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.
2007-12-06
high order well-balanced schemes to a class of hyperbolic systems with source terms, Boletin de la Sociedad Espanola de Matematica Aplicada, v34 (2006...schemes to a class of hyperbolic systems with source terms, Boletin de la Sociedad Espanola de Matematica Aplicada, v34 (2006), pp.69-80. 39. Y. Xu and C.-W
High Order Accurate Algorithms for Shocks, Rapidly Changing Solutions and Multiscale Problems
2014-11-13
positivity-preserving property for such high speed flows. As an application to traffic flow modeling and simulations, we study a predictive continuum...related numerical methods, which are high order accurate numerical methods for solving problems with shocks and other complicated solution structures...New algorithm aspects include subcell resolution for non-conservative systems, high order well balanced schemes, stable Lagrangian schemes, schemes
S66: A Well-balanced Database of Benchmark Interaction Energies Relevant to Biomolecular Structures
2011-01-01
With numerous new quantum chemistry methods being developed in recent years and the promise of even more new methods to be developed in the near future, it is clearly critical that highly accurate, well-balanced, reference data for many different atomic and molecular properties be available for the parametrization and validation of these methods. One area of research that is of particular importance in many areas of chemistry, biology, and material science is the study of noncovalent interactions. Because these interactions are often strongly influenced by correlation effects, it is necessary to use computationally expensive high-order wave function methods to describe them accurately. Here, we present a large new database of interaction energies calculated using an accurate CCSD(T)/CBS scheme. Data are presented for 66 molecular complexes, at their reference equilibrium geometries and at 8 points systematically exploring their dissociation curves; in total, the database contains 594 points: 66 at equilibrium geometries, and 528 in dissociation curves. The data set is designed to cover the most common types of noncovalent interactions in biomolecules, while keeping a balanced representation of dispersion and electrostatic contributions. The data set is therefore well suited for testing and development of methods applicable to bioorganic systems. In addition to the benchmark CCSD(T) results, we also provide decompositions of the interaction energies by means of DFT-SAPT calculations. The data set was used to test several correlated QM methods, including those parametrized specifically for noncovalent interactions. Among these, the SCS-MI-CCSD method outperforms all other tested methods, with a root-mean-square error of 0.08 kcal/mol for the S66 data set. PMID:21836824
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; ...
2015-06-01
In this study, 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 show how HOLO approaches, in particular the implicit-explicit method, can provide a solid route for ocean simulation to heterogeneous computing and exascale environments.
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.
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.
Multiscale high-order/low-order (HOLO) algorithms and applications
Chacon, Luis; Chen, Guangye; Knoll, Dana Alan; ...
2016-11-11
Here, 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. Themore » 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.« less
Multiscale high-order/low-order (HOLO) algorithms and applications
Chacon, Luis; Chen, Guangye; Knoll, Dana Alan; Newman, Christopher Kyle; Park, HyeongKae; Taitano, William; Willert, Jeff A.; Womeldorff, Geoffrey Alan
2016-11-11
Here, 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.
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.
Building fast well-balanced two-stage numerical schemes for a model of two-phase flows
NASA Astrophysics Data System (ADS)
Thanh, Mai Duc
2014-06-01
We present a set of well-balanced two-stage schemes for an isentropic model of two-phase flows arisen from the modeling of deflagration-to-detonation transition in granular materials. The first stage is to absorb the source term in nonconservative form into equilibria. Then in the second stage, these equilibria will be composed into a numerical flux formed by using a convex combination of the numerical flux of a stable Lax-Friedrichs-type scheme and the one of a higher-order Richtmyer-type scheme. Numerical schemes constructed in such a way are expected to get the interesting property: they are fast and stable. Tests show that the method works out until the parameter takes on the value CFL, and so any value of the parameter between zero and this value is expected to work as well. All the schemes in this family are shown to capture stationary waves and preserves the positivity of the volume fractions. The special values of the parameter 0,1/2,1/(1+CFL), and CFL in this family define the Lax-Friedrichs-type, FAST1, FAST2, and FAST3 schemes, respectively. These schemes are shown to give a desirable accuracy. The errors and the CPU time of these schemes and the Roe-type scheme are calculated and compared. The constructed schemes are shown to be well-balanced and faster than the Roe-type scheme.
High-Order 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
High-Order Methods for Computational Physics
1999-03-01
some techniques to construct high order MUSCL type schemes on general meshes : the ENO and WENO type schemes. Special attention is given to the...years, a growing interest has emerged for constructing high order accurate and robust schemes for simulations of compressible fluid flow. One of the...reconstruction technique may be applied either to the nodal values [34] or to a particular function constructed from cell averages in control volumes [18,19]. In
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.
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.
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.
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 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.
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.
High order Nystrom method for acoustic scattering
NASA Astrophysics Data System (ADS)
Chen, Kun; Yang, Siming; Song, Jiming; Roberts, Ron
2015-03-01
While high frequency approximation methods are widely used to solve flaw scattering in ultrasonic nondestructive evaluation, full wave approaches based on integral equations have great potentials due to their high accuracy. In this work, boundary integral equations for acoustic wave scattering are solved using high order Nyström method. Compared with boundary elements method, it features the coincidence of the samples for interpolation basis and quadrature, which makes the far-field interaction free from numerical integration. The singular integral is dealt with using the Duffy transformation, while efficient singularity subtraction techniques are employed to evaluate the near singular integrals. This approach has the ease to go high order so highly accurate results can be obtained with fewer unknowns and faster convergence, and it is also amenable to incorporate fast algorithms like the multi-level fast multi-pole algorithm. The convergence of the approach for different orders of elements and interpolation basis functions is investigated. Numerical results are shown to validate this approach.
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.
Coherence properties of high order harmonic radiation
Ditmire, T.; Budil, K.S.; Crane, J.K.; Nguyen, H.; Perry, M.D.; Salieres, P.; Huillier, A.L.
1994-05-01
The results of a series of experiments to characterize the coherence properties of xuv radiation produced by high-order harmonic generation in helium, neon and argon are reported and compared to predictions from an effective order model. The harmonics exhibit smooth, near gaussian spatial profiles, and have a divergence that is approximately constant ( < 12 mrad) in the plateau region and decreases ({approx}4 mrad) in the cutoff for f/17 focusing. For a bandwidth limited, 140 fsec incident pulse, we measure a harmonic line width of {Delta}{lambda}/{lambda} {approx} 2 {times} 10{sup {minus}3} at 30.3 nm. By reducing the spectral width of the driving pulse, harmonics with {Delta}{lambda}/{lambda} {approx} 2 {times} 10{sup {minus}4} can be produced. Absolute conversion efficiency as high as 10{sup {minus}7} for harmonic radiation as short as 20 nm has been achieved by using 400 fsec, 526 nm pulses from an Nd:Glass laser.
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.
High-order counting statistics and interactions
NASA Astrophysics Data System (ADS)
Flindt, Christian
2012-02-01
Full counting statistics concerns the stochastic transport of electrons in mesoscopic structures [1]. Recently it has been shown that the charge transport statistics for noninteracting electrons in a two-terminal system is always generalized binomial: it can be decomposed into independent single-particle events, and the zeros of the generating function are real and negative [2]. In this talk I show how the zeros of the generating function move into the complex plane due to interactions and demonstrate how the positions of the zeros can be detected using high-order factorial cumulants [3]. As an illustrative example I discuss electron transport through a Coulomb blockade quantum dot for which the interactions on the quantum dot are clearly visible in the high-order factorial cumulants. These findings are important for understanding the influence of interactions on counting statistics, and the characterization in terms of zeros of the generating function provides a simple interpretation of recent experiments, where high-order statistics have been measured [4]. [4pt] [1] Yu. V. Nazarov, ed., Quantum Noise in Mesoscopic Physics, NATO Science Series, Vol. 97 (Kluwer, Dordrecht, 2003) [2] A. G. Abanov and D. A. Ivanov, Phys. Rev. Lett. 100, 086602 (2008), Phys. Rev. B 79, 205315 (2009) [3] D. Kambly, C. Flindt, and M. B"uttiker, Phys. Rev. B 83, 075432 (2011) -- Editors' Suggestion [4] C. Flindt, C. Fricke, F. Hohls, T. Novotn'y, K. Netocn'y, T. Brandes, and R. J. Haug, Proc. Natl. Acad. Sci. USA 106, 10116 (2009)
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.
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.
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.
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.
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.
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.
High order harmonics from relativistic electron spikes
NASA Astrophysics Data System (ADS)
Pirozhkov, Alexander S.; Kando, Masaki; Esirkepov, Timur Zh; Gallegos, Pablo; Ahmed, Hamad; Ragozin, Eugene N.; Faenov, Anatoly Ya; Pikuz, Tatiana A.; Kawachi, Tetsuya; Sagisaka, Akito; Koga, James K.; Coury, Mireille; Green, James; Foster, Peta; Brenner, Ceri; Dromey, Brendan; Symes, Dan R.; Mori, Michiaki; Kawase, Keigo; Kameshima, Takashi; Fukuda, Yuji; Chen, Liming; Daito, Izuru; Ogura, Koichi; Hayashi, Yukio; Kotaki, Hideyuki; Kiriyama, Hiromitsu; Okada, Hajime; Nishimori, Nobuyuki; Imazono, Takashi; Kondo, Kiminori; Kimura, Toyoaki; Tajima, Toshiki; Daido, Hiroyuki; Rajeev, Pattathil; McKenna, Paul; Borghesi, Marco; Neely, David; Kato, Yoshiaki; Bulanov, Sergei V.
2014-09-01
A new regime of relativistic high-order harmonic generation has been discovered (Pirozhkov 2012 Phys. Rev. Lett. 108 135004). Multi-terawatt relativistic-irradiance (>1018 W cm-2) femtosecond (˜30-50 fs) lasers focused to underdense (few × 1019 cm-3) plasma formed in gas jet targets produce comb-like spectra with hundreds of even and odd harmonic orders reaching the photon energy of 360 eV, including the ‘water window’ spectral range. Harmonics are generated either by linearly or circularly polarized pulses from the J-KAREN (KPSI, JAEA) and Astra Gemini (CLF, RAL, UK) lasers. The photon number scalability has been demonstrated with a 120 TW laser, producing 40 μJ sr-1 per harmonic at 120 eV. The experimental results are explained using particle-in-cell simulations and catastrophe theory. A new mechanism of harmonic generation by sharp, structurally stable, oscillating electron spikes at the joint of the boundaries of the wake and bow waves excited by a laser pulse is introduced. In this paper, detailed descriptions of the experiments, simulations and model are provided and new features are shown, including data obtained with a two-channel spectrograph, harmonic generation by circularly polarized laser pulses and angular distribution.
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.
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.
High School Order and Academic Achievement.
ERIC Educational Resources Information Center
Gaddy, Gary D.
In contrast to public opinion, the relationship between school order and achievement is neither simple nor certain. While research shows individuals who misbehave perform poorly in school, it has not made clear why. Further, the evidence on order and achievement at the school level is even more limited. One inference drawn here is that failure to…
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 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.
A high performance totally ordered multicast protocol
NASA Technical Reports Server (NTRS)
Montgomery, Todd; Whetten, Brian; Kaplan, Simon
1995-01-01
This paper presents the Reliable Multicast Protocol (RMP). RMP provides a totally ordered, reliable, atomic multicast service on top of an unreliable multicast datagram service such as IP Multicasting. RMP is fully and symmetrically distributed so that no site bears un undue portion of the communication load. RMP provides a wide range of guarantees, from unreliable delivery to totally ordered delivery, to K-resilient, majority resilient, and totally resilient atomic delivery. These QoS guarantees are selectable on a per packet basis. RMP provides many communication options, including virtual synchrony, a publisher/subscriber model of message delivery, an implicit naming service, mutually exclusive handlers for messages, and mutually exclusive locks. It has commonly been held that a large performance penalty must be paid in order to implement total ordering -- RMP discounts this. On SparcStation 10's on a 1250 KB/sec Ethernet, RMP provides totally ordered packet delivery to one destination at 842 KB/sec throughput and with 3.1 ms packet latency. The performance stays roughly constant independent of the number of destinations. For two or more destinations on a LAN, RMP provides higher throughput than any protocol that does not use multicast or broadcast.
High-order tail in Schwarzschild spacetime
NASA Astrophysics Data System (ADS)
Casals, Marc; Ottewill, Adrian
2015-12-01
We present an analysis of the behavior at late times of linear field perturbations of a Schwarzschild black hole spacetime. In particular, we give explicit analytic expressions for the field perturbations (for a specific ℓ-multipole) of general spin up to the first four orders at late times. These expressions are valid at arbitrary radius and include, apart from the well-known power-law tail decay at leading order (˜t-2 ℓ-3), a new logarithmic behavior at third leading order (˜t-2 ℓ-5ln t ). We obtain these late-time results by developing an analytical formalism initially formulated by Mano, Suzuki and Takasugi (MST) [Prog. Theor. Phys. 95, 1079 (1996); 96, 549 (1996)] formalism and by expanding the various MST Fourier-mode quantities for small frequency. While we give explicit expansions up to the first four leading orders (for small frequency for the Fourier modes, for late time for the field perturbation), we give a prescription for obtaining expressions to arbitrary order within a "perturbative regime."
Periodicity of high-order neural functions
NASA Technical Reports Server (NTRS)
Kellaway, P.; Borda, R. P.; Frost, J. D.; Carrie, J. R. G.; Coats, A. C.
1973-01-01
The results of recent studies on higher order, integrative processes in the central nervous system are reported. Attempts were made to determine whether these processes exhibit any ongoing rhythmicity which might manifest itself in alterations of attention and alertness. Experiments were also designed to determine if a periodicity approximating that of the REM could be detected in various parameters of brain electrical activity.
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.
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.
Ennequin, Gaël; Boisseau, Nathalie; Caillaud, Kevin; Chavanelle, Vivien; Gerbaix, Maude; Metz, Lore; Etienne, Monique; Walrand, Stéphane; Masgrau, Aurélie; Guillet, Christelle; Courteix, Daniel; Niu, Airu; Li, Yi-Ping; Capel, Fréderic; Sirvent, Pascal
2015-01-01
Some studies suggest that the signalling pathway of neuregulin 1 (NRG1), a protein involved in the regulation of skeletal muscle metabolism, could be altered by nutritional and exercise interventions. We hypothesized that diet-induced obesity could lead to alterations of the NRG1 signalling pathway and that chronic exercise could improve NRG1 signalling in rat skeletal muscle. To test this hypothesis, male Wistar rats received a high fat/high sucrose (HF/HS) diet for 16 weeks. At the end of this period, NRG1 and ErbB expression/activity in skeletal muscle was assessed. The obese rats then continued the HF/HS diet or were switched to a well-balanced diet. Moreover, in both groups, half of the animals also performed low intensity treadmill exercise training. After another 8 weeks, NRG1 and ErbB expression/activity in skeletal muscle were tested again. The 16 week HF/HS diet induced obesity, but did not significantly affect the NRG1/ErbB signalling pathway in rat skeletal muscle. Conversely, after the switch to a well-balanced diet, NRG1 cleavage ratio and ErbB4 amount were increased. Chronic exercise training also promoted NRG1 cleavage, resulting in increased ErbB4 phosphorylation. This result was associated with increased protein expression and phosphorylation ratio of the metalloprotease ADAM17, which is involved in NRG1 shedding. Similarly, in vitro stretch-induced activation of ADAM17 in rat myoblasts induced NRG1 cleavage and ErbB4 activation. These results show that low intensity endurance training and well-balanced diet activate the NRG1-ErbB4 pathway, possibly via the metalloprotease ADAM17, in skeletal muscle of diet-induced obese rats. PMID:25820551
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 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.
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
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.
Designing Adaptive Low Dissipative High Order Schemes
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sjoegreen, B.; Parks, John W. (Technical Monitor)
2002-01-01
Proper control of the numerical dissipation/filter to accurately resolve all relevant multiscales of complex flow problems while still maintaining nonlinear stability and efficiency for long-time numerical integrations poses a great challenge to the design of numerical methods. The required type and amount of numerical dissipation/filter are not only physical problem dependent, but also vary from one flow region to another. This is particularly true for unsteady high-speed shock/shear/boundary-layer/turbulence/acoustics interactions and/or combustion problems since the dynamics of the nonlinear effect of these flows are not well-understood. Even with extensive grid refinement, it is of paramount importance to have proper control on the type and amount of numerical dissipation/filter in regions where it is needed.
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.
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)
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.
Frances, Oriane; Fatemi, Fataneh; Pompon, Denis; Guittet, Eric; Sizun, Christina; Pérez, Javier; Lescop, Ewen; Truan, Gilles
2015-01-01
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. PMID:25809265
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.
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
Second-order accurate difference schemes on highly irregular meshes
Manteuffel, T.A.; White, A.B. Jr.
1988-01-01
In this paper compact-as-possible second-order accurate difference schemes will be constructed for boundary-value problems of arbitrary order on highly irregular meshes. It will be shown that for equations of order (K) these schemes will have truncation error of order (3/endash/K). This phenomena is known as supraconvergence. 7 refs.
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 phase-lag order Runge Kutta pairs of orders 8(7)
NASA Astrophysics Data System (ADS)
Tsitouras, Ch.; Famelis, Ioannis Th.
2017-07-01
In this work we present a representative of a new wider family of high phase-lag order 16 Runge-Kutta pairs of orders 8(7) with smaller principal local truncation term than the methods suggested in the literature. Numerical experiments justify the characteristics of the new method.
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.
High-order dispersion suppression for FFAG-based optics
NASA Astrophysics Data System (ADS)
Fenning, R.; Machida, S.; Kelliher, D.; Khan, A.; Edgecock, R.
2012-05-01
The resurgence of interest in FFAG type magnets has motivated the desire for high-order dispersion suppression to aid the development of dispersion-free straight sections to currently circular designs. In scaling FFAGs, dispersion suppression can only be achieved over a limited momentum range and breaks down as high-order chromatic aberration terms become significant. However by breaking the scaling law and varying the individual multipole components, these can be compensated for and a design for high-order dispersion suppression achieved. This paper presents a process for doing so and discusses the impact on beta functions, as well as the effect of magnet positioning errors.
Efficient Unsteady Flow Visualization with High-Order Access Dependencies
Zhang, Jiang; Guo, Hanqi; Yuan, Xiaoru
2016-04-19
We present a novel high-order access dependencies based model for efficient pathline computation in unsteady flow visualization. By taking longer access sequences into account to model more sophisticated data access patterns in particle tracing, our method greatly improves the accuracy and reliability in data access prediction. In our work, high-order access dependencies are calculated by tracing uniformly-seeded pathlines in both forward and backward directions in a preprocessing stage. The effectiveness of our proposed approach is demonstrated through a parallel particle tracing framework with high-order data prefetching. Results show that our method achieves higher data locality and hence improves the efficiency of pathline computation.
High Spin-Chern Insulators with Magnetic Order
NASA Astrophysics Data System (ADS)
Ezawa, Motohiko
2013-12-01
As a topological insulator, the quantum Hall (QH) effect is indexed by the Chern and spin-Chern numbers and . We have only in conventional QH systems. We investigate QH effects in generic monolayer honeycomb systems. We search for spin-resolved characteristic patterns by exploring Hofstadter's butterfly diagrams in the lattice theory and fan diagrams in the low-energy Dirac theory. It is shown that the spin-Chern number can takes an arbitrary high value for certain QH systems. This is a new type of topological insulators, which we may call high spin-Chern insulators. Samples may be provided by graphene on the SiC substrate with ferromagnetic order, transition-metal dichalcogenides with ferromagnetic order, transition-metal oxide with antiferromagnetic order and silicene with ferromagnetic order. Actually high spin-Chern insulators are ubiquitous in any systems with magnetic order. Nevertheless, the honeycomb system would provide us with unique materials for practical materialization.
High Spin-Chern Insulators with Magnetic Order
Ezawa, Motohiko
2013-01-01
As a topological insulator, the quantum Hall (QH) effect is indexed by the Chern and spin-Chern numbers and . We have only in conventional QH systems. We investigate QH effects in generic monolayer honeycomb systems. We search for spin-resolved characteristic patterns by exploring Hofstadter's butterfly diagrams in the lattice theory and fan diagrams in the low-energy Dirac theory. It is shown that the spin-Chern number can takes an arbitrary high value for certain QH systems. This is a new type of topological insulators, which we may call high spin-Chern insulators. Samples may be provided by graphene on the SiC substrate with ferromagnetic order, transition-metal dichalcogenides with ferromagnetic order, transition-metal oxide with antiferromagnetic order and silicene with ferromagnetic order. Actually high spin-Chern insulators are ubiquitous in any systems with magnetic order. Nevertheless, the honeycomb system would provide us with unique materials for practical materialization. PMID:24310394
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.
Reduced Order Modeling For High Speed Flows with Moving Shocks
2001-12-03
use of Proper Orthogonal Decomposition ( POD ) for reduced order modeling (ROM)of fluid problems is extended to high-speed compressible fluid flows. The...challenge in using POD for high-speed flows is presented by the presence of moving discontinuities in the flow field. To ovecome these difficulties...difficulty. The accuracy and order reduction of the domain decomposition POD /ROM approach is quantified for each application. ROMs with as large as three
An explicit high order method for fractional advection diffusion equations
NASA Astrophysics Data System (ADS)
Sousa, Ercília
2014-12-01
We propose a high order explicit finite difference method for fractional advection diffusion equations. These equations can be obtained from the standard advection diffusion equations by replacing the second order spatial derivative by a fractional operator of order α with 1<α≤2. This operator is defined by a combination of the left and right Riemann-Liouville fractional derivatives. We study the convergence of the numerical method through consistency and stability. The order of convergence varies between two and three and for advection dominated flows is close to three. Although the method is conditionally stable, the restrictions allow wide stability regions. The analysis is confirmed by numerical examples.
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.
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.
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.
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.
Transient L1 error estimates for well-balanced schemes on non-resonant scalar balance laws
NASA Astrophysics Data System (ADS)
Amadori, Debora; Gosse, Laurent
The ability of Well-Balanced (WB) schemes to capture very accurately steady-state regimes of non-resonant hyperbolic systems of balance laws has been thoroughly illustrated since its introduction by Greenberg and LeRoux (1996) [15] (see also the anterior WB Glimm scheme in E, 1992 [8]). This paper aims at showing, by means of rigorous Ct0(Lx1) estimates, that these schemes deliver an increased accuracy in transient regimes too. Namely, after explaining that for the vast majority of non-resonant scalar balance laws, the Ct0(Lx1) error of conventional fractional-step (Tang and Teng, 1995 [45]) numerical approximations grows exponentially in time like exp(max(g')t)√{Δx} (as a consequence of the use of Gronwall's lemma), it is shown that WB schemes involving an exact Riemann solver suffer from a much smaller error amplification: thanks to strict hyperbolicity, their error grows at most only linearly in time (see also Layton, 1984 [30]). Numerical results on several test-cases of increasing difficulty (including the classical LeVeque-Yee's benchmark problem (LeVeque and Yee, 1990 [34]) in the non-stiff case) confirm the analysis.
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.
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.
Reconstructing a High School Society After Court-Ordered Desegregation.
ERIC Educational Resources Information Center
Collins, Thomas W.
A recently desegregated high school student subsystem in a Deep South urban center is examined in this paper. It was found that although court ordered desegregation paired two high school populations, it did not effect racial boundaries. The whites, largely because they had been attending the school prior to desegregation, have been able to…
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.
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.
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.
Theory of intertwined orders in high temperature superconductors
Fradkin, Eduardo; Tranquada, John M.; Kivelson, Steven A.
2015-03-26
The electronic phase diagrams of many highly correlated systems, and in particular the cuprate high temperature superconductors, are complex, with many different phases appearing with similar—sometimes identical—ordering temperatures even as material properties, such as a dopant concentration, are varied over wide ranges. This complexity is sometimes referred to as “competing orders.” However, since the relation is intimate, and can even lead to the existence of new phases of matter such as the putative “pair-density-wave,” the general relation is better thought of in terms of “intertwined orders.” We selectively analyze some of the experiments in the cuprates which suggest that essentialmore » aspects of the physics are reflected in the intertwining of multiple orders—not just in the nature of each order by itself. We also summarize and critique several theoretical ideas concerning the origin and implications of this complexity.« less
The Observation of Highly Ordered Domains in Membranes with Cholesterol
Armstrong, Clare L; Marquardt, Drew; Dies, Hannah; Kucerka, Norbert; Yamani, Zahra; Harroun, Thad; Katsaras, John; Shi, A-C; Rheinstadter, Maikel C
2013-01-01
Rafts, or functional domains, are transient nano- or mesoscopic structures in the exoplasmic leaflet of the plasma membrane, and are thought to be essential for many cellular processes. Using neutron diffraction and computer modelling, we present evidence for the existence of highly ordered lipid domains in the cholesterol-rich (32.5 mol%) liquid-ordered (lo) phase of dipalmitoylphosphatidylcholine membranes. The liquid ordered phase in one-component lipid membranes has previously been thought to be a homogeneous phase. The presence of highly ordered lipid domains embedded in a disordered lipid matrix implies non-uniform distribution of cholesterol between the two phases. The experimental results are in excellent agreement with recent computer simulations of DPPC/cholesterol complexes [Meinhardt, Vink and Schmid (2013). Proc Natl Acad Sci USA 110(12): 4476 4481], which reported the existence of nanometer size lo domains in a liquid disordered lipid environment.
The Observation of Highly Ordered Domains in Membranes with Cholesterol
Armstrong, Clare L.; Marquardt, Drew; Dies, Hannah; Kučerka, Norbert; Yamani, Zahra; Harroun, Thad A.; Katsaras, John; Shi, An-Chang; Rheinstädter, Maikel C.
2013-01-01
Rafts, or functional domains, are transient nano- or mesoscopic structures in the exoplasmic leaflet of the plasma membrane, and are thought to be essential for many cellular processes. Using neutron diffraction and computer modelling, we present evidence for the existence of highly ordered lipid domains in the cholesterol-rich (32.5 mol%) liquid-ordered () phase of dipalmitoylphosphatidylcholine membranes. The liquid ordered phase in one-component lipid membranes has previously been thought to be a homogeneous phase. The presence of highly ordered lipid domains embedded in a disordered lipid matrix implies non-uniform distribution of cholesterol between the two phases. The experimental results are in excellent agreement with recent computer simulations of DPPC/cholesterol complexes [Meinhardt, Vink and Schmid (2013). Proc Natl Acad Sci USA 110(12): 4476–4481], which reported the existence of nanometer size domains in a liquid disordered lipid environment. PMID:23823623
Adaptive Numerical Dissipation Controls for High Order Methods
NASA Technical Reports Server (NTRS)
Yee, Helen C.; Sjogreen, B.; Sandham, N. D.; Mansour, Nagi (Technical Monitor)
2001-01-01
A numerical scheme for direct numerical simulation of shock-turbulence interactions of high speed compressible flows would ideally not be significantly more expensive than the standard fourth or sixth-order compact or non-compact central differencing scheme. It should be possible to resolve all scales down to scales of order of the Kolmogorov scales of turbulence accurately and efficiently, while at the same time being able to capture steep gradients occurring at much smaller scales efficiently. The goal of this lecture is to review the progress and new development of the low dissipative high order shock-capturing schemes proposed by Yee et al. Comparison on the efficiency and accuracy of this class of schemes with spectral and the fifth-order WENO (weighted essentially nonoscillatory) scheme will be presented. A new approach to dynamically sense the appropriate amount of numerical dissipation to be added at each grid point using non-orthogonal wavelets will be discussed.
Theory of intertwined orders in high temperature superconductors
Fradkin, Eduardo; Tranquada, John M.; Kivelson, Steven A.
2015-03-26
The electronic phase diagrams of many highly correlated systems, and in particular the cuprate high temperature superconductors, are complex, with many different phases appearing with similar—sometimes identical—ordering temperatures even as material properties, such as a dopant concentration, are varied over wide ranges. This complexity is sometimes referred to as “competing orders.” However, since the relation is intimate, and can even lead to the existence of new phases of matter such as the putative “pair-density-wave,” the general relation is better thought of in terms of “intertwined orders.” We selectively analyze some of the experiments in the cuprates which suggest that essential aspects of the physics are reflected in the intertwining of multiple orders—not just in the nature of each order by itself. We also summarize and critique several theoretical ideas concerning the origin and implications of this complexity.
Separation of High Order Harmonics with Fluoride Windows
Allison, Tom; van Tilborg, Jeroen; Wright, Travis; Hertlein, Marcus; Falcone, Roger; Belkacem, Ali
2010-08-02
The lower orders produced in high order harmonic generation can be effciently temporally separated into monochromatic pulses by propagation in a Fluoride window while still preserving their femtosecond pulse duration. We present calculations for MgF2, CaF2, and LiF windows for the third, fifth, and seventh harmonics of 800 nm. We demonstrate the use of this simple and inexpensive technique in a femtosecond pump/probe experiment using the fifth harmonic.
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.
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.
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.
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.
Hyperspectral target detection using regularized high-order matched filter
NASA Astrophysics Data System (ADS)
Shi, Zhenwei; Yang, Shuo; Jiang, Zhiguo
2011-05-01
Automatic target detection is an important application in the hyperspectral image processing field. Most statistics-based detection algorithms use second-order statistics to construct detectors. However, for target detection in a real hyperspectral image, targets of interest usually occupy a few pixels with small population. In this case, high-order statistics could characterize targets more effectively than second-order statistics. Also, the inherent variation of spectra of targets is an obstacle to successful target detection. In this paper, we propose a regularized high-order matched filter (RHF) which uses high-order statistics to build an objective function and uses a regularized term to make the algorithm robust to target spectral variation. A gradient descent method is used to solve this optimization problem, and we obtain the convergence properties of the RHF. According to the experimental hyperspectral data, the results have shown that the proposed algorithm performed better than those classical second-order statistics-based algorithms and some kernel-based methods.
Atomic short-range order and incipient long-range order in high-entropy alloys
NASA Astrophysics Data System (ADS)
Singh, Prashant; Smirnov, A. V.; Johnson, D. D.
2015-06-01
Within density-functional theory, we apply an electronic-structure-based thermodynamic theory to calculate short-ranged order (SRO) in homogeneously disordered substitutional N -component alloys, and its electronic origin. Using the geometric properties of an (N -1 ) simplex that describes the Gibbs (compositional) space, we derive the analytic transform of the SRO eigenvectors that provides a unique description of high-temperature SRO in N -component alloys and the incipient low-temperature long-range order. We apply the electronic-based thermodynamic theory and the new general analysis to ternaries (A 1 Cu-Ni-Zn and A 2 Nb-Al-Ti) for validation, and then to quinary Al-Co-Cr-Fe-Ni high-entropy alloys for predictive assessment.
Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows
NASA 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
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
Nonreflective boundary conditions for high-order methods
NASA Technical Reports Server (NTRS)
Atkins, H.; Casper, Jay
1994-01-01
A different approach to nonreflective boundary conditions for the Euler equations is presented. This work is motivated by a need for inflow and outflow boundary conditions that do not limit the useful accuracy of high-order accurate methods. The primary interest is in the propagation and convection of continuous acoustic and convective waves. This new approach employs the exact solution to finite waves to relate interior values and ambient conditions to boundary values. The method is first presented in one dimension and then generalized to multidimensions. Grid refinement studies are used to demonstrate high-order convergence for both one-dimensional and two-dimensional flows.
Nonreflective boundary conditions for high-order methods
NASA Technical Reports Server (NTRS)
Atkins, H. L.; Casper, Jay
1993-01-01
A different approach to nonreflective boundary conditions for the Euler equations is presented. This work is motivated by a need for in and outflow boundary conditions that do not limit the useful accuracy of high-order accurate methods. The primary interest is in the propagation and convection of continuous acoustic and convective waves. This new approach employs the exact solution to finite waves to relate interior values and ambient conditions to boundary values. The method is first presented in one dimension and then generalized to multidimensions. Grid refinement studies are used to demonstrate high-order convergence for both one-dimensional and two-dimensional flows.
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.
High-order anisotropic diffraction in photoreflective crystals
Temple, D.A.; Warde, C.
1988-08-01
High-order anisotropic diffraction and anisotropic self-diffraction in barium titanate (BaTiO/sub 3/), strontium barium niobate (Sr/sub x/Ba/sub 1-//sub x/Nb/sub 2/O/sub 6/, or SBN), and barium strontium potassium sodium niobate (Ba/sub 2//sub -//sub x/Sr/sub x/K/sub 1-//sub y/Na/sub y/Nb/sub 5/O/sub 15/, or BSKNN) have been observed: up to fourth order in BaTiO/sub 3/ and SBN and up to fifth order in BSKNN. It is shown that the scattered beams arising from anisotropic self-diffraction are composed of multiple orders. To model anisotropic diffraction, high-order terms have been included in Kukhtarev's solution of the transport equations for diffusion-dominated transport. Light-induced grating decay rates and diffraction efficiencies were measured as a function of grating vector and modulation index for the first three orders in BaTiO/sub 3/ and were found to be in good agreement with the model.
High spin-Chern insulators with magnetic order.
Ezawa, Motohiko
2013-12-06
As a topological insulator, the quantum Hall (QH) effect is indexed by the Chern and spin-Chern numbers C and Cspin. We have only Cspin = 0 or ± 1/2 in conventional QH systems. We investigate QH effects in generic monolayer honeycomb systems. We search for spin-resolved characteristic patterns by exploring Hofstadter's butterfly diagrams in the lattice theory and fan diagrams in the low-energy Dirac theory. It is shown that the spin-Chern number can takes an arbitrary high value for certain QH systems. This is a new type of topological insulators, which we may call high spin-Chern insulators. Samples may be provided by graphene on the SiC substrate with ferromagnetic order, transition-metal dichalcogenides with ferromagnetic order, transition-metal oxide with antiferromagnetic order and silicene with ferromagnetic order. Actually high spin-Chern insulators are ubiquitous in any systems with magnetic order. Nevertheless, the honeycomb system would provide us with unique materials for practical materialization.
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.
Developing High-Order Weighted Compact Nonlinear Schemes
NASA Astrophysics Data System (ADS)
Deng, Xiaogang; Zhang, Hanxin
2000-11-01
The weighted technique is introduced in the compact high-order nonlinear schemes (CNS) and three fourth- and fifth-order weighted compact nonlinear schemes (WCNS) are developed in this paper. By Fourier analysis, the dissipative and dispersive features of WCNS are discussed. In view of the modified wave number, the WCNS are equivalent to fifth-order upwind biased explicit schemes in smooth regions and the interpolations at cell-edges dominate the properties of WCNS. Both flux difference splitting and flux vector splitting methods can be applied in WCNS, though they are finite difference schemes. Boundary and near boundary schemes are developed and the asymptotic stability of WCNS is analyzed. Several numerical results are given which show the good performances of WCNS for discontinuity capture high accuracy for boundary layer calculation, and good convergent rate. We also compare WCNS with MUSCL scheme and spectral solutions. WCNS are more accurate than MUSCL, as expected, especially for heat transfer calculations.
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.
A New Low Dissipative High Order Schemes for MHD Equations
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sjoegreen, Bjoern; Mansour, Nagi (Technical Monitor)
2002-01-01
The goal of this talk is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls to limit the amount and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids.
Automated Approach to Very High-Order Aeroacoustic Computations. Revision
NASA Technical Reports Server (NTRS)
Dyson, Rodger W.; Goodrich, John W.
2001-01-01
Computational aeroacoustics requires efficient, high-resolution simulation tools. For smooth problems, this is best accomplished with very high-order in space and time methods on small stencils. However, the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewski recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that am located near wall boundaries. These procedures are used to develop automatically and to implement very high-order methods (> 15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.
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 \
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.}
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 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.
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 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.
A Highly-Ordered 3D Covalent Fullerene Framework**
Minar, Norma K; Hou, Kun; Westermeier, Christian; Döblinger, Markus; Schuster, Jörg; Hanusch, Fabian C; Nickel, Bert; Ozin, Geoffrey A; Bein, Thomas
2015-01-01
A highly-ordered 3D covalent fullerene framework is presented with a structure based on octahedrally functionalized fullerene building blocks in which every fullerene is separated from the next by six functional groups and whose mesoporosity is controlled by cooperative self-assembly with a liquid-crystalline block copolymer. The new fullerene-framework material was obtained in the form of supported films by spin coating the synthesis solution directly on glass or silicon substrates, followed by a heat treatment. The fullerene building blocks coassemble with a liquid-crystalline block copolymer to produce a highly ordered covalent fullerene framework with orthorhombic Fmmm symmetry, accessible 7.5 nm pores, and high surface area, as revealed by gas adsorption, NMR spectroscopy, small-angle X-ray scattering (SAXS), and TEM. We also note that the 3D covalent fullerene framework exhibits a dielectric constant significantly lower than that of the nonporous precursor material. PMID:25958846
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.
High-order parabolic beam approximation for aero-optics
White, Michael D.
2010-08-01
The parabolic beam equations are solved using high-order compact differences for the Laplacians and Runge-Kutta integration along the beam path. The solution method is verified by comparison to analytical solutions for apertured beams and both constant and complex index of refraction. An adaptive 4th-order Runge-Kutta using an embedded 2nd-order method is presented that has demonstrated itself to be very robust. For apertured beams, the results show that the method fails to capture near aperture effects due to a violation of the paraxial approximation in that region. Initial results indicate that the problem appears to be correctable by successive approximations. A preliminary assessment of the effect of turbulent scales is undertaken using high-order Lagrangian interpolation. The results show that while high fidelity methods are necessary to accurately capture the large scale flow structure, the method may not require the same level of fidelity in sampling the density for the index of refraction. The solution is used to calculate a phase difference that is directly compared with that commonly calculated via the optical path difference. Propagation through a supersonic boundary layer shows that for longer wavelengths, the traditional method to calculate the optical path is less accurate than for shorter wavelengths. While unlikely to supplant more traditional methods for most aero-optics applications, the current method can be used to give a quantitative assessment of the other methods as well as being amenable to the addition of more physics.
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.
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.
Effect of Under-Resolved Grids on High Order Methods
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sjoegreen, B.; Mansour, Nagi (Technical Monitor)
2001-01-01
There has been much discussion on verification and validation processes for establishing the credibility of CFD simulations. Since the early 1990s, many of the aeronautical and mechanical engineering related reference journals mandated that any accepted articles in numerical simulations (without known solutions to compared with) need to perform a minimum of one level of grid refinement and time step reduction. Due to the difficulty in analysis, the effect of under-resolved grids and the nonlinear behavior of available spatial discretizations, are scarcely discussed in the literature. Here, an under-resolved numerical simulation is one where the grid spacing being used is too coarse to resolve the smallest physically relevant scales of the chosen continuum governing equations that are of interest to the numerical modeler. With the advent of new developments in fourth-order or higher spatial schemes, it has become common to regard high order schemes as more accurate, reliable and require less grid points. The danger comes when one tries to perform computations with the coarsest grid possible while still hoping to maintain numerical results sufficiently accurate for complex flows, and especially, data-limited problems. On one hand, high order methods when applies to highly coupled multidimensional complex nonlinear problems might have different stability, convergence and reliability behavior than their well studied low order counterparts, especially for nonlinear schemes such as TVD, MUSCL with limiters, ENO, WENO and discrete Galerkin. On the other hand, high order methods involve more operation counts and systematic grid convergence study can be time consuming and prohibitively expansive. At the same time it is difficult to fully understand or categorize the different nonlinear behavior of finite discretizations, especially at the limits of under-resolution when different types of bifurcation phenomena might occur, depending on the combination of grid spacings, time
A Low Order and a High Order Solution for a Converging-Diverging Nozzle Problem
NASA Technical Reports Server (NTRS)
Goodrich, John W.
2000-01-01
The Computational Aeroacoustics Workshops on Benchmark problems are conducted in order to generate solutions with a variety of methods for problems that are chosen both to be representative of significant and relevant acoustic phenomena. It is generally recognized that CAA applications require the resolution in time and in space of solution details over a significantly broader range of scales than typical computational fluid dynamics applications. These requirements are forcing the development of new methodologies for CAA applications. This paper presents numerical results from a third and a seventh order algorithm for the propagation of an acoustic signal through a converging-diverging nozzle. These two algorithms are members of a new family of high accuracy methods that have the same order accuracy in both space and time, and are an extension of previous work for linearized Euler equations to fully nonlinear time dependent problems. The simulations are all with the fully nonlinear quasi-1D Euler equations for the total solution, which includes both the fluid dynamics and the acoustics. The acoustic solution is obtained from the time dependent nonlinear solution by subtracting the steady solution.
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 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 regularization in lattice-Boltzmann equations
NASA Astrophysics Data System (ADS)
Mattila, Keijo K.; Philippi, Paulo C.; Hegele, Luiz A.
2017-04-01
A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order non-equilibrium moments are filtered, i.e., only the corresponding advective parts are retained after a given rank. The decomposition of moments into diffusive and advective parts is based directly on analytical relations between Hermite polynomial tensors. The resulting, refined regularization procedure leads to recurrence relations where high-order non-equilibrium moments are expressed in terms of low-order ones. The procedure is appealing in the sense that stability can be enhanced without local variation of transport parameters, like viscosity, or without tuning the simulation parameters based on embedded optimization steps. The improved stability properties are here demonstrated using the perturbed double periodic shear layer flow and the Sod shock tube problem as benchmark cases.
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.
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.
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.
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
Sensitivity of high-order-harmonic generation to aromaticity
NASA Astrophysics Data System (ADS)
Alharbi, A. F.; Boguslavskiy, A. E.; Thiré, N.; Schmidt, B. E.; Légaré, F.; Brabec, T.; Spanner, M.; Bhardwaj, V. R.
2015-10-01
The influence of cyclic electron delocalization associated with aromaticity on the high-order-harmonic generation (HHG) process is investigated in organic molecules. We show that the aromatic molecules benzene (C6H6 ) and furan (C4H4O ) produce high-order harmonics more efficiently than nonaromatic systems having the same ring structure. We also demonstrate that the relative strength of plateau harmonics is sensitive to the aromaticity in five-membered-ring molecules using furan, pyrrole (C4H4NH ), and thiophene (C4H4S ). Numerical time-dependent Schrödinger equation simulations of total orientation-averaged strong-field ionization yields show that the HHG from aromatic molecules comes predominantly from the two highest π molecular orbitals, which contribute to the aromatic character of the systems.
High Performance Parallel Algorithms for Improved Reduced-Order Modeling
2008-05-04
HIGH PERFORMANCE PARALLEL ALGORITHMS FOR IMPROVED REDUCED-ORDER MODELING AFOSR FA9550-05-1-0449 FINAL REPORT Chris Beattie, Jeff Borggaard, Serkan ... Serkan Gugercin and Traian Iliescu (co-PIs) Post-Docs Andrew Duggelby, Alexander Hay and Sonja Schlaugh Students Weston Hunter, Denis Kovacs, Miroslav...internship to discuss his research. [Contacts: Chris Camphouse (937) 255-6326, James Myatt (937) 255-8498] Synergistic Activities 1. Serkan Gugerin, with
Conditional High-Order Boltzmann Machines for Supervised Relation Learning.
Huang, Yan; Wang, Wei; Wang, Liang; Tan, Tieniu
2017-09-01
Relation learning is a fundamental problem in many vision tasks. Recently, high-order Boltzmann machine and its variants have shown their great potentials in learning various types of data relation in a range of tasks. But most of these models are learned in an unsupervised way, i.e., without using relation class labels, which are not very discriminative for some challenging tasks, e.g., face verification. In this paper, with the goal to perform supervised relation learning, we introduce relation class labels into conventional high-order multiplicative interactions with pairwise input samples, and propose a conditional high-order Boltzmann Machine (CHBM), which can learn to classify the data relation in a binary classification way. To be able to deal with more complex data relation, we develop two improved variants of CHBM: 1) latent CHBM, which jointly performs relation feature learning and classification, by using a set of latent variables to block the pathway from pairwise input samples to output relation labels and 2) gated CHBM, which untangles factors of variation in data relation, by exploiting a set of latent variables to multiplicatively gate the classification of CHBM. To reduce the large number of model parameters generated by the multiplicative interactions, we approximately factorize high-order parameter tensors into multiple matrices. Then, we develop efficient supervised learning algorithms, by first pretraining the models using joint likelihood to provide good parameter initialization, and then finetuning them using conditional likelihood to enhance the discriminant ability. We apply the proposed models to a series of tasks including invariant recognition, face verification, and action similarity labeling. Experimental results demonstrate that by exploiting supervised relation labels, our models can greatly improve the performance.
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
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.
An extreme ultraviolet interferometer using high order harmonic generation
NASA Astrophysics Data System (ADS)
Laban, D. E.; Palmer, A. J.; Wallace, W. C.; Gaffney, N. S.; Notermans, R. P. M. J. W.; Clevis, T. T. J.; Pullen, M. G.; Jiang, D.; Quiney, H. M.; Litvinyuk, I. V.; Kielpinski, D.; Sang, R. T.
2014-04-01
We present a new interferometer technique based on the interference of high-order harmonic generation radiation from translatable successive gas jets. The phase shifts in the apparatus are shown to originate from the Gouy phase shift of the driving laser. The technique can be used to deliver time delays between light pulses and we demonstrate the unprecedented capability of delivering pulses of extreme ultraviolet light delayed in time by as small as 100 zeptoseconds.
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
High order spectral difference lattice Boltzmann method for incompressible hydrodynamics
NASA Astrophysics Data System (ADS)
Li, Weidong
2017-09-01
This work presents a lattice Boltzmann equation (LBE) based high order spectral difference method for incompressible flows. In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy. Because the SD scheme represents the solution as cell local polynomials and the solution polynomials have good tensor-product property, the present spectral difference lattice Boltzmann method (SD-LBM) can be implemented on arbitrary unstructured quadrilateral meshes for effective and efficient treatment of complex geometries. Thanks to only first oder PDEs involved in the LBE, no special techniques, such as hybridizable discontinuous Galerkin method (HDG), local discontinuous Galerkin method (LDG) and so on, are needed to discrete diffusion term, and thus, it simplifies the algorithm and implementation of the high order spectral difference method for simulating viscous flows. The proposed SD-LBM is validated with four incompressible flow benchmarks in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the lid-driven cavity flow without singularity at the two top corners-Burggraf flow; and (c) the unsteady Taylor-Green vortex flow; (d) the Blasius boundary-layer flow past a flat plate. Computational results are compared with analytical solutions of these cases and convergence studies of these cases are also given. The designed accuracy of the proposed SD-LBM is clearly verified.
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 harmonic generation via multicolor beam superposition
NASA Astrophysics Data System (ADS)
Sarikhani, S.; Batebi, S.
2017-09-01
In this article, femtosecond pulses, especially designed by multicolor beam superposition are used for high-order harmonic generation. To achieve this purpose, the spectral difference between the beams, and their width are taken to be small values, i.e., less than 1 nm. Applying a Gaussian distribution to the beam intensities leads to a more distinct pulses. Also, it is seen that these pulses have an intrinsic linear chirp. By changing the width of the Gaussian distributions, we can have several pulses with different bandwidths and hence various pulse duration. Thus, the study of these broadband pulse influences, in contrast with monochromatic pulses, on the atomic or molecular targets was achievable. So, we studied numerically the effect of these femtosecond pulses on behavior of the high-order harmonics generated after interaction between the pulse and the atomic hydrogen. For this study, we adjusted the beam intensities so that the produced pulse intensity be in the over-barrier ionization region. This makes the power spectrum of high-order harmonics more extensive. Cutoff frequency of the power spectrum along with the first harmonic intensity and its shift from the incident pulse are investigated. Additionally, maximum ionization probability with respect to the pulse bandwidth was also studied.
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.
TWave: high-order analysis of functional MRI.
Barnathan, Michael; Megalooikonomou, Vasileios; Faloutsos, Christos; Faro, Scott; Mohamed, Feroze B
2011-09-15
The traditional approach to functional image analysis models images as matrices of raw voxel intensity values. Although such a representation is widely utilized and heavily entrenched both within neuroimaging and in the wider data mining community, the strong interactions among space, time, and categorical modes such as subject and experimental task inherent in functional imaging yield a dataset with "high-order" structure, which matrix models are incapable of exploiting. Reasoning across all of these modes of data concurrently requires a high-order model capable of representing relationships between all modes of the data in tandem. We thus propose to model functional MRI data using tensors, which are high-order generalizations of matrices equivalent to multidimensional arrays or data cubes. However, several unique challenges exist in the high-order analysis of functional medical data: naïve tensor models are incapable of exploiting spatiotemporal locality patterns, standard tensor analysis techniques exhibit poor efficiency, and mixtures of numeric and categorical modes of data are very often present in neuroimaging experiments. Formulating the problem of image clustering as a form of Latent Semantic Analysis and using the WaveCluster algorithm as a baseline, we propose a comprehensive hybrid tensor and wavelet framework for clustering, concept discovery, and compression of functional medical images which successfully addresses these challenges. Our approach reduced runtime and dataset size on a 9.3GB finger opposition motor task fMRI dataset by up to 98% while exhibiting improved spatiotemporal coherence relative to standard tensor, wavelet, and voxel-based approaches. Our clustering technique was capable of automatically differentiating between the frontal areas of the brain responsible for task-related habituation and the motor regions responsible for executing the motor task, in contrast to a widely used fMRI analysis program, SPM, which only detected the
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.
High-order above-threshold ionization beyond the first-order Born approximation
NASA Astrophysics Data System (ADS)
Čerkić, A.; Hasović, E.; Milošević, D. B.; Becker, W.
2009-03-01
In the improved strong-field approximation, which describes high-order above-threshold ionization (HATI), the rescattering of the ionized electron on the parent ion is described within the first-order Born approximation. The low-frequency approximation for laser-assisted scattering goes beyond the first Born approximation. In the present paper, we derive the low-frequency approximation for HATI. The rescattering amplitude in the first Born approximation is replaced by the exact scattering amplitude calculated on the energy shell. Our numerical results for the angle-resolved HATI energy spectra show that the difference between the improved strong-field approximation and the low-frequency approximation is significant for scattering away from the laser polarization axis. In the context of quantum-orbit theory and the uniform approximation, we also show that on the back-rescattering ridge, the rescattering T -matrix element can be factorized into the product of the incoming flux and the elastic-scattering cross section so that the latter can be extracted from the angle- and energy-resolved HATI spectra.
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)
Rad-Hydro with a High-Order, Low-Order Method
Wollaber, Allan Benton; Park, HyeongKae; Lowrie, Robert Byron; Rauenzahn, Rick M.; Cleveland, Mathew Allen
2015-08-04
Moment-based acceleration via the development of “high-order, low-order” (HO-LO) algorithms has provided substantial accuracy and efficiency enhancements for solutions of the nonlinear, thermal radiative transfer equations by CCS-2 and T-3 staff members. Accuracy enhancements over traditional, linearized methods are obtained by solving a nonlinear, timeimplicit HO-LO system via a Jacobian-free Newton Krylov procedure. This also prevents the appearance of non-physical maximum principle violations (“temperature spikes”) associated with linearization. Efficiency enhancements are obtained in part by removing “effective scattering” from the linearized system. In this highlight, we summarize recent work in which we formally extended the HO-LO radiation algorithm to include operator-split radiation-hydrodynamics.
High-order harmonics from laser-irradiated plasma surfaces
Teubner, U.; Gibbon, P.
2009-04-15
The investigation of high-order harmonic generation (HHG) of femtosecond laser pulses by means of laser-produced plasmas is surveyed. This kind of harmonic generation is an alternative to the HHG in gases and shows significantly higher conversion efficiency. Furthermore, with plasma targets there is no limitation on applicable laser intensity and thus the generated harmonics can be much more intense. In principle, harmonic light may also be generated at relativistic laser intensity, in which case their harmonic intensities may even exceed that of the focused laser pulse by many orders of magnitude. This phenomenon presents new opportunities for applications such as nonlinear optics in the extreme ultraviolet region, photoelectron spectroscopy, and opacity measurements of high-density matter with high temporal and spatial resolution. On the other hand, HHG is strongly influenced by the laser-plasma interaction itself. In particular, recent results show a strong correlation with high-energy electrons generated during the interaction process. The harmonics are a promising tool for obtaining information not only on plasma parameters such as the local electron density, but also on the presence of large electric and magnetic fields, plasma waves, and the (electron) transport inside the target. This paper reviews the theoretical and experimental progress on HHG via laser-plasma interactions and discusses the prospects for applying HHG as a short-wavelength, coherent optical tool.
Shaping Neural Circuits by High Order Synaptic Interactions
Ravid Tannenbaum, Neta; Burak, Yoram
2016-01-01
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
NASA Astrophysics Data System (ADS)
Matsui, Yoshitaka; Nishio, Kazuyuki; Masuda, Hideki
2005-10-01
Anodic porous alumina with a highly ordered pore arrangement was prepared by imprinting using a metal (Ni) mold prepared from a two-dimensional ordered array of polystyrene particles as a template. The ordered array of shallow concaves of Al prepared by imprinting could initiate pore development and could guide pore growth during anodization. This process enables the high-throughput preparation of highly ordered anodic porous alumina because the metal mold can be used repeatedly.
On high-order perturbative calculations at finite density
Ghisoiu, Ioan; Gorda, Tyler; Kurkela, Aleksi; ...
2016-12-01
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 — aresult 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 perturbativemore » orders.« less
High-order harmonic generation from the dressed autoionizing states
NASA Astrophysics Data System (ADS)
Fareed, M. A.; Strelkov, V. V.; Thiré, N.; Mondal, S.; Schmidt, B. E.; Légaré, F.; Ozaki, T.
2017-07-01
In high-order harmonic generation, resonant harmonics (RH) are sources of intense, coherent extreme-ultraviolet radiation. However, intensity enhancement of RH only occurs for a single harmonic order, making it challenging to generate short attosecond pulses. Moreover, the mechanism involved behind such RH was circumstantial, because of the lack of direct experimental proofs. Here, we demonstrate the exact quantum paths that electron follows for RH generation using tin, showing that it involves not only the autoionizing state, but also a harmonic generation from dressed-AIS that appears as two coherent satellite harmonics at frequencies +/-2Ω from the RH (Ω represents laser frequency). Our observations of harmonic emission from dressed states open the possibilities of generating intense and broadband attosecond pulses, thus contributing to future applications in attosecond science, as well as the perspective of studying the femtosecond and attosecond dynamics of autoionizing states.
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.
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 test bench for extreme adaptive optics system optimization
NASA Astrophysics Data System (ADS)
Aller-Carpentier, Emmanuel; Kasper, Markus; Martinez, Patrice; Vernet, Elise; Fedrigo, Enrico; Soenke, Christian; Tordo, Sébastien; Hubin, Norbert; Verinaud, Christophe; Esposito, Simone; Pinna, Enrico; Puglisi, Alfio; Tozzi, Andrea; Quiros, Fernando; Basden, Alastair G.; Goodsell, Stephen J.; Love, Gordon D.; Myers, Richard M.
2008-07-01
High-contrast imagers dedicated to the search for extrasolar planets are currently being developed for the VLT (SPHERE) and Gemini (GPI) observatories. A vital part of such a high-contrast imager is the extreme adaptive optics (XAO) system that very efficiently removes effects of atmospheric turbulence and instrument aberrations. The high order test bench (HOT) implements an XAO system under realistic telescope conditions reproduced by star and turbulence generators. New technological developments (32x32 actuator micro deformable mirror, read-noise free electron multiplying CCD60, SPARTA real time computer) are used to study and compare two potential XAO wave front sensors: The Pyramid- and the Shack-Hartmann wave front sensors. We will describe the overall design of HOT including the sub-systems. We will present the closed loop study results of the behavior of the Shack-Hartmann wave front sensor in terms of linearity, sensitivity to calibration errors, performance and other specific issues.
On High-Order Upwind Methods for Advection
NASA Technical Reports Server (NTRS)
Huynh, H. T.
2017-01-01
In the fourth installment of the celebrated series of five papers entitled "Towards the ultimate conservative difference scheme", Van Leer (1977) introduced five schemes for advection, the first three are piecewise linear, and the last two, piecewise parabolic. Among the five, scheme I, which is the least accurate, extends with relative ease to systems of equations in multiple dimensions. As a result, it became the most popular and is widely known as the MUSCL scheme (monotone upstream-centered schemes for conservation laws). Schemes III and V have the same accuracy, are the most accurate, and are closely related to current high-order methods. Scheme III uses a piecewise linear approximation that is discontinuous across cells, and can be considered as a precursor of the discontinuous Galerkin methods. Scheme V employs a piecewise quadratic approximation that is, as opposed to the case of scheme III, continuous across cells. This method is the basis for the on-going "active flux scheme" developed by Roe and collaborators. Here, schemes III and V are shown to be equivalent in the sense that they yield identical (reconstructed) solutions, provided the initial condition for scheme III is defined from that of scheme V in a manner dependent on the CFL number. This equivalence is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The finding also shows a key connection between the approaches of discontinuous and continuous polynomial approximations. In addition to the discussed equivalence, a framework using both projection and interpolation that extends schemes III and V into a single family of high-order schemes is introduced. For these high-order extensions, it is demonstrated via Fourier analysis that schemes with the same number of degrees of freedom ?? per cell, in spite of the different piecewise polynomial degrees, share the same
Thin high-order shims for small dipole NMR magnets
NASA Astrophysics Data System (ADS)
McDowell, Andrew; Conradi, Mark
2017-08-01
An NMR shim coil design method that addresses the severe spatial constraints of miniaturized dipole magnets is introduced. The fundamental design element, a collection of straight wires, is shown to be sufficient for producing a complete set of shim fields of high mathematical order. In accord with these theoretical considerations, a shim set is constructed using four wires in each of four directions to create all first through fourth order fields, except one. This shim set, with its supporting structure, occupies only 2 mm of the available 5 mm gap in a small 1.6 T magnet. However, the fields produced by the individual wires are found to differ significantly from theoretical expectations. To produce the desired harmonic shim fields, the magnetic field of each of the 32 wires is mapped in three dimensions, and linear combinations of these maps are formed. The resulting shim fields are found to be very pure. The shims are used in a prototype high-resolution NMR magnet in which the 1.0 mm sample size is only possible due to the thinness of the shim set. The resulting spectra demonstrate shimming to high resolution (<25 ppb FWHM) without undue heating effects.
Thin high-order shims for small dipole NMR magnets.
McDowell, Andrew; Conradi, Mark
2017-08-01
An NMR shim coil design method that addresses the severe spatial constraints of miniaturized dipole magnets is introduced. The fundamental design element, a collection of straight wires, is shown to be sufficient for producing a complete set of shim fields of high mathematical order. In accord with these theoretical considerations, a shim set is constructed using four wires in each of four directions to create all first through fourth order fields, except one. This shim set, with its supporting structure, occupies only 2mm of the available 5mm gap in a small 1.6T magnet. However, the fields produced by the individual wires are found to differ significantly from theoretical expectations. To produce the desired harmonic shim fields, the magnetic field of each of the 32 wires is mapped in three dimensions, and linear combinations of these maps are formed. The resulting shim fields are found to be very pure. The shims are used in a prototype high-resolution NMR magnet in which the 1.0mm sample size is only possible due to the thinness of the shim set. The resulting spectra demonstrate shimming to high resolution (<25ppb FWHM) without undue heating effects. Copyright © 2017 Elsevier Inc. All rights reserved.
High-order harmonic generation in a capillary discharge
Rocca, Jorge J.; Kapteyn, Henry C.; Mumane, Margaret M.; Gaudiosi, David; Grisham, Michael E.; Popmintchev, Tenio V.; Reagan, Brendan A.
2010-06-01
A pre-ionized medium created by a capillary discharge results in more efficient use of laser energy in high-order harmonic generation (HHG) from ions. It extends the cutoff photon energy, and reduces the distortion of the laser pulse as it propagates down the waveguide. The observed enhancements result from a combination of reduced ionization energy loss and reduced ionization-induced defocusing of the driving laser as well as waveguiding of the driving laser pulse. The discharge plasma also provides a means to spectrally tune the harmonics by tailoring the initial level of ionization of the medium.
High Order Filter Methods for Shock/Turbulence MHD Flows
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sjoegreen, Bjoern
2003-01-01
Low-dissipative high order filter finite difference methods for shock/turbulence/combustion compressible viscous MHD flows has been constructed. Several variants of the filter approach that cater to different flow types are proposed. These filters provide a natural and efficient way for the minimization of the divergence of the magnetic field (del (raided dot) B) numerical error in the sense that no standard divergence cleaning is required. For certain 2-D MHD test problems, divergence free preservation of the magnetic fields of these filter schemes has been achieved.
Quantum Path Interferences in High-Order Harmonic Generation
Zaier, A.; Holler, M.; Guandalini, A.; Schapper, F.; Biegert, J.; Gallmann, L.; Keller, U.; Wyatt, A. S.; Monmayrant, A.; Walmsley, I. A.; Cormier, E.; Auguste, T.; Caumes, J. P.; Salieres, P.
2008-04-11
We have investigated the intensity dependence of high-order harmonic generation in argon when the two shortest quantum paths contribute to the harmonic emission. For the first time to our knowledge, experimental conditions were found to clearly observe interference between these two quantum paths that are in excellent agreement with theoretical predictions. This result is a first step towards the direct experimental characterization of the full single-atom dipole moment and demonstrates an unprecedented accuracy of quantum path control on an attosecond time scale.
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.
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.
High-order pseudo-Gaussian scalar acoustical beams.
Mitri, Farid
2014-01-01
Exact solutions of the scalar Helmholtz equation describing tightly spherically-focused beams are introduced without any approximations using the complex source point method in spherical coordinates. The generalized solutions, valid for any integer degree n and order m, describe high-order pseudo-Gaussian vortex, intermediate (vortex), hollow (nonvortex), and trigonometric (non-vortex) beams having an arbitrary beam waist w0. A very useful property of these beams is the efficient and fast computational modeling of tightly focused or quasi-collimated wave-fronts depending on the dimensionless waist parameter kw0, where k is the wave number of the acoustical radiation. Examples that illustrate hollow vortex and non-vortex beams are provided, and numerical simulations for the magnitude, isosurface, and phase plots of the pressure wave field of higher-order quasi-Gaussian beams are evaluated with particular emphasis on kw0 for strongly (kw0 = 3) to weakly focused (i.e., quasi-collimated) beams (kw0 = 7). Potential applications are in beam-forming design, imaging, particle sizing and manipulation in acoustical tweezers, and phenomena related to scattering, radiation force, and torque.
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
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
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.
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.
Highly ordered periodic mesoporous organosilica nanoparticles with controllable pore structures
NASA Astrophysics Data System (ADS)
Guan, Buyuan; Cui, Yan; Ren, Zhongyuan; Qiao, Zhen-An; Wang, Li; Liu, Yunling; Huo, Qisheng
2012-09-01
A general synthetic procedure for highly ordered and well-dispersed periodic mesoporous organosilica (PMO) nanoparticles is reported based on a single cationic surfactant cetyltrimethylammonium bromide (CTAB) and simple silica sources with organic bridging groups via an ammonia-catalyzed sol-gel reaction. By changing the bridging group in the silica sources, the pore structures of the as-made particles with three-dimensional hexagonal (P63/mmc), cubic (Pm3n), two-dimensional hexagonal (P6mm), and wormlike structure were evidenced by powder X-ray diffraction analysis (XRD) and transmission electron microscopy (TEM). The size range of the nanoparticles can be adjusted from 30 nm to 500 nm by variation of the ammonia concentration or the co-solvent content of the reaction medium. The PMO nanoparticles with high concentration of organic groups in the framework offered good thermal stability, good dispersion in low polarity solvent and high adsorption of small hydrophobic molecules. Finally, the dye functionalized PMO nanoparticles show low cytotoxicity and excellent cell permeability, which offers great potential for biomedical applications.A general synthetic procedure for highly ordered and well-dispersed periodic mesoporous organosilica (PMO) nanoparticles is reported based on a single cationic surfactant cetyltrimethylammonium bromide (CTAB) and simple silica sources with organic bridging groups via an ammonia-catalyzed sol-gel reaction. By changing the bridging group in the silica sources, the pore structures of the as-made particles with three-dimensional hexagonal (P63/mmc), cubic (Pm3n), two-dimensional hexagonal (P6mm), and wormlike structure were evidenced by powder X-ray diffraction analysis (XRD) and transmission electron microscopy (TEM). The size range of the nanoparticles can be adjusted from 30 nm to 500 nm by variation of the ammonia concentration or the co-solvent content of the reaction medium. The PMO nanoparticles with high concentration of organic
Blind Image Quality Assessment based on High Order Statistics Aggregation.
Xu, Jingtao; Ye, Peng; Li, Qiaohong; Du, Haiqing; Liu, Yong; Doermann, David
2016-06-28
Blind image quality assessment (BIQA) research aims to develop a perceptual model to evaluate the quality of distorted images automatically and accurately without access to the non-distorted reference images. State-of-the-art general purpose BIQA methods can be classified into two categories according to the types of features used. The first includes handcrafted features which rely on the statistical regularities of natural images. These, however, are not suitable for images containing text and artificial graphics. The second includes learning based features which invariably require large codebook or supervised codebook updating procedures to obtain satisfactory performance. These are time consuming and not applicable in practice. In this paper, we propose a novel general purpose BIQA method based on High Order Statistics Aggregation (HOSA), requiring only a small codebook. HOSA consists of three steps. First, local normalized image patches are extracted as local features through a regular grid and a codebook containing 100 codewords is constructed by K-means clustering. In addition to the mean of each cluster, the diagonal covariance and coskewness (i.e., dimension wise variance and skewness) of clusters are also calculated. Second, each local feature is softly assigned to several nearest clusters and the differences of high order statistics (mean, variance and skewness) between local features and corresponding clusters are softly aggregated to build the global quality aware image representation. Finally, support vector regression (SVR) is adopted to learn the mapping between perceptual features and subjective opinion scores. The proposed method has been extensively evaluated on ten image databases with both simulated and realistic image distortions, and shows highly competitive performance to state-of-the-art BIQA methods.
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
Crossing Fibers Detection with an Analytical High Order Tensor Decomposition
Megherbi, T.; Kachouane, M.; Oulebsir-Boumghar, F.; Deriche, R.
2014-01-01
Diffusion magnetic resonance imaging (dMRI) is the only technique to probe in vivo and noninvasively the fiber structure of human brain white matter. Detecting the crossing of neuronal fibers remains an exciting challenge with an important impact in tractography. In this work, we tackle this challenging problem and propose an original and efficient technique to extract all crossing fibers from diffusion signals. To this end, we start by estimating, from the dMRI signal, the so-called Cartesian tensor fiber orientation distribution (CT-FOD) function, whose maxima correspond exactly to the orientations of the fibers. The fourth order symmetric positive definite tensor that represents the CT-FOD is then analytically decomposed via the application of a new theoretical approach and this decomposition is used to accurately extract all the fibers orientations. Our proposed high order tensor decomposition based approach is minimal and allows recovering the whole crossing fibers without any a priori information on the total number of fibers. Various experiments performed on noisy synthetic data, on phantom diffusion, data and on human brain data validate our approach and clearly demonstrate that it is efficient, robust to noise and performs favorably in terms of angular resolution and accuracy when compared to some classical and state-of-the-art approaches. PMID:25246940
Recursive regularization step for high-order lattice Boltzmann methods
NASA Astrophysics Data System (ADS)
Coreixas, Christophe; Wissocq, Gauthier; Puigt, Guillaume; Boussuge, Jean-François; Sagaut, Pierre
2017-09-01
A lattice Boltzmann method (LBM) with enhanced stability and accuracy is presented for various Hermite tensor-based lattice structures. The collision operator relies on a regularization step, which is here improved through a recursive computation of nonequilibrium Hermite polynomial coefficients. In addition to the reduced computational cost of this procedure with respect to the standard one, the recursive step allows to considerably enhance the stability and accuracy of the numerical scheme by properly filtering out second- (and higher-) order nonhydrodynamic contributions in under-resolved conditions. This is first shown in the isothermal case where the simulation of the doubly periodic shear layer is performed with a Reynolds number ranging from 104 to 106, and where a thorough analysis of the case at Re=3 ×104 is conducted. In the latter, results obtained using both regularization steps are compared against the Bhatnagar-Gross-Krook LBM for standard (D2Q9) and high-order (D2V17 and D2V37) lattice structures, confirming the tremendous increase of stability range of the proposed approach. Further comparisons on thermal and fully compressible flows, using the general extension of this procedure, are then conducted through the numerical simulation of Sod shock tubes with the D2V37 lattice. They confirm the stability increase induced by the recursive approach as compared with the standard one.
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).
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 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.
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}.
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.
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.
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.
Electrochemical synthesis of highly ordered magnetic multilayered nanowire arrays
NASA Astrophysics Data System (ADS)
Kok, Kuan-Ying; Ng, Inn-Khuan; Saidin, Nur Ubaidah; Zali, Nurazila Mat; Bustamam, Farah Khuwailah Ahmad; Shaari, Abdul Halim
2012-06-01
Electrochemical deposition is a versatile technique that has been employed to synthesize various types of onedimensional nanostructures such as nanorods, nanotubes and nanowires to meet different requirements for applications. Magnetic nanowires in the form of multilayered structures, such as Co/Cu and permalloy (Ni80Fe20)/Cu, with ferromagnetic materials alternating with non-magnetic materials exhibit giant magnetoresistance (GMR) property that can be utilized in sensors and mass memory devices. This study focuses on the synthesis of highly ordered magnetic multilayered nanowire arrays using template-directed electrochemical deposition technique. The nanowires were electrodeposited within the nanopores of anodized alumina from sulphate baths via pulse potential technique. The structures and compositions of the wires were characterized using various microscopy and probe-based techniques. Magnetoresistance measurement was performed on the multilayered nanowire arrays.
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
Cluster size dependence of high-order harmonic generation
NASA Astrophysics Data System (ADS)
Tao, Y.; Hagmeijer, R.; Bastiaens, H. M. J.; Goh, S. J.; van der Slot, P. J. M.; Biedron, S. G.; Milton, S. V.; Boller, K.-J.
2017-08-01
We investigate high-order harmonic generation (HHG) from noble gas clusters in a supersonic gas jet. To identify the contribution of harmonic generation from clusters versus that from gas monomers, we measure the high-order harmonic output over a broad range of the total atomic number density in the jet (from 3×1016 to 3 × 1018 {{cm}}-3) at two different reservoir temperatures (303 and 363 K). For the first time in the evaluation of the harmonic yield in such measurements, the variation of the liquid mass fraction, g, versus pressure and temperature is taken into consideration, which we determine, reliably and consistently, to be below 20% within our range of experimental parameters. By comparing the measured harmonic yield from a thin jet with the calculated corresponding yield from monomers alone, we find an increased emission of the harmonics when the average cluster size is less than 3000. Using g, under the assumption that the emission from monomers and clusters add up coherently, we calculate the ratio of the average single-atom response of an atom within a cluster to that of a monomer and find an enhancement of around 100 for very small average cluster size (∼200). We do not find any dependence of the cut-off frequency on the composition of the cluster jet. This implies that HHG in clusters is based on electrons that return to their parent ions and not to neighboring ions in the cluster. To fully employ the enhanced average single-atom response found for small average cluster sizes (∼200), the nozzle producing the cluster jet must provide a large liquid mass fraction at these small cluster sizes for increasing the harmonic yield. Moreover, cluster jets may allow for quasi-phase matching, as the higher mass of clusters allows for a higher density contrast in spatially structuring the nonlinear medium.
Ultrafast nanoscale imaging using high order harmonic generation (Conference Presentation)
NASA Astrophysics Data System (ADS)
Merdji, Hamed
2017-05-01
Ultrafast coherent diffraction using soft and hard X-rays is actually revolutionizing imaging science thanks to new sources recently available. This powerful technique extends standard X-ray diffraction towards imaging of non-crystalline objects and leads actually to a strong impact in physics, chemistry and biology. New ultrashort pulses recently available hold the promise of watching matter evolving with unprecedented space and time resolution. Femtosecond coherent and intense radiation in the soft X-ray (λ = 10-40 nm) is currently produced in our laboratory, from highly non linear frequency conversion (high harmonic generation). A high intensity UV-X coherent beam is obtained using a loose focusing geometry, which allows coupling a very high amount of Ti:Sapphire laser system energy in the HHG process. Using a long gas cell and a long focal length lens, the emitting volume can be increased by orders of magnitude compared to standard HHG set-ups. This approach, allows reaching up to 1x1011 photons per shot for the 25th harmonic (λ=32nm). We have already demonstrated nanoscale imaging in a single shot mode reaching 70 nm spatial resolution and 20 femtoseconds snapshot [1]. We then implemented a recently proposed holographic technique using extended references. This technique, easy to implement, allows a direct non iterative image reconstruction. In the single shot regime, we demonstrated a spatial resolution of 110nm [2].This opens fascinating perspectives in imaging dynamical phenomena to be spread over a large scientific community. I will present recent results in the investigation of femtosecond phase spin-reversals of magnetic nano-domains [3]. Finally, I will report on recent development on noise sensitivity of the technique and perspectives in attosecond coherent imaging [4]. [1] A. Ravasio et al., Physical Review Letters 103, 028104 (2009). [2] D. Gauthier et al., Physical Review Letters 105, 093901 (2010). [3] Vodungbo et al., Nature Communications 3
Guo, Zhongyi; Zhu, Lie; Guo, Kai; Shen, Fei; Yin, Zhiping
2017-08-29
In this paper, a high-order dielectric metasurface based on silicon nanobrick array is proposed and investigated. By controlling the length and width of the nanobricks, the metasurfaces could supply two different incremental transmission phases for the X-linear-polarized (XLP) and Y-linear-polarized (YLP) light with extremely high efficiency over 88%. Based on the designed metasurface, two polarization beam splitters working in high-order diffraction modes have been designed successfully, which demonstrated a high transmitted efficiency. In addition, we have also designed two vortex-beam generators working in high-order diffraction modes to create vortex beams with the topological charges of 2 and 3. The employment of dielectric metasurfaces operating in high-order diffraction modes could pave the way for a variety of new ultra-efficient optical devices.
NASA Astrophysics Data System (ADS)
Guo, Zhongyi; Zhu, Lie; Guo, Kai; Shen, Fei; Yin, Zhiping
2017-08-01
In this paper, a high-order dielectric metasurface based on silicon nanobrick array is proposed and investigated. By controlling the length and width of the nanobricks, the metasurfaces could supply two different incremental transmission phases for the X-linear-polarized (XLP) and Y-linear-polarized (YLP) light with extremely high efficiency over 88%. Based on the designed metasurface, two polarization beam splitters working in high-order diffraction modes have been designed successfully, which demonstrated a high transmitted efficiency. In addition, we have also designed two vortex-beam generators working in high-order diffraction modes to create vortex beams with the topological charges of 2 and 3. The employment of dielectric metasurfaces operating in high-order diffraction modes could pave the way for a variety of new ultra-efficient optical devices.
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
A Well-Balanced Path-Integral f-Wave Method for Hyperbolic Problems with Source Terms
2014-01-01
Systems of hyperbolic partial differential equations with source terms (balance laws) arise in many applications where it is important to compute accurate time-dependent solutions modeling small perturbations of equilibrium solutions in which the source terms balance the hyperbolic part. The f-wave version of the wave-propagation algorithm is one approach, but requires the use of a particular averaged value of the source terms at each cell interface in order to be “well balanced” and exactly maintain steady states. A general approach to choosing this average is developed using the theory of path conservative methods. A scalar advection equation with a decay or growth term is introduced as a model problem for numerical experiments. PMID:24563581
ERIC Educational Resources Information Center
Kubota, Mikio
1993-01-01
This study investigated the accuracy order of English relative clauses in the usage of 199 Japanese high school students of English as a foreign language (EFL). Specifically, it looked at: (1) whether the Accessibility Hierarchy conform to the accuracy order by Japanese senior high school students of EFL; and (2) how frequently this population…
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 And High Resolution Methods For a Model CAA Problem
NASA Technical Reports Server (NTRS)
Goodrich, John W.
2004-01-01
The initial value problem for the first order linear wave equation in one space dimension is treated for two cases with specified initial data and grid, and data from solutions at t = 400 and t = 800 are presented, as prescribed for Problem 1 in Category 1. Results are shown from computations with a sequence of recently developed high order and high resolution methods which combine Hermite interpolation, Cauchy-Kowaleskya recursion for time derivatives, and Taylor series time advancement. These methods have the same order of accuracy in time as in space. Results are shown from methods that range from third to nineteenth order. The stated problems with the prescribed coarse grid can be simulated with errors that are at the level of machine accuracy if the method is sufficiently high order. In addition, the growth of the maximum absolute error out to t = 100,000 is given for simulations with the stated problem data.
Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence
NASA Technical Reports Server (NTRS)
Sandham, N. D.; Yee, H. C.; Kwak, Dochan (Technical Monitor)
2000-01-01
A stable high order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy splitting approach splits the inviscid flux derivatives into conservative and non-conservative portions. The spatial difference operators satisfy a summation by parts condition leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier-Stokes equations is used to ensure that any tendency to odd-even decoupling associated with central schemes can be countered by the fluid viscosity. A special formulation of the continuity equation is used, based on similar arguments. The resulting methods are able to minimize spurious high frequency oscillation producing nonlinear instability associated with pure central schemes, especially for long time integration simulation such as DNS. For validation purposes, the methods are tested in a DNS of compressible turbulent plane channel flow at a friction Mach number of 0.1 where a very accurate turbulence data base exists. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with incompressible channel data, as expected at this Mach number. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.
Stirling Analysis Comparison of Commercial vs. High-Order Methods
NASA Technical Reports Server (NTRS)
Dyson, Rodger W.; Wilson, Scott D.; Tew, Roy C.; Demko, Rikako
2007-01-01
Recently, three-dimensional Stirling engine simulations have been accomplished utilizing commercial Computational Fluid Dynamics software. The validations reported can be somewhat inconclusive due to the lack of precise time accurate experimental results from engines, export control/ proprietary concerns, and the lack of variation in the methods utilized. The last issue may be addressed by solving the same flow problem with alternate methods. In this work, a comprehensive examination of the methods utilized in the commercial codes is compared with more recently developed high-order methods. Specifically, Lele's Compact scheme and Dyson s Ultra Hi-Fi method will be compared with the SIMPLE and PISO methods currently employed in CFD-ACE, FLUENT, CFX, and STAR-CD (all commercial codes which can in theory solve a three-dimensional Stirling model although sliding interfaces and their moving grids limit the effective time accuracy). We will initially look at one-dimensional flows since the current standard practice is to design and optimize Stirling engines with empirically corrected friction and heat transfer coefficients in an overall one-dimensional model. This comparison provides an idea of the range in which commercial CFD software for modeling Stirling engines may be expected to provide accurate results. In addition, this work provides a framework for improving current one-dimensional analysis codes.
Stirling Analysis Comparison of Commercial Versus High-Order Methods
NASA Technical Reports Server (NTRS)
Dyson, Rodger W.; Wilson, Scott D.; Tew, Roy C.; Demko, Rikako
2005-01-01
Recently, three-dimensional Stirling engine simulations have been accomplished utilizing commercial Computational Fluid Dynamics software. The validations reported can be somewhat inconclusive due to the lack of precise time accurate experimental results from engines, export control/proprietary concerns, and the lack of variation in the methods utilized. The last issue may be addressed by solving the same flow problem with alternate methods. In this work, a comprehensive examination of the methods utilized in the commercial codes is compared with more recently developed high-order methods. Specifically, Lele's compact scheme and Dyson's Ultra Hi-Fi method will be compared with the SIMPLE and PISO methods currently employed in CFD-ACE, FLUENT, CFX, and STAR-CD (all commercial codes which can in theory solve a three-dimensional Stirling model with sliding interfaces and their moving grids limit the effective time accuracy). We will initially look at one-dimensional flows since the current standard practice is to design and optimize Stirling engines with empirically corrected friction and heat transfer coefficients in an overall one-dimensional model. This comparison provides an idea of the range in which commercial CFD software for modeling Stirling engines may be expected to provide accurate results. In addition, this work provides a framework for improving current one-dimensional analysis codes.
Central Command Architecture for High Order Autonomous Unmanned Systems
NASA Astrophysics Data System (ADS)
Bieber, Chad Michael
This dissertation describes a High-Order Central Command (HOCC) architecture and presents a flight demonstration where a single user coordinates 4 unmanned fixed-wing aircraft. HOCC decouples the user from control of individual vehicles, eliminating human limits on the size of the system, and uses a non-iterative sequence of algorithms that permit easy estimation of how computational complexity scales. The Hungarian algorithm used to solve a min-sum assignment with a one-task planning horizon becomes the limiting complexity, scaling at O(x3) where x is the larger number of vehicles or tasks in the assignment. This method is shown to have a unique property of creating non-intersecting routes which is used to drastically reduce the computational cost of deconflicting planned routes. Results from several demonstration flights are presented where a single user commands a system of 4 fixed-wing aircraft. The results confirm that autonomous flight of a large number of UAVs is a bona fide engineering sub-discipline, which is expected to be of interest to engineers who will find its utility in the aviation industry and in other emerging markets.
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.
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).
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.
Adapting to blur produced by ocular high-order aberrations
Sawides, Lucie; de Gracia, Pablo; Dorronsoro, Carlos; Webster, Michael; Marcos, Susana
2011-01-01
The perceived focus of an image can be strongly biased by prior adaptation to a blurred or sharpened image. We examined whether these adaptation effects can occur for the natural patterns of retinal image blur produced by high-order aberrations (HOAs) in the optics of the eye. Focus judgments were measured for 4 subjects to estimate in a forced choice procedure (sharp/blurred) their neutral point after adaptation to different levels of blur produced by scaled increases or decreases in their HOAs. The optical blur was simulated by convolution of the PSFs from the 4 different HOA patterns, with Zernike coefficients (excluding tilt, defocus, and astigmatism) multiplied by a factor between 0 (diffraction limited) and 2 (double amount of natural blur). Observers viewed the images through an Adaptive Optics system that corrected their aberrations and made settings under neutral adaptation to a gray field or after adapting to 5 different blur levels. All subjects adapted to changes in the level of blur imposed by HOA regardless of which observer’s HOA was used to generate the stimuli, with the perceived neutral point proportional to the amount of blur in the adapting image. PMID:21712375
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.
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 Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order
2014-06-01
Number of nodes RD Scheme Order GS relaxations /Newton iteration Newton iteration High-Order Technique High-Order Technique 50 3rd RD-D RD-GT RD-D RD-GT 168...over every physical time step. In this paper, two techniques for the source term discretiza- tion are proposed; 1) reformulation of the source terms...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
Humanities and High Order Thinking Skills. Task Force Report.
ERIC Educational Resources Information Center
Colorado State Dept. of Education, Denver. Office of Federal Relations and Instructional Services.
Responding to the Colorado State Board of Education's request for recommendations concerning the need to improve humanities instruction and its relationship to the development of higher-order thinking skills, this task force report specifies a scope for humanities teaching; defines higher-order thinking skills as the ability to judge information,…
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.
High-Order Numerical Simulations of Wind Turbine Wakes
NASA Astrophysics Data System (ADS)
Kleusberg, E.; Mikkelsen, R. F.; Schlatter, P.; Ivanell, S.; Henningson, D. S.
2017-05-01
Previous attempts to describe the structure of wind turbine wakes and their mutual interaction were mostly limited to large-eddy and Reynolds-averaged Navier-Stokes simulations using finite-volume solvers. We employ the higher-order spectral-element code Nek5000 to study the influence of numerical aspects on the prediction of the wind turbine wake structure and the wake interaction between two turbines. The spectral-element method enables an accurate representation of the vortical structures, with lower numerical dissipation than the more commonly used finite-volume codes. The wind-turbine blades are modeled as body forces using the actuator-line method (ACL) in the incompressible Navier-Stokes equations. Both tower and nacelle are represented with appropriate body forces. An inflow boundary condition is used which emulates homogeneous isotropic turbulence of wind-tunnel flows. We validate the implementation with results from experimental campaigns undertaken at the Norwegian University of Science and Technology (NTNU Blind Tests), investigate parametric influences and compare computational aspects with existing numerical simulations. In general the results show good agreement between the experiments and the numerical simulations both for a single-turbine setup as well as a two-turbine setup where the turbines are offset in the spanwise direction. A shift in the wake center caused by the tower wake is detected similar to experiments. The additional velocity deficit caused by the tower agrees well with the experimental data. The wake is captured well by Nek5000 in comparison with experiments both for the single wind turbine and in the two-turbine setup. The blade loading however shows large discrepancies for the high-turbulence, two-turbine case. While the experiments predicted higher thrust for the downstream turbine than for the upstream turbine, the opposite case was observed in Nek5000.
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.
Low Dissipative High Order Numerical Simulations of Supersonic Reactive Flows
NASA Technical Reports Server (NTRS)
Sjoegreen, B.; Yee, H. C.; Mansour, Nagi (Technical Monitor)
2001-01-01
The objective of this paper is to evaluate the performance of a newly developed low dissipative sixth-order spatial and fourth-order temporal scheme for viscous reactive flows interacting with shock waves that contain fine scale flow structures. The accuracy and efficiency of the scheme, and to what degree the scheme can capture the correct physical wave speeds of stiff reactive flows will be included.
High-order 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.
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.}
Compact high-order schemes for the Euler equations
NASA Technical Reports Server (NTRS)
Abarbanel, Saul; Kumar, Ajay
1988-01-01
An implicit approximate factorization (AF) algorithm is constructed which has the following characteristics. In 2-D: the scheme is unconditionally stable, has a 3 x 3 stencil and at steady state has a fourth order spatial accuracy. The temporal evolution is time accurate either to first or second order through choice of parameter. In 3-D: the scheme has almost the same properties as in 2-D except that it is now only conditionally stable, with the stability condition (the CFL number) being dependent on the cell aspect ratios, delta y/delta x and delta z/delta x. The stencil is still compact and fourth order accuracy at steady state is maintained.
High-order numerical solutions using cubic splines
NASA Technical Reports Server (NTRS)
Rubin, S. G.; Khosla, P. K.
1975-01-01
The cubic spline collocation procedure for the numerical solution of partial differential equations was reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a nonuniform mesh and overall fourth-order accuracy for a uniform mesh. Application of the technique was made to the Burger's equation, to the flow around a linear corner, to the potential flow over a circular cylinder, and to boundary layer problems. The results confirmed the higher-order accuracy of the spline method and suggest that accurate solutions for more practical flow problems can be obtained with relatively coarse nonuniform meshes.
Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.
2017-09-01
High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemannmore » problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. The upwind scheme is shown to be robust and provide high-order accuracy.« less
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.
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.
High-order harmonics from bow wave caustics driven by a high-intensity laser
Pirozhkov, A.S.; Kando, M.; Esirkepov, T.Zh.; and others
2012-07-11
We propose a new mechanism of high-order harmonic generation during an interaction of a high-intensity laser pulse with underdense plasma. A tightly focused laser pulse creates a cavity in plasma pushing electrons aside and exciting the wake wave and the bow wave. At the joint of the cavity wall and the bow wave boundary, an annular spike of electron density is formed. This spike surrounds the cavity and moves together with the laser pulse. Collective motion of electrons in the spike driven by the laser field generates high-order harmonics. A strong localization of the electron spike, its robustness to oscillations imposed by the laser field and, consequently, its ability to produce high-order harmonics is explained by catastrophe theory. The proposed mechanism explains the experimental observations of high-order harmonics with the 9 TW J-KAREN laser (JAEA, Japan) and the 120 TW Astra Gemini laser (CLF RAL, UK) [A. S. Pirozhkov, et al., arXiv:1004.4514 (2010); A. S. Pirozhkov et al, AIP Proceedings, this volume]. The theory is corroborated by high-resolution two-and three-dimensional particle-in-cell simulations.
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.
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.
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.
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.
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.
Encoding high-order cylindrically polarized light beams.
Moreno, Ignacio; Davis, Jeffrey A; Cottrell, Don M; Donoso, Ramiro
2014-08-20
In this work we present a setup for the experimental production of cylindrically polarized beams, as well as other variations of polarized light beams. The optical system uses a single transmissive phase-only spatial light modulator, which is used to apply different spatial phase modulation to two output collinear R and L circularly polarized components. Different cylindrically polarized light beams can be obtained by applying different phase shifts to these two circularly polarized components. The system is very efficient since modulation is directly applied to the light beam (as opposed to other common methods operating in the first order of encoded diffraction gratings). Different variations to the cylindrically polarized light beams are also reported, obtained by adding linear or quadratic relative phase shifts between the two circular polarization components of the light beam. Experimental results are provided in all cases.
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.
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.
Highly ordered Ag-TiO2 nanocomposited arrays with high visible-light photocatalytic activity
NASA Astrophysics Data System (ADS)
Zhao, Cong; Zhu, Da-chuan; Cheng, Xiao-yao; Cao, Shi-xiu
2017-06-01
TiO2 is active only in the ultraviolet region. To enhance the active ability, a combined method consisting of the anodic oxidation method and the hydrothermal method was developed to prepare highly ordered Ag-TiO2 nanocomposited arrays. The anodic oxidation was used to synthesize amorphous nanotubes with high chemical activity that subsequently served as highly ordered templates in preparing the final sample. The amorphous nanotubes got converted to highly ordered Ag-TiO2 (anatase) arrays in the silver nitrate & glucose aqueous solution via hydrothermal treatment. SEM and TEM results show that the Ag-TiO2 nanocomposite was composed of a large number of Ag nanoparticles and anatase TiO2 nanoparticles, and the morphology of those at the top of the arrays was found different from that of its trunk. The morphology evolution mechanism of the obtained sample was discussed. It is also revealed that the Ag-TiO2 nanocomposite has high visible-light photocatalytic activity.
Highly ordered Ag-TiO2 nanocomposited arrays with high visible-light photocatalytic activity
NASA Astrophysics Data System (ADS)
Zhao, Cong; Zhu, Da-chuan; Cheng, Xiao-yao; Cao, Shi-xiu
2017-09-01
TiO2 is active only in the ultraviolet region. To enhance the active ability, a combined method consisting of the anodic oxidation method and the hydrothermal method was developed to prepare highly ordered Ag-TiO2 nanocomposited arrays. The anodic oxidation was used to synthesize amorphous nanotubes with high chemical activity that subsequently served as highly ordered templates in preparing the final sample. The amorphous nanotubes got converted to highly ordered Ag-TiO2 (anatase) arrays in the silver nitrate & glucose aqueous solution via hydrothermal treatment. SEM and TEM results show that the Ag-TiO2 nanocomposite was composed of a large number of Ag nanoparticles and anatase TiO2 nanoparticles, and the morphology of those at the top of the arrays was found different from that of its trunk. The morphology evolution mechanism of the obtained sample was discussed. It is also revealed that the Ag-TiO2 nanocomposite has high visible-light photocatalytic activity.
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.
A high-order staggered meshless method for elliptic problems
Trask, Nathaniel; Perego, Mauro; Bochev, Pavel Blagoveston
2017-03-21
Here, we present a new meshless method for scalar diffusion equations, which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of nearby neighbor connectivity of the discretization points. This graph defines a local primal-dual grid complex with a virtual dual grid, in the sense that specification of the dual metric attributes is implicit in the method's construction. Our method combines a topological gradient operator on the local primal grid with a generalized moving least squares approximation of the divergence on the local dual grid. We show that the resulting approximation of the div-grad operator maintains polynomial reproduction to arbitrary orders and yields a meshless method, which attainsmore » $$O(h^{m})$$ convergence in both $L^2$- and $H^1$-norms, similar to mixed finite element methods. We demonstrate this convergence on curvilinear domains using manufactured solutions in two and three dimensions. Application of the new method to problems with discontinuous coefficients reveals solutions that are qualitatively similar to those of compatible mesh-based discretizations.« less
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
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.
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
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 ⌉.
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.
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.
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)
Status of the PALM-3000 high order adaptive optics instrument
NASA Astrophysics Data System (ADS)
Burruss, Rick S.; Dekany, Richard G.; Roberts, Jennifer E.; Shelton, J. C.; Wallace, J. K.; Tesch, Jonathan A.; Palmer, Dean L.; Hale, David; Bartos, Randall; Rykoski, Kevin M.; Heffner, Carolyn M.; Eriksen, Jamey E.; Vescelus, Fred
2014-07-01
We report on the status of PALM-3000, the second generation adaptive optics instrument for the 5.1 meter Hale telescope at Palomar Observatory. PALM-3000 was released as a facility class instrument in October 2011, and has since been used on the Hale telescope a total of over 250 nights. In the past year, the PALM-3000 team introduced several instrument upgrades, including the release of the 32x32 pupil sampling mode which allows for correction on fainter guide stars, the upgrade of wavefront sensor relay optics, the diagnosis and repair of hardware problems, and the release of software improvements. We describe the performance of the PALM-3000 instrument as a result of these upgrades, and provide on-sky results. In the 32x32 pupil sampling mode (15.8 cm per subaperture), we have achieved K-band strehl ratios as high as 11% on a 14.4 mv star, and in the 64x64 pupil sampling mode (8.1 cm per subaperture), we have achieved K-band strehl ratios as high as 86% on stars brighter than 7th mv.
NASA Astrophysics Data System (ADS)
Tomita, Yasuo; Matsushima, Shun-suke; Yamagami, Ryu-ichi; Jinzenji, Taka-aki; Sakuma, Shohei; Liu, Xiangming; Izuishi, Takuya; Shen, Qing
2017-06-01
We describe the nonlinear optical properties of inorganic-organic nanocomposite films in which semiconductor CdSe quantum dots as high as 6.8 vol.% are dispersed. Open/closed Z-scan measurements, degenerate multi-wave mixing and femtosecond pump-probe/transient grating measurements are conducted. It is shown that the observed fifth-order optical nonlinearity has the cascaded third-order contribution that becomes prominent at high concentrations of CdSe QDs. It is also shown that there are picosecond-scale intensity-dependent and nanosecond-scale intensity-independent decay components in absorptive and refractive nonlinearities. The former is caused by the Auger process, while the latter comes from the electron-hole recombination process.
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
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.
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.
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
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 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.
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.
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
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
Formal Solutions for Polarized Radiative Transfer. II. High-order Methods
NASA Astrophysics Data System (ADS)
Janett, Gioele; Steiner, Oskar; Belluzzi, Luca
2017-08-01
When integrating the radiative transfer equation for polarized light, the necessity of high-order numerical methods is well known. In fact, well-performing high-order formal solvers enable higher accuracy and the use of coarser spatial grids. Aiming to provide a clear comparison between formal solvers, this work presents different high-order numerical schemes and applies the systematic analysis proposed by Janett et al., emphasizing their advantages and drawbacks in terms of order of accuracy, stability, and computational cost.
High-order multilayer coated blazed gratings for high resolution soft x-ray spectroscopy
Voronov, Dmitriy L.; Goray, Leonid I.; Warwick, Tony; ...
2015-02-17
A grand challenge in soft x-ray spectroscopy is to drive the resolving power of monochromators and spectrometers from the 104 achieved routinely today to well above 105. This need is driven mainly by the requirements of a new technique that is set to have enormous impact in condensed matter physics, Resonant Inelastic X-ray Scattering (RIXS). Unlike x-ray absorption spectroscopy, RIXS is not limited by an energy resolution dictated by the core-hole lifetime in the excitation process. Using much higher resolving power than used for normal x-ray absorption spectroscopy enables access to the energy scale of soft excitations in matter. Thesemore » excitations such as magnons and phonons drive the collective phenomena seen in correlated electronic materials such as high temperature superconductors. RIXS opens a new path to study these excitations at a level of detail not formerly possible. However, as the process involves resonant excitation at an energy of around 1 keV, and the energy scale of the excitations one would like to see are at the meV level, to fully utilize the technique requires the development of monochromators and spectrometers with one to two orders of magnitude higher energy resolution than has been conventionally possible. Here we investigate the detailed diffraction characteristics of multilayer blazed gratings. These elements offer potentially revolutionary performance as the dispersive element in ultra-high resolution x-ray spectroscopy. In doing so, we have established a roadmap for the complete optimization of the grating design. Traditionally 1st order gratings are used in the soft x-ray region, but we show that as in the optical domain, one can work in very high spectral orders and thus dramatically improve resolution without significant loss in efficiency.« less
High-order multilayer coated blazed gratings for high resolution soft x-ray spectroscopy
Voronov, Dmitriy L.; Goray, Leonid I.; Warwick, Tony; Yashchuk, Valeriy V.; Padmore, Howard A.
2015-02-17
A grand challenge in soft x-ray spectroscopy is to drive the resolving power of monochromators and spectrometers from the 10^{4} achieved routinely today to well above 10^{5}. This need is driven mainly by the requirements of a new technique that is set to have enormous impact in condensed matter physics, Resonant Inelastic X-ray Scattering (RIXS). Unlike x-ray absorption spectroscopy, RIXS is not limited by an energy resolution dictated by the core-hole lifetime in the excitation process. Using much higher resolving power than used for normal x-ray absorption spectroscopy enables access to the energy scale of soft excitations in matter. These excitations such as magnons and phonons drive the collective phenomena seen in correlated electronic materials such as high temperature superconductors. RIXS opens a new path to study these excitations at a level of detail not formerly possible. However, as the process involves resonant excitation at an energy of around 1 keV, and the energy scale of the excitations one would like to see are at the meV level, to fully utilize the technique requires the development of monochromators and spectrometers with one to two orders of magnitude higher energy resolution than has been conventionally possible. Here we investigate the detailed diffraction characteristics of multilayer blazed gratings. These elements offer potentially revolutionary performance as the dispersive element in ultra-high resolution x-ray spectroscopy. In doing so, we have established a roadmap for the complete optimization of the grating design. Traditionally 1st order gratings are used in the soft x-ray region, but we show that as in the optical domain, one can work in very high spectral orders and thus dramatically improve resolution without significant loss in efficiency.
High-order multilayer coated blazed gratings for high resolution soft x-ray spectroscopy.
Voronov, Dmitriy L; Goray, Leonid I; Warwick, Tony; Yashchuk, Valeriy V; Padmore, Howard A
2015-02-23
A grand challenge in soft x-ray spectroscopy is to drive the resolving power of monochromators and spectrometers from the 10(4) achieved routinely today to well above 10(5). This need is driven mainly by the requirements of a new technique that is set to have enormous impact in condensed matter physics, Resonant Inelastic X-ray Scattering (RIXS). Unlike x-ray absorption spectroscopy, RIXS is not limited by an energy resolution dictated by the core-hole lifetime in the excitation process. Using much higher resolving power than used for normal x-ray absorption spectroscopy enables access to the energy scale of soft excitations in matter. These excitations such as magnons and phonons drive the collective phenomena seen in correlated electronic materials such as high temperature superconductors. RIXS opens a new path to study these excitations at a level of detail not formerly possible. However, as the process involves resonant excitation at an energy of around 1 keV, and the energy scale of the excitations one would like to see are at the meV level, to fully utilize the technique requires the development of monochromators and spectrometers with one to two orders of magnitude higher energy resolution than has been conventionally possible. Here we investigate the detailed diffraction characteristics of multilayer blazed gratings. These elements offer potentially revolutionary performance as the dispersive element in ultra-high resolution x-ray spectroscopy. In doing so, we have established a roadmap for the complete optimization of the grating design. Traditionally 1st order gratings are used in the soft x-ray region, but we show that as in the optical domain, one can work in very high spectral orders and thus dramatically improve resolution without significant loss in efficiency.
Convergency analysis of the high-order mimetic finite difference method
Lipnikov, Konstantin; Veiga Da Beirao, L; Manzini, G
2008-01-01
We prove second-order convergence of the conservative variable and its flux in the high-order MFD method. The convergence results are proved for unstructured polyhedral meshes and full tensor diffusion coefficients. For the case of non-constant coefficients, we also develop a new family of high-order MFD methods. Theoretical result are confirmed through numerical experiments.
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.
Solid state microwave synthesis of highly crystalline ordered mesoporous hausmannite Mn 3 O 4 films
Xia, Yanfeng; Qiang, Zhe; Lee, Byeongdu; ...
2017-06-23
Microwave calcination of ordered micelle templated manganese carbonate films leads to highly crystalline, ordered mesoporous manganese oxide, while similar temperatures in a furnace lead to disordered, amorphous manganese oxide.
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.
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.
NASA Astrophysics Data System (ADS)
Conde, Sidafa; Gottlieb, Sigal; Grant, Zachary J.; Shadid, John N.
2017-07-01
High order strong stability preserving (SSP) time discretizations have proven beneficial for use with spatial discretizations with nonlinear stability properties for the solution of hyperbolic PDEs. Implicit SSP Runge-Kutta methods exist only up to sixth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: implicit SSP Runge-Kutta methods of any linear order exist. In the current work we aim to find implicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have varying designed orders of accuracy for nonlinear order. In this work we also extend the concept of varying orders of accuracy for linear and non linear components to the class of implicit-explicit (IMEX) Runge-Kutta methods methods, and present a method of this type.
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.
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 numerical differentiation and approximation of Laplace fields using regular grid data
NASA Astrophysics Data System (ADS)
Berdnikov, A. S.
2011-07-01
Specialized numerical schemes for calculation of high order field derivatives are considered. The input data are a regular rectangular mesh with potential values at its nodes, the output data are high order derivative values at grid nodes and associated expressions which enable the calculation of potentials, field values or high order derivatives inside a grid cell with high accuracy. An important feature is that differentiation and approximation techniques are based on a priori knowledge about the Laplace equation which allow the production of numerical schemes with higher order properties.
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.
Determination of coefficients of high-order schemes for Riemann-Liouville derivative.
Wu, Rifang; Ding, Hengfei; Li, Changpin
2014-01-01
Although there have existed some numerical algorithms for the fractional differential equations, developing high-order methods (i.e., with convergence order greater than or equal to 2) is just the beginning. Lubich has ever proposed the high-order schemes when he studied the fractional linear multistep methods, where he constructed the pth order schemes (p = 2, 3, 4, 5, 6) for the αth order Riemann-Liouville integral and αth order Riemann-Liouville derivative. In this paper, we study such a problem and develop recursion formulas to compute these coefficients in the higher-order schemes. The coefficients of higher-order schemes (p = 7,8, 9,10) are also obtained. We first find that these coefficients are oscillatory, which is similar to Runge's phenomenon. So, they are not suitable for numerical calculations. Finally, several numerical examples are implemented to testify the efficiency of the numerical schemes for p = 3,…, 6.
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.
High reprint orders in medical journals and pharmaceutical industry funding: case-control study.
Handel, Adam E; Patel, Sunil V; Pakpoor, Julia; Ebers, George C; Goldacre, Ben; Ramagopalan, Sreeram V
2012-06-28
To assess the extent to which funding and study design are associated with high reprint orders. Case-control study. Top articles by size of reprint orders in seven journals, 2002-09. Lancet, Lancet Neurology, Lancet Oncology (Lancet Group), BMJ, Gut, Heart, and Journal of Neurology, Neurosurgery & Psychiatry (BMJ Group) matched to contemporaneous articles not in the list of high reprint orders. Funding and design of randomised controlled trials or other study designs. Median reprint orders for the seven journals ranged from 3000 to 126,350. Papers with high reprint orders were more likely to be funded by the pharmaceutical industry than were control papers (industry funding versus other or none: odds ratio 8.64, 95% confidence interval 5.09 to 14.68, and mixed funding versus other or none: 3.72, 2.43 to 5.70). Funding by the pharmaceutical industry is associated with high numbers of reprint orders.
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.
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
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.
Zou, Ling; Zhao, Haihua; Kim, Seung Jun
2016-11-16
In this study, the classical Welander’s oscillatory natural circulation problem is investigated using high-order numerical methods. As originally studied by Welander, the fluid motion in a differentially heated fluid loop can exhibit stable, weakly instable, and strongly instable modes. A theoretical stability map has also been originally derived from the stability analysis. Numerical results obtained in this paper show very good agreement with Welander’s theoretical derivations. For stable cases, numerical results from both the high-order and low-order numerical methods agree well with the non-dimensional flow rate analytically derived. The high-order numerical methods give much less numerical errors compared to themore » low-order methods. For stability analysis, the high-order numerical methods could perfectly predict the stability map, while the low-order numerical methods failed to do so. For all theoretically unstable cases, the low-order methods predicted them to be stable. The result obtained in this paper is a strong evidence to show the benefits of using high-order numerical methods over the low-order ones, when they are applied to simulate natural circulation phenomenon that has already gain increasing interests in many future nuclear reactor designs.« less
Zou, Ling; Zhao, Haihua; Kim, Seung Jun
2016-11-16
In this study, the classical Welander’s oscillatory natural circulation problem is investigated using high-order numerical methods. As originally studied by Welander, the fluid motion in a differentially heated fluid loop can exhibit stable, weakly instable, and strongly instable modes. A theoretical stability map has also been originally derived from the stability analysis. Numerical results obtained in this paper show very good agreement with Welander’s theoretical derivations. For stable cases, numerical results from both the high-order and low-order numerical methods agree well with the non-dimensional flow rate analytically derived. The high-order numerical methods give much less numerical errors compared to the low-order methods. For stability analysis, the high-order numerical methods could perfectly predict the stability map, while the low-order numerical methods failed to do so. For all theoretically unstable cases, the low-order methods predicted them to be stable. The result obtained in this paper is a strong evidence to show the benefits of using high-order numerical methods over the low-order ones, when they are applied to simulate natural circulation phenomenon that has already gain increasing interests in many future nuclear reactor designs.
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.
A High-Order High-Accuracy Geometric Block Interface Treatment for Computational Aeroacoustics Codes
NASA Astrophysics Data System (ADS)
Mansouri, Nima
Numerical performance in computational aeroacoustics (CAA) has been driven the use of structured multi-block codes for modeling problems in the aeronautic industry. Structured grids reduce the amount of communication in a numerical simulation, leading to higher computational speeds and lower cost. CAA codes are applied to real problems, so they must be capable of handling complex geometries. The structure of the complex geometries may lead to grid discontinuities and/or singularities at block interfaces. These discontinuities are the primary sources of error in the codes, significantly reducing a codes performance. The geometric block interface treatment (GBIT) is a new approach to improve grid block discontinuity issues at block interfaces for structured multi-block codes. This article first reviews what researchers have done to treat block interfaces. Then, the mathematical model of our geometry-based treatment is proposed. This method was implemented in the high-order, high-accuracy NASA Glenn Research Center Broadband Aeroacoustic Stator Simulation (BASS) CAA code. Here, the initial results for two-dimensional test cases are shown. To determine the performance of the new method, the results are verified by Ingraham's External Verification Approach (EVA). Initial results are promising and reach expected convergence rate. However, instability and inaccuracy appear in the solution. Artificial dissipation and special differencing schemes are revealed to be the main causes of instability and inaccuracy, respectively. To overcome these problems, interior dissipation stencils replace biased stencils at interface regions. Smooth grid clustering is proposed to improve the accuracy of the spatial schemes performance near interfaces, which consequently strengthens the accuracy of the solution. All these new results are laid out, verified, and implemented in basic form.
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.
Extension of Efficient Low Dissipative High Order Schemes for 3-D Curvilinear Moving Grids
NASA Technical Reports Server (NTRS)
Vinokur, Marcel; Yee H. C.; Koga, Dennis (Technical Monitor)
2000-01-01
The efficient low dissipative high order schemes proposed by Yee et al. is formulated for 3-D curvilinear moving grids. These schemes consists of a high order base schemes combined with nonlinear characteristic filters. The amount of numerical dissipation is minimized by applying the schemes to the entropy splitting form of the inviscid flux derivatives. The analysis is given for a thermally perfect gas. The main difficulty in the extension of higher order schemes that were formulated in Cartesian coordinates to curvilinear moving grids is the higher order transformed metric evaluations. The higher order numerical evaluation of the transformed metric terms to insure freestream preservation is done in a coordinate invariant manner. The formulation is an improvement over existing formulation of high order scheme in curvilinear moving grids.
High-Order Discontinuous Galerkin Solution of Low-Re Viscous Flows
NASA Astrophysics Data System (ADS)
Lu, Hongqiang
In this paper, the BR2 high-order Discontinuous Galerkin (DG) method is used to discretize the 2D Navier-Stokes (N-S) equations. The nonlinear discrete system is solved using a Newton method. Both preconditioned GMRES methods and block Gauss-Seidel method can be used to solve the resulting sparse linear system at each nonlinear step in low-order cases. In order to save memory and accelerate the convergence in high-order cases, a linear p-multigrid is developed based on the Taylor basis instead of the GMRES method and the block Gauss-Seidel method. Numerical results indicate that highly accurate solutions can be obtained on very coarse grids when using high order schemes and the linear p-multigrid works well when the implicit backward Euler method is employed to improve the robustness.
High-Order Compact Difference Scheme for the Numerical Solution of Time Fractional Heat Equations
Karatay, Ibrahim; Bayramoglu, Serife R.
2014-01-01
A high-order finite difference scheme is proposed for solving time fractional heat equations. The time fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme a new second-order discretization, which is based on Crank-Nicholson method, is applied for the time fractional part and fourth-order accuracy compact approximation is applied for the second-order space derivative. The spectral stability and the Fourier stability analysis of the difference scheme are shown. Finally a detailed numerical analysis, including tables, figures, and error comparison, is given to demonstrate the theoretical results and high accuracy of the proposed scheme. PMID:24696040
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
2017-03-01
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.
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
High-order neural networks and kernel methods for peptide-MHC binding prediction.
Kuksa, Pavel P; Min, Martin Renqiang; Dugar, Rishabh; Gerstein, Mark
2015-11-15
Effective computational methods for peptide-protein binding prediction can greatly help clinical peptide vaccine search and design. However, previous computational methods fail to capture key nonlinear high-order dependencies between different amino acid positions. As a result, they often produce low-quality rankings of strong binding peptides. To solve this problem, we propose nonlinear high-order machine learning methods including high-order neural networks (HONNs) with possible deep extensions and high-order kernel support vector machines to predict major histocompatibility complex-peptide binding. The proposed high-order methods improve quality of binding predictions over other prediction methods. With the proposed methods, a significant gain of up to 25-40% is observed on the benchmark and reference peptide datasets and tasks. In addition, for the first time, our experiments show that pre-training with high-order semi-restricted Boltzmann machines significantly improves the performance of feed-forward HONNs. Moreover, our experiments show that the proposed shallow HONN outperform the popular pre-trained deep neural network on most tasks, which demonstrates the effectiveness of modelling high-order feature interactions for predicting major histocompatibility complex-peptide binding. There is no associated distributable software. renqiang@nec-labs.com or mark.gerstein@yale.edu Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
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 harmonic spectroscopy of the Cooper minimum in argon: Experimental and theoretical study
Higuet, J.; Ruf, H.; Constant, E.; Cormier, E.; Descamps, D.; Mevel, E.; Petit, S.; Pons, B.; Mairesse, Y.; Fabre, B.; Thire, N.; Cireasa, R.
2011-05-15
We study the Cooper minimum in high-order-harmonic generation from argon atoms by using long wavelength laser pulses. We find that the minimum in high-order-harmonic spectra is systematically shifted with respect to total photoionization cross section measurements. We use a semiclassical theoretical approach based on classical trajectory Monte Carlo and quantum electron scattering methods to model the experiment. Our study reveals that the shift between photoionization and high-order-harmonic emission is due to several effects: the directivity of the recombining electrons and emitted polarization, and the shape of the recolliding electron wave packet.
Optimization design of an adaptive CFRC reflector for high order wave-front error control
NASA Astrophysics Data System (ADS)
Lan, Lan; Fang, Houfei; Wu, Ke; Jiang, Shuidong; Zhou, Yang
2017-04-01
The trend in future space high precision reflectors is going towards large aperture, lightweight and actively controlled deformable antennas. An adaptive shape control system for a Carbon Fiber Reinforced Composite (CFRC) reflector is conducted by Piezoelectric Ceramic Transducer (PZT) actuators. This adaptive shape control system has been shown to effectively mitigate common low order wave-front error, but it is inevitably plagued by high order wave-front error control. In order to improve the controllability of the adaptive CFRC reflector control system for high order wave-front error, the design of adaptive CFRC reflector requires optimizing further. According to numerical and experimental results, the print-through error induced by manufacturing and PZT actuators actuation is a type of predominant high order wave-front error. This paper describes a design which some secondary rib elements are embedded within the triangular cells of the primary ribs. These small secondary ribs are designed to support the reflector surface's weak region. Controllability of this new adaptive CFRC reflector control system with small secondary ribs is evaluated by generalized Zernike functions. This new design scheme can reduce high order residual error and suppress the high order wave-front error such as print-through error. Finally, design parameters of the adaptive CFRC reflector control system with small secondary ribs, such as primary rib height, secondary rib height, cut-out height of primary rib, are optimized.
Pencil lead plasma for generating multimicrojoule high-order harmonics with a broad spectrum
Pertot, Y.; Elouga Bom, L. B.; Ozaki, T.; Bhardwaj, V. R.
2011-03-07
Using the plasma harmonic method, we show the generation of efficient and intense high-order harmonics from plasma of pencil lead. We demonstrate multimicrojoule energy in each harmonic order for the 11th to the 17th order of a Ti:sapphire laser. By analyzing the target morphology and the plasma composition, we conclude that these intense harmonics are generated from nanoparticles of graphitic carbon.
High-Order Central WENO Schemes for 1D Hamilton-Jacobi Equations
NASA Technical Reports Server (NTRS)
Bryson, Steve; Levy, Doron; Biegel, Bryan A. (Technical Monitor)
2002-01-01
In this paper we derive fully-discrete Central WENO (CWENO) schemes for approximating solutions of one dimensional Hamilton-Jacobi (HJ) equations, which combine our previous works. We introduce third and fifth-order accurate schemes, which are the first central schemes for the HJ equations of order higher than two. The core ingredient is the derivation of our schemes is a high-order CWENO reconstructions in space.
High-Order Ghost-Fluid Method for Compressible Flow in Complex Geometry
NASA Astrophysics Data System (ADS)
Al Marouf, Mohamad; Samtaney, Ravi
2014-11-01
We present a high-order embedded boundary method for numerical solutions of the Compressible Navier Stokes (CNS) equations in arbitrary domains. A high-order ghost fluid method based on the PDEs multidimensional extrapolation approach of Aslam (J. Comput. Phys. 2003) is utilized to extrapolate the solution across the fluid-solid interface to impose boundary conditions. A fourth order accurate numerical time integration for the CNS is achieved by fourth order Runge-Kutta scheme, and a fourth order conservative finite volume scheme by McCorquodale & Colella (Comm. in App. Math. & Comput. Sci. 2011) is used to evaluate the fluxes. Resolution at the embedded boundary and high gradient regions is accomplished by applying block-structured adaptive mesh refinement. A number of numerical examples with different Reynolds number for a low Mach number flow over an airfoil and circular cylinder will be presented. Supported by OCRF-CRG grant at KAUST.
78 FR 65744 - High End Ventures, Inc., Order of Suspension of Trading
Federal Register 2010, 2011, 2012, 2013, 2014
2013-11-01
... COMMISSION High End Ventures, Inc., Order of Suspension of Trading October 21, 2013. It appears to the... investors require a suspension of trading in the securities of the above-listed company. Therefore, it is ordered, pursuant to Section 12(k) of the Securities Exchange Act of 1934, that trading in the...
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…
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).
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.
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-Energy Amplitudes in the Next-to-Leading Order
Ian Balitsky
2011-03-01
High-energy scattering in the saturation region is described by the evolution of color dipoles. In the leading order this evolution is governed by the non-linear BK equation. To see if this equation is relevant for existing or future accelerators (like EIC or LHeC) one needs to know how big are the next-to-leading order (NLO) corrections. I review the calculation of the NLO corrections to high-energy amplitudes in QCD.
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.
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
(YIP-10) Efficient and Robust High-Order Methods for Fluid and Solid Mechanics
2013-08-01
viscous and convective model problems, as well as the full compressible Navier - Stokes equations. An example of a turbulent flow is shown in figure 2...designs, which are validated using our high-order Navier - Stokes code. The deforming domain is discretized using our mapping- based ALE approach. The need...Peraire. Numerical simulation of flapping wings using a panel method and a high-order Navier - Stokes solver. Internat. J. Numer. Methods Engrg., 89(10):1296
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
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.
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.
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.
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.
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.
Ultrahigh-resolution soft-x-ray microscopy with zone plates in high orders of diffraction.
Rehbein, S; Heim, S; Guttmann, P; Werner, S; Schneider, G
2009-09-11
We present an x-ray optical approach to overcome the current limitations in spatial resolution of x-ray microscopes. Our new BESSY full-field x-ray microscope operates with an energy resolution up to E/DeltaE=10(4). We demonstrate that under these conditions it is possible to employ high orders of diffraction for imaging. Using the third order of diffraction of a zone plate objective with 25 nm outermost zone width, 14 nm lines and spaces of a multilayer test structure were clearly resolved. We believe that high-order imaging paves the way towards sub-10-nm real space x-ray imaging.
Formation of high-order oligomers by a hyperthemostable Fe-superoxide dismutase (tcSOD).
Wang, Sha; Dong, Zhi-Yang; Yan, Yong-Bin
2014-01-01
Hyperthermostable proteins are highly resistant to various extreme conditions. Many factors have been proposed to contribute to their ultrahigh structural stability. Some thermostable proteins have larger oligomeric size when compared to their mesophilic homologues. The formation of compact oligomers can minimize the solvent accessible surface area and increase the changes of Gibbs free energy for unfolding. Similar to mesophilic proteins, hyperthermostable proteins also face the problem of unproductive aggregation. In this research, we investigated the role of high-order oligomerization in the fight against aggregation by a hyperthermostable superoxide dismutase identified from Tengchong, China (tcSOD). Besides the predominant tetramers, tcSOD could also form active high-order oligomers containing at least eight subunits. The dynamic equilibrium between tetramers and high-order oligomers was not significantly affected by pH, salt concentration or moderate temperature. The secondary and tertiary structures of tcSOD remained unchanged during heating, while cross-linking experiments showed that there were conformational changes or structural fluctuations at high temperatures. Mutational analysis indicated that the last helix at the C-terminus was involved in the formation of high-order oligomers, probably via domain swapping. Based on these results, we proposed that the reversible conversion between the active tetramers and high-order oligomers might provide a buffering system for tcSOD to fight against the irreversible protein aggregation pathway. The formation of active high-order oligomers not only increases the energy barrier between the native state and unfolded/aggregated state, but also provides the enzyme the ability to reproduce the predominant oligomers from the active high-order oligomers.
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).
Chen, Feng; Zhu, Ying-Jie
2016-12-27
Practical applications of nanostructured materials have been largely limited by the difficulties in controllable and scaled-up synthesis, large-sized highly ordered self-assembly, and macroscopic processing of nanostructures. Hydroxyapatite (HAP), the major inorganic component of human bone and tooth, is an important biomaterial with high biocompatibility, bioactivity, and high thermal stability. Large-sized highly ordered HAP nanostructures are of great significance for applications in various fields and for understanding the formation mechanisms of bone and tooth. However, the synthesis of large-sized highly ordered HAP nanostructures remains a great challenge, especially for the preparation of large-sized highly ordered ultralong HAP nanowires because ultralong HAP nanowires are easily tangled and aggregated. Herein, we report our three main research findings: (1) the large-scale synthesis of highly flexible ultralong HAP nanowires with lengths up to >100 μm and aspect ratios up to >10000; (2) the demonstration of a strategy for the rapid automated production of highly flexible, fire-resistant, large-sized, self-assembled highly ordered ultralong HAP nanowires (SHOUHNs) at room temperature; and (3) the successful construction of various flexible fire-resistant HAP ordered architectures using the SHOUHNs, such as high-strength highly flexible nanostructured ropes (nanoropes), highly flexible textiles, and 3-D printed well-defined highly ordered patterns. The SHOUHNs are successively formed from the nanoscale to the microscale then to the macroscale, and the ordering direction of the ordered HAP structure is controllable. These ordered HAP architectures made from the SHOUHNs, such as highly flexible textiles, may be engineered into advanced functional products for applications in various fields, for example, fireproof clothing.
Manipulating the wavefront of light by plasmonic metasurfaces operating in high order modes.
Li, Zhiwei; Hao, Jiaming; Huang, Lirong; Li, Hu; Xu, Hao; Sun, Yan; Dai, Ning
2016-04-18
In this work, plasmonic metasurfaces with abrupt phase discontinuities operating in high order modes are investigated for manipulating the wavefront of light. We first design two types of meta-super-cells consisting of V-shaped antennas with the phase shift coverage larger than 2π. And then, we create two linear gradient phased metasurfaces using the designed cells, which exhibit exceptional abilities for light-steering functioned as meta-echelette gratings operating in high order diffraction modes, may be valuable for using in high resolution spectrographs and advantage to achieve high numerical aperture plasmonic lenses. Based on the new designed super cells we further build another two azimuthal gradient phased metasurfaces that are able to generate high order optical vortex beams. Our results could lead to wide applications in photonic research.
High-order accurate difference schemes for the Hodgkin-Huxley equations
NASA Astrophysics Data System (ADS)
Amsallem, David; Nordström, Jan
2013-11-01
A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate difference schemes using the Summation-By-Parts operators with weak boundary and interface conditions applied to the Hodgkin-Huxley equations. This work is the first demonstrating high accuracy for that equation. Several boundary conditions are considered including the non-standard one accounting for the soma presence, which is characterized by its own partial differential equation. Well-posedness for the continuous problem as well as stability of the discrete approximation is proved for all the boundary conditions. Gains in terms of CPU times are observed when high-order operators are used, demonstrating the advantage of the high-order schemes for simulating potential propagation in large neuronal trees.
Extending the high-order-harmonic spectrum using surface plasmon polaritons
NASA Astrophysics Data System (ADS)
Ebadian, H.; Mohebbi, M.
2017-08-01
Nanoparticle assisted high-order-harmonic generation by low-intensity ultrashort laser pulses in hydrogen atomic gas is studied. This work is based on surface plasmon-polariton coupling in metal-insulator-metal structures. The necessary laser intensity is provided by enhancement of the incident laser power in the vicinity of bowtie nanoparticles installed on an insulator-metal structure. The inhomogeneous electric field distribution in the Au nanobowtie gap region is investigated. Simulations show that the insulator layer installed on the Au metal film that supports the plasmon-polariton interactions has a dramatic effect on the field enhancement factor. High-order-harmonic generation cutoffs for different arrangements are calculated and results show that the metal-insulator-metal structure is an excellent device for high-order-harmonic generation purposes. Also, the harmonic cutoff order is extended to more than 170, which is a considerable value and will be an efficient source for extreme ultraviolet radiation.
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 Technical Reports Server (NTRS)
Weinan, E.; Shu, Chi-Wang
1992-01-01
High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth order central differences through Fast Fourier Transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large-scale features, such as the total circulation around the roll-up region, are adequately resolved.
Rezaee, Hamed; Abdollahi, Farzaneh
2016-12-06
The leaderless consensus problem over a class of high-order nonlinear multiagent systems (MASs) is studied. A robust protocol is proposed which guarantees achieving consensus in the network in the presences of uncertainties in agents models. Achieving consensus in the case of stochastic links failure is studied as well. Based on the concept super-martingales, it is shown that if the probability of the network connectivity is not zero, under some conditions, achieving almost sure consensus in the network can be guaranteed. Despite existing consensus protocols for high-order stochastic networks, the proposed consensus protocol in this paper is robust to uncertain nonlinearities in the agents models, and it can be designed independent of knowledge on the set of feasible topologies (topologies with nonzero probabilities). Numerical examples for a team of single-link flexible joint manipulators with fourth-order models verify the accuracy of the proposed strategy for consensus control of high-order MASs with uncertain nonlinearities.
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.
Decomposition of conditional probability for high-order symbolic Markov chains
NASA Astrophysics Data System (ADS)
Melnik, S. S.; Usatenko, O. V.
2017-07-01
The main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high-order Markov chains. We represent the conditional probability function as the sum of multilinear memory function monomials of different orders (from zero up to the chain order). This allows us to introduce a family of Markov chain models and to construct artificial sequences via a method of successive iterations, taking into account at each step increasingly high correlations among random elements. At weak correlations, the memory functions are uniquely expressed in terms of the high-order symbolic correlation functions. The proposed method fills the gap between two approaches, namely the likelihood estimation and the additive Markov chains. The obtained results may have applications for sequential approximation of artificial neural network training.
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
Determination of Coefficients of High-Order Schemes for Riemann-Liouville Derivative
Wu, Rifang; Li, Changpin
2014-01-01
Although there have existed some numerical algorithms for the fractional differential equations, developing high-order methods (i.e., with convergence order greater than or equal to 2) is just the beginning. Lubich has ever proposed the high-order schemes when he studied the fractional linear multistep methods, where he constructed the pth order schemes (p = 2, 3, 4, 5, 6) for the αth order Riemann-Liouville integral and αth order Riemann-Liouville derivative. In this paper, we study such a problem and develop recursion formulas to compute these coefficients in the higher-order schemes. The coefficients of higher-order schemes (p = 7,8, 9,10) are also obtained. We first find that these coefficients are oscillatory, which is similar to Runge's phenomenon. So, they are not suitable for numerical calculations. Finally, several numerical examples are implemented to testify the efficiency of the numerical schemes for p = 3,…, 6. PMID:24883394
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.
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.
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.
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.
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.
Stability Switches of Arbitrary High-Order Consensus in Multiagent Networks with Time Delays
2013-01-01
High-order consensus seeking, in which individual high-order dynamic agents share a consistent view of the objectives and the world in a distributed manner, finds its potential broad applications in the field of cooperative control. This paper presents stability switches analysis of arbitrary high-order consensus in multiagent networks with time delays. By employing a frequency domain method, we explicitly derive analytical equations that clarify a rigorous connection between the stability of general high-order consensus and the system parameters such as the network topology, communication time-delays, and feedback gains. Particularly, our results provide a general and a fairly precise notion of how increasing communication time-delay causes the stability switches of consensus. Furthermore, under communication constraints, the stability and robustness problems of consensus algorithms up to third order are discussed in details to illustrate our central results. Numerical examples and simulation results for fourth-order consensus are provided to demonstrate the effectiveness of our theoretical results. PMID:24109207
High reprint orders in medical journals and pharmaceutical industry funding: case-control study
Handel, Adam E; Patel, Sunil V; Pakpoor, Julia; Ebers, George C; Goldacre, Ben
2012-01-01
Objectives To assess the extent to which funding and study design are associated with high reprint orders. Design Case-control study. Setting Top articles by size of reprint orders in seven journals, 2002-09. Participants Lancet, Lancet Neurology, Lancet Oncology (Lancet Group), BMJ, Gut, Heart, and Journal of Neurology, Neurosurgery & Psychiatry (BMJ Group) matched to contemporaneous articles not in the list of high reprint orders. Main outcome measures Funding and design of randomised controlled trials or other study designs. Results Median reprint orders for the seven journals ranged from 3000 to 126 350. Papers with high reprint orders were more likely to be funded by the pharmaceutical industry than were control papers (industry funding versus other or none: odds ratio 8.64, 95% confidence interval 5.09 to 14.68, and mixed funding versus other or none: 3.72, 2.43 to 5.70). Conclusions Funding by the pharmaceutical industry is associated with high numbers of reprint orders. PMID:22745328
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.
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.
High-energy amplitudes in N = 4 SYM in the next-to-leading order
Chirilli, Giovanni; Balitsky, Ian
2010-03-16
In this study, the high-energy behavior of the N = 4 SYM amplitudes in the Regge limit can be calculated order by order in perturbation theory using the high-energy operator expansion in Wilson lines. At large $N_c$, a typical four-point amplitude is determined by a single BFKL pomeron. The conformal structure of the four-point amplitude is fixed in terms of two functions: pomeron intercept and the coefficient function in front of the pomeron (the product of two residues). The pomeron intercept is universal while the coefficient function depends on the correlator in question. The intercept is known in the first two orders in coupling constant: BFKL intercept and NLO BFKL intercept calculated in Ref. 1. As an example of using the Wilson-line OPE, we calculate the coefficient function in front of the pomeron for the correlator of four $Z^2$ currents in the first two orders in perturbation theory.
High Order Numerical Simulation of Sound Generated by the Kirchhoff Vortex
NASA Technical Reports Server (NTRS)
Mueller, Bernhard; Yee, H. C.
2001-01-01
An improved high order finite difference method for low Mach number computational aeroacoustics (CAA) is described. The improvements involve the conditioning of the Euler equations in perturbation form to minimize numerical cancellation error, and the use of a stable non-dissipative sixth-order central spatial differencing for the interior points and third-order at the boundary points. The spatial difference operator satisfies the summation-by-parts property to guarantee strict stability for linear hyperbolic systems. Spurious high frequency oscillations are damped by a third-order characteristic-based filter. The objective of this paper is to apply these improvements in the simulation of sound generated by the Kirchhoff vortex.
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.
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.
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.
Highly ordered self-assembled nanoscale periodic faceting in GaAs(631) homoepitaxial growth
Cruz-Hernandez, E.; Mendez-Garcia, V. H.; Shimomura, S.
2012-08-13
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 Multiplication-Sign 1.7 {mu}m{sup 2} 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.
Skew-Symmetric Splitting and Stability of High Order Central Schemes
NASA Astrophysics Data System (ADS)
Sjögreen, Björn; Yee, H. C.; Kotov, Dmitry
2017-05-01
Skew-symmetric splittings of the inviscid flux derivative for high order central schemes are studied and developed to improve their numerical stability without added high order numerical dissipation for long time wave propagations and long time integration of compressible turbulent flows. For flows containing discontinuities and multiscale turbulence fluctuations the Yee & Sjogreen [33] and Kotov et al. [15, 14] high order nonlinear filter approach is utilized in conjunction with the skew-symmetric form of high order central schemes. Due to the incomplete hyperbolic nature of the conservative ideal magnetohydrodynamics (MHD) governing equations, not all of the skew-symmetric splittings for gas dynamics can be extended to the ideal MHD. For the MHD the Ducros et al. [6] variants are constructed. In addition, four formulations of the MHD are considered: (a) the conservative MHD, (b) the Godunov/Powell non-conservative form, (c) the Janhunen MHD with magnetic field source terms [13], and (d) a MHD with source terms of [3]. The different formulation of the equations in conjunction with the variants of Ducros et al. type skew-symmetric splitting will be shown to have a strong effect on the stability of non-dissipative approximations. Representative test cases for both smooth flows and problems containing discontinuities for the ideal MHD are included. The results illustrate the improved stability by using the skew-symmetric splitting as part of the central base scheme instead of the pure high order central scheme.
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.
An Investigation of High-Order Shock-Capturing Methods for Computational Aeroacoustics
NASA Technical Reports Server (NTRS)
Casper, Jay; Baysal, Oktay
1997-01-01
Topics covered include: Low-dispersion scheme for nonlinear acoustic waves in nonuniform flow; Computation of acoustic scattering by a low-dispersion scheme; Algorithmic extension of low-dispersion scheme and modeling effects for acoustic wave simulation; The accuracy of shock capturing in two spatial dimensions; Using high-order methods on lower-order geometries; and Computational considerations for the simulation of discontinuous flows.
High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids
NASA Technical Reports Server (NTRS)
Mazaheri, Alireza; Nishikawa, Hiroaki
2015-01-01
In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.
High order 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 energy x-ray scattering studies of the local order in liquid Al
Mauro, N.A.; Bendert, J.C.; Vogt, A.J.; Gewin, J.M.; Kelton, K.F.
2012-10-23
The x-ray structure factors and densities for liquid aluminum from 1123 K to 1273 K have been measured using the beamline electrostatic levitator. Atomic structures as a function of temperature have been constructed from the diffraction data with reverse Monte Carlo simulations. An analysis of the local atomic structures in terms of the Honeycutt-Andersen indices indicates a high degree of icosahedral and distorted icosahedral order, a modest amount of body-centered cubic order, and marginal amounts of face-centered cubic and hexagonal close-packed order.
High-order diffraction gratings for high-power semiconductor lasers
Vasil'eva, V. V.; Vinokurov, D. A.; Zolotarev, V. V.; Leshko, A. Yu.; Petrunov, A. N.; Pikhtin, N. A.; Rastegaeva, M. G.; Sokolova, Z. N. Shashkin, I. S.; Tarasov, I. S.
2012-02-15
A deep diffraction grating with a large period ({approx}2 {mu}m) within one of the cladding layers is proposed for the implementation of selective feedback in a semiconductor laser. Frequency dependences of reflectance in the 12th diffraction order for rectangular, triangular, and trapezoidal diffraction gratings are calculated. It is shown that the maximum reflectance of the waveguide mode is attained using a rectangular or trapezoidal grating {approx}2 {mu}m deep in the laser structure. Deep trapezoidal diffraction gratings with large periods are fabricated in the Al{sub 0.3}Ga{sub 0.7}As cladding layer of a GaAs/AlGaAs laser structure using photolithography and reactive ion etching.
A High-Order Accurate Parallel Solver for Maxwell's Equations on Overlapping Grids
Henshaw, W D
2005-09-23
A scheme for the solution of the time dependent Maxwell's equations on composite overlapping grids is described. The method uses high-order accurate approximations in space and time for Maxwell's equations written as a second-order vector wave equation. High-order accurate symmetric difference approximations to the generalized Laplace operator are constructed for curvilinear component grids. The modified equation approach is used to develop high-order accurate approximations that only use three time levels and have the same time-stepping restriction as the second-order scheme. Discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed. The implementation is optimized for component grids that are Cartesian, resulting in a fast and efficient method. The solver runs on parallel machines with each component grid distributed across one or more processors. Numerical results in two- and three-dimensions are presented for the fourth-order accurate version of the method. These results demonstrate the accuracy and efficiency of the approach.
Estimate Low and High Order Wavefront Using P1640 Calibrator Measurements
NASA Technical Reports Server (NTRS)
Zhai, C.; Vasisht, G.; Shao, M.; Lockhart, T.; Cady, E.; Oppenheimer, B.; Burruss, R.; Roberts, J.; Beichman, C.; Brenner, D.; Crepp, J.; Dekany, R.; Hillenbrand, L.; Hinkley, S.; Parry, I.; Pueyo, L.; Rice, E.; Roberts, L. C. Jr.; Sivaramakrishnan, A.; Soummer, R.; Tang, H.; Vescelus, F.; Wallace, K.; Zimmerman, N.
2013-01-01
P1640 high contrast imaging system on the Palomar 200 inch Telescope consists of an apodized-pupil Lyot coronagraph, the PALM-3000 adaptive optics (P3K-AO), and P1640 Calibrator (CAL). Science images are recorded by an integral field spectrograph covering J-H bands for detecting and characterizing stellar companions. With aberrations from atmosphere corrected by the P3K-AO, instrument performance is limited mainly by the quasi-static speckles due to noncommon path wavefront aberrations for the light to propagate to the P3K-AO wavefront sensor and to the coronagraph mask. The non-common path wavefront aberrations are sensed by CAL, which measures the post-coronagraph E-field using interferometry, and can be effectively corrected by offsetting the P3K-AO deformable mirror target position accordingly. Previously, we have demonstrated using CAL measurements to correct high order wavefront aberrations, which is directly connected to the static speckles in the image plane. Low order wavefront, on the other hand, usually of larger amplitudes, causes light to leak through the coronagraph making the whole image plane brighter. Knowledge error in low order wavefront aberrations can also affect the estimation of the high order wavefront. Even though, CAL is designed to sense efficiently high order wavefront aberrations, the low order wavefront front can be inferred with less sensitivity. Here, we describe our method for estimating both low and high order wavefront aberrations using CAL measurements by propagating the post-coronagraph E-field to a pupil before the coronagraph. We present the results from applying this method to both simulated and experiment data.
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.;
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
Efficient nonlinear generation of high power, higher order, ultrafast "perfect" vortices in green.
Apurv Chaitanya, N; Jabir, M V; Samanta, G K
2016-04-01
We report on efficient nonlinear generation of ultrafast, higher order "perfect" vortices at the green wavelength. Based on Fourier transformation of the higher order Bessel-Gauss (BG) beam generated through the combination of the spiral phase plate and axicon, we have transformed the Gaussian beam of the ultrafast Yb-fiber laser at 1060 nm into perfect vortices of power 4.4 W and order up to 6. Using single-pass second-harmonic generation (SHG) of such vortices in 5 mm long chirped MgO-doped, periodically poled congruent LiNbO_{3} crystal, we have generated perfect vortices at green wavelength (530 nm) with output power of 1.2 W and vortex order up to 12 at a single-pass conversion efficiency of 27%, independent of the orders. This is the highest single-pass SHG efficiency of any optical beams other than Gaussian beams. Unlike the disintegration of higher order vortices due to spatial walk-off effect in birefringent crystals, here, the use of the quasi-phase-matching process enables generation of high-quality vortices, even at higher orders. The green perfect vortices of all orders have temporal and spectral widths of 507 fs and 1.9 nm, respectively, corresponding to a time-bandwidth product of 1.02.
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.
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.
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.
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.
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.
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.
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.
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.
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
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
2014-07-07
discretization. In this paper, two techniques for the source term discretization are proposed; (1) reformulation of the source terms with their divergence...modifying the source term discretization. In this paper, two techniques for the source term discretization are proposed; (1) reformulation of the...and fourth-order schemes from the former technique . These schemes require computations of the gradients and second-derivatives of the source terms
An optimization-based method for high order gradient calculation on unstructured meshes
NASA Astrophysics Data System (ADS)
Busatto, Alcides Dallanora
A new implicit and compact optimization-based method is presented for high order derivative calculation for finite-volume numerical method on unstructured meshes. High-order approaches to gradient calculation are often based on variants of the Least-Squares (L-S) method, an explicit method that requires a stencil large enough to accommodate the necessary variable information to calculate the derivatives. The new scheme proposed here is applicable for an arbitrary order of accuracy (demonstrated here up to 3rd order), and uses just the first level of face neighbors to compute all derivatives, thus reducing stencil size and avoiding stiffness in the calculation matrix. Preliminary results for a static variable field example and solution of a simple scalar transport (advection) equation show that the proposed method is able to deliver numerical accuracy equivalent to (or better than) the nominal order of accuracy for both 2nd and 3rd order schemes in the presence of a smoothly distributed variable field (i.e., in the absence of discontinuities). This new Optimization-based Gradient REconstruction (herein denoted OGRE) scheme produces, for the simple scalar transport test case, lower error and demands less computational time (for a given level of required precision) for a 3rd order scheme when compared to an equivalent L-S approach on a two-dimensional framework. For three-dimensional simulations, where the L-S scheme fails to obtain convergence without the help of limiters, the new scheme obtains stable convergence and also produces lower error solution when compared to a third order MUSCL scheme. Furthermore, spectral analysis of results from the advection equation shows that the new scheme is better able to accurately resolve high wave number modes, which demonstrates its potential to better solve problems presenting a wide spectrum of wavelengths, for example unsteady turbulent flow simulations.
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.
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.
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.
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.
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
A perspective on high-order methods in computational fluid dynamics
NASA Astrophysics Data System (ADS)
Wang, ZhiJian
2016-01-01
There has been an intensive international effort to develop high-order Computational Fluid Dynamics (CFD) methods into design tools in aerospace engineering during the last one and half decades. These methods offer the potential to significantly improve solution accuracy and efficiency for vortex dominated turbulent flows. Enough progresses have been made in algorithm development, mesh generation and parallel computing that these methods are on the verge of being applied in a production design environment. Since many review papers have been written on the subject, I decide to offer a personal perspective on the state-of-the-art in high-order CFD methods and the challenges that must be overcome.
A high-order 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
2014-11-04
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.
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.
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.
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
2014-01-01
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
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.
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.
A high-order spatial filter for a cubed-sphere spectral element model
NASA Astrophysics Data System (ADS)
Kang, Hyun-Gyu; Cheong, Hyeong-Bin
2017-04-01
A high-order spatial filter is developed for the spectral-element-method dynamical core on the cubed-sphere grid which employs the Gauss-Lobatto Lagrange interpolating polynomials (GLLIP) as orthogonal basis functions. The filter equation is the high-order Helmholtz equation which corresponds to the implicit time-differencing of a diffusion equation employing the high-order Laplacian. The Laplacian operator is discretized within a cell which is a building block of the cubed sphere grid and consists of the Gauss-Lobatto grid. When discretizing a high-order Laplacian, due to the requirement of C0 continuity along the cell boundaries the grid-points in neighboring cells should be used for the target cell: The number of neighboring cells is nearly quadratically proportional to the filter order. Discrete Helmholtz equation yields a huge-sized and highly sparse matrix equation whose size is N*N with N the number of total grid points on the globe. The number of nonzero entries is also almost in quadratic proportion to the filter order. Filtering is accomplished by solving the huge-matrix equation. While requiring a significant computing time, the solution of global matrix provides the filtered field free of discontinuity along the cell boundaries. To achieve the computational efficiency and the accuracy at the same time, the solution of the matrix equation was obtained by only accounting for the finite number of adjacent cells. This is called as a local-domain filter. It was shown that to remove the numerical noise near the grid-scale, inclusion of 5*5 cells for the local-domain filter was found sufficient, giving the same accuracy as that obtained by global domain solution while reducing the computing time to a considerably lower level. The high-order filter was evaluated using the standard test cases including the baroclinic instability of the zonal flow. Results indicated that the filter performs better on the removal of grid-scale numerical noises than the explicit
Highly ordered Zn-doped mesoporous silica: An efficient catalyst for transesterification reaction
Pal, Nabanita; Paul, Manidipa; Bhaumik, Asim
2011-07-15
Designing highly ordered material with nanoscale periodicity is of great significance in the field of solid state chemistry. Herein, we report the synthesis of highly ordered 2D-hexagonal mesoporous zinc-doped silica using a mixture of anionic and cationic surfactants under hydrothermal conditions. Powder XRD, N{sub 2} sorption, TEM analysis revealed highly ordered 2D-hexagonal arrangements of the pores with very good surface area (762 m{sup 2} g{sup -1}) in this Zn-rich mesoporous material. Chemical analysis shows very high loading of zinc (ca. 12.0 wt%) in the material together with retention of hexagonal pore structure. Interestingly, high temperature calcination resulted into zinc silicate phase, unlike any ZnO phase, which otherwise is expected under heat treatments. High surface area together with Zn loading in this mesoporous material has been found useful for the catalytic activity of the materials in the acid-catalyzed transesterification reactions of various esters under mild liquid phase conditions. - Graphical abstract: Zn-rich 2D-hexagonal mesoporous materials are synthesized hydrothermally, which show very good catalytic activity in the transesterification reaction under mild liquid phase reaction conditions. Highlights: > Zn-rich 2D-hexagonal mesoporous silica. > High surface area material. > Efficient catalyst in liquid phase transesterification reaction. > Biodiesel production.
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.
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 staggered finite-element vertical discretization for non-hydrostatic atmospheric models
NASA Astrophysics Data System (ADS)
Guerra, Jorge E.; Ullrich, Paul A.
2016-06-01
Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δx) modes. Furthermore, high-order accuracy also eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.
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.
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
Enhancement of the Nernst effect by stripe order in a high-T(c) superconductor.
Cyr-Choinière, Olivier; Daou, R; Laliberté, Francis; LeBoeuf, David; Doiron-Leyraud, Nicolas; Chang, J; Yan, J-Q; Cheng, J-G; Zhou, J-S; Goodenough, J B; Pyon, S; Takayama, T; Takagi, H; Tanaka, Y; Taillefer, Louis
2009-04-09
The Nernst effect in metals is highly sensitive to two kinds of phase transition: superconductivity and density-wave order. The large, positive Nernst signal observed in hole-doped high-T(c) superconductors above their transition temperature (T(c)) has so far been attributed to fluctuating superconductivity. Here we report that in some of these materials the large Nernst signal is in fact the result of stripe order, a form of spin/charge modulation that causes a reconstruction of the Fermi surface. In La(2-x)Sr(x)CuO(4) (LSCO) doped with Nd or Eu, the onset of stripe order causes the Nernst signal to change from being small and negative to being large and positive, as revealed either by lowering the hole concentration across the quantum critical point in Nd-doped LSCO (refs 6-8) or by lowering the temperature across the ordering temperature in Eu-doped LSCO (refs 9, 10). In the second case, two separate peaks are resolved, respectively associated with the onset of stripe order at high temperature and superconductivity near T(c).
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.
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.
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.
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
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.
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.
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.
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).
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
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.
Generation of high-order harmonics with ultra-short pulses from filamentation.
Steingrube, Daniel S; Schulz, Emilia; Binhammer, Thomas; Vockerodt, Tobias; Morgner, Uwe; Kovacev, Milutin
2009-08-31
7-fs-pulses with 0.3 mJ are obtained after filamentation in argon and compression by double-chirped-mirrors. These pulses are used to generate high-order harmonics in a semi-infinite gas cell in different noble gases. Spectral broadening of high-order harmonics in xenon and argon is observed. In neon, an extended continuous cut-off region down to 10 nm (124 eV) is observed which is to the best of our knowledge the highest cut-off energy obtained by filamented pulses. Our result suggests the feasibility of single attosecond-pulse-generation at both high photon flux and high cut-off energy.
Quantum Key Distribution with High Order Fibonacci-like Orbital Angular Momentum States
NASA Astrophysics Data System (ADS)
Pan, Ziwen; Cai, Jiarui; Wang, Chuan
2017-08-01
The coding space in quantum communication could be expanded to high-dimensional space by using orbital angular momentum (OAM) states of photons, as both the capacity of the channel and security are enhanced. Here we present a novel approach to realize high-capacity quantum key distribution (QKD) by exploiting OAM states. The innovation of the proposed approach relies on a unique type of entangled-photon source which produces entangled photons with OAM randomly distributed among high order Fiboncci-like numbers and a new physical mechanism for efficiently sharing keys. This combination of entanglement with mathematical properties of high order Fibonacci sequences provides the QKD protocol immunity to photon-number-splitting attacks and allows secure generation of long keys from few photons. Unlike other protocols, reference frame alignment and active modulation of production and detection bases are unnecessary.
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.
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.
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.
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.
Resonancelike enhancement in high-order above-threshold ionization of molecules
NASA Astrophysics Data System (ADS)
Quan, Wei; Lai, XuanYang; Chen, YongJu; Wang, ChuanLiang; Hu, ZiLong; Liu, XiaoJun; Hao, XiaoLei; Chen, Jing; Hasović, Elvedin; Busuladžić, Mustafa; Becker, Wilhelm; Milošević, Dejan B.
2013-08-01
Rresonancelike enhancement of groups of adjacent peaks in the photoelectron spectrum of high-order above-threshold ionization has been well documented for noble-gas atoms subjected to intense infrared laser pulses. However, its physical origin is still under debate. In this Rapid Communication, we investigate experimentally and theoretically high-order above-threshold ionization of diatomic nitrogen and oxygen molecules in order to shed more light on the underlying mechanism. The resonancelike enhancement is experimentally observed for N2 but is absent for O2 molecules. A simulation on the basis of S-matrix theory and the strong-field approximation reproduces the experimental observations. This implies that the resonancelike enhancement can be attributed to the channel-closing effect. The specific molecular structure plays a decisive role for the presence or absence of this enhancement in molecular systems.
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.
Pramanik, Malay; Li, Cuiling; Imura, Masataka; Malgras, Victor; Kang, Yong-Mook; Yamauchi, Yusuke
2016-04-06
A hexagonally ordered mesoporous cobalt phosphate (CoPi) material is prepared by a facile one-pot soft-templating strategy using cetyltrimethylammonium bromide template. Because of its highly accessible surface area and crystalline framework with abundant active sites, the mesoporous CoPi shows a high catalytic activity for the oxygen evolution reaction compared to previously reported noble/transition-metal and nonmetal catalysts. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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.
A high order multi-resolution solver for the Poisson equation with application to vortex methods
NASA Astrophysics Data System (ADS)
Hejlesen, Mads Mølholm; Spietz, Henrik Juul; Walther, Jens Honore
2015-11-01
A high order method is presented for solving the Poisson equation subject to mixed free-space and periodic boundary conditions by using fast Fourier transforms (FFT). The high order convergence is achieved by deriving mollified Green's functions from a high order regularization function which provides a correspondingly smooth solution to the Poisson equation. The high order regularization function may be obtained analogous to the approximate deconvolution method used in turbulence models and strongly relates to deblurring algorithms used in image processing. At first we show that the regularized solver can be combined with a short range particle-particle correction for evaluating discrete particle interactions in the context of a particle-particle particle-mesh (P3M) method. By a similar approach we extend the regularized solver to handle multi-resolution patches in continuum field simulations by super-positioning an inter-mesh correction. For sufficiently smooth vector fields this multi-resolution correction can be achieved without the loss of convergence rate. An implementation of the multi-resolution solver in a two-dimensional re-meshed particle-mesh based vortex method is presented and validated.
Bounded Skew High-Order Resolution Schemes for the Discrete Ordinates Method
NASA Astrophysics Data System (ADS)
Coelho, P. J.
2002-01-01
The discrete ordinates method for the solution of the radiative heat transfer equation suffers from two main shortcomings, namely ray effects and numerical smearing. Spatial discretization, which is the cause of numerical smearing, constitutes the subject of the present work. Bounded skew high-order resolution schemes are applied to the discrete ordinate equations and compared with standard bounded high-order resolution schemes (CLAM, MUSCL, and SMART), as well as with the step scheme. Calculations are performed for two- and three-dimensional enclosures with transparent, emitting-absorbing, and emitting-absorbing-scattering media. One of the walls of the enclosure is hot, while the others are cold. The results demonstrate that the bounded skew high-order schemes are more accurate than the bounded high-order ones, regardless of the radiative properties of the medium. The improved accuracy is more significant for the radiation intensity along directions oblique to the coordinate lines, but it is also observed for the incident radiation. The difference between the results of the skewed and the standard schemes is attenuated as the optical thickness of the medium increases. A drawback of the skewed schemes is their higher computational requirements, associated with an increased number of iterations required for convergence.
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.
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.
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,…
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.
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…
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…
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…
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.
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.
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
Identification of interactions in fractional-order systems with high dimensions
Ji, Xiaoxi; Wu, Yu; Sheng, Wenbo; Lin, Wei
2014-06-15
This article proposes an approach to identify fractional-order systems with sparse interaction structures and high dimensions when observation data are supposed to be experimentally available. This approach includes two steps: first, it is to estimate the value of the fractional order by taking into account the solution properties of fractional-order systems; second, it is to identify the interaction coefficients among the system variables by employing the compressed sensing technique. An error analysis is provided analytically for this approach and a further improved approach is also proposed. Moreover, the applicability of the proposed approach is fully illustrated by two examples: one is to estimate the mutual interactions in a complex dynamical network described by fractional-order systems, and the other is to identify a high fractional-order and homogeneous sequential differential equation, which is frequently used to describe viscoelastic phenomena. All the results demonstrate the feasibility of figuring out the system mechanisms behind the data experimentally observed in physical or biological systems with viscoelastic evolution characters.
High-order moments of spin-orbit energy in a multielectron configuration
NASA Astrophysics Data System (ADS)
Na, Xieyu; Poirier, M.
2016-07-01
In order to analyze the energy-level distribution in complex ions such as those found in warm dense plasmas, this paper provides values for high-order moments of the spin-orbit energy in a multielectron configuration. Using second-quantization results and standard angular algebra or fully analytical expressions, explicit values are given for moments up to 10th order for the spin-orbit energy. Two analytical methods are proposed, using the uncoupled or coupled orbital and spin angular momenta. The case of multiple open subshells is considered with the help of cumulants. The proposed expressions for spin-orbit energy moments are compared to numerical computations from Cowan's code and agree with them. The convergence of the Gram-Charlier expansion involving these spin-orbit moments is analyzed. While a spectrum with infinitely thin components cannot be adequately represented by such an expansion, a suitable convolution procedure ensures the convergence of the Gram-Charlier series provided high-order terms are accounted for. A corrected analytical formula for the third-order moment involving both spin-orbit and electron-electron interactions turns out to be in fair agreement with Cowan's numerical computations.
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.
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).
Sun, J. P.; Matsuura, K.; Ye, G. Z.; Mizukami, Y.; Shimozawa, M.; Matsubayashi, K.; Yamashita, M.; Watashige, T.; Kasahara, S.; Matsuda, Y.; Yan, J. -Q.; Sales, B. C.; Uwatoko, Y.; Cheng, J. -G.; Shibauchi, T.
2016-01-01
The coexistence and competition between superconductivity and electronic orders, such as spin or charge density waves, have been a central issue in high transition-temperature (Tc) superconductors. Unlike other iron-based superconductors, FeSe exhibits nematic ordering without magnetism whose relationship with its superconductivity remains unclear. Moreover, a pressure-induced fourfold increase of Tc has been reported, which poses a profound mystery. Here we report high-pressure magnetotransport measurements in FeSe up to ∼15 GPa, which uncover the dome shape of magnetic phase superseding the nematic order. Above ∼6 GPa the sudden enhancement of superconductivity (Tc≤38.3 K) accompanies a suppression of magnetic order, demonstrating their competing nature with very similar energy scales. Above the magnetic dome, we find anomalous transport properties suggesting a possible pseudogap formation, whereas linear-in-temperature resistivity is observed in the normal states of the high-Tc phase above 6 GPa. The obtained phase diagram highlights unique features of FeSe among iron-based superconductors, but bears some resemblance to that of high-Tc cuprates. PMID:27431724
NASA Astrophysics Data System (ADS)
Sun, J. P.; Matsuura, K.; Ye, G. Z.; Mizukami, Y.; Shimozawa, M.; Matsubayashi, K.; Yamashita, M.; Watashige, T.; Kasahara, S.; Matsuda, Y.; Yan, J.-Q.; Sales, B. C.; Uwatoko, Y.; Cheng, J.-G.; Shibauchi, T.
2016-07-01
The coexistence and competition between superconductivity and electronic orders, such as spin or charge density waves, have been a central issue in high transition-temperature (Tc) superconductors. Unlike other iron-based superconductors, FeSe exhibits nematic ordering without magnetism whose relationship with its superconductivity remains unclear. Moreover, a pressure-induced fourfold increase of Tc has been reported, which poses a profound mystery. Here we report high-pressure magnetotransport measurements in FeSe up to ~15 GPa, which uncover the dome shape of magnetic phase superseding the nematic order. Above ~6 GPa the sudden enhancement of superconductivity (Tc<=38.3 K) accompanies a suppression of magnetic order, demonstrating their competing nature with very similar energy scales. Above the magnetic dome, we find anomalous transport properties suggesting a possible pseudogap formation, whereas linear-in-temperature resistivity is observed in the normal states of the high-Tc phase above 6 GPa. The obtained phase diagram highlights unique features of FeSe among iron-based superconductors, but bears some resemblance to that of high-Tc cuprates.
Sun, J P; Matsuura, K; Ye, G Z; Mizukami, Y; Shimozawa, M; Matsubayashi, K; Yamashita, M; Watashige, T; Kasahara, S; Matsuda, Y; Yan, J-Q; Sales, B C; Uwatoko, Y; Cheng, J-G; Shibauchi, T
2016-07-19
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.; ...
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
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.
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.
High order mode long-period fiber grating refractive index sensor based on intensity measurement
NASA Astrophysics Data System (ADS)
Lan, Xinwei; Han, Qun; Huang, Jie; Fang, Xia; Wei, Tao; Gao, Zhan; Xiao, Hai
2012-02-01
Long-period fiber gratings have been used for refractive index measurements under different conditions. Normally, this kind of sensor is based on measuring resonance wavelength shift with respect to different refractive index environments. As high order mode long period fiber gratings are attracting more attention, a new methodology based on intensity measurement of turning points is introduced, which involves simple experiment setup and straightforward demodulation process compared with wavelength shift based method. By using CO2 laser point by point irradiation method, high order mode gratings working at turning point can be easily fabricated. This type of grating has a very high sensitive response to surrounding refractive index, which can be used in chemical, medical and bio applications. In this paper, high sensitive refractive index sensor is demonstrated based on high order mode using intensity measurement. Phase match curve and couple mode theory are combined to analyze the intensity response to refractive index change at turning point of LPFG. This sensor is also demonstrated as an effective refractive index based glucose sensor with a range from 0 to 40 mM concentration of glucose solution, which can fulfill the medical requirement.
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.
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.
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.
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.
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.
High-order lattice Boltzmann models for wall-bounded flows at finite Knudsen numbers.
Feuchter, C; Schleifenbaum, W
2016-07-01
We analyze a large number of high-order discrete velocity models for solving the Boltzmann-Bhatnagar-Gross-Krook equation for finite Knudsen number flows. Using the Chapman-Enskog formalism, we prove for isothermal flows a relation identifying the resolved flow regimes for low Mach numbers. Although high-order lattice Boltzmann models recover flow regimes beyond the Navier-Stokes level, we observe for several models significant deviations from reference results. We found this to be caused by their inability to recover the Maxwell boundary condition exactly. By using supplementary conditions for the gas-surface interaction it is shown how to systematically generate discrete velocity models of any order with the inherent ability to fulfill the diffuse Maxwell boundary condition accurately. Both high-order quadratures and an exact representation of the boundary condition turn out to be crucial for achieving reliable results. For Poiseuille flow, we can reproduce the mass flow and slip velocity up to the Knudsen number of 1. Moreover, for small Knudsen numbers, the Knudsen layer behavior is recovered.
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.
A comparison of two formulations for high-order accurate essentially non-oscillatory schemes
NASA Technical Reports Server (NTRS)
Casper, J.; Shu, Chi-Wang; Atkins, H.
1993-01-01
The finite-volume and finite-difference implementations of high-order accurate essentially nonoscillatory 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.
Application of organic compounds for high-order harmonic generation of ultrashort pulses
NASA Astrophysics Data System (ADS)
Ganeev, R. A.
2016-02-01
The studies of the high-order nonlinear optical properties of a few organic compounds (polyvinyl alcohol, polyethylene, sugar, coffee, and leaf) are reported. Harmonic generation in the laser-produced plasmas containing the molecules and large particles of above materials is demonstrated. These studies showed that the harmonic distributions and harmonic cutoffs from organic compound plasmas were similar to those from the graphite ablation. The characteristic feature of observed harmonic spectra was the presence of bluesided lobes near the lower-order harmonics.
Gkortsas, Vasileios-Marios; Bhardwaj, Siddharth; Lai, Chien-Jen; Hong, Kyung-Han; Falcao-Filho, Edilson L.; Kaertner, Franz X.
2011-07-15
High-order harmonic generation efficiency is theoretically modeled and compared with experiments using 400 and 800 nm driver pulses. It is shown that, for a short drive wavelength and a Keldysh parameter larger than 1, the Ammosov-Delone-Krainov (ADK) ionization model does not give a good agreement between theory and experiment. Since the ADK ionization model only accounts for tunnel ionization, it underestimates the yield of low-order harmonics from the wings of the driver pulse. In contrast, the Yudin-Ivanov ionization model [Phys. Rev. A 64, 013409 (2001)], which accounts for both tunnel and multiphoton ionization, gives much better agreement with the experimental results.
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.
Optimal error estimates for high order Runge-Kutta methods applied to evolutionary equations
McKinney, W.R.
1989-01-01
Fully discrete approximations to 1-periodic solutions of the Generalized Korteweg de-Vries and the Cahn-Hilliard equations are analyzed. These approximations are generated by an Implicit Runge-Kutta method for the temporal discretization and a Galerkin Finite Element method for the spatial discretization. Furthermore, these approximations may be of arbitrarily high order. In particular, it is shown that the well-known order reduction phenomenon afflicting Implicit Runge Kutta methods does not occur. Numerical results supporting these optimal error estimates for the Korteweg-de Vries equation and indicating the existence of a slow motion manifold for the Cahn-Hilliard equation are also provided.
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 $N$.
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.