among neural responses as potentially important; (2) the dependence tree decoder also considered all possible relations as potentially important, but it approximated high-order statistical correlations using a computationally tractable procedure; and (3) the independent response decoder, which assumed that neural responses are statistically independent, meaning that all correlations should be zero and thus can be ignored. Simulation results indicate that high-order correlations among model neuron responses contain significant information about binocular disparities and that the amount of this high-order information increases rapidly as a function of neural population size. Furthermore, the results highlight the potential importance of the dependence tree decoder to neuroscientists as a powerful but still practical way of approximating high-order correlations among neural responses.
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
An, Tae Kyu; Kang, Il; Yun, Hui-jun; Cha, Hyojung; Hwang, Jihun; Park, Seonuk; Kim, Jiye; Kim, Yu Jin; Chung, Dae Sung; Kwon, Soon-Ki; Kim, Yun-Hi; Park, Chan Eon
2013-12-23
A facile spin-coating method in which a small percentage of the solvent additive, 1-chloronaphthalene (CN), is found to increase the drying time during film deposition, is reported. The field-effect mobility of a PDPPDBTE film cast from a chloroform-CN mixed solution is 0.46 cm(2) V(-1) s(-1). The addition of CN to the chloroform solution facilitates the formation of highly crystalline polymer structures.
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.
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.
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.
An immersed boundary method for aeroacoustic flow using a high-order finite difference method
NASA Astrophysics Data System (ADS)
Olson, Britton
2016-11-01
An immersed boundary method that achieves second order accuracy in space on acoustic reflection problems is introduced and tested on a number of aero-acoustic related problems. The method follows a continuous forcing approach and uses existing solver operators to smoothly extend the flow solution though the immersed boundary. Both no-slip and free-slip boundary conditions are demonstrated on complex geometries using a high-order finite difference code on a Cartesian grid. High Mach number test problems are also shown, demonstrating the method's robustness in the presence of shock waves.
A high-order Immersed Boundary method for solving fluid problems on arbitrary smooth domains
NASA Astrophysics Data System (ADS)
Stein, David; Guy, Robert; Thomases, Becca
2015-11-01
We present a robust, flexible, and high-order Immersed Boundary method for solving the equations of fluid motion on domains with smooth boundaries using FFT-based spectral methods. The solution to the PDE is coupled with an equation for a smooth extension of the unknown solution; high-order accuracy is a natural consequence of this additional global regularity. The method retains much of the simplicity of the original Immersed Boundary method, and enables the use of simple implicit and implicit/explicit timestepping schemes to be used to solve a wide range of problems. We show results for the Stokes, Navier-Stokes, and Oldroyd-B equations.
A high-order Immersed Boundary method for the simulation of polymeric flow
NASA Astrophysics Data System (ADS)
Stein, David; Thomases, Becca; Guy, Robert
2016-11-01
We present a robust, flexible, and high-order Immersed Boundary method for simulating fluid flow, including the Incompressible Navier-Stokes equations and certain models of viscoelastic flow, e.g. the Stokes-Oldroyd-B equations. The solution to the PDE is coupled with an equation for a smooth extension of the unknown solution; high-order accuracy is a natural consequence of this additional global regularity. Low and zero Reynolds number problems are handled efficiently and accurately. We demonstrate pointwise convergence of the polymeric stress for flows in complex domains, in contrast to the standard Immersed Boundary method, which generates large errors in the polymeric stress near to the boundaries.
Development of high-order harmonic focusing system based on ellipsoidal mirror.
Motoyama, H; Sato, T; Iwasaki, A; Takei, Y; Kume, T; Egawa, S; Hiraguri, K; Hashizume, H; Yamanouchi, K; Mimura, H
2016-05-01
We have developed a focusing system for extreme ultraviolet light produced by high-order harmonic generation. An ellipsoidal mirror with a precise surface shape was fabricated and installed into the focusing system. A rigid mirror manipulator and a beam profiler were employed to perform precise and stable mirror alignment. As a demonstration of the focusing performance, high-order harmonics in the wavelength range of 13.5-19.5 nm were successfully focused into a 2.4 × 2.3 μm(2) spot.
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
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.
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 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.
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.
Quasi-phase-matched high-order harmonic generation using tunable pulse trains.
O'Keeffe, Kevin; Lloyd, David T; Hooker, Simon M
2014-04-07
A simple technique for generating trains of ultrafast pulses is demonstrated in which the linear separation between pulses can be varied continuously over a wide range. These pulse trains are used to achieve tunable quasi-phase-matching of high harmonic generation over a range of harmonic orders up to the harmonic cut-off, resulting in enhancements of the harmonic intensity in excess of an order of magnitude. The peak enhancement of the harmonics is clearly shown to depend on the separation between pulses, as well as the number of pulses in the train, representing an easily tunable source of quasi-phase-matched high harmonic generation.
Fast Growth of Highly Ordered TiO2 Nanotube Arrays on Si Substrate under High-Field Anodization
NASA Astrophysics Data System (ADS)
Song, Jingnan; Zheng, Maojun; Zhang, Bin; Li, Qiang; Wang, Faze; Ma, Liguo; Li, Yanbo; Zhu, Changqing; Ma, Li; Shen, Wenzhong
2017-04-01
Highly ordered TiO2 nanotube arrays (NTAs) on Si substrate possess broad applications due to its high surface-to-volume ratio and novel functionalities, however, there are still some challenges on facile synthesis. Here, we report a simple and cost-effective high-field (90-180 V) anodization method to grow highly ordered TiO2 NTAs on Si substrate, and investigate the effect of anodization time, voltage, and fluoride content on the formation of TiO2 NTAs. The current density-time curves, recorded during anodization processes, can be used to determine the optimum anodization time. It is found that the growth rate of TiO2 NTAs is improved significantly under high field, which is nearly 8 times faster than that under low fields (40-60 V). The length and growth rate of the nanotubes are further increased with the increase of fluoride content in the electrolyte.
Bernerd, Francoise; Marionnet, Claire; Duval, Christine
2012-06-01
Cutaneous damages such as sunburn, pigmentation, and photoaging are known to be induced by acute as well as repetitive sun exposure. Not only for basic research, but also for the design of the most efficient photoprotection, it is crucial to understand and identify the early biological events occurring after ultraviolet (UV) exposure. Reconstructed human skin models provide excellent and reliable in vitro tools to study the UV-induced alterations of the different skin cell types, keratinocytes, fibroblasts, and melanocytes in a dose- and time-dependent manner. Using different in vitro human skin models, the effects of UV light (UVB and UVA) were investigated. UVB-induced damages are essentially epidermal, with the typical sunburn cells and DNA lesions, whereas UVA radiation-induced damages are mostly located within the dermal compartment. Pigmentation can also be obtained after solar simulated radiation exposure of pigmented reconstructed skin model. Those models are also highly adequate to assess the potential of sunscreens to protect the skin from UV-associated damage, sunburn reaction, photoaging, and pigmentation. The results showed that an effective photoprotection is provided by broad-spectrum sunscreens with a potent absorption in both UVB and UVA ranges.
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.
Adaptive two-pass rank order filter to remove impulse noise in highly corrupted images.
Xu, Xiaoyin; Miller, Eric L; Chen, Dongbin; Sarhadi, Mansoor
2004-02-01
In this paper, we present an adaptive two-pass rank order filter to remove impulse noise in highly corrupted images. When the noise ratio is high, rank order filters, such as the median filter for example, can produce unsatisfactory results. Better results can be obtained by applying the filter twice, which we call two-pass filtering. To further improve the performance, we develop an adaptive two-pass rank order filter. Between the passes of filtering, an adaptive process is used to detect irregularities in the spatial distribution of the estimated impulse noise. The adaptive process then selectively replaces some pixels changed by the first pass of filtering with their original observed pixel values. These pixels are then kept unchanged during the second filtering. In combination, the adaptive process and the second filter eliminate more impulse noise and restore some pixels that are mistakenly altered by the first filtering. As a final result, the reconstructed image maintains a higher degree of fidelity and has a smaller amount of noise. The idea of adaptive two-pass processing can be applied to many rank order filters, such as a center-weighted median filter (CWMF), adaptive CWMF, lower-upper-middle filter, and soft-decision rank-order-mean filter. Results from computer simulations are used to demonstrate the performance of this type of adaptation using a number of basic rank order filters.
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.
Evaluation of Euler fluxes by a high-order CFD scheme: shock instability
NASA Astrophysics Data System (ADS)
Tu, Guohua; Zhao, Xiaohui; Mao, Meiliang; Chen, Jianqiang; Deng, Xiaogang; Liu, Huayong
2014-05-01
The construction of Euler fluxes is an important step in shock-capturing/upwind schemes. It is well known that unsuitable fluxes are responsible for many shock anomalies, such as the carbuncle phenomenon. Three kinds of flux vector splittings (FVSs) as well as three kinds of flux difference splittings (FDSs) are evaluated for the shock instability by a fifth-order weighted compact nonlinear scheme. The three FVSs are Steger-Warming splitting, van Leer splitting and kinetic flux vector splitting (KFVS). The three FDSs are Roe's splitting, advection upstream splitting method (AUSM) type splitting and Harten-Lax-van Leer (HLL) type splitting. Numerical results indicate that FVSs and high dissipative FDSs undergo a relative lower risk on the shock instability than that of low dissipative FDSs. However, none of the fluxes evaluated in the present study can entirely avoid the shock instability. Generally, the shock instability may be caused by any of the following factors: low dissipation, high Mach number, unsuitable grid distribution, large grid aspect ratio, and the relative shock-internal flow state (or position) between upstream and downstream shock waves. It comes out that the most important factor is the relative shock-internal state. If the shock-internal state is closer to the downstream state, the computation is at higher susceptibility to the shock instability. Wall-normal grid distribution has a greater influence on the shock instability than wall-azimuthal grid distribution because wall-normal grids directly impact on the shock-internal position. High shock intensity poses a high risk on the shock instability, but its influence is not as much as the shock-internal state. Large grid aspect ratio is also a source of the shock instability. Some results of a second-order scheme and a first-order scheme are also given. The comparison between the high-order scheme and the two low-order schemes indicates that high-order schemes are at a higher risk of the shock
Unconventional charge order in a co-doped high-Tc superconductor
NASA Astrophysics Data System (ADS)
Pelc, D.; Vučković, M.; Grafe, H.-J.; Baek, S.-H.; Požek, M.
2016-09-01
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.
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.
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
Second-order hot image from a scatterer in high-power laser systems
Xie Liangping; Zhao Jianlin; Jing Feng
2005-05-01
A theory is developed for predicting a second-order hot-image formation in high-power laser systems. Light diffracted from a small optical scatterer interferes with an intense original wave in the nonlinear medium to produce a hologram like a Fresnel-zone plate. The theoretical model shows that the hologram produces a negative first-order diffractive wave focused to the traditional hot image and negative second-order diffraction that causes another intense image, namely, a second-order hot image. It is found by analysis that the location of the second-order hot image arises in a downstream plane with a half-distance from the medium to the scatterer. Results of the numerical calculations show that the peak intensity of the nonlinear image may reach a level high enough to damage optical components with the increase of the breakup integral (B integral), indicating that the image may also potentially damage expensive optical components in high-power laser systems.
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
Prediction model of sinoatrial node field potential using high order partial least squares.
Feng, Yu; Cao, Hui; Zhang, Yanbin
2015-01-01
High order partial least squares (HOPLS) is a novel data processing method. It is highly suitable for building prediction model which has tensor input and output. The objective of this study is to build a prediction model of the relationship between sinoatrial node field potential and high glucose using HOPLS. The three sub-signals of the sinoatrial node field potential made up the model's input. The concentration and the actuation duration of high glucose made up the model's output. The results showed that on the premise of predicting two dimensional variables, HOPLS had the same predictive ability and a lower dispersion degree compared with partial least squares (PLS).
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
A high order characteristic discontinuous Galerkin scheme for advection on unstructured meshes
NASA Astrophysics Data System (ADS)
Lee, D.; Lowrie, R.; Petersen, M.; Ringler, T.; Hecht, M.
2016-11-01
A new characteristic discontinuous Galerkin (CDG) advection scheme is presented. In contrast to standard discontinuous Galerkin schemes, the test functions themselves follow characteristics in order to ensure conservation and the edges of each element are also traced backwards along characteristics in order to create a swept region, which is integrated in order to determine the mass flux across the edge. Both the accuracy and performance of the scheme are greatly improved by the use of large Courant-Friedrichs-Lewy numbers for a shear flow test case and the scheme is shown to scale sublinearly with the number of tracers being advected, outperforming a standard flux corrected transport scheme for 10 or more tracers with a linear basis. Moreover the CDG scheme may be run to arbitrarily high order spatial accuracy and on unstructured grids, and is shown to give the correct order of error convergence for piecewise linear and quadratic bases on regular quadrilateral and hexahedral planar grids. Using a modal Taylor series basis, the scheme may be made monotone while preserving conservation with the use of a standard slope limiter, although this reduces the formal accuracy of the scheme to first order. The second order scheme is roughly as accurate as the incremental remap scheme with nonlocal gradient reconstruction at half the horizontal resolution. The scheme is being developed for implementation within the Model for Prediction Across Scales (MPAS) Ocean model, an unstructured grid finite volume ocean model.
Molecular order in high-efficiency polymer/fullerene bulk heterojunction solar cells.
Hammond, Matthew R; Kline, R Joseph; Herzing, Andrew A; Richter, Lee J; Germack, David S; Ro, Hyun-Wook; Soles, Christopher L; Fischer, Daniel A; Xu, Tao; Yu, Luping; Toney, Michael F; Delongchamp, Dean M
2011-10-25
We report quantitative measurements of ordering, molecular orientation, and nanoscale morphology in the active layer of bulk heterojunction (BHJ) organic photovoltaic cells based on a thieno[3,4-b]thiophene-alt-benzodithiophene copolymer (PTB7), which has been shown to yield very high power conversion efficiency when blended with [6,6]-phenyl-C71-butyric acid methyl ester (PC(71)BM). A surprisingly low degree of order was found in the polymer-far lower in the bulk heterojunction than in pure PTB7. X-ray diffraction data yielded a nearly full orientation distribution for the polymer π-stacking direction within well-ordered regions, revealing a moderate preference for π-stacking in the vertical direction ("face-on"). By combining molecular orientation information from polarizing absorption spectroscopies with the orientation distribution of ordered material from diffraction, we propose a model describing the PTB7 molecular orientation distribution (ordered and disordered), with the fraction of ordered polymer as a model parameter. This model shows that only a small fraction (≈20%) of the polymer in the PTB7/PC(71)BM blend is ordered. Energy-filtered transmission electron microscopy shows that the morphology of PTB7/PC(71)BM is composed of nanoscale fullerene-rich aggregates separated by polymer-rich regions. The addition of diiodooctane (DIO) to the casting solvent, as a processing additive, results in smaller domains and a more finely interpenetrating BHJ morphology, relative to blend films cast without DIO.
ESR study of order and dynamics in lecithin liposomes with high cholesterol content
NASA Astrophysics Data System (ADS)
Costanzo, R.; De Paoli, T.; Ihlo, J. E.; Hager, A. A.; Farach, H. A.; Poole, C. P.; Knight, J. M.
1994-02-01
Previous studies have shown that increasing amounts of cholesterol in phosphatidyl choline liposomes (involving cholesterol/lecithin ratios up to 1), produce an increase in order and a decrease in mobility of the phospholipids in the bilayer. The present work focuses on the order and dynamics of the phospholipids in soybean and egg yolk liposomes with cholesterol/lecithin (chol/lec) ratios as high as 2. The influence of cholesterol on the order parameter and correlation times of 5-, 12- and 16-doxyl stearic acid probes, is analyzed for both types of liposomes. The order parameter increases continuously with the increase of the amount of cholesterol although the correlation time at first increases, then it levels off at a chol/lec ratio of 1, and thereafter shows a small, gradual decrease up to a ratio of 2. A statistical model of cholesterol substitution on the lecithin lattice was employed to explain the correlation time results.
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.
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.
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.
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
High-order finite-volume methods for the shallow-water equations on the sphere
NASA Astrophysics Data System (ADS)
Ullrich, Paul A.; Jablonowski, Christiane; van Leer, Bram
2010-08-01
This paper presents a third-order and fourth-order finite-volume method for solving the shallow-water equations on a non-orthogonal equiangular cubed-sphere grid. Such a grid is built upon an inflated cube placed inside a sphere and provides an almost uniform grid point distribution. The numerical schemes are based on a high-order variant of the Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) pioneered by van Leer. In each cell the reconstructed left and right states are either obtained via a dimension-split piecewise-parabolic method or a piecewise-cubic reconstruction. The reconstructed states then serve as input to an approximate Riemann solver that determines the numerical fluxes at two Gaussian quadrature points along the cell boundary. The use of multiple quadrature points renders the resulting flux high-order. Three types of approximate Riemann solvers are compared, including the widely used solver of Rusanov, the solver of Roe and the new AUSM +-up solver of Liou that has been designed for low-Mach number flows. Spatial discretizations are paired with either a third-order or fourth-order total-variation-diminishing Runge-Kutta timestepping scheme to match the order of the spatial discretization. The numerical schemes are evaluated with several standard shallow-water test cases that emphasize accuracy and conservation properties. These tests show that the AUSM +-up flux provides the best overall accuracy, followed closely by the Roe solver. The Rusanov flux, with its simplicity, provides significantly larger errors by comparison. A brief discussion on extending the method to arbitrary order-of-accuracy is included.
Platonenko, Viktor T
2001-01-31
The amplitudes of harmonics of the atomic response are determined as functions of the intensity of the pump light wave within the range of intensities of 4.9x10{sup 13} - 2.1x10{sup 14} W cm{sup -2} through the numerical solution of the Schrodinger equation for a hydrogen atom in an oscillating electric field. For the amplitudes of harmonics starting from the 5th up to at least the 55th order, these dependences display a deep modulation. Generation of high-order harmonics is analysed within the framework of semiclassical theory including several factors that were ignored in earlier studies. Relatively simple formulas for the amplitudes of high-order harmonics are derived. These formulas agree well with the results of numerical simulations in the range of tunnelling ionisation and provide a satisfactory agreement with numerical simulations in the range of barrier-suppression ionisation. (nonlinear optical phenomena)
Monitoring in a predator-prey systems via a class of high order observer design.
Mata-Machuca, Juan Luis; Martínez-Guerra, Rafael; Aguilar-López, Ricardo
2010-04-01
The goal of this work is the monitoring of the corresponding species in a class of predator-prey systems, this issue is important from the ecology point of view to analyze the population dynamics. The above is done via a nonlinear observer design which contains on its structure a high order polynomial form of the estimation error. A theoretical frame is provided in order to show the convergence characteristics of the proposed observer, where it can be concluded that the performance of the observer is improved as the order of the polynomial is high. The proposed methodology is applied to a class of Lotka-Volterra systems with two and three species. Finally, numerical simulations present the performance of the proposed observer.
An a posteriori-driven adaptive Mixed High-Order method with application to electrostatics
NASA Astrophysics Data System (ADS)
Di Pietro, Daniele A.; Specogna, Ruben
2016-12-01
In this work we propose an adaptive version of the recently introduced Mixed High-Order method and showcase its performance on a comprehensive set of academic and industrial problems in computational electromagnetism. The latter include, in particular, the numerical modeling of comb-drive and MEMS devices. Mesh adaptation is driven by newly derived, residual-based error estimators. The resulting method has several advantageous features: It supports fairly general meshes, it enables arbitrary approximation orders, and has a moderate computational cost thanks to hybridization and static condensation. The a posteriori-driven mesh refinement is shown to significantly enhance the performance on problems featuring singular solutions, allowing to fully exploit the high-order of approximation.
Integration of single-crystalline nanocolumns into highly ordered nanopore arrays
NASA Astrophysics Data System (ADS)
Ding, G. Q.; Shen, W. Z.; Zheng, M. J.; Zhou, Z. B.
2006-05-01
The arrangement of nanostructures into desired well-ordered architectures is crucial for the realization of functional nanodevices and has been the focus of current nanotechnology. Existing physical and chemical approaches have the ability to assemble nanostructures, but it is still a challenge to arrange basic nanostructures into a highly ordered designed pattern. Here, we report a novel method to integrate tin-doped indium oxide single-crystalline nanocolumns into highly ordered two-dimensional nanopore patterns through radio-frequency magnetron sputtering by the aid of porous alumina membranes (PAMs). We have further demonstrated that the morphology of the assembled nanopore arrays is controllable by adjusting either the PAM configurations or sputtering conditions. Our present method provides the possibility of a general approach for nanounit integration, and these assembled regular nanopore arrays pave the way for the application of novel filters and sensors.
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.
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.
Gravitational waves from the first order phase transition of the Higgs field at high energy scales
NASA Astrophysics Data System (ADS)
Jinno, Ryusuke; Nakayama, Kazunori; Takimoto, Masahiro
2016-02-01
In a wide class of new physics models, there exist scalar fields that obtain vacuum expectation values of high energy scales. We study the possibility that the standard model Higgs field has experienced first order phase transition at the high energy scale due to the couplings with these scalar fields. We estimate the amount of gravitational waves produced by the phase transition, and discuss observational consequences.
Performance-Based Task Assessment of Higher-Order Proficiencies in Redesigned STEM High Schools
ERIC Educational Resources Information Center
Ernst, Jeremy V.; Glennie, Elizabeth; Li, Songze
2017-01-01
This study explored student abilities in applying conceptual knowledge when presented with structured performance tasks. Specifically, the study gauged proficiency in higher-order applications of students enrolled in earth and environmental science or biology. The student sample was drawn from a Redesigned STEM high school model where a tested…
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.
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.
ERIC Educational Resources Information Center
Tanujaya, Benidiktus
2016-01-01
The purpose of this research was to develop an instrument that can be used to measure higher-order thinking skills (HOTS) in mathematics instruction of high school students. This research was conducted using a standard procedure of instrument development, from the development of conceptual definitions, development of operational definitions,…
Photonic generation of high order uniform QAM signals based on IQ modulators
NASA Astrophysics Data System (ADS)
Zhao, Qiang
2016-01-01
A pre-distortion algorithm of generating driving signals was proposed for high-order QAM modulation based on IQ modulator. IQ modulator working in the nonlinear area and driving by non-uniform signals was employed. The pre-distorted driving signal requires lower signal-to-noise ratio than the common uniform driving signal in QAM modulation.
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…
Filamentation of arbitrary polarized femtosecond laser pulses in case of high-order Kerr effect.
Panov, Nikolay A; Makarov, Vladimir A; Fedorov, Vladimir Y; Kosareva, Olga G
2013-02-15
We developed a model of femtosecond filamentation which includes high-order Kerr effect and an arbitrary polarization of a laser pulse. We show that a circularly polarized pulse has maximum filament intensity. Also, we show that, independently of the initial pulse polarization, the value of a maximum filament intensity tends to the maximum intensity of either linearly or circularly polarized pulse.
Marker Re-Distancing and Sharp Reconstruction for High-Order Multi-Material Interface Evolution
NASA Astrophysics Data System (ADS)
Nourgaliev, Robert; Greene, Patrick; Schofield, Sam
2016-11-01
A new method for high-order front evolution on arbitrary meshes is introduced. The method is a hybrid of a Lagrangian marker tracking with a Discontinuous Galerkin projection based level set re-distancing. This Marker-Re-Distancing (MRD) method is designed to work accurately and robustly on unstructured, generally highly distorted meshes, necessitated by applications within ALE-based hydro-codes. Since no PDE is solved for re-distancing, the method does not have stability time step restrictions, which is particularly useful in combination with AMR, used here to efficiently resolve fine interface features. A high-order (implemented up to the 6th-order) level set approach is utilized for a new sharp treatment of mix elements, which reconstructs multiple-per-element solution fields (one for each material present in the mix element). Reconstruction incorporates interfacial jump conditions, which are enforced in the least-squares sense at the interfacial marker positions provided by MRD. Since no explicit differentiation across the interface is involved in the assembly of residuals for mass, momentum and energy equations, the method is capable of capturing discontinuous solutions at multi-material interfaces with high order, and without Gibbs oscillations. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
2007-12-06
problems studied in this project involve numerically solving partial differential equations with either discontinuous or rapidly changing solutions ...REPORT Algorithm Development and Application of High Order Numerical Methods for Shocked and Rapid Changing Solutions 14. ABSTRACT 16. SECURITY...discontinuous Galerkin finite element methods, for solving partial differential equations with discontinuous or rapidly changing solutions . Algorithm
High-order Hybridized Discontinuous Galerkin methods for Large-Eddy Simulation
NASA Astrophysics Data System (ADS)
Fernandez, Pablo; Nguyen, Ngoc-Cuong; Peraire, Jaime
2016-11-01
With the increase in computing power, Large-Eddy Simulation emerges as a promising technique to improve both knowledge of complex flow physics and reliability of flow predictions. Most LES works, however, are limited to simple geometries and low Reynolds numbers due to high computational cost. While most existing LES codes are based on 2nd-order finite volume schemes, the efficient and accurate prediction of complex turbulent flows may require a paradigm shift in computational approach. This drives a growing interest in the development of Discontinuous Galerkin (DG) methods for LES. DG methods allow for high-order, conservative implementations on complex geometries, and offer opportunities for improved sub-grid scale modeling. Also, high-order DG methods are better-suited to exploit modern HPC systems. In the spirit of making them more competitive, researchers have recently developed the hybridized DG methods that result in reduced computational cost and memory footprint. In this talk we present an overview of high-order hybridized DG methods for LES. Numerical accuracy, computational efficiency, and SGS modeling issues are discussed. Numerical results up to Re=460k show rapid grid convergence and excellent agreement with experimental data at moderate computational cost.
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.
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
Liu, Yong; Lan, Kun; Bagabas, Abdulaziz A; Zhang, Pengfei; Gao, Wenjun; Wang, Jingxiu; Sun, Zhenkun; Fan, Jianwei; Elzatahry, Ahmed A; Zhao, Dongyuan
2016-02-17
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).
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.
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
2016-07-19
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.
2016-07-19
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 (T_{c}) 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 T_{c} 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 (T_{c} ≤ 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-T_{c} phase above 6 GPa. In conclusion, the obtained phase diagram highlights unique features of FeSe among iron-based superconductors, but bears some resemblance to that of high-T_{c} cuprates.
Sun, J. P.; Matsuura, K.; Ye, G. Z.; ...
2016-07-19
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,more » 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. In conclusion, the obtained phase diagram highlights unique features of FeSe among iron-based superconductors, but bears some resemblance to that of high-Tc cuprates.« less
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
NASA Astrophysics Data System (ADS)
Miyazaki, Narumasa; Lo, Yu-Chieh; Wakeda, Masato; Ogata, Shigenobu
2016-08-01
We applied gigapascal-level compressive hydrostatic pressure to the melt-quenching process of metallic glass to obtain a unique high-pressure glass state with high density that is well-ordered yet has high energy. This state contradicts the common understanding that high-density, well-ordered metallic glass states have low energy. Through molecular dynamics simulations, we found that the high-pressure glass state of the metallic glass Zr50Cu40Al10 has a rich anti-free volume and that its relaxation is dominated by the annihilation of full icosahedra and the rich anti-free volume. The aging rate of the high-pressure metallic glass state (energy reduction rate) is almost the same as that of typical high-energy metallic glass, suggesting that it has a lifetime similar to that of a typical high-energy metallic glass that has been experimentally realized and reported previously [Wakeda et al., Sci. Rep. 5, 10545 (2015)]. Thus, the high-pressure phase can be realized even under the experimental cooling rate, suggesting its suitability for practical applications.
On the freestream preservation of high-order conservative flux-reconstruction schemes
NASA Astrophysics Data System (ADS)
Abe, Yoshiaki; Haga, Takanori; Nonomura, Taku; Fujii, Kozo
2015-01-01
The appropriate procedure for constructing the symmetric conservative metric is presented with which both the freestream preservation and global conservation properties are satisfied in the high-order conservative flux-reconstruction scheme on a three-dimensional stationary-curvilinear grid. A freestream preservation test is conducted, and the symmetric conservative metric constructed by the appropriate procedure preserves the freestream regardless of the order of shape functions, while other metrics cannot always preserve the freestream. Also a convecting vortex is computed on three-dimensional wavy grids, and the formal order of accuracy is achieved when the symmetric conservative metric is appropriately constructed, while it is not when they are inappropriately constructed. In addition, although the sufficient condition for the freestream preservation with the nonconservative (cross product form) metric was reported in the previous study to be that the order of solution polynomial has to be greater than or equal to the twice of the order of a shape function, a special case is newly found in the present study: when the Radau polynomial is used for the correction function, the freestream is preserved even if the solution order is lower than the known condition. Using the properties of Legendre polynomials, the mechanism for this special case is analytically explained, considering the cancellation of aliasing errors.
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.
Violi, Ianina L; Perez, M Dolores; Fuertes, M Cecilia; Soler-Illia, Galo J A A
2012-08-01
Highly porous (V(mesopore) = 25-50%) and ordered mesoporous titania thin films (MTTF) were prepared on ITO (indium tin oxide)-covered glass by a fast two-step method. The effects of substrate surface modification and thermal treatment on pore order, accessibility and crystallinity of the MTTF were systematically studied for MTTF deposited onto bare and titania-modified ITO. MTTF exposed briefly to 550 °C resulted in highly ordered films with grid-like structures, enlarged pore size, and increased accessible pore volume when prepared onto the modified ITO substrate. Mesostructure collapse and no significant change in pore volume were observed for MTTF deposited on bare ITO substrates. Highly crystalline anatase was obtained for MTTF prepared on the modified-ITO treated at high temperatures, establishing the relationship between grid-like structures and titania crystallization. Photocatalytic activity was maximized for samples with increased crystallization and high accessible pore volume. In this manner, a simple way of designing materials with optimized characteristics for optoelectronic applications was achieved through the modification of the ITO surface and a controlled thermal treatment.
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.
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.
Selective suppression of high-order harmonics within phase-matched spectral regions.
Lerner, Gavriel; Diskin, Tzvi; Neufeld, Ofer; Kfir, Ofer; Cohen, Oren
2017-04-01
Phase matching in high-harmonic generation leads to enhancement of multiple harmonics. It is sometimes desired to control the spectral structure within the phase-matched spectral region. We propose a scheme for selective suppression of high-order harmonics within the phase-matched spectral region while weakly influencing the other harmonics. The method is based on addition of phase-mismatched segments within a phase-matched medium. We demonstrate the method numerically in two examples. First, we show that one phase-mismatched segment can significantly suppress harmonic orders 9, 15, and 21. Second, we show that two phase-mismatched segments can efficiently suppress circularly polarized harmonics with one helicity over the other when driven by a bi-circular field. The new method may be useful for various applications, including the generation of highly helical bright attosecond pulses.
A high-order discontinuous Galerkin method for unsteady advection-diffusion problems
NASA Astrophysics Data System (ADS)
Borker, Raunak; Farhat, Charbel; Tezaur, Radek
2017-03-01
A high-order discontinuous Galerkin method with Lagrange multipliers is presented for the solution of unsteady advection-diffusion problems in the high Péclet number regime. It operates directly on the second-order form of the governing equation and does not require any stabilization. Its spatial basis functions are chosen among the free-space solutions of the homogeneous form of the partial differential equation obtained after time-discretization. It also features Lagrange multipliers for enforcing a weak continuity of the approximated solution across the element interface boundaries. This leads to a system of differential-algebraic equations which are time-integrated by an implicit family of schemes. The numerical stability of these schemes and the well-posedness of the overall discretization method are supported by a theoretical analysis. The performance of this method is demonstrated for various high Péclet number constant-coefficient model flow problems.
Strong-field ionization via a high-order Coulomb-corrected strong-field approximation
NASA Astrophysics Data System (ADS)
Klaiber, Michael; Daněk, Jiří; Yakaboylu, Enderalp; Hatsagortsyan, Karen Z.; Keitel, Christoph H.
2017-02-01
Signatures of the Coulomb corrections in the photoelectron momentum distribution during laser-induced ionization of atoms or ions in tunneling and multiphoton regimes are investigated analytically in the case of a one-dimensional problem. A high-order Coulomb-corrected strong-field approximation is applied, where the exact continuum state in the S matrix is approximated by the eikonal Coulomb-Volkov state including the second-order corrections to the eikonal. Although without high-order corrections our theory coincides with the known analytical R -matrix (ARM) theory, we propose a simplified procedure for the matrix element derivation. Rather than matching the eikonal Coulomb-Volkov wave function with the bound state as in the ARM theory to remove the Coulomb singularity, we calculate the matrix element via the saddle-point integration method by time as well as by coordinate, and in this way avoiding the Coulomb singularity. The momentum shift in the photoelectron momentum distribution with respect to the ARM theory due to high-order corrections is analyzed for tunneling and multiphoton regimes. The relation of the quantum corrections to the tunneling delay time is discussed.
NASA Astrophysics Data System (ADS)
Guo, Yan; Xiong, Tao; Shi, Yufeng
2014-10-01
In this paper, a positivity-preserving fifth-order finite volume compact-WENO scheme is proposed for solving compressible Euler equations. As it is known, conservative compact finite volume schemes have high resolution properties while WENO (Weighted Essentially Non-Oscillatory) schemes are essentially non-oscillatory near flow discontinuities. We extend the idea of WENO schemes to some classical finite volume compact schemes [30], where lower order compact stencils are combined with WENO nonlinear weights to get a higher order finite volume compact-WENO scheme. The newly developed positivity-preserving limiter [43,42] is used to preserve positive density and internal energy for compressible Euler equations of fluid dynamics. The HLLC (Harten, Lax, and van Leer with Contact) approximate Riemann solver [37,4] is used to get the numerical flux at the cell interfaces. Numerical tests are presented to demonstrate the high-order accuracy, positivity-preserving, high-resolution and robustness of the proposed scheme.
Vector Brillouin optical time-domain analyzer for high-order acoustic modes.
Dossou, Michel; Bacquet, Denis; Szriftgiser, Pascal
2010-11-15
Thanks to a double-frequency phase modulation scheme, we report a vector Brillouin optical time-domain analyzer (BOTDA). This BOTDA has a high immunity level to noise, and it features a phase spectrogram capability. It is well suited for complex situations involving several acoustic resonances, such as high-order longitudinal modes. It has notably been used to characterize a dispersion-shifted fiber, allowing us to report spectrograms with multiple acoustic resonances. A very high 57 dB dynamic range is also reported for 100-ns-long pulses simultaneously with a 16 cm numerical resolution.
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.
High order mode beam waveguide for technological medium power millimeter wave applications
Rio, C. del; Gonzalo, R.; Marin, M.; Sorolla, M.; Moebius, A.; Thumm, M.
1995-12-31
The use of medium power millimeter CW gyrotrons (10-30 kW and 30-100 GHz) has several potential applications in advanced materials processing. Since a stochastic field distribution in the applicator is desirable no pencil beam is necessary. Then the possibility to couple the circular symmetric gyrotron output to a higher order free space mode can be considered. Beam waveguides based on iterative reflection of such high order beams on properly disigned mirrors opens the possibility to increase the efficiency and to reduce costs of present compact transmission lines in gyrotron technological systems.
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.
Goyal, Amit , Kang; Sukill, [Knoxville, TN
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.
A comparison of two formulations for high-order accurate essentially non-oscillatory schemes
NASA Technical Reports Server (NTRS)
Casper, Jay; Shu, Chi-Wang; Atkins, H. L.
1993-01-01
The finite-volume and finite-difference implementations of high-order accurate essentially non-oscillatory shock-capturing schemes are discussed and compared. Results obtained with fourth-order accurate algorithms based on both formulations are examined for accuracy, sensitivity to grid irregularities, resolution of waves that are oblique to the mesh, and computational efficiency. Some algorithm modifications that may be required for a given application are suggested. Conclusions that pertain to the relative merits of both formulations are drawn, and some circumstances for which each might be useful are noted.
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.
Optimum plasma conditions for the efficient high-order harmonic generation in platinum plasma
Ganeev, Rashid A.; Elouga Bom, Luc B.; Kieffer, Jean-Claude; Ozaki, Tsuneyuki
2007-06-15
We studied the optimum plasma conditions that are required for efficient high-order harmonic generation in platinum plume. Harmonics up to the 49th order ({lambda}=16.32 nm) are analyzed under various conditions of laser-plasma interaction. Time-resolved ultraviolet spectra of platinum plasma at both optimum and nonoptimum conditions of harmonic generation are presented. We calculated the ionization states of the plasma, free electron density, and singly charged ion density at different prepulse intensities and compared them with experimental results.
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.
High-Order Entropy-Based Closures for Linear Transport in Slab Geometries
Hauck, Cory D
2011-01-01
We compute, for the first time, high-order entropy-based ($M_N$) models for a linear transport equation on a one-dimensional, slab geometry. We simulate two test problems from the literature: the two-beam instability and the plane-source problem. In the former case we compute solutions for systems up to order $N=5$ ; in the latter, up to $N=15$. The most notable outcome of these results is the existence of shocks in the steady-state profiles of the two-beam instability for all odd values of $N$.
High-order wide-band frequency domain identification using composite curve fitting
NASA Technical Reports Server (NTRS)
Bayard, D. S.
1992-01-01
A method is presented for curve fitting nonparametric frequency domain data so as to identify a parametric model composed of two models in parallel, where each model has dynamics in a specified portion of the frequency band. This decomposition overcomes the problem of numerical sensitivity since lower order polynomials can be used compared to existing methods which estimate the model as a single entity. Consequently, composite curve fitting is useful for frequency domain identification of high-order systems and/or systems whose dynamics are spread over a large bandwidth. The approach can be extended to identify an arbitrary number of parallel subsystems in specified frequency regimes.
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.
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
Zeng, Zhaoli; Qu, Xueming; Tan, Yidong; Tan, Runtao; Zhang, Shulian
2015-06-29
A simple and high-accuracy self-mixing interferometer based on single high-order orthogonally polarized feedback effects is presented. The single high-order feedback effect is realized when dual-frequency laser reflects numerous times in a Fabry-Perot cavity and then goes back to the laser resonator along the same route. In this case, two orthogonally polarized feedback fringes with nanoscale resolution are obtained. This self-mixing interferometer has the advantages of higher sensitivity to weak signal than that of conventional interferometer. In addition, two orthogonally polarized fringes are useful for discriminating the moving direction of measured object. The experiment of measuring 2.5nm step is conducted, which shows a great potential in nanometrology.
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.
Bayati, Basil S; Eckhoff, Philip A
2012-12-01
We perform a high-order analytical expansion of the epidemiological susceptible-infectious-recovered multivariate master equation and include terms up to and beyond single-particle fluctuations. It is shown that higher order approximations yield qualitatively different results than low-order approximations, which is incident to the influence of additional nonlinear fluctuations. The fluctuations can be related to a meaningful physical parameter, the basic reproductive number, which is shown to dictate the rate of divergence in absolute terms from the ordinary differential equations more so than the total number of persons in the system. In epidemiological terms, the effect of single-particle fluctuations ought to be taken into account as the reproductive number approaches unity.
High-order power series expansion of the elastic interaction between conical membrane inclusions.
Fournier, Jean-Baptiste; Galatola, Paolo
2015-08-01
We revisit the problem of the long-range interaction between two conical proteins inserted into a lipid membrane and interacting via the induced deformation of the membrane, first considered by Goulian et al. (M. Goulian, R. Bruinsma, P. Pincus, Europhys. Lett. 22, 145 (1993); Europhys. Lett. 23, 155 (1993)). By means of a complex variables formulation and an iterative solution, we determine analytically an arbitrary high-order expansion of the interaction energy in powers of the inverse distance between two inclusions of different sizes. At leading order and for inclusions of equal sizes, we recover the result obtained by Goulian et al.. We generalize the development to inclusions of different sizes and give explicit formulas that increase the precision by ten orders in the inverse distance.
Matković, Aleksandar; Genser, Jakob; Lüftner, Daniel; Kratzer, Markus; Gajić, Radoš; Puschnig, Peter; Teichert, Christian
2016-01-01
This study focuses on hexagonal boron nitride as an ultra-thin van der Waals dielectric substrate for the epitaxial growth of highly ordered crystalline networks of the organic semiconductor parahexaphenyl. Atomic force microscopy based morphology analysis combined with density functional theory simulations reveal their epitaxial relation. As a consequence, needle-like crystallites of parahexaphenyl grow with their long axes oriented five degrees off the hexagonal boron nitride zigzag directions. In addition, by tuning the deposition temperature and the thickness of hexagonal boron nitride, ordered networks of needle-like crystallites as long as several tens of micrometers can be obtained. A deeper understanding of the organic crystallites growth and ordering at ultra-thin van der Waals dielectric substrates will lead to grain boundary-free organic field effect devices, limited only by the intrinsic properties of the organic semiconductors. PMID:27929042
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.
Attosecond-pulse production using resonantly enhanced high-order harmonics
NASA Astrophysics Data System (ADS)
Strelkov, V. V.
2016-12-01
We study theoretically the effect of giant resonance in Xe on the phase difference between consecutive resonantly enhanced high-order harmonics and calculate the duration of the attosecond pulses produced by these harmonics. For certain conditions, resonantly induced dephasing compensates the phase difference which is intrinsic for off-resonance harmonics. We find these conditions analytically and compare them with numerical results. This harmonic synchronization allows attosecond-pulse shortening in conjunction with the resonance-induced intensity increase of more than an order of magnitude. The latter enhancement relaxes the requirements for the UV filtering needed for attosecond-pulse production. Using a two-color driving field allows a further increase of the intensity. In particular, a causticlike feature in the harmonic spectrum leads to a generation efficiency growth of up to two orders of magnitude, which is, however, accompanied by an elongation of the XUV pulse.
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.
Stripe order in La2-xBaxCuO4 in high magnetic fields
NASA Astrophysics Data System (ADS)
Huecker, M.; von Zimmermann, M.; Xu, Z. J.; Wen, J. S.; Gu, G. D.; Zaliznyak, I. A.; Chung, J.-H.; Choi, E. S.; Tranquada, J. M.
2012-02-01
The observation of enhanced spin stripe order in the vortex cores of La2-xSrxCuO4 has been a landmark experiment that revealed the intimate connection between superconductivity and incommensurate antiferromagnetism. Only recently we have observed a corresponding field dependence of the spin and, more importantly, of the charge stripe order in La2-xBaxCuO4. Here we present our recent results from neutron diffraction, x-ray diffraction, and torque measurements in high magnetic fields. These helped us to establish the field versus temperature and doping phase diagrams for spin and charge order, and to further corroborate the stripe model as the more appropriate description than for example spiral and vortex states.
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.
Shin, Yongsoon; Tao, Jinhui; Arey, Bruce W.; Wang, Chongmin; Exarhos, Gregory J.; De Yoreo, James J.; Sushko, Maria L.; Liu, Jun
2016-08-30
Molecular templating and self-assembly are fundamental mechanisms for controlling the morphology of biominerals, while in synthetic two-dimensional layered materials similar levels of control over materials structure can be achieved through the epitaxial relationship with the substrate. In this study these two concepts are combined to provide an approach for the nucleation and growth of three-dimensional ordered mesophases on solid surfaces. A combined experimental and theoretical study revealed how atomic ordering of the substrate controls the structure of surfactant template and the orientation and morphology of the epitaxially grown inorganic material. Such dual epitaxial relationship between the substrate, surfactant template and inorganic mesophase gives rise to a highly ordered porous mesophase with a well-defined cubic lattice of pores. The level of control over material’s three-dimensional architecture achieved in this one-step synthesis is reminiscent to that in biomineralization.
New Stability Criteria for High-Order Neural Networks with Proportional Delays
NASA Astrophysics Data System (ADS)
Xu, Chang-Jin; Li, Pei-Luan
2017-03-01
This paper is concerned with high-order neural networks with proportional delays. The proportional delay is a time-varying unbounded delay which is different from the constant delay, bounded time-varying delay and distributed delay. By the nonlinear transformation {y}i(t)={u}i({{{e}}}t){{ }}(i=1,2,\\ldots ,n), we transform a class of high-order neural networks with proportional delays into a class of high-order neural networks with constant delays and time-varying coefficients. With the aid of Brouwer fixed point theorem and constructing the delay differential inequality, we obtain some delay-independent and delay-dependent sufficient conditions to ensure the existence, uniqueness and global exponential stability of equilibrium of the network. Two examples with their simulations are given to illustrate the theoretical findings. Our results are new and complement previously known results. Supported by National Natural Science Foundation of China under Grant Nos. 61673008 and 11261010, and Project of High-level Innovative Talents of Guizhou Province ([2016]5651)
Mei, Peng; Pramanik, Malay; Lee, Jaewoo; Ide, Yusuke; Alothman, Zeid Abdullah; Kim, Jung Ho; Yamauchi, Yusuke
2017-03-28
Highly ordered mesostructured vanadium phosphonates (VP) have been synthesized in the presence of cetyltrimethylammonium bromide (CTAB) as a structure-directing agent. Nitrilotris(methylene)triphosphonic acid (NMPA) and (ammonium/sodium) metavanadate (NH4 VO3 /NaVO3 ) have been used for the construction of pore walls. The CTAB templates are removed from the materials by an extraction process without destroying the parent mesostructure. The formation mechanism for the ordered mesoporous structure and its impact on electrochemical application in lithium ion batteries (LIBs) are explained by considering the structural and electrochemical stability of the framework. The results demonstrate that the counter cations (NH4(+) /Na(+) ) of the metavanadate precursors have a crucial role in stabilizing the mesoporous structure of the mesoporous VP materials. Mesoporous VP materials with highly ordered structure have great applicability as high-performance electrode materials in LIBs due to the advantages of their large contact area with electrolyte and short transport paths for lithium ions. Mesoporous VP electrodes exhibit high reversible specific capacity with superb cycling stability (100 cycles) and excellent retention of capacity (92 %).
A high-order mode extended interaction klystron at 0.34 THz
NASA Astrophysics Data System (ADS)
Wang, Dongyang; Wang, Guangqiang; Wang, Jianguo; Li, Shuang; Zeng, Peng; Teng, Yan
2017-02-01
We propose the concept of high-order mode extended interaction klystron (EIK) at the terahertz band. Compared to the conventional fundamental mode EIK, it operates at the TM31-2π mode, and its remarkable advantage is to obtain a large structure and good performance. The proposed EIK consists of five identical cavities with five gaps in each cavity. The method is discussed to suppress the mode competition and self-oscillation in the high-order mode cavity. Particle-in-cell simulation demonstrates that the EIK indeed operates at TM31-2π mode without self-oscillation while other modes are well suppressed. Driven by the electron beam with a voltage of 15 kV and a current of 0.3 A, the saturation gain of 43 dB and the output power of 60 W are achieved at the center frequency of 342.4 GHz. The EIK operating at high-order mode seems a promising approach to generate high power terahertz waves.
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
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.
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.
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.
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.
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 largemore » $$N_c$$, 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.« less
Stripe order in La2-xBaxCuO4 at ambient and high pressure.
NASA Astrophysics Data System (ADS)
Huecker, M.; Wen, J. S.; Xu, Z. J.; Gu, G. D.; Tranquada, J. M.; Zimmermann, M. V.
2009-03-01
The pronounced stability of the charge and spin stripe order in La2-xBaxCuO4 at x=1/8 doping still is a poorly understood peculiarity. A combination of electronic and structural interactions is likely, however it has been difficult to clearly separate the involved mechanisms. One approach is to explore how stripe order fades away for dopings x !=1/8. We have performed high energy (100 keV) x-ray diffraction and static magnetization experiments on single crystals between x=0.095 and 0.155. To our surprise, at ambient pressure stripes exist in a much broader range of doping around x=1/8 than expected. In the underdoped region charge stripe order always coincides with a structural transition associated with a rotation of the octahedral tilt axis. However, for x=1/8 and high pressure we have been able to show that stripe order also occurs in the absence of this structural phase, which motivates us to discuss stripes in terms of an electronic liquid crystal phase.
Grid Convergence of High Order Methods for Multiscale Complex Unsteady Viscous Compressible Flows
NASA Technical Reports Server (NTRS)
Sjoegreen, B.; Yee, H. C.
2001-01-01
Grid convergence of several high order methods for the computation of rapidly developing complex unsteady viscous compressible flows with a wide range of physical scales is studied. The recently developed adaptive numerical dissipation control high order methods referred to as the ACM and wavelet filter schemes are compared with a fifth-order weighted ENO (WENO) scheme. The two 2-D compressible full Navier-Stokes models considered do not possess known analytical and experimental data. Fine grid solutions from a standard second-order TVD scheme and a MUSCL scheme with limiters are used as reference solutions. The first model is a 2-D viscous analogue of a shock tube problem which involves complex shock/shear/boundary-layer interactions. The second model is a supersonic reactive flow concerning fuel breakup. The fuel mixing involves circular hydrogen bubbles in air interacting with a planar moving shock wave. Both models contain fine scale structures and are stiff in the sense that even though the unsteadiness of the flows are rapidly developing, extreme grid refinement and time step restrictions are needed to resolve all the flow scales as well as the chemical reaction scales.
High-Order Topology Modeling of Visual Words for Image Classification.
Huang, Kaiqi; Wang, Chong; Tao, Dacheng
2015-11-01
Modeling relationship between visual words in feature encoding is important in image classification. Recent methods consider this relationship in either image or feature space, and most of them incorporate only pairwise relationship (between visual words). However, in situations involving large variability in images, one cannot capture intrinsic invariance of intra-class images using low-order pairwise relationship. The result is not robust to larger variations in images. In addition, as the number of potential pairings grows exponentially with the number of visual words, the task of learning becomes computationally expensive. To overcome these two limitations, we propose an efficient classification framework that exploits high-order topology of visual words in the feature space, as follows. First, we propose a search algorithm that seeks dependence between the visual words. This dependence is used to construct higher order topology in the feature space. Then, the local features are encoded according to this higher order topology to improve the image classification. Experiments involving four common data sets, namely PASCAL VOC 2007, 15 Scenes, Caltech 101, and UIUC Sport Event, demonstrate that the dependence search significantly improves the efficiency of higher order topological construction, and consequently increases the image classification in all these data sets.
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).
A corrected particle method with high-order Taylor expansion for solving the viscoelastic fluid flow
NASA Astrophysics Data System (ADS)
Jiang, T.; Ren, J. L.; Lu, W. G.; Xu, B.
2017-02-01
In this paper, a corrected particle method based on the smoothed particle hydrodynamics (SPH) method with high-order Taylor expansion (CSPH-HT) for solving the viscoelastic flow is proposed and investigated. The validity and merits of the CSPH-HT method are first tested by solving the nonlinear high order Kuramoto-Sivishinsky equation and simulating the drop stretching, respectively. Then the flow behaviors behind two stationary tangential cylinders of polymer melt, which have been received little attention, are investigated by the CSPH-HT method. Finally, the CSPH-HT method is extended to the simulation of the filling process of the viscoelastic fluid. The numerical results show that the CSPH-HT method possesses higher accuracy and stability than other corrected SPH methods and is more reliable than other corrected SPH methods.
A high-order fast method for computing convolution integral with smooth kernel
NASA Astrophysics Data System (ADS)
Qiang, Ji
2010-02-01
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), 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.
NASA Astrophysics Data System (ADS)
Trask, Nathaniel; Maxey, Martin; Hu, Xiaozhe
2016-12-01
A generalization of the optimization framework typically used in moving least squares is presented that provides high-order approximation while maintaining compact stencils and a consistent treatment of boundaries. The approach, which we refer to as compact moving least squares, resembles the capabilities of compact finite differences but requires no structure in the underlying set of nodes. An efficient collocation scheme is used to demonstrate the capabilities of the method to solve elliptic boundary value problems in strong form stably without the need for an expensive weak form. The flexibility of the approach is demonstrated by using the same framework to both solve a variety of elliptic problems and to generate implicit approximations to derivatives. Finally, an efficient preconditioner is presented for the steady Stokes equations, and the approach's efficiency and high order of accuracy is demonstrated for domains with curvi-linear boundaries.
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.
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-Dimensional Hermite Filters Simplify the Description of High-Order Statistics of Natural Images.
Hu, Qin; Victor, Jonathan D
2016-09-01
Natural image statistics play a crucial role in shaping biological visual systems, understanding their function and design principles, and designing effective computer-vision algorithms. High-order statistics are critical for conveying local features, but they are challenging to study - largely because their number and variety is large. Here, via the use of two-dimensional Hermite (TDH) functions, we identify a covert symmetry in high-order statistics of natural images that simplifies this task. This emerges from the structure of TDH functions, which are an orthogonal set of functions that are organized into a hierarchy of ranks. Specifically, we find that the shape (skewness and kurtosis) of the distribution of filter coefficients depends only on the projection of the function onto a 1-dimensional subspace specific to each rank. The characterization of natural image statistics provided by TDH filter coefficients reflects both their phase and amplitude structure, and we suggest an intuitive interpretation for the special subspace within each rank.
Negative-index metamaterial at visible frequencies based on high order plasmon resonance.
Cong, Jiawei; Yun, Binfeng; Cui, Yiping
2012-05-01
A type of negative-index metamaterial composed of periodic arrays of SRRs is proposed and numerically investigated in the visible frequencies. Employing the high order magnetic resonance to induce negative permeability, negative refractive index is obtained between 395 THz and 430 THz with the maximum FOM=4.59. The effective permeability exhibits a rapid convergence with increasing number of metamaterial layers. Different responses from the electric and magnetic resonances to the changing geometric parameters are compared and analyzed in terms of the field distribution. Simulation results show that the high order magnetic resonance can be greatly enhanced at visible frequencies as well as effectively tuned over a wide spectral range without notably altering the coupling between unit cells.
Titanium-rich highly ordered mesoporous silica synthesized by using a mixed surfactant system
NASA Astrophysics Data System (ADS)
Chandra, Debraj; Kishor Mal, Nawal; Mukherjee, Manabendra; Bhaumik, Asim
2006-06-01
A new titanium-rich highly ordered 2-D hexagonal mesoporous titanium silicate has been synthesized using a mixture of cationic (cetyltrimethylammonium bromide, CTAB) and non-ionic (Brij-35, C 12H 25-(OC 2H 4) 23-OH, a polyether and aliphatic hydrocarbon chain surfactant) mixed surfactant system as the supramolecular structure directing agent (SDA) in the presence of tartaric acid (TA) as a mineralizer of Ti(IV). XRD, N 2 adsorption and TEM data suggested the presence of mesophase with hexagonal pore arrangements and the UV-visible, FT IR and XPS studies suggested the incorporation of mostly tetrahedral titanium (IV) species in the highly ordered silica network. This mesoporous titanium silicate material showed excellent catalytic activity and selectivity in the epoxidation of styrene using dilute aqueous H 2O 2 as oxidant.
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 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.
Impact of two-electron dynamics and correlations on high-order-harmonic generation in He
NASA Astrophysics Data System (ADS)
Artemyev, Anton N.; Cederbaum, Lorenz S.; Demekhin, Philipp V.
2017-03-01
The interaction of a helium atom with an intense, short, 800-nm, laser pulse is studied theoretically beyond the single-active-electron approximation. For this purpose, the time-dependent Schrödinger equation for a two-electron wave packet driven by a linearly polarized infrared pulse is solved by the time-dependent restricted-active-space configuration-interaction method in the dipole velocity gauge. By systematically extending the space of active configurations, we investigate the role of the collective two-electron dynamics in the strong-field ionization and high-order-harmonic generation processes. Our numerical results demonstrate that allowing both electrons in He to be dynamically active results in a considerable extension of the computed high-order-harmonic generation spectrum.
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.
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.
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.
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.
An overset mesh approach for 3D mixed element high-order discretizations
NASA Astrophysics Data System (ADS)
Brazell, Michael J.; Sitaraman, Jayanarayanan; Mavriplis, Dimitri J.
2016-10-01
A parallel high-order Discontinuous Galerkin (DG) method is used to solve the compressible Navier-Stokes equations in an overset mesh framework. The DG solver has many capabilities including: hp-adaption, curved cells, support for hybrid, mixed-element meshes, and moving meshes. Combining these capabilities with overset grids allows the DG solver to be used in problems with bodies in relative motion and in a near-body off-body solver strategy. The overset implementation is constructed to preserve the design accuracy of the baseline DG discretization. Multiple simulations are carried out to validate the accuracy and performance of the overset DG solver. These simulations demonstrate the capability of the high-order DG solver to handle complex geometry and large scale parallel simulations in an overset framework.
A corrected particle method with high-order Taylor expansion for solving the viscoelastic fluid flow
NASA Astrophysics Data System (ADS)
Jiang, T.; Ren, J. L.; Lu, W. G.; Xu, B.
2016-12-01
In this paper, a corrected particle method based on the smoothed particle hydrodynamics (SPH) method with high-order Taylor expansion (CSPH-HT) for solving the viscoelastic flow is proposed and investigated. The validity and merits of the CSPH-HT method are first tested by solving the nonlinear high order Kuramoto-Sivishinsky equation and simulating the drop stretching, respectively. Then the flow behaviors behind two stationary tangential cylinders of polymer melt, which have been received little attention, are investigated by the CSPH-HT method. Finally, the CSPH-HT method is extended to the simulation of the filling process of the viscoelastic fluid. The numerical results show that the CSPH-HT method possesses higher accuracy and stability than other corrected SPH methods and is more reliable than other corrected SPH methods.
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.
Numerical solution of multiparameter spectral problems by high order finite different schemes
NASA Astrophysics Data System (ADS)
Amodio, Pierluigi; Settanni, Giuseppina
2016-10-01
We report on the progress achieved in the numerical simulation of self-adjoint multiparameter spectral problems for ordinary differential equations. We describe how to obtain a discrete problem by means of High Order Finite Difference Schemes and discuss its numerical solution. Based on this approach, we also define a recursive algorithm to compute approximations of the parameters by means of the solution of a set of problems converging to the original one.
NASA Astrophysics Data System (ADS)
Dimitrovski, Darko; Madsen, Lars Bojer; Pedersen, Thomas Garm
2017-01-01
We consider the interaction of gapped graphene in the two-band approximation using an explicit time-dependent approach. In addition to the full high-order harmonic generation (HHG) spectrum, we also obtain the perturbative harmonic response using the time-dependent method at photon energies covering all the significant features in the responses. The transition from the perturbative to the fully nonperturbative regime of HHG at these photon energies is studied in detail.
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.
2014-10-01
Approved for public release; distribution unlimited. Between single sweep measurements Eddy Current excitation will not run, to prevent heating the...AFRL-RX-WP-TR-2015-0004 RESEARCH INITIATIVES FOR MATERIALS STATE SENSING (RIMSS) Task Order 0020: High Frequency Eddy Current NDE...Frequency Eddy Current NDE 5a. CONTRACT NUMBER FA8650-10-D-5210-0020 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 62102F 6. AUTHOR(S) See
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.
High order harmonic generation from SF6: Deconvolution of macroscopic effects
NASA Astrophysics Data System (ADS)
Wilson, B. P.; Fulfer, K. D.; Mondal, S.; Ren, X.; Tross, J.; Poliakoff, E. D.; Jose, J.; Le, Anh-Thu; Lucchese, R. R.; Trallero-Herrero, C.
2016-12-01
We measure high order harmonics from the molecule SF6 over a large range of phase matching conditions and observe several features in the harmonics that are largely independent of such macroscopic conditions. The experimental data are then compared to the quantitative rescattering theory for the generation of harmonics from three orbitals. With this comparison, we are able to assign spectroscopic features in the harmonics to contributions from 1t1g (HOMO) and 5t1u (HOMO-1) orbitals.
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
A Method for Measuring Distortion in Wide-Field Imaging with High Order Polynomials
NASA Astrophysics Data System (ADS)
Yasuda, N.; Okura, Y.; Takata, T.; Furusawa, H.
2011-07-01
In analyzing wide-field images, for example those from the Hyper Suprime-Cam on the Subaru telescope, determining World Coordinate System (WCS) information (for example position and angle) of each CCD is very important. In this paper, we show a method for determining the distortion with high-order polynomials using the TAN-SIP convention, utilizing all of the CCDs in a field of view (FOV) at once.
Degenerate Four-Wave Mixing Measurements of High Order Nonlinearities in Semiconductors
1991-10-01
2274 IEEE JOURNAL OF QUANTUM ELECTRONICS. VOL. 27, NO. IO. OCTOBER 1991 Degenerate Four -Wave Mixing Measurements of High Order Nonlinearities in... four -wave mixing experi- ments on ZnSe and CdTe semiconductor samples with pico- second laser pulses at wavelengths below the bandgap. Nonlin- earities...three-photon absorption. I. INTRODUCTION WE repo~ ~ series of picose~ond degenerate four -wave mixmg (DFWM) studies conducted in ZnSe and CdTe at
Utilizing liquid crystal phases to obtain highly ordered thin films for organic electronics
NASA Astrophysics Data System (ADS)
Springer, Mike T.
Organic electronic materials offer several advantages when compared to inorganic materials, but they suffer from low charge carrier mobility. Two major factors hindering effective charge transport in organic materials are: 1) effective wavefunction overlap in organic crystals and 2) the domain morphology of thin films. Charge transport in organic materials occurs via a hopping mechanism along the conjugated pi system. Often, rigid, aromatic organic materials crystallize in a herringbone, edge-to-face orientation, limiting pi-pi stacking and decreasing charge carrier mobility. Face-to-face orientation of aromatic rings decreases intermolecular pi-pi distances and increases wavefunction overlap. Control of the crystal structure can be achieved to some extent by tuning structural features of the molecule, like increasing the ratio of carbon atoms to hydrogen atoms in the aromatic rings; this is often achieved by introducing heteroatoms like sulfur and oxygen into the aromatic ring structure. Thin films of organic materials often contain many unaligned domains; this is caused by rapid crystallization. Control of the domain morphology of thin films has been shown to increase charge carrier mobility by 6 orders of magnitude for thin films of the same material. Liquid crystal phases allow a slow process of crystallization, whereby the molecules in a thin film can be slowly aligned into a monodomain before crystallization. The crystal-smectic phases, like smectic E, are particularly attractive for this strategy due to their high degree of intermolecular order. This project describes the synthesis and characterization of organic semiconductors designed to exhibit short pi-pi distances and highly ordered crystal-smectic phases to obtain thin films with high charge carrier mobility. The n,2-OBTTT series contains 15 newly designed and synthesized mesogens. The liquid crystal and solid crystal structures of these mesogens are examined and deposition conditions are optimized for
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.
Properties-preserving high order numerical methods for a kinetic eikonal equation
NASA Astrophysics Data System (ADS)
Luo, Songting; Payne, Nicholas
2017-02-01
For the BGK (Bhatnagar-Gross-Krook) equation in the large scale hyperbolic limit, the density of particles can be transformed as the Hopf-Cole transformation, where the phase function converges uniformly to the viscosity solution of an effective Hamilton-Jacobi equation, referred to as the kinetic eikonal equation. In this work, we present efficient high order finite difference methods for numerically solving the kinetic eikonal equation. The methods are based on monotone schemes such as the Godunov scheme. High order weighted essentially non-oscillatory techniques and Runge-Kutta procedures are used to obtain high order accuracy in both space and time. The effective Hamiltonian is determined implicitly by a nonlinear equation given as integrals with respect to the velocity variable. Newton's method is applied to solve the nonlinear equation, where integrals with respect to the velocity variable are evaluated either by a Gauss quadrature formula or as expansions with respect to moments of the Maxwellian. The methods are designed such that several key properties such as the positivity of the viscosity solution and the positivity of the effective Hamiltonian are preserved. Numerical experiments are presented to demonstrate the effectiveness of the methods.
Lu, Guo-Wei; Albuquerque, André; Puttnam, Benjamin J; Sakamoto, Takahide; Drummond, Miguel; Nogueira, Rogério; Kanno, Atsushi; Shinada, Satoshi; Wada, Naoya; Kawanishi, Tetsuya
2014-03-10
Optical wavelength conversion (OWC) is expected to be a desirable function in future optical transparent networks. Since high-order quadrature amplitude modulation (QAM) is more sensitive to the phase noise, in the OWC of high-order QAM signals, it is crucial to suppress the extra noise introduced in the OWC subsystem, especially for the scenario with multiple cascaded OWCs. Here, we propose and experimentally demonstrate a pump-linewidth-tolerant OWC scheme suitable for high-order QAM signals using coherent two-tone pumps. Using 3.5-MHz-linewidth distributed feedback (DFB) lasers as pump sources, our scheme enables wavelength conversion of both 16QAM and 64QAM signals with negligible power penalty, in a periodically-poled Lithium Niobate (PPLN) waveguide based OWC. We also demonstrate the performance of pump phase noise cancellation, showing that such coherent two-tone pump schemes can eliminate the need for ultra-narrow linewidth pump lasers and enable practical implementation of low-cost OWC in future dynamic optical networks.
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.
NASA Astrophysics Data System (ADS)
Pan, Yong-dong; Jin, Jian; Yang, Feng; Chen, Wei-zhen
2017-02-01
High order longitudinal guided waves (HOLGW) are studied for the damage detection in the anchorage zone of stayed cable through the theoretical analysis, numerical simulation and experimental validation. First, based on the theory of elastic wave propagation in cylinder, the dispersion curves of longitudinal modes were obtained and calculated analytically and the high-frequency such as 5MHz corresponding to the higher order longitudinal guided wave modes are identified for the damage detection. Then, the ultrasonic guided waves propagating in a steel wire with or without defects were simulated by using the finite element method and the effects of defect depth and length on the reflection coefficient are studied. Finally, the free wires and a tested cable were studied experimentally. The results show that the finite element method is able to model the high-order guided wave propagation in the steel wire. The agreement between the experiment and theory has demonstrated that the HOLGW is a potential candidate for the damage detection in anchorage zones of stayed-cables.
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
Coulomb-interaction-dependent effect of high-order sideband generation in an optomechanical system
NASA Astrophysics Data System (ADS)
Kong, Cui; Xiong, Hao; Wu, Ying
2017-03-01
High-order sideband generation in an optomechanical system coupled to a charged object is discussed, and the features of Coulomb-interaction-dependent effect are identified. We show that the Coulomb-interaction-dependent effect of high-order sideband generation exhibits essential difference between the case of weak control field and strong control field. In the weak control field case, the output spectra are in the perturbative regime and there is hardly any Coulomb-interaction-dependent effect in an optomechanical system coupling to an object with a small amount of charge. In the strong control field case, the output spectra are in the nonperturbative regime and robust Coulomb-interaction-dependent effect arises even if there are few charges. The amplitudes of specific sidebands are also discussed, and it is shown that Coulomb interaction plays an important role in achieving optomechanical control. Due to the extremely sensitive charge number, the Coulomb-interaction-dependent effect of high-order sideband generation is remarkable in many aspects and may be used to precision measurement of electrical charges beyond the linearized optomechanical interaction.
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
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.
Femtosecond Dynamics and Multiphoton Ionization driven with an Intense High Order Harmonic Source
NASA Astrophysics Data System (ADS)
van Tilborg, Jeroen; Allison, Tom; Wright, Travis; Hertlein, Marc; Falcone, Roger; Liu, Yanwei; Merdji, Hamed; Belkacem, Ali
2009-05-01
We have constructed a high intensity high order harmonic source at the Lawrence Berkeley National Lab delivering ˜10^9 extreme ultraviolet photons/shot on a gas target and used it to observe multiphoton ionization and conduct femtosecond EUV-pump IR-probe experiments. Following excitation by 20-25 eV photons, we observed that the excited ethylene cation (H2C-CH2)^+ experienced isomerization to the ethylidene configuration (HC-CH3)^+ in 50±25 fs, followed by an H2 stretch motion. Experimental data and analysis from several experiments as well as a future outlook of our efforts will be presented.
Femtosecond dynamics and multiphoton ionization driven with an intense high order harmonic source
NASA Astrophysics Data System (ADS)
van Tilborg, J.; Allison, T. K.; Wright, T. W.; Hertlein, M. P.; Liu, Y.; Merdji, H.; Falcone, R. W.; Belkacem, A.
2009-11-01
We have constructed a high intensity high order harmonic source delivering ~ 109 extreme ultraviolet photons/shot on a gas target and used it to observe multiphoton ionization and conduct femtosecond EUV-pump IR-probe experiments. Following excitation by 20-25 eV photons, we observed that the excited ethylene cation (H2C-CH2)+ experienced isomerization to the ethylidene configuration (HC-CHs)+ in 50±25 fs, followed by an H2 stretch motion. Experimental data and analysis from several other performed and planned experiments will be presented as well.
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.
Maximizing the yield and cutoff of high-order harmonic generation from plasma plume
Ganeev, Rashid A.; Elouga Bom, Luc B.; Ozaki, Tsuneyuki; Redkin, Pavel V.
2007-11-15
We study high-order harmonic generation (HHG) from various lowly ionized laser plasmas. We study harmonic generation from targets of Al (Z=13) to Bi (Z=83). Varying the wavelength, chirp, and pulse duration of the femtosecond pump laser resulted in the change in the harmonic distribution, cutoff, and conversion efficiency of HHG. We also study the use of doubly charged ions, and resonances for some materials. We were able to obtain high HHG conversion efficiency and harmonic cutoff by implementing the above approaches and by observing the time-resolved spectra of the laser plasma.
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.
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.
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 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-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.
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.
NASA Astrophysics Data System (ADS)
Kozdon, J. E.; Wilcox, L.; Aranda, A. R.
2014-12-01
The goal of this work is to develop a new set of simulation tools for earthquake rupture dynamics based on state-of-the-art high-order, adaptive numerical methods capable of handling complex geometries. High-order methods are ideal for earthquake rupture simulations as the problems are wave-dominated and the waves excited in simulations propagate over distance much larger than their fundamental wavelength. When high-order methods are used for such problems significantly fewer degrees of freedom are required as compared with low-order methods. The base numerical method in our new software elements is a discontinuous Galerkin method based on curved, Kronecker product hexahedral elements. We currently use MPI for off-node parallelism and are in the process of exploring strategies for on-node parallelism. Spatial mesh adaptivity is handled using the p4est library and temporal adaptivity is achieved through an Adams-Bashforth based local time stepping method; we are presently in the process of including dynamic spatial adaptivity which we believe will be valuable for capturing the small-scale features around the propagating rupture front. One of the key features of our software elements is that the method is provably stable, even after the inclusion of the nonlinear frictions laws which govern rupture dynamics. In this presentation we will both outline the structure of the software elements as well as validate the rupture dynamics with SCEC benchmark test problems. We are also presently developing several realistic simulation geometries which may also be reported on. Finally, the software elements that we have designed are fully public domain and have been designed with tightly coupled, wave dominated multiphysics applications in mind. This latter design decisions means the software elements are applicable to many other geophysical and non-geophysical applications.
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; Sabok, S A; Dabrowski, B; Lonzarich, G G; Sebastian, Suchitra E
2015-08-04
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.
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.
High-Order Integral Equation Methods for Diffraction Problems Involving Screens and Apertures
NASA Astrophysics Data System (ADS)
Lintner, Stephane K.
This thesis presents a novel approach for the numerical solution of problems of diffraction by infinitely thin screens and apertures. The new methodology relies on combination of weighted versions of the classical operators associated with the Dirichlet and Neumann open-surface problems. In the two-dimensional case, a rigorous proof is presented, establishing that the new weighted formulations give rise to second-kind Fredholm integral equations, thus providing a generalization to open surfaces of the classical closed-surface Calderon formulae. High-order quadrature rules are introduced for the new weighted operators, both in the two-dimensional case as well as the scalar three-dimensional case. Used in conjunction with Krylov subspace iterative methods, these rules give rise to efficient and accurate numerical solvers which produce highly accurate solutions in small numbers of iterations, and whose performance is comparable to that arising from efficient high-order integral solvers recently introduced for closed-surface problems. Numerical results are presented for a wide range of frequencies and a variety of geometries in two- and three-dimensional space, including complex resonating structures as well as, for the first time, accurate numerical solutions of classical diffraction problems considered by the 19th-century pioneers: diffraction of high-frequency waves by the infinitely thin disc, the circular aperture, and the two-hole geometry inherent in Young's experiment.
Optimization of multi-color laser waveform for high-order harmonic generation
NASA Astrophysics Data System (ADS)
Jin, Cheng; Lin, C. D.
2016-09-01
With the development of laser technologies, multi-color light-field synthesis with complete amplitude and phase control would make it possible to generate arbitrary optical waveforms. A practical optimization algorithm is needed to generate such a waveform in order to control strong-field processes. We review some recent theoretical works of the optimization of amplitudes and phases of multi-color lasers to modify the single-atom high-order harmonic generation based on genetic algorithm. By choosing different fitness criteria, we demonstrate that: (i) harmonic yields can be enhanced by 10 to 100 times, (ii) harmonic cutoff energy can be substantially extended, (iii) specific harmonic orders can be selectively enhanced, and (iv) single attosecond pulses can be efficiently generated. The possibility of optimizing macroscopic conditions for the improved phase matching and low divergence of high harmonics is also discussed. The waveform control and optimization are expected to be new drivers for the next wave of breakthrough in the strong-field physics in the coming years. Project supported by the Fundamental Research Funds for the Central Universities of China (Grant No. 30916011207), Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U. S. Department of Energy (Grant No. DE-FG02-86ER13491), and Air Force Office of Scientific Research, USA (Grant No. FA9550-14-1-0255).
NASA Astrophysics Data System (ADS)
Tang, Lin; Cai, Ye; Yang, Guide; Liu, Yuanyuan; Zeng, Guangming; Zhou, Yaoyu; Li, Sisi; Wang, Jiajia; Zhang, Sheng; Fang, Yan; He, Yibin
2014-09-01
Cobalt nanoparticles-embedded magnetic ordered mesoporous carbon (Co/OMC), prepared through a simple method involving infusing and calcination, was used as a highly effective adsorbent for rhodamine B (Rh B) removal. Several techniques, including SEM, HRTEM, nitrogen adsorption-desorption isotherms, XRD, Raman spectra, EDX, zeta potential and VSM measurement, were applied to characterize the adsorbent. Batch tests were conducted to investigate the adsorption performance. The adsorption capacity of the resultant adsorbent was relatively high compared with raw ordered mesoporous carbon (OMC) and reached an equilibrium value of 468 mg/g at 200 mg/L initial Rh B concentration. Removal efficiency even reached 96% within 25 min at 100 mg/L initial Rh B concentration. Besides, the adsorption amount increased with the increase of solution pH, adsorbent dose and initial Rh B concentration. Kinetics study showed that the adsorption agreed well with pseudo-second-order model (R2 = 0.999) and had a significant correlation with intra-particle diffusion model in the both two adsorption periods. Furthermore, thermodynamics research indicated that the adsorption process was endothermic and spontaneous in nature. The adsorption isotherms fitted well with Langmuir model, demonstrating the formation of mono-molecular layer on the surface of Co/OMC during adsorption process. The results confirmed that Co/OMC has the potential superiority in removal of Rh B from aqueous solution.
A high-order kinetic flux-splitting method for the relativistic magnetohydrodynamics
Qamar, Shamsul . E-mail: shamsul.qamar@mathematik.uni-magdeburg.de; Warnecke, Gerald . E-mail: gerald.warnecke@mathematik.uni-magdeburg.de
2005-05-01
In this paper we extend the special relativistic hydrodynamic (SRHD) equations [L.D. Landau, E.M. Lifshitz, Fluid Mechanics, Pergamon, New York, 1987] and as a limiting case the ultra-relativistic hydrodynamic equations [M. Kunik, S. Qamar, G. Warnecke, J. Comput. Phys. 187 (2003) 572-596] to the special relativistic magnetohydrodynamics (SRMHD). We derive a flux splitting method based on gas-kinetic theory in order to solve these equations in one space dimension. The scheme is based on the direct splitting of macroscopic flux functions with consideration of particle transport. At the same time, particle 'collisions' are implemented in the free transport process to reduce numerical dissipation. To achieve high-order accuracy we use a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. For the direct comparison of the numerical results, we also solve the SRMHD equations with the well-developed second-order central schemes. The 1D computations reported in this paper have comparable accuracy to the already published results. The results verify the desired accuracy, high resolution, and robustness of the kinetic flux splitting method and central schemes.
Response properties of ON-OFF retinal ganglion cells to high-order stimulus statistics.
Xiao, Lei; Gong, Han-Yan; Gong, Hai-Qing; Liang, Pei-Ji; Zhang, Pu-Ming
2014-10-17
The visual stimulus statistics are the fundamental parameters to provide the reference for studying visual coding rules. In this study, the multi-electrode extracellular recording experiments were designed and implemented on bullfrog retinal ganglion cells to explore the neural response properties to the changes in stimulus statistics. The changes in low-order stimulus statistics, such as intensity and contrast, were clearly reflected in the neuronal firing rate. However, it was difficult to distinguish the changes in high-order statistics, such as skewness and kurtosis, only based on the neuronal firing rate. The neuronal temporal filtering and sensitivity characteristics were further analyzed. We observed that the peak-to-peak amplitude of the temporal filter and the neuronal sensitivity, which were obtained from either neuronal ON spikes or OFF spikes, could exhibit significant changes when the high-order stimulus statistics were changed. These results indicate that in the retina, the neuronal response properties may be reliable and powerful in carrying some complex and subtle visual information.
Non-linear stabilization of high-order Flux Reconstruction schemes via Fourier-spectral filtering
NASA Astrophysics Data System (ADS)
Asthana, Kartikey; López-Morales, Manuel R.; Jameson, Antony
2015-12-01
High-order Flux Reconstruction (FR) schemes have been limited in their application to transonic and supersonic problems on account of numerical instabilities related to the resolution of jump discontinuities. These instabilities arise from aliasing errors associated with the collocation projection of the flux corresponding to the numerical solution onto the polynomial basis of the numerical flux. In this paper, we obtain energy bounds on the numerical solution via FR to prove that stability can be ensured for any polynomial order by the addition of adequate artificial dissipation such that the solution is energy-stable beyond a critical grid resolution. This artificial viscosity is then approximately posed as a Fourier filtering operation which is implemented in the physical space via a strictly local convolution integral. The filter is selectively applied to 'troubled' cells as indicated by a discontinuity sensor based on the spectral concentration method. Numerous numerical tests in 1-D and 2-D have been performed. The proposed approach captures shock discontinuities while preserving accuracy in smooth regions of the solution, even for very high polynomial orders such as P = 119. The filtered solution provides reduced total variation, reduced maximum overshoot/undershoot, and even allows sub-element shocks to be localized in the interior of an element.
A set of high-order spatiotemporal stimuli that elicit motion and reverse-phi percepts.
Hu, Qin; Victor, Jonathan D
2010-03-25
Detection of motion is a crucial component of visual processing. To probe the computations underlying motion perception, we created a new class of non-Fourier motion stimuli, characterized by their third- and fourth-order spatiotemporal correlations. As with other non-Fourier stimuli, they lack second-order correlations, and therefore their motion cannot be detected by standard Fourier mechanisms. Additionally, these stimuli lack pairwise spatiotemporal correlation of edges or flicker-and thus, also cannot be detected by extraction of one of these features, followed by standard motion analysis. Nevertheless, many of these stimuli produced apparent motion in human observers. The pattern of responses-i.e., which specific spatiotemporal correlations led to a percept of motion-was highly consistent across subjects. For many of these stimuli, inverting the overall contrast of the stimulus reversed the direction of apparent motion. This "reverse-phi" phenomenon challenges existing models, including models that correlate low-level features and gradient models. Our findings indicate that current knowledge of the computations underlying motion processing is as yet incomplete, and that understanding how high-order spatiotemporal correlations lead to motion percepts will illuminate the computations underlying early motion processing.
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.
Highly ordered alignment of a vinyl polymer by host-guest cross-polymerization.
Distefano, Gaetano; Suzuki, Hirohito; Tsujimoto, Masahiko; Isoda, Seiji; Bracco, Silvia; Comotti, Angiolina; Sozzani, Piero; Uemura, Takashi; Kitagawa, Susumu
2013-04-01
Chain alignment can significantly influence the macroscopic properties of a polymeric material, but no general and versatile methodology has yet been reported to obtain highly ordered crystalline packing of polymer chains, with high stability. Here, we disclose a strategy that relies on 'ordered crosslinks' to produce polymeric materials that exhibit a crystalline arrangement. Divinyl crosslinkers (2,5-divinyl-terephthalate) were first embedded, as substitutional ligands, into the structure of a porous coordination polymer (PCP), [Cu(terephthalate)triethylenediamine0.5]n. A representative vinyl monomer, styrene, was subsequently polymerized inside the channels of the host PCP. The polystyrene chains that form within the PCP channels also crosslink with the divinyl species. This bridges together the polymer chains of adjacent channels and ensures that, on selective removal of the PCP, the polymer chains remain aligned. Indeed, the resulting material exhibits long-range order and is stable to thermal and solvent treatments, as demonstrated by X-ray powder diffraction and transmission electron microscopy.
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)
Caskey, Terrence Colin
This thesis describes the development and subsequent characterization of a series of oriented, highly ordered laminated composite materials. These laminated composite materials all possess order over varying length-scales from angstrom level molecular chain orientation to macro-scale order in woven fabrics. In each case, supercritical carbon dioxide (SC CO2) is used as a unique reaction medium and processing aid allowing for the development of structures not previously attainable with standard techniques. The goal of this research is two-fold, the first goal involves the proof of concept, exhibiting the ability to attain novel composite structures using unique SC CO2 chemistries and processes. The second goal of this research is aimed at developing a thorough understanding of how these unique structures and morphologies translate into an overall mechanical response for the material. This work will be divided into three distinct but interrelated projects. The first project involves the development of a unique SC CO2 assisted solvent welding technique. This technique is then applied towards the fabrication of a quasi-isotropic laminate comprised of a series of solvent-welded uniaxially-oriented linear low density polyethylene films (LLDPE). The geometry of this laminate is designed to exploit the improved strength and rigidity of uniaxially oriented LLDPE films while suppressing undesireable transverse properties. The second project to be addressed in this project involves the development of fiber-reinforced composites with unique nano-scale morphologies. The long-range order in these composites has profound effects on both the individual fiber properties as well as the overall composite properties. The final project of interest in this work involves the development of intercalated silicate nano-composites with high clay content. In order to achieve the desired morphologies it is necessary to create polymer/clay nano-composites with very high clay content
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
Highly ordered vertical GaAs nanowire arrays with dry etching and their optical properties.
Dhindsa, Navneet; Chia, Andrew; Boulanger, Jonathan; Khodadad, Iman; LaPierre, Ray; Saini, Simarjeet S
2014-08-01
We report fabrication methods, including metal masks and dry etching, and demonstrate highly ordered vertical gallium arsenide nanowire arrays. The etching process created high aspect ratio, vertical nanowires with insignificant undercutting from the mask, allowing us to vary the diameter from 30 nm to 400 nm with a pitch from 250 nm to 1100 nm and length up to 2.2 μm. A diameter to pitch ratio of ∼68% was achieved. We also measured the reflectance from the nanowire arrays and show experimentally diameter-dependent strong absorption peaks resulting from resonant optical mode excitations within these nanowires. The reflectance curves match very well with simulations. The work done here paves the way towards achieving high efficiency solar cells and tunable photodetectors using III-V nanowires.
Influence of gas pressure on high-order-harmonic generation of Ar and Ne
Wang Guoli; Jin Cheng; Le, Anh-Thu; Lin, C. D.
2011-11-15
We study the effect of gas pressure on the generation of high-order harmonics where harmonics due to individual atoms are calculated using the recently developed quantitative rescattering theory, and the propagation of the laser and harmonics in the medium is calculated by solving the Maxwell's wave equation. We illustrate that the simulated spectra are very sensitive to the laser focusing conditions at high laser intensity and high pressure since the fundamental laser field is severely reshaped during the propagation. By comparing the simulated results with several experiments we show that the pressure dependence can be qualitatively explained. The lack of quantitative agreement is tentatively attributed to the failure of the complete knowledge of the experimental conditions.
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
NASA Astrophysics Data System (ADS)
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.
Highly ordered Pb(Zr₀.₅₂ Ti₀.₄₈)O₃ piezoelectric nanorod arrays.
Yang, Su Chul; Sanghadasa, Mohan; Priya, Shashank
2013-06-07
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.
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.
Formation of high-order acoustic Bessel beams by spiral diffraction gratings
NASA Astrophysics Data System (ADS)
Jiménez, Noé; Picó, R.; Sánchez-Morcillo, V.; Romero-García, V.; García-Raffi, L. M.; Staliunas, K.
2016-11-01
The formation of high-order Bessel beams by a passive acoustic device consisting of an Archimedes' spiral diffraction grating is theoretically, numerically, and experimentally reported in this paper. These beams are propagation-invariant solutions of the Helmholtz equation and are characterized by an azimuthal variation of the phase along its annular spectrum producing an acoustic vortex in the near field. In our system, the scattering of plane acoustic waves by the spiral grating leads to the formation of the acoustic vortex with zero pressure on axis and the angular phase dislocations characterized by the spiral geometry. The order of the generated Bessel beam and, as a consequence, the size of the generated vortex can be fixed by the number of arms in the spiral diffraction grating. The obtained results allow for obtaining Bessel beams with controllable vorticity by a passive device, which has potential applications in low-cost acoustic tweezers and acoustic radiation force devices.
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.
Efficient simulation of cardiac electrical propagation using high order finite elements.
Arthurs, Christopher J; Bishop, Martin J; Kay, David
2012-05-20
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.
Assessment of a high-order accurate Discontinuous Galerkin method for turbomachinery flows
NASA Astrophysics Data System (ADS)
Bassi, F.; Botti, L.; Colombo, A.; Crivellini, A.; Franchina, N.; Ghidoni, A.
2016-04-01
In this work the capabilities of a high-order Discontinuous Galerkin (DG) method applied to the computation of turbomachinery flows are investigated. The Reynolds averaged Navier-Stokes equations coupled with the two equations k-ω turbulence model are solved to predict the flow features, either in a fixed or rotating reference frame, to simulate the fluid flow around bodies that operate under an imposed steady rotation. To ensure, by design, the positivity of all thermodynamic variables at a discrete level, a set of primitive variables based on pressure and temperature logarithms is used. The flow fields through the MTU T106A low-pressure turbine cascade and the NASA Rotor 37 axial compressor have been computed up to fourth-order of accuracy and compared to the experimental and numerical data available in the literature.
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.
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.
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.
Efficient simulation of cardiac electrical propagation using high order finite elements
Arthurs, Christopher J.; Bishop, Martin J.; Kay, David
2012-01-01
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. PMID:24976644
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.
Construction of minimum energy high-order Helmholtz bases for structured elements
NASA Astrophysics Data System (ADS)
Rodrigues, Caio F.; Suzuki, Jorge L.; Bittencourt, Marco L.
2016-02-01
We present a construction procedure for high-order expansion bases for structured finite elements specific for the operator under consideration. The procedure aims to obtain bases in such way that the condition numbers for the element matrices are almost constant or have a moderate increase in terms of the polynomial order. The internal modes of the mass and stiffness matrices are made simultaneously diagonal and the minimum energy concept is used to make the boundary modes orthogonal to the internal modes. The performance of the proposed bases is compared to the standard basis using Jacobi polynomials. This is performed through numerical examples for Helmholtz problem and transient linear elasticity employing explicit and implicit time integration algorithms and the conjugate gradient method with diagonal, SSOR and Gauss-Seidel pre-conditioners. The sparsity patterns, conditioning and solution costs are investigated. A significant speedup and reduction in the number of iterations are obtained when compared to the standard basis.
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.
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.
Probe of Multielectron Dynamics in Xenon by Caustics in High-Order Harmonic Generation
NASA Astrophysics Data System (ADS)
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.
2016-08-01
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.
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.
Output Feedback Distributed Containment Control for High-Order Nonlinear Multiagent Systems.
Li, Yafeng; Hua, Changchun; Wu, Shuangshuang; Guan, Xinping
2017-01-31
In this paper, we study the problem of output feedback distributed containment control for a class of high-order nonlinear multiagent systems under a fixed undirected graph and a fixed directed graph, respectively. Only the output signals of the systems can be measured. The novel reduced order dynamic gain observer is constructed to estimate the unmeasured state variables of the system with the less conservative condition on nonlinear terms than traditional Lipschitz one. Via the backstepping method, output feedback distributed nonlinear controllers for the followers are designed. By means of the novel first virtual controllers, we separate the estimated state variables of different agents from each other. Consequently, the designed controllers show independence on the estimated state variables of neighbors except outputs information, and the dynamics of each agent can be greatly different, which make the design method have a wider class of applications. Finally, a numerical simulation is presented to illustrate the effectiveness of the proposed method.
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.
GPU-based interactive cut-surface extraction from high-order finite element fields.
Nelson, Blake; Haimes, Robert; Kirby, Robert M
2011-12-01
We present a GPU-based ray-tracing system for the accurate and interactive visualization of cut-surfaces through 3D simulations of physical processes created from spectral/hp high-order finite element methods. When used by the numerical analyst to debug the solver, the ability for the imagery to precisely reflect the data is critical. In practice, the investigator interactively selects from a palette of visualization tools to construct a scene that can answer a query of the data. This is effective as long as the implicit contract of image quality between the individual and the visualization system is upheld. OpenGL rendering of scientific visualizations has worked remarkably well for exploratory visualization for most solver results. This is due to the consistency between the use of first-order representations in the simulation and the linear assumptions inherent in OpenGL (planar fragments and color-space interpolation). Unfortunately, the contract is broken when the solver discretization is of higher-order. There have been attempts to mitigate this through the use of spatial adaptation and/or texture mapping. These methods do a better job of approximating what the imagery should be but are not exact and tend to be view-dependent. This paper introduces new rendering mechanisms that specifically deal with the kinds of native data generated by high-order finite element solvers. The exploratory visualization tools are reassessed and cast in this system with the focus on image accuracy. This is accomplished in a GPU setting to ensure interactivity.
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)
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.
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.
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.
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.
Zhang, Daohong; Xu, Zhicai; Li, Junna; Chen, Sufang; Cheng, Juan; Zhang, Aiqing; Chen, Shenghui; Miao, Menghe
2014-09-24
Self-assemblies fabricated from dendrimers and amphiphilic polymers have demonstrated remarkable performances and a wide range of applications. Direct self-assembly of hyperbranched polymers into highly ordered macrostructures with heat-resistance remains a big challenge due to the weak amphiphilicity of the polymers. Here, we report the self-assembly of amphiphilic amido-ended hyperbranched polyester (HTDA-2) into millimeter-size dendritic films using combined hydrogen bond interaction and solvent induction. The self-assembly process and mechanism have been studied. Hydrogen bond interaction between amido-ended groups assists the aggregation of inner and outer chains of the HTDA-2, resulting in phase separation and micelle formation. Some micelles attach to and grow on the glass substrate like seedlings. Other micelles move to the seedlings and connect with their branches via solvent induction and hydrogen bond interaction, leading to the fabrication of highly ordered crystalline dendritic films that show high heat-resistance. HTDA-2 can further self-assemble into sheet crystals on the dendritic films.
Impact of electron ionization on the generation of high-order harmonics from molecules
Brener, S.; Moiseyev, N.; Ivanov, M. V.
2003-08-01
When the laser frequency is tuned to be equal to the molecular electronic excitation, high-order harmonics are generated due to the electronic dipole transitions between the corresponding two potential-energy surfaces (PES). A natural, often taken, choice is the PES of the field-free molecular system. In this special choice the ionization phenomenon is not considered. Only the effect of the dissociation is considered. The method we developed enables one to remain within the framework of the 2-PES approximation and yet to include also the ionization effect in the calculations of molecular high-order harmonic generation spectra. In this approach the coupling between the electronic and nuclear motions is taken into consideration by using coupled complex adiabatic PES. As an illustrative numerical example, we calculated the high harmonic generation (HHG) spectra of H{sub 2}{sup +} in a 730-nm laser with the intensity of 8.77x10{sup 13} W/cm{sup 2}. The inclusion of the ionization in our approach not only enables the electrons to tunnel through the effective static potential barrier, but also apply an asymmetric force which accelerates the electron before ionization takes place. Therefore, indirectly the inclusion of the ionization by the laser field may lead eventually to an enhanced HHG spectra in comparison with the calculated one when the ''natural'' choice of the field-free 2PES is taken.
Inhomogeneity of charge-density-wave order and quenched disorder in a high-Tc superconductor
NASA Astrophysics Data System (ADS)
Campi, G.; Bianconi, A.; Poccia, N.; Bianconi, G.; Barba, L.; Arrighetti, G.; Innocenti, D.; Karpinski, J.; Zhigadlo, N. D.; Kazakov, S. M.; Burghammer, M.; Zimmermann, M. V.; Sprung, M.; Ricci, A.
2015-09-01
It has recently been established that the high-transition-temperature (high-Tc) superconducting state coexists with short-range charge-density-wave order and quenched disorder arising from dopants and strain. This complex, multiscale phase separation invites the development of theories of high-temperature superconductivity that include complexity. The nature of the spatial interplay between charge and dopant order that provides a basis for nanoscale phase separation remains a key open question, because experiments have yet to probe the unknown spatial distribution at both the nanoscale and mesoscale (between atomic and macroscopic scale). Here we report micro X-ray diffraction imaging of the spatial distribution of both short-range charge-density-wave `puddles' (domains with only a few wavelengths) and quenched disorder in HgBa2CuO4 + y, the single-layer cuprate with the highest Tc, 95 kelvin (refs 26, 27, 28). We found that the charge-density-wave puddles, like the steam bubbles in boiling water, have a fat-tailed size distribution that is typical of self-organization near a critical point. However, the quenched disorder, which arises from oxygen interstitials, has a distribution that is contrary to the usually assumed random, uncorrelated distribution. The interstitial-oxygen-rich domains are spatially anticorrelated with the charge-density-wave domains, because higher doping does not favour the stripy charge-density-wave puddles, leading to a complex emergent geometry of the spatial landscape for superconductivity.
Multi-Material Closure Model for High-Order Finite Element Lagrangian Hydrodynamics
Dobrev, V. A.; Kolev, T. V.; Rieben, R. N.; ...
2016-04-27
We present a new closure model for single fluid, multi-material Lagrangian hydrodynamics and its application to high-order finite element discretizations of these equations [1]. The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a high-order variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial non-instantaneous pressure equilibration, while the full pressure equilibration is achieved bymore » both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard one-dimensional two-material problems, followed by two-dimensional and three-dimensional multi-material high-velocity impact arbitrary Lagrangian–Eulerian calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.« less
Multi-Material Closure Model for High-Order Finite Element Lagrangian Hydrodynamics
Dobrev, V. A.; Kolev, T. V.; Rieben, R. N.; Tomov, V. Z.
2016-04-27
We present a new closure model for single fluid, multi-material Lagrangian hydrodynamics and its application to high-order finite element discretizations of these equations [1]. The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a high-order variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial non-instantaneous pressure equilibration, while the full pressure equilibration is achieved by both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard one-dimensional two-material problems, followed by two-dimensional and three-dimensional multi-material high-velocity impact arbitrary Lagrangian–Eulerian calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.
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.
A comparison of high-order polynomial and wave-based methods for Helmholtz problems
NASA Astrophysics Data System (ADS)
Lieu, Alice; Gabard, Gwénaël; Bériot, Hadrien
2016-09-01
The application of computational modelling to wave propagation problems is hindered by the dispersion error introduced by the discretisation. Two common strategies to address this issue are to use high-order polynomial shape functions (e.g. hp-FEM), or to use physics-based, or Trefftz, methods where the shape functions are local solutions of the problem (typically plane waves). Both strategies have been actively developed over the past decades and both have demonstrated their benefits compared to conventional finite-element methods, but they have yet to be compared. In this paper a high-order polynomial method (p-FEM with Lobatto polynomials) and the wave-based discontinuous Galerkin method are compared for two-dimensional Helmholtz problems. A number of different benchmark problems are used to perform a detailed and systematic assessment of the relative merits of these two methods in terms of interpolation properties, performance and conditioning. It is generally assumed that a wave-based method naturally provides better accuracy compared to polynomial methods since the plane waves or Bessel functions used in these methods are exact solutions of the Helmholtz equation. Results indicate that this expectation does not necessarily translate into a clear benefit, and that the differences in performance, accuracy and conditioning are more nuanced than generally assumed. The high-order polynomial method can in fact deliver comparable, and in some cases superior, performance compared to the wave-based DGM. In addition to benchmarking the intrinsic computational performance of these methods, a number of practical issues associated with realistic applications are also discussed.