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Sample records for dynamical approximation schemes

  1. On the dynamics of approximating schemes for dissipative nonlinear equations

    NASA Technical Reports Server (NTRS)

    Jones, Donald A.

    1993-01-01

    Since one can rarely write down the analytical solutions to nonlinear dissipative partial differential equations (PDE's), it is important to understand whether, and in what sense, the behavior of approximating schemes to these equations reflects the true dynamics of the original equations. Further, because standard error estimates between approximations of the true solutions coming from spectral methods - finite difference or finite element schemes, for example - and the exact solutions grow exponentially in time, this analysis provides little value in understanding the infinite time behavior of a given approximating scheme. The notion of the global attractor has been useful in quantifying the infinite time behavior of dissipative PDEs, such as the Navier-Stokes equations. Loosely speaking, the global attractor is all that remains of a sufficiently large bounded set in phase space mapped infinitely forward in time under the evolution of the PDE. Though the attractor has been shown to have some nice properties - it is compact, connected, and finite dimensional, for example - it is in general quite complicated. Nevertheless, the global attractor gives a way to understand how the infinite time behavior of approximating schemes such as the ones coming from a finite difference, finite element, or spectral method relates to that of the original PDE. Indeed, one can often show that such approximations also have a global attractor. We therefore only need to understand how the structure of the attractor for the PDE behaves under approximation. This is by no means a trivial task. Several interesting results have been obtained in this direction. However, we will not go into the details. We mention here that approximations generally lose information about the system no matter how accurate they are. There are examples that show certain parts of the attractor may be lost by arbitrary small perturbations of the original equations.

  2. Comparison of dynamical approximation schemes for nonlinear gravitaional clustering

    NASA Technical Reports Server (NTRS)

    Melott, Adrian L.

    1994-01-01

    We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the lognormal approximation, the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by smoothing the initial conditions with various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was cross-correlation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(sub G(exp 2)), where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present. This in turn provides a natural explanation for the presence of sheets and filaments in the observed galaxy distribution. Use of the approximation scheme can permit extremely rapid generation of large numbers of realizations of model universes with good accuracy down to galaxy group mass scales.

  3. Stable boundary approximations for a class of implicit schemes for the one-dimensional inviscid equations of gas dynamics

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Beam, R. M.; Warming, R. F.

    1981-01-01

    The applicability to practical calculations of recent theoretical developments in the stability analysis of difference approximations for initial-boundary-value problems of the hyperbolic type. For the numerical experiments, select the one-dimensional inviscid gas-dynamic equations in conservation-law form is selected. A class of implicit schemes based on linear multistep methods for ordinary differential equations is chosen and the use of space or space-time extrapolations as implicit or explicit boundary schemes is emphasized. Some numerical examples with various inflow-outflow conditions highlight the commonly discussed issues: explicit versus implicit boundary schemes, unconditionally stable schemes, and underspecification or overspecification of boundary conditions.

  4. Comparison of dynamical approximation schemes for non-linear gravitational clustering

    NASA Technical Reports Server (NTRS)

    Melott, Adrian L.

    1994-01-01

    We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of approximation by truncation, i.e., smoothing the initial conditions by various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was crosscorrelation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(exp 2, sub G)) where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. All other schemes, including those proposed as generalizations of the Zel'dovich approximation created by adding forces, were in fact generally worse by this measure. By explicitly checking, we verified that the success of our best-choice was a result of the best treatment of the phases of nonlinear Fourier components. Of all schemes tested, the adhesion approximation produced the most accurate nonlinear power spectrum and density distribution, but its phase errors suggest mass condensations were moved to slightly the wrong location. Due to its better reproduction of the mass density distribution function and power spectrum, it might be preferred for some uses. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even

  5. Approximate particle spectra in the pyramid scheme

    NASA Astrophysics Data System (ADS)

    Banks, Tom; Torres, T. J.

    2012-12-01

    We construct a minimal model inspired by the general class of pyramid schemes [T. Banks and J.-F. Fortin, J. High Energy Phys. 07 (2009) 046JHEPFG1029-8479], which is consistent with both supersymmetry breaking and electroweak symmetry breaking. In order to do computations, we make unjustified approximations to the low energy Kähler potential. The phenomenological viability of the resultant mass spectrum is then examined and compared with current collider limits. We show that for certain regimes of parameters, the model, and thus generically the pyramid scheme, can accommodate the current collider mass constraints on physics beyond the standard model with a tree-level light Higgs mass near 125 GeV. However, in this regime the model exhibits a little hierarchy problem, and one must permit fine-tunings that are of order 5%.

  6. Quark propagator in a truncation scheme beyond the rainbow approximation

    NASA Astrophysics Data System (ADS)

    Fu, Hui-Feng; Wang, Qing

    2016-01-01

    The quark propagator is studied under a truncation scheme beyond the rainbow approximation by dressing the quark-gluon vertex nonperturbatively. It is found that, in the chiral limit with dynamical symmetry breaking, the dynamical quark mass and the quark condensate are significantly enhanced due to the non-Abelian contribution arising from the three-gluon interaction compared to those under the rainbow approximation, and the critical strength of the dynamical chiral symmetry breaking is much lowered. The Abelian contribution is much smaller than the non-Abelian contribution. A technical issue on removing the ultraviolet divergences, including the overlapping divergences, is discussed.

  7. An Approximation Scheme for Delay Equations.

    DTIC Science & Technology

    1980-06-16

    AD-Am" 155 BtO~i UNkIV PROVIDENCE RI LEFSCI4ETZ CENTER FOR DYNAMI-flO F/f 12/ 1 AN APPROXIMATION SCIEME FOR DELAY EQUATIONS (U) JUN 80 F KAPPEL DAA629...for publ.ic release IAM 19.. and 1s aftnaotaton in unhi tea.0 ( f) 1 DDC UtB Distwifeaton A_._il .rd/or 1 . Introduction. In recent years one can see...Banach spaces. Fundamental for our approach is the following approximation theorem for semigroups of type W: Theorem 1 ([10]). Let AN, N - 1,2,..., and A

  8. Stochastic population dynamics: The Poisson approximation

    NASA Astrophysics Data System (ADS)

    Solari, Hernán G.; Natiello, Mario A.

    2003-03-01

    We introduce an approximation to stochastic population dynamics based on almost independent Poisson processes whose parameters obey a set of coupled ordinary differential equations. The approximation applies to systems that evolve in terms of events such as death, birth, contagion, emission, absorption, etc., and we assume that the event-rates satisfy a generalized mass-action law. The dynamics of the populations is then the result of the projection from the space of events into the space of populations that determine the state of the system (phase space). The properties of the Poisson approximation are studied in detail. Especially, error bounds for the moment generating function and the generating function receive particular attention. The deterministic approximation for the population fractions and the Langevin-type approximation for the fluctuations around the mean value are recovered within the framework of the Poisson approximation as particular limit cases. However, the proposed framework allows to treat other limit cases and general situations with small populations that lie outside the scope of the standard approaches. The Poisson approximation can be viewed as a general (numerical) integration scheme for this family of problems in population dynamics.

  9. A piecewise linear approximation scheme for hereditary optimal control problems

    NASA Technical Reports Server (NTRS)

    Cliff, E. M.; Burns, J. A.

    1977-01-01

    An approximation scheme based on 'piecewise linear' approximations of L2 spaces is employed to formulate a numerical method for solving quadratic optimal control problems governed by linear retarded functional differential equations. This piecewise linear method is an extension of the so called averaging technique. It is shown that the Riccati equation for the linear approximation is solved by simple transformation of the averaging solution. Thus, the computational requirements are essentially the same. Numerical results are given.

  10. A piecewise linear approximation scheme for hereditary optimal control problems

    NASA Technical Reports Server (NTRS)

    Cliff, E. M.; Burns, J. A.

    1977-01-01

    An approximation scheme based on 'piecewise linear' approximations of L2 spaces is employed to formulate a numerical method for solving quadratic optimal control problems governed by linear retarded functional differential equations. This piecewise linear method is an extension of the so called averaging technique. It is shown that the Riccati equation for the linear approximation is solved by simple transformation of the averaging solution. Thus, the computational requirements are essentially the same. Numerical results are given.

  11. Ab initio dynamical vertex approximation

    NASA Astrophysics Data System (ADS)

    Galler, Anna; Thunström, Patrik; Gunacker, Patrik; Tomczak, Jan M.; Held, Karsten

    2017-03-01

    Diagrammatic extensions of dynamical mean-field theory (DMFT) such as the dynamical vertex approximation (DΓ A) allow us to include nonlocal correlations beyond DMFT on all length scales and proved their worth for model calculations. Here, we develop and implement an Ab initio DΓ A approach (AbinitioDΓ A ) for electronic structure calculations of materials. The starting point is the two-particle irreducible vertex in the two particle-hole channels which is approximated by the bare nonlocal Coulomb interaction and all local vertex corrections. From this, we calculate the full nonlocal vertex and the nonlocal self-energy through the Bethe-Salpeter equation. The AbinitioDΓ A approach naturally generates all local DMFT correlations and all nonlocal G W contributions, but also further nonlocal correlations beyond: mixed terms of the former two and nonlocal spin fluctuations. We apply this new methodology to the prototypical correlated metal SrVO3.

  12. On Approximate Factorization Schemes for Solving the Full Potential Equation

    NASA Technical Reports Server (NTRS)

    Holst, Terry L.

    1997-01-01

    An approximate factorization scheme based on the AF2 algorithm is presented for solving the three-dimensional full potential equation for the transonic flow about isolated wings. Two spatial discretization variations are presented, one using a hybrid first-order/second-order-accurate scheme and the second using a fully second-order-accurate scheme. The present algorithm utilizes a C-H grid topology to map the flow field about the wing. One version of the AF2 iteration scheme is used on the upper wing surface and another slightly modified version is used on the lower surface. These two algorithm variations are then connected at the wing leading edge using a local iteration technique. The resulting scheme has improved linear stability characteristics and improved time-like damping characteristics relative to previous implementations of the AF2 algorithm. The presentation is highlighted with a grid refinement study and a number of numerical results.

  13. A class of difference schemes with flexible local approximation

    SciTech Connect

    Tsukerman, Igor . E-mail: igor@uakron.edu

    2006-01-20

    Solutions of many physical problems have salient local features that are qualitatively known a priori (for example, singularities at point sources, edge and corners; boundary layers; derivative jumps at material interfaces; strong dipole field components near polarized spherical particles; cusps of electronic wavefunctions at the nuclei; electrostatic double layers around colloidal particles, etc.) The known methods capable of providing flexible local approximation of such features include the generalized finite element - partition of unity method, special variational-difference schemes in broken Sobolev spaces, and a few other specialized techniques. In the proposed new class of Flexible Local Approximation MEthods (FLAME), a desirable set of local approximating functions (such as cylindrical or spherical harmonics, plane waves, harmonic polynomials, etc.) defines a finite difference scheme on a chosen grid stencil. One motivation is to minimize the notorious 'staircase' effect at curved and slanted interface boundaries. However, the new approach has much broader applications. As illustrative examples, the paper presents arbitrarily high order 3-point schemes for the 1D Schroedinger equation and a 1D singular equation, schemes for electrostatic interactions of colloidal particles, electromagnetic wave propagation and scattering, plasmon resonances. Moreover, many classical finite difference schemes, including the Collatz 'Mehrstellen' schemes, are direct particular cases of FLAME.

  14. Implicit lower-upper/approximate-factorization schemes for incompressible flows

    SciTech Connect

    Briley, W.R.; Neerarambam, S.S.; Whitfield, D.L.

    1996-10-01

    A lower-upper/approximate-factorization (LU/AF) scheme is developed for the incompressible Euler or Navier-Stokes equations. The LU/AF scheme contains an iteration parameter that can be adjusted to improve iterative convergence rate. The LU/AF scheme is to be used in conjunction with linearized implicit approximations and artificial compressibility to compute steady solutions, and within sub-iterations to compute unsteady solutions. Formulations based on time linearization with and without sub-iteration and on Newton linearization are developed using spatial difference operators. The spatial approximation used includes upwind differencing based on Roe`s approximate Riemann solver and van Leer`s MUSCL scheme, with numerically computed implicit flux linearizations. Simple one-dimensional diffusion and advection/diffusion problems are first studied analytically to provide insight for development of the Navier-Stokes algorithm. The optimal values of both time step and LU/AF parameter are determined for a test problem consisting of two-dimensional flow past a NACA 0012 airfoil, with a highly stretched grid. The optimal parameter provides a consistent improvement in convergence rate for four test cases having different grids and Reynolds numbers and, also, for an inviscid case. The scheme can be easily extended to three dimensions and adapted for compressible flows. 24 refs., 11 figs., 2 tabs.

  15. Approximation schemes for viscosity solutions of Hamilton-Jacobi equations

    NASA Astrophysics Data System (ADS)

    Souganidis, Panagiotis E.

    Equations of Hamilton-Jacobi type arise in many areas of applications, including the calculus of variations, control theory and differential games. Recently M. G. Crandall and P.-L. Lions established the correct notion of generalized solutions for these equations. This article discusses the convergence of general approximation schemes to this solution and gives, under certain hypotheses, explicit error estimates. These results are then applied to obtain various representations as limits of solutions of general explicit and implicit finite difference schemes, with error estimates.

  16. Level-treewidth property, exact algorithms and approximation schemes

    SciTech Connect

    Marathe, M.V.; Hunt, H.B.; Stearns, R.E.

    1997-06-01

    Informally, a class of graphs Q is said to have the level-treewidth property (LT-property) if for every G {element_of} Q there is a layout (breadth first ordering) L{sub G} such that the subgraph induced by the vertices in k-consecutive levels in the layout have treewidth O(f (k)), for some function f. We show that several important and well known classes of graphs including planar and bounded genus graphs, (r, s)-civilized graphs, etc, satisfy the LT-property. Building on the recent work, we present two general types of results for the class of graphs obeying the LT-property. (1) All problems in the classes MPSAT, TMAX and TMIN have polynomial time approximation schemes. (2) The problems considered in Eppstein have efficient polynomial time algorithms. These results can be extended to obtain polynomial time approximation algorithms and approximation schemes for a number of PSPACE-hard combinatorial problems specified using different kinds of succinct specifications studied in. Many of the results can also be extended to {delta}-near genus and {delta}-near civilized graphs, for any fixed {delta}. Our results significantly extend the work in and affirmatively answer recent open questions.

  17. Accuracy of approximate inversion schemes in quantitative photacoustic imaging

    NASA Astrophysics Data System (ADS)

    Hochuli, Roman; Beard, Paul C.; Cox, Ben

    2014-03-01

    Five numerical phantoms were developed to investigate the accuracy of approximate inversion schemes in the reconstruction of oxygen saturation in photoacoustic imaging. In particular, two types of inversion are considered: Type I, an inversion that assumes fluence is unchanged between illumination wavelengths, and Type II, a method that assumes known background absorption and scattering coefficients to partially correct for the fluence. These approaches are tested in tomography (PAT) and acoustic-resolution microscopy mode (AR-PAM). They are found to produce accurate values of oxygen saturation in a blood vessel of interest at shallow depth - less than 3mm for PAT and less than 1mm for AR-PAM.

  18. Rational approximation schemes for bi-continuous semigroups

    NASA Astrophysics Data System (ADS)

    Jara, Patricio

    2008-08-01

    This paper extends the Hille-Phillips functional calculus and rational approximations results due to R. Hersh, T. Kato, P. Brenner, and V. Thomée to generators of bi-continuous semigroups. The method yields error estimates for rational time-discretization schemes for such semigroups, in particular for dual semigroups, Feller semigroups such as the Ornstein-Uhlenbeck semigroup, the heat semigroup, semigroups induced by nonlinear flows, implemented semigroups, and evolution semigroups. Furthermore, the results provide error estimates for a new class of inversion formulas for the Laplace transform.

  19. Approximate dynamic model of a turbojet engine

    NASA Technical Reports Server (NTRS)

    Artemov, O. A.

    1978-01-01

    An approximate dynamic nonlinear model of a turbojet engine is elaborated on as a tool in studying the aircraft control loop, with the turbojet engine treated as an actuating component. Approximate relationships linking the basic engine parameters and shaft speed are derived to simplify the problem, and to aid in constructing an approximate nonlinear dynamic model of turbojet engine performance useful for predicting aircraft motion.

  20. Stability analysis of intermediate boundary conditions in approximate factorization schemes

    NASA Technical Reports Server (NTRS)

    South, J. C., Jr.; Hafez, M. M.; Gottlieb, D.

    1986-01-01

    The paper discusses the role of the intermediate boundary condition in the AF2 scheme used by Holst for simulation of the transonic full potential equation. It is shown that the treatment suggested by Holst led to a restriction on the time step and ways to overcome this restriction are suggested. The discussion is based on the theory developed by Gustafsson, Kreiss, and Sundstrom and also on the von Neumann method.

  1. Robust Synchronization Schemes for Dynamic Channel Environments

    NASA Technical Reports Server (NTRS)

    Xiong, Fugin

    2003-01-01

    Professor Xiong will investigate robust synchronization schemes for dynamic channel environment. A sliding window will be investigated for symbol timing synchronizer and an open loop carrier estimator for carrier synchronization. Matlab/Simulink will be used for modeling and simulations.

  2. Dynamic Restarting Schemes for Eigenvalue Problems

    SciTech Connect

    Wu, Kesheng; Simon, Horst D.

    1999-03-10

    In studies of restarted Davidson method, a dynamic thick-restart scheme was found to be excellent in improving the overall effectiveness of the eigen value method. This paper extends the study of the dynamic thick-restart scheme to the Lanczos method for symmetric eigen value problems and systematically explore a range of heuristics and strategies. We conduct a series of numerical tests to determine their relative strength and weakness on a class of electronic structure calculation problems.

  3. Monotonicity of the CABARET scheme approximating a hyperbolic equation with a sign-changing characteristic field

    NASA Astrophysics Data System (ADS)

    Kovyrkina, O. A.; Ostapenko, V. V.

    2016-05-01

    The monotonicity of the CABARET scheme approximating a hyperbolic differential equation with a sign-changing characteristic field is analyzed. Monotonicity conditions for this scheme are obtained in domains where the characteristics have a sign-definite propagation velocity and near sonic lines, on which the propagation velocity changes its sign. These properties of the CABARET scheme are illustrated by test computations.

  4. Evaluating the Accuracy of Hessian Approximations for Direct Dynamics Simulations.

    PubMed

    Zhuang, Yu; Siebert, Matthew R; Hase, William L; Kay, Kenneth G; Ceotto, Michele

    2013-01-08

    Direct dynamics simulations are a very useful and general approach for studying the atomistic properties of complex chemical systems, since an electronic structure theory representation of a system's potential energy surface is possible without the need for fitting an analytic potential energy function. In this paper, recently introduced compact finite difference (CFD) schemes for approximating the Hessian [J. Chem. Phys.2010, 133, 074101] are tested by employing the monodromy matrix equations of motion. Several systems, including carbon dioxide and benzene, are simulated, using both analytic potential energy surfaces and on-the-fly direct dynamics. The results show, depending on the molecular system, that electronic structure theory Hessian direct dynamics can be accelerated up to 2 orders of magnitude. The CFD approximation is found to be robust enough to deal with chaotic motion, concomitant with floppy and stiff mode dynamics, Fermi resonances, and other kinds of molecular couplings. Finally, the CFD approximations allow parametrical tuning of different CFD parameters to attain the best possible accuracy for different molecular systems. Thus, a direct dynamics simulation requiring the Hessian at every integration step may be replaced with an approximate Hessian updating by tuning the appropriate accuracy.

  5. Approximation of Dynamical System's Separatrix Curves

    NASA Astrophysics Data System (ADS)

    Cavoretto, Roberto; Chaudhuri, Sanjay; De Rossi, Alessandra; Menduni, Eleonora; Moretti, Francesca; Rodi, Maria Caterina; Venturino, Ezio

    2011-09-01

    In dynamical systems saddle points partition the domain into basins of attractions of the remaining locally stable equilibria. This problem is rather common especially in population dynamics models, like prey-predator or competition systems. In this paper we construct programs for the detection of points lying on the separatrix curve, i.e. the curve which partitions the domain. Finally, an efficient algorithm, which is based on the Partition of Unity method with local approximants given by Wendland's functions, is used for reconstructing the separatrix curve.

  6. Dynamical entanglement versus symmetry and dynamics of classical approximations

    SciTech Connect

    Buric, Nikola

    2006-05-15

    It is shown that dynamical entanglement between two qubits depends on the symmetry of the quantum model. On the other hand, the latter is reflected in the qualitative properties of the dynamics of a classical approximation of the quantum system. For generic separable pure initial states, the dynamical entanglement is larger if the system is less symmetric and its classical approximation is chaotic. The influence of different types of Markov environments on the established relation between the dynamical entanglement, symmetry and the classical dynamics is also studied.

  7. Dynamical exchange-correlation potentials beyond the local density approximation

    NASA Astrophysics Data System (ADS)

    Tao, Jianmin; Vignale, Giovanni

    2006-03-01

    Approximations for the static exchange-correlation (xc) potential of density functional theory (DFT) have reached a high level of sophistication. By contrast, time-dependent xc potentials are still being treated in a local (although velocity-dependent) approximation [G. Vignale, C. A. Ullrich and S. Conti, PRL 79, 4879 (1997)]. Unfortunately, one of the assumptions upon which the dynamical local approximation is based appears to break down in the important case of d.c. transport. Here we propose a new approximation scheme, which should allow a more accurate treatment of molecular transport problems. As a first step, we separate the exact adiabatic xc potential, which has the same form as in the static theory and can be treated by a generalized gradient approximation (GGA) or a meta-GGA. In the second step, we express the high-frequency limit of the xc stress tensor (whose divergence gives the xc force density) in terms of the exact static xc energy functional. Finally, we develop a perturbative scheme for the calculation of the frequency dependence of the xc stress tensor in terms of the ground-state Kohn-Sham orbitals and eigenvalues.

  8. Phase field approximation of dynamic brittle fracture

    NASA Astrophysics Data System (ADS)

    Schlüter, Alexander; Willenbücher, Adrian; Kuhn, Charlotte; Müller, Ralf

    2014-11-01

    Numerical methods that are able to predict the failure of technical structures due to fracture are important in many engineering applications. One of these approaches, the so-called phase field method, represents cracks by means of an additional continuous field variable. This strategy avoids some of the main drawbacks of a sharp interface description of cracks. For example, it is not necessary to track or model crack faces explicitly, which allows a simple algorithmic treatment. The phase field model for brittle fracture presented in Kuhn and Müller (Eng Fract Mech 77(18):3625-3634, 2010) assumes quasi-static loading conditions. However dynamic effects have a great impact on the crack growth in many practical applications. Therefore this investigation presents an extension of the quasi-static phase field model for fracture from Kuhn and Müller (Eng Fract Mech 77(18):3625-3634, 2010) to the dynamic case. First of all Hamilton's principle is applied to derive a coupled set of Euler-Lagrange equations that govern the mechanical behaviour of the body as well as the crack growth. Subsequently the model is implemented in a finite element scheme which allows to solve several test problems numerically. The numerical examples illustrate the capabilities of the developed approach to dynamic fracture in brittle materials.

  9. Configuring Airspace Sectors with Approximate Dynamic Programming

    NASA Technical Reports Server (NTRS)

    Bloem, Michael; Gupta, Pramod

    2010-01-01

    In response to changing traffic and staffing conditions, supervisors dynamically configure airspace sectors by assigning them to control positions. A finite horizon airspace sector configuration problem models this supervisor decision. The problem is to select an airspace configuration at each time step while considering a workload cost, a reconfiguration cost, and a constraint on the number of control positions at each time step. Three algorithms for this problem are proposed and evaluated: a myopic heuristic, an exact dynamic programming algorithm, and a rollouts approximate dynamic programming algorithm. On problem instances from current operations with only dozens of possible configurations, an exact dynamic programming solution gives the optimal cost value. The rollouts algorithm achieves costs within 2% of optimal for these instances, on average. For larger problem instances that are representative of future operations and have thousands of possible configurations, excessive computation time prohibits the use of exact dynamic programming. On such problem instances, the rollouts algorithm reduces the cost achieved by the heuristic by more than 15% on average with an acceptable computation time.

  10. Feedback optimal control of distributed parameter systems by using finite-dimensional approximation schemes.

    PubMed

    Alessandri, Angelo; Gaggero, Mauro; Zoppoli, Riccardo

    2012-06-01

    Optimal control for systems described by partial differential equations is investigated by proposing a methodology to design feedback controllers in approximate form. The approximation stems from constraining the control law to take on a fixed structure, where a finite number of free parameters can be suitably chosen. The original infinite-dimensional optimization problem is then reduced to a mathematical programming one of finite dimension that consists in optimizing the parameters. The solution of such a problem is performed by using sequential quadratic programming. Linear combinations of fixed and parameterized basis functions are used as the structure for the control law, thus giving rise to two different finite-dimensional approximation schemes. The proposed paradigm is general since it allows one to treat problems with distributed and boundary controls within the same approximation framework. It can be applied to systems described by either linear or nonlinear elliptic, parabolic, and hyperbolic equations in arbitrary multidimensional domains. Simulation results obtained in two case studies show the potentials of the proposed approach as compared with dynamic programming.

  11. Spline Approximation of Thin Shell Dynamics

    NASA Technical Reports Server (NTRS)

    delRosario, R. C. H.; Smith, R. C.

    1996-01-01

    A spline-based method for approximating thin shell dynamics is presented here. While the method is developed in the context of the Donnell-Mushtari thin shell equations, it can be easily extended to the Byrne-Flugge-Lur'ye equations or other models for shells of revolution as warranted by applications. The primary requirements for the method include accuracy, flexibility and efficiency in smart material applications. To accomplish this, the method was designed to be flexible with regard to boundary conditions, material nonhomogeneities due to sensors and actuators, and inputs from smart material actuators such as piezoceramic patches. The accuracy of the method was also of primary concern, both to guarantee full resolution of structural dynamics and to facilitate the development of PDE-based controllers which ultimately require real-time implementation. Several numerical examples provide initial evidence demonstrating the efficacy of the method.

  12. Scheme for approximate conditional teleportation of an unknown atomic state without the Bell-state measurement

    SciTech Connect

    Zheng Shibiao

    2004-06-01

    We propose a scheme for approximately and conditionally teleporting an unknown atomic state in cavity QED. Our scheme does not involve the Bell-state measurement and thus an additional atom is unnecessary. Only two atoms and one single-mode cavity are required. The scheme may be used to teleport the state of a cavity mode to another mode using a single atom. The idea may also be used to teleport the state of a trapped ion.

  13. An efficient approximate factorization implicit scheme for the equations of gasdynamics

    NASA Technical Reports Server (NTRS)

    Barth, T. J.; Steger, J. L.

    1984-01-01

    An efficient implicit finite-difference algorithm for the gas dynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved while maintaining the same favorable stability characteristics and generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows about a NACA 0012 airfoil. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations. It is shown that the method offers advantages over the conventional Beam and Warming scheme and can retrofit existing Beam and Warming codes with minimal effort.

  14. Revisiting approximate dynamic programming and its convergence.

    PubMed

    Heydari, Ali

    2014-12-01

    Value iteration-based approximate/adaptive dynamic programming (ADP) as an approximate solution to infinite-horizon optimal control problems with deterministic dynamics and continuous state and action spaces is investigated. The learning iterations are decomposed into an outer loop and an inner loop. A relatively simple proof for the convergence of the outer-loop iterations to the optimal solution is provided using a novel idea with some new features. It presents an analogy between the value function during the iterations and the value function of a fixed-final-time optimal control problem. The inner loop is utilized to avoid the need for solving a set of nonlinear equations or a nonlinear optimization problem numerically, at each iteration of ADP for the policy update. Sufficient conditions for the uniqueness of the solution to the policy update equation and for the convergence of the inner-loop iterations to the solution are obtained. Afterwards, the results are formed as a learning algorithm for training a neurocontroller or creating a look-up table to be used for optimal control of nonlinear systems with different initial conditions. Finally, some of the features of the investigated method are numerically analyzed.

  15. Dynamical Vertex Approximation for the Hubbard Model

    NASA Astrophysics Data System (ADS)

    Toschi, Alessandro

    A full understanding of correlated electron systems in the physically relevant situations of three and two dimensions represents a challenge for the contemporary condensed matter theory. However, in the last years considerable progress has been achieved by means of increasingly more powerful quantum many-body algorithms, applied to the basic model for correlated electrons, the Hubbard Hamiltonian. Here, I will review the physics emerging from studies performed with the dynamical vertex approximation, which includes diagrammatic corrections to the local description of the dynamical mean field theory (DMFT). In particular, I will first discuss the phase diagram in three dimensions with a special focus on the commensurate and incommensurate magnetic phases, their (quantum) critical properties, and the impact of fluctuations on electronic lifetimes and spectral functions. In two dimensions, the effects of non-local fluctuations beyond DMFT grow enormously, determining the appearance of a low-temperature insulating behavior for all values of the interaction in the unfrustrated model: Here the prototypical features of the Mott-Hubbard metal-insulator transition, as well as the existence of magnetically ordered phases, are completely overwhelmed by antiferromagnetic fluctuations of exponentially large extension, in accordance with the Mermin-Wagner theorem. Eventually, by a fluctuation diagnostics analysis of cluster DMFT self-energies, the same magnetic fluctuations are identified as responsible for the pseudogap regime in the holed-doped frustrated case, with important implications for the theoretical modeling of the cuprate physics.

  16. Comparison of hybrid schemes for the combination of shallow approximations in numerical simulations of the Antarctic Ice Sheet

    NASA Astrophysics Data System (ADS)

    Bernales, Jorge; Rogozhina, Irina; Greve, Ralf; Thomas, Maik

    2017-01-01

    The shallow ice approximation (SIA) is commonly used in ice-sheet models to simplify the force balance equations within the ice. However, the SIA cannot adequately reproduce the dynamics of the fast flowing ice streams usually found at the margins of ice sheets. To overcome this limitation, recent studies have introduced heuristic hybrid combinations of the SIA and the shelfy stream approximation. Here, we implement four different hybrid schemes into a model of the Antarctic Ice Sheet in order to compare their performance under present-day conditions. For each scheme, the model is calibrated using an iterative technique to infer the spatial variability in basal sliding parameters. Model results are validated against topographic and velocity data. Our analysis shows that the iterative technique compensates for the differences between the schemes, producing similar ice-sheet configurations through quantitatively different results of the sliding coefficient calibration. Despite this we observe a robust agreement in the reconstructed patterns of basal sliding parameters. We exchange the calibrated sliding parameter distributions between the schemes to demonstrate that the results of the model calibration cannot be straightforwardly transferred to models based on different approximations of ice dynamics. However, easily adaptable calibration techniques for the potential distribution of basal sliding coefficients can be implemented into ice models to overcome such incompatibility, as shown in this study.

  17. Stable schemes for dissipative particle dynamics with conserved energy

    NASA Astrophysics Data System (ADS)

    Stoltz, Gabriel

    2017-07-01

    This article presents a new numerical scheme for the discretization of dissipative particle dynamics with conserved energy. The key idea is to reduce elementary pairwise stochastic dynamics (either fluctuation/dissipation or thermal conduction) to effective single-variable dynamics, and to approximate the solution of these dynamics with one step of a Metropolis-Hastings algorithm. This ensures by construction that no negative internal energies are encountered during the simulation, and hence allows to increase the admissible timesteps to integrate the dynamics, even for systems with small heat capacities. Stability is only limited by the Hamiltonian part of the dynamics, which suggests resorting to multiple timestep strategies where the stochastic part is integrated less frequently than the Hamiltonian one.

  18. Iterated upwind schemes for gas dynamics

    NASA Astrophysics Data System (ADS)

    Smolarkiewicz, Piotr K.; Szmelter, Joanna

    2009-01-01

    A class of high-resolution schemes established in integration of anelastic equations is extended to fully compressible flows, and documented for unsteady (and steady) problems through a span of Mach numbers from zero to supersonic. The schemes stem from iterated upwind technology of the multidimensional positive definite advection transport algorithm (MPDATA). The derived algorithms employ standard and modified forms of the equations of gas dynamics for conservation of mass, momentum and either total or internal energy as well as potential temperature. Numerical examples from elementary wave propagation, through computational aerodynamics benchmarks, to atmospheric small- and large-amplitude acoustics with intricate wave-flow interactions verify the approach for both structured and unstructured meshes, and demonstrate its flexibility and robustness.

  19. A simple scheme for calculating approximate transition moments within the equation of motion expectation value formalism

    NASA Astrophysics Data System (ADS)

    Dutta, Achintya Kumar; Neese, Frank; Izsák, Róbert

    2017-06-01

    A simple scheme for calculating approximate transition moments within the framework of the equation of motion coupled cluster method is proposed. It relies on a matrix inversion technique to calculate the excited state left eigenvectors and requires no additional cost over that of the excitation energy calculation. The new approximation gives almost identical UV-Vis spectra to that obtained using the standard equation of motion coupled cluster method with single and double excitations for molecules in a standard test set.

  20. Coupled-cluster method: A lattice-path-based subsystem approximation scheme for quantum lattice models

    SciTech Connect

    Bishop, R. F.; Li, P. H. Y.

    2011-04-15

    An approximation hierarchy, called the lattice-path-based subsystem (LPSUBm) approximation scheme, is described for the coupled-cluster method (CCM). It is applicable to systems defined on a regular spatial lattice. We then apply it to two well-studied prototypical (spin-(1/2) Heisenberg antiferromagnetic) spin-lattice models, namely, the XXZ and the XY models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the ground-state sublattice magnetization, and the quantum critical point. They are all in good agreement with those from such alternative methods as spin-wave theory, series expansions, quantum Monte Carlo methods, and the CCM using the alternative lattice-animal-based subsystem (LSUBm) and the distance-based subsystem (DSUBm) schemes. Each of the three CCM schemes (LSUBm, DSUBm, and LPSUBm) for use with systems defined on a regular spatial lattice is shown to have its own advantages in particular applications.

  1. An improved approximation scheme for the centrifugal term and the Hulthén potential

    NASA Astrophysics Data System (ADS)

    Ikhdair, S. M.

    2009-03-01

    We present a new approximation scheme for the centrifugal term to solve the Schrödinger equation with the Hulthén potential for any arbitrary l -state by means of a mathematical Nikiforov-Uvarov (NU) method. We obtain the bound-state energy eigenvalues and the normalized corresponding eigenfunctions expressed in terms of the Jacobi polynomials or hypergeometric functions for a particle exposed to this potential field. Our numerical results of the energy eigenvalues are found to be in high agreement with those results obtained by using the program based on a numerical integration procedure. The s -wave ( l = 0analytic solution for the binding energies and eigenfunctions of a particle are also calculated. The physical meaning of the approximate analytical solution is discussed. The present approximation scheme is systematic and accurate.

  2. On approximating hereditary dynamics by systems of ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Cliff, E. M.; Burns, J. A.

    1978-01-01

    The paper deals with methods of obtaining approximate solutions to linear retarded functional differential equations (hereditary systems). The basic notion is to project the infinite dimensional space of initial functions for the hereditary system onto a finite dimensional subspace. Within this framework, two particular schemes are discussed. The first uses well-known piecewise constant approximations, while the second is a new method based on piecewise linear approximating functions. Numerical results are given.

  3. On approximating hereditary dynamics by systems of ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Cliff, E. M.; Burns, J. A.

    1978-01-01

    The paper deals with methods of obtaining approximate solutions to linear retarded functional differential equations (hereditary systems). The basic notion is to project the infinite dimensional space of initial functions for the hereditary system onto a finite dimensional subspace. Within this framework, two particular schemes are discussed. The first uses well-known piecewise constant approximations, while the second is a new method based on piecewise linear approximating functions. Numerical results are given.

  4. Approximated solutions to Born-Infeld dynamics

    NASA Astrophysics Data System (ADS)

    Ferraro, Rafael; Nigro, Mauro

    2016-02-01

    The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.

  5. Implicit approximate-factorization schemes for the low-frequency transonic equation

    NASA Technical Reports Server (NTRS)

    Ballhaus, W. F.; Steger, J. L.

    1975-01-01

    Two- and three-level implicit finite-difference algorithms for the low-frequency transonic small disturbance-equation are constructed using approximate factorization techniques. The schemes are unconditionally stable for the model linear problem. For nonlinear mixed flows, the schemes maintain stability by the use of conservatively switched difference operators for which stability is maintained only if shock propagation is restricted to be less than one spatial grid point per time step. The shock-capturing properties of the schemes were studied for various shock motions that might be encountered in problems of engineering interest. Computed results for a model airfoil problem that produces a flow field similar to that about a helicopter rotor in forward flight show the development of a shock wave and its subsequent propagation upstream off the front of the airfoil.

  6. Relaxation approximations to second-order traffic flow models by high-resolution schemes

    SciTech Connect

    Nikolos, I.K.; Delis, A.I.; Papageorgiou, M.

    2015-03-10

    A relaxation-type approximation of second-order non-equilibrium traffic models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms with the attractive feature that neither Riemann solvers nor characteristic decompositions are in need. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. To discretize the resulting relaxation system, high-resolution reconstructions in space are considered. Emphasis is given on a fifth-order WENO scheme and its performance. The computations reported demonstrate the simplicity and versatility of relaxation schemes as numerical solvers.

  7. Gas Evolution Dynamics in Godunov-Type Schemes and Analysis of Numerical Shock Instability

    NASA Technical Reports Server (NTRS)

    Xu, Kun

    1999-01-01

    In this paper we are going to study the gas evolution dynamics of the exact and approximate Riemann solvers, e.g., the Flux Vector Splitting (FVS) and the Flux Difference Splitting (FDS) schemes. Since the FVS scheme and the Kinetic Flux Vector Splitting (KFVS) scheme have the same physical mechanism and similar flux function, based on the analysis of the discretized KFVS scheme the weakness and advantage of the FVS scheme are closely observed. The subtle dissipative mechanism of the Godunov method in the 2D case is also analyzed, and the physical reason for shock instability, i.e., carbuncle phenomena and odd-even decoupling, is presented.

  8. The Dynamics of Some Iterative Implicit Schemes

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Sweby, P. K.

    1994-01-01

    The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations is analyzed using the theory of dynamical systems. With the aid of parallel Connection Machines (CM-2 and CM-5), the associated bifurcation diagrams as a function of the time step, and the complex behavior of the associated 'numerical basins of attraction' of these iterative implicit schemes are revealed and compared. Studies showed that all of the four implicit LMMs exhibit a drastic distortion and segmentation but less shrinkage of the basin of attraction of the true solution than standard explicit methods. The numerical basins of attraction of a noniterative implicit procedure mimic more closely the basins of attraction of the differential equations than the iterative implicit procedures for the four implicit LMMs.

  9. Approximation of acoustic waves by explicit Newmark's schemes and spectral element methods

    NASA Astrophysics Data System (ADS)

    Zampieri, Elena; Pavarino, Luca F.

    2006-01-01

    A numerical approximation of the acoustic wave equation is presented. The spatial discretization is based on conforming spectral elements, whereas we use finite difference Newmark's explicit integration schemes for the temporal discretization. A rigorous stability analysis is developed for the discretized problem providing an upper bound for the time step [Delta]t. We present several numerical results concerning stability and convergence properties of the proposed numerical methods.

  10. Improved sampling and validation of frozen Gaussian approximation with surface hopping algorithm for nonadiabatic dynamics

    NASA Astrophysics Data System (ADS)

    Lu, Jianfeng; Zhou, Zhennan

    2016-09-01

    In the spirit of the fewest switches surface hopping, the frozen Gaussian approximation with surface hopping (FGA-SH) method samples a path integral representation of the non-adiabatic dynamics in the semiclassical regime. An improved sampling scheme is developed in this work for FGA-SH based on birth and death branching processes. The algorithm is validated for the standard test examples of non-adiabatic dynamics.

  11. Scheme for accelerating quantum tunneling dynamics

    NASA Astrophysics Data System (ADS)

    Khujakulov, Anvar; Nakamura, Katsuhiro

    2016-02-01

    We propose a scheme of the exact fast forwarding of standard quantum dynamics for a charged particle. The present idea allows the acceleration of both the amplitude and the phase of the wave function throughout the fast-forward time range and is distinct from that of Masuda and Nakamura [Proc. R. Soc. A 466, 1135 (2010), 10.1098/rspa.2009.0446], which enabled acceleration of only the amplitude of the wave function on the way. We apply the proposed method to the quantum tunneling phenomena and obtain the electromagnetic field to ensure the rapid penetration of wave functions through a tunneling barrier. Typical examples described here are (1) an exponential wave packet passing through the δ -function barrier and (2) the opened Moshinsky shutter with a δ -function barrier just behind the shutter. We elucidate the tunneling current in the vicinity of the barrier and find a remarkable enhancement of the tunneling rate (tunneling power) due to the fast forwarding. In the case of a very high barrier, in particular, we present the asymptotic analysis and exhibit a suitable driving force to recover a recognizable tunneling current. The analysis is also carried out on the exact acceleration of macroscopic quantum tunneling with use of the nonlinear Schrödinger equation, which accommodates a tunneling barrier.

  12. Core polarization effects in the Hartree--Fock--random phase approximation schemes

    SciTech Connect

    Lipparini, E.; Stringari, S.

    1987-02-01

    Core polarization effects in odd nuclei are investigated in the framework of the Hartree--Fock and random phase approximation schemes. The results of the particle vibration coupling model are recovered by linearizing the equations of motion in the interaction Hamiltonian between the external and the core particles. The formalism is used to study the renormalization of diagonal and off-diagonal M1 matrix elements. It is found that M1 polarization effects exhibit a very strong dependence on the range of the force. Copyright 1987 Academic Press, Inc.

  13. Gravitational-wave dynamics and black-hole dynamics: second quasi-spherical approximation

    NASA Astrophysics Data System (ADS)

    Hayward, Sean A.

    2001-12-01

    Gravitational radiation with roughly spherical wavefronts, produced by roughly spherical black holes or other astrophysical objects, is described by an approximation scheme. The first quasi-spherical approximation, describing radiation propagation on a background, is generalized to include additional non-linear effects, due to the radiation itself. The gravitational radiation is locally defined and admits an energy tensor, satisfying all standard local energy conditions and entering the truncated Einstein equations as an effective energy tensor. This second quasi-spherical approximation thereby includes gravitational radiation reaction, such as the back-reaction on the black hole. With respect to a canonical flow of time, the combined energy-momentum of the matter and gravitational radiation is covariantly conserved. The corresponding Noether charge is a local gravitational mass-energy. Energy conservation is formulated as a local first law relating the gradient of the gravitational mass to work and energy-supply terms, including the energy flux of the gravitational radiation. Zeroth, first and second laws of black-hole dynamics are given, involving a dynamic surface gravity. Local gravitational-wave dynamics is described by a non-linear wave equation. In terms of a complex gravitational-radiation potential, the energy tensor has a scalar-field form and the wave equation is an Ernst equation, holding independently at each spherical angle. The strain to be measured by a distant detector is simply defined.

  14. Development of highly accurate approximate scheme for computing the charge transfer integral

    NASA Astrophysics Data System (ADS)

    Pershin, Anton; Szalay, Péter G.

    2015-08-01

    The charge transfer integral is a key parameter required by various theoretical models to describe charge transport properties, e.g., in organic semiconductors. The accuracy of this important property depends on several factors, which include the level of electronic structure theory and internal simplifications of the applied formalism. The goal of this paper is to identify the performance of various approximate approaches of the latter category, while using the high level equation-of-motion coupled cluster theory for the electronic structure. The calculations have been performed on the ethylene dimer as one of the simplest model systems. By studying different spatial perturbations, it was shown that while both energy split in dimer and fragment charge difference methods are equivalent with the exact formulation for symmetrical displacements, they are less efficient when describing transfer integral along the asymmetric alteration coordinate. Since the "exact" scheme was found computationally expensive, we examine the possibility to obtain the asymmetric fluctuation of the transfer integral by a Taylor expansion along the coordinate space. By exploring the efficiency of this novel approach, we show that the Taylor expansion scheme represents an attractive alternative to the "exact" calculations due to a substantial reduction of computational costs, when a considerably large region of the potential energy surface is of interest. Moreover, we show that the Taylor expansion scheme, irrespective of the dimer symmetry, is very accurate for the entire range of geometry fluctuations that cover the space the molecule accesses at room temperature.

  15. Development of highly accurate approximate scheme for computing the charge transfer integral.

    PubMed

    Pershin, Anton; Szalay, Péter G

    2015-08-21

    The charge transfer integral is a key parameter required by various theoretical models to describe charge transport properties, e.g., in organic semiconductors. The accuracy of this important property depends on several factors, which include the level of electronic structure theory and internal simplifications of the applied formalism. The goal of this paper is to identify the performance of various approximate approaches of the latter category, while using the high level equation-of-motion coupled cluster theory for the electronic structure. The calculations have been performed on the ethylene dimer as one of the simplest model systems. By studying different spatial perturbations, it was shown that while both energy split in dimer and fragment charge difference methods are equivalent with the exact formulation for symmetrical displacements, they are less efficient when describing transfer integral along the asymmetric alteration coordinate. Since the "exact" scheme was found computationally expensive, we examine the possibility to obtain the asymmetric fluctuation of the transfer integral by a Taylor expansion along the coordinate space. By exploring the efficiency of this novel approach, we show that the Taylor expansion scheme represents an attractive alternative to the "exact" calculations due to a substantial reduction of computational costs, when a considerably large region of the potential energy surface is of interest. Moreover, we show that the Taylor expansion scheme, irrespective of the dimer symmetry, is very accurate for the entire range of geometry fluctuations that cover the space the molecule accesses at room temperature.

  16. Development of highly accurate approximate scheme for computing the charge transfer integral

    SciTech Connect

    Pershin, Anton; Szalay, Péter G.

    2015-08-21

    The charge transfer integral is a key parameter required by various theoretical models to describe charge transport properties, e.g., in organic semiconductors. The accuracy of this important property depends on several factors, which include the level of electronic structure theory and internal simplifications of the applied formalism. The goal of this paper is to identify the performance of various approximate approaches of the latter category, while using the high level equation-of-motion coupled cluster theory for the electronic structure. The calculations have been performed on the ethylene dimer as one of the simplest model systems. By studying different spatial perturbations, it was shown that while both energy split in dimer and fragment charge difference methods are equivalent with the exact formulation for symmetrical displacements, they are less efficient when describing transfer integral along the asymmetric alteration coordinate. Since the “exact” scheme was found computationally expensive, we examine the possibility to obtain the asymmetric fluctuation of the transfer integral by a Taylor expansion along the coordinate space. By exploring the efficiency of this novel approach, we show that the Taylor expansion scheme represents an attractive alternative to the “exact” calculations due to a substantial reduction of computational costs, when a considerably large region of the potential energy surface is of interest. Moreover, we show that the Taylor expansion scheme, irrespective of the dimer symmetry, is very accurate for the entire range of geometry fluctuations that cover the space the molecule accesses at room temperature.

  17. Parallelization of implicit finite difference schemes in computational fluid dynamics

    NASA Technical Reports Server (NTRS)

    Decker, Naomi H.; Naik, Vijay K.; Nicoules, Michel

    1990-01-01

    Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed.

  18. Dynamical systems - A unified colored-noise approximation

    NASA Astrophysics Data System (ADS)

    Jung, Peter; Hanggi, Peter

    1987-05-01

    An adiabatic elimination procedure and a particular time scaling are used to derive a novel colored-noise approximation in the form of a Smoluchowski dynamics which is exact both for correlation times of colored noise (tau) equal to zero and to infinity. This dynamics combines the advantageous features of a recent decoupling theory that does not restrict the value of tau with those occurring in the small-correlation-time theory of Fox (1986). The approximative theory is applied to a nonlinear model for a dye laser driven by multiplicative noise. Excellent agreement for the stationary probability is obtained between the numerically exact solution and the novel approximative theory.

  19. Collisions of Halo Nuclei within a Dynamical Eikonal Approximation

    SciTech Connect

    Baye, D.; Goldstein, G.

    2005-08-19

    The dynamical eikonal approximation unifies the semiclassical time-dependent and eikonal methods. It allows calculating differential cross sections for elastic scattering and breakup in a quantal way by taking into account interference effects. Good agreement is obtained with experiment for {sup 11}Be breakup on {sup 208}Pb. Dynamical effects are weak for elastic scattering.

  20. Dynamical cluster approximation plus semiclassical approximation study for a Mott insulator and d-wave pairing

    NASA Astrophysics Data System (ADS)

    Kim, SungKun; Lee, Hunpyo

    2017-06-01

    Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.

  1. Approximate Bisimulation-Based Reduction of Power System Dynamic Models

    SciTech Connect

    Stankovic, AM; Dukic, SD; Saric, AT

    2015-05-01

    In this paper we propose approximate bisimulation relations and functions for reduction of power system dynamic models in differential- algebraic (descriptor) form. The full-size dynamic model is obtained by linearization of the nonlinear transient stability model. We generalize theoretical results on approximate bisimulation relations and bisimulation functions, originally derived for a class of constrained linear systems, to linear systems in descriptor form. An algorithm for transient stability assessment is proposed and used to determine whether the power system is able to maintain the synchronism after a large disturbance. Two benchmark power systems are used to illustrate the proposed algorithm and to evaluate the applicability of approximate bisimulation relations and bisimulation functions for reduction of the power system dynamic models.

  2. On the dynamics of some grid adaption schemes

    NASA Technical Reports Server (NTRS)

    Sweby, Peter K.; Yee, Helen C.

    1994-01-01

    The dynamics of a one-parameter family of mesh equidistribution schemes coupled with finite difference discretisations of linear and nonlinear convection-diffusion model equations is studied numerically. It is shown that, when time marched to steady state, the grid adaption not only influences the stability and convergence rate of the overall scheme, but can also introduce spurious dynamics to the numerical solution procedure.

  3. Dynamical nonlocal coherent-potential approximation for itinerant electron magnetism.

    PubMed

    Rowlands, D A; Zhang, Yu-Zhong

    2014-11-26

    A dynamical generalisation of the nonlocal coherent-potential approximation is derived based upon the functional integral approach to the interacting electron problem. The free energy is proven to be variational with respect to the self-energy provided a self-consistency condition on a cluster of sites is satisfied. In the present work, calculations are performed within the static approximation and the effect of the nonlocal physics on the formation of the local moment state in a simple model is investigated. The results reveal the importance of the dynamical correlations.

  4. Approximation of stochastic equilibria for dynamic systems with colored noise

    SciTech Connect

    Bashkirtseva, Irina

    2015-03-10

    We consider nonlinear dynamic systems forced by colored noise. Using first approximation systems, we study dynamics of deviations of stochastic solutions from stable deterministic equilibria. Equations for the stationary second moments of deviations of random states are derived. An application of the elaborated theory to Van der Pol system driven by colored noise is given. A dependence of the dispersion on the time correlation of the colored noise is studied.

  5. Approximation schemes to dispersion and linear problems for 3D systems on shear current of arbitrary direction and depth dependence

    NASA Astrophysics Data System (ADS)

    Ådnøy Ellingsen, Simen; Li, Yan; Smeltzer, Benjamin K.

    2017-04-01

    We compare different methods of approximating the dispersion relation for waves on top of currents whose direction and magnitude may vary arbitrarily with depth. Two fundamentally different approximation philosophies are in use: analytical approximation schemes, and what we term the N-layer procedure in which the velocity profile is approximated by a continuous, piecewise linear function of depth. The relative virtues of both schemes are reviewed. The N-layer procedure yields the dispersion relation with arbitrary accuracy. We present the details and subtleties of implementing this procedure in practice. We find with a good choice of layer boundaries, 4-5 layers are sufficient for accuracy of about 1%. For inhomogeneous systems with a specified source, implementation is straightforward and most complications are eschewed. Analytical approximation schemes are reviewed, and criteria of applicability are derived for the first time. In particular the much used approximation by Kirby & Chen (1989) (KCA) is compared with a new approximation which we propose. The two give similar predictions when the KCA is applicable, but our new scheme is more robust and can handle several special but realistic cases where the KCA fails. Once the dispersion relation is calculated, 3D linear problems such as initial value problems, or problems with stationary or periodic time dependence can be readily solved.

  6. Dynamic flow-driven erosion - An improved approximate solution

    NASA Astrophysics Data System (ADS)

    Yu, Bofu; Guo, Dawei; Rose, Calvin W.

    2017-09-01

    Rose et al. (2007) published an approximate solution of dynamic sediment concentration for steady and uniform flows, and this approximate solution shows a peak sediment concentration at the early stage of a runoff event, which can be used to describe and explain the first flush effect, a commonly observed phenomenon, especially in the urban environment. However the approximate solution does not converge to the steady state solution that is known exactly. The purpose of the note is to improve the approximate solution of Rose et al. (2007) by maintaining its functional form while forcing its steady state behaviour for sediment concentration to converge to the known steady state solution. The quality of the new approximate solution was assessed by comparing the new approximate solution with an exact solution for the single size class case, and with the numerical solution for the multiple size classes. It was found that 1) the relative error, or discrepancy, decreases as the stream power increases for all three soils considered; 2) the largest discrepancy occurs for the peak sediment concentration, and the average discrepancy in the peak concentration is less than 10% for the three soils considered; 3) for the majority of the 27 slope-flow combinations and for the three soils considered, the new approximate solution modestly underestimates the peak sediment concentration.

  7. Implicit Time Integration for Multiscale Molecular Dynamics Using Transcendental Padé Approximants.

    PubMed

    Abi Mansour, Andrew; Ortoleva, Peter J

    2016-04-12

    Molecular dynamics systems evolve through the interplay of collective and localized disturbances. As a practical consequence, there is a restriction on the time step imposed by the broad spectrum of time scales involved. To resolve this restriction, multiscale factorization was introduced for molecular dynamics as a method that exploits the separation of time scales by coevolving the coarse-grained and atom-resolved states via Trotter factorization. Developing a stable time-marching scheme for this coevolution, however, is challenging because the coarse-grained dynamical equations depend on the microstate; therefore, these equations cannot be expressed in closed form. The objective of this paper is to develop an implicit time integration scheme for multiscale simulation of large systems over long periods of time and with high accuracy. The scheme uses Padé approximants to account for both the stochastic and deterministic features of the coarse-grained dynamics. The method is demonstrated for a protein either undergoing a conformational change or migrating under the influence of an external force. The method shows promise in accelerating multiscale molecular dynamics without a loss of atomic precision or the need to conjecture the form of coarse-grained governing equations.

  8. Systematic Approximations to Susceptible-Infectious-Susceptible Dynamics on Networks

    PubMed Central

    Cooper, Alison J.

    2016-01-01

    Network-based infectious disease models have been highly effective in elucidating the role of contact structure in the spread of infection. As such, pair- and neighbourhood-based approximation models have played a key role in linking findings from network simulations to standard (random-mixing) results. Recently, for SIR-type infections (that produce one epidemic in a closed population) on locally tree-like networks, these approximations have been shown to be exact. However, network models are ideally suited for Sexually Transmitted Infections (STIs) due to the greater level of detail available for sexual contact networks, and these diseases often possess SIS-type dynamics. Here, we consider the accuracy of three systematic approximations that can be applied to arbitrary disease dynamics, including SIS behaviour. We focus in particular on low degree networks, in which the small number of neighbours causes build-up of local correlations between the state of adjacent nodes that are challenging to capture. By examining how and when these approximation models converge to simulation results, we generate insights into the role of network structure in the infection dynamics of SIS-type infections. PMID:27997542

  9. Approximating common fixed points of asymptotically quasi-nonexpansive mappings by a k+1-step iterative scheme with error terms

    NASA Astrophysics Data System (ADS)

    Xiao, Jian-Zhong; Sun, Jing; Huang, Xuan

    2010-02-01

    In this paper a k+1-step iterative scheme with error terms involving k+1 asymptotically quasi-nonexpansive mappings is studied. In usual Banach spaces, some sufficient and necessary conditions are given for the iterative scheme to approximate a common fixed point. In uniformly convex Banach spaces, power equicontinuity for a mapping is introduced and a series of new convergence theorems are established. Several known results in the current literature are extended and refined.

  10. Dynamical scheme for hadronization with first-order phase transition

    NASA Astrophysics Data System (ADS)

    Feng, Bohao; Xu, Zhe; Greiner, Carsten

    2017-02-01

    We present a dynamical scheme for hadronization with first-order confinement phase transition. The thermodynamical conditions of phase equilibrium, the fluid velocity profile, and the dissipative effect determine the macroscopic changes of the parton volume and the corresponding hadron volume during the phase transition. The macroscopic volume changes are the basis for building up a dynamical scheme by considering microscopic transition processes from partons to hadrons and backwards. The established scheme is proved by comparing the numerical results with the analytical solutions in the case of a one-dimensional expansion of a dissipative fluid with Bjorken boost invariance. The comparisons show almost perfect agreements, which demonstrate the applicability of the introduced scheme.

  11. Numerical approximation of boundary conditions with applications to inviscid equations of gas dynamics

    NASA Technical Reports Server (NTRS)

    Yee, H. C.

    1981-01-01

    A comprehensive overview of the state of the art of well-posedness and stability analysis of difference approximations for initial boundary value problems of the hyperbolic type is presented. The applicability of recent theoretical development to practical calculations for nonlinear gas dynamics is examined. The one dimensional inviscid gas dynamics equations in conservation law form are selected for numerical experiments. The class of implicit schemes developed from linear multistep methods in ordinary differential equations is chosen and the use of linear extrapolation as an explicit or implicit boundary scheme is emphasized. Specification of boundary data in the primitive variables and computation in terms of the conservative variables in the interior is discussed. Some numerical examples for the quasi-one-dimensional nozzle are given.

  12. On approximate reasoning and minimal models for the development of robust outdoor vehicle navigation schemes

    SciTech Connect

    Pin, F.G.

    1993-11-01

    Outdoor sensor-based operation of autonomous robots has revealed to be an extremely challenging problem, mainly because of the difficulties encountered when attempting to represent the many uncertainties which are always present in the real world. These uncertainties are primarily due to sensor imprecisions and unpredictability of the environment, i.e., lack of full knowledge of the environment characteristics and dynamics. Two basic principles, or philosophies, and their associated methodologies are proposed in an attempt to remedy some of these difficulties. The first principle is based on the concept of ``minimal model`` for accomplishing given tasks and proposes to utilize only the minimum level of information and precision necessary to accomplish elemental functions of complex tasks. This approach diverges completely from the direction taken by most artificial vision studies which conventionally call for crisp and detailed analysis of every available component in the perception data. The paper will first review the basic concepts of this approach and will discuss its pragmatic feasibility when embodied in a behaviorist framework. The second principle which is proposed deals with implicit representation of uncertainties using Fuzzy Set Theory-based approximations and approximate reasoning, rather than explicit (crisp) representation through calculation and conventional propagation techniques. A framework which merges these principles and approaches is presented, and its application to the problem of sensor-based outdoor navigation of a mobile robot is discussed. Results of navigation experiments with a real car in actual outdoor environments are also discussed to illustrate the feasibility of the overall concept.

  13. An Energy Decaying Scheme for Nonlinear Dynamics of Shells

    NASA Technical Reports Server (NTRS)

    Bottasso, Carlo L.; Bauchau, Olivier A.; Choi, Jou-Young; Bushnell, Dennis M. (Technical Monitor)

    2000-01-01

    A novel integration scheme for nonlinear dynamics of geometrically exact shells is developed based on the inextensible director assumption. The new algorithm is designed so as to imply the strict decay of the system total mechanical energy at each time step, and consequently unconditional stability is achieved in the nonlinear regime. Furthermore, the scheme features tunable high frequency numerical damping and it is therefore stiffly accurate. The method is tested for a finite element spatial formulation of shells based on mixed interpolations of strain tensorial components and on a two-parameter representation of director rotations. The robustness of the, scheme is illustrated with the help of numerical examples.

  14. Approximating the dynamic response of strain-hardening structures

    SciTech Connect

    Youngdahl, C.K.

    1991-01-01

    A mode approximation method is being developed to predict the dynamic plastic deformation of strain-hardening structures. A mode shape having time-dependent coefficients is based on quasi-static deformation profiles. Two stress fields are associated with the modal shape, one satisfying the dynamic relations and the other satisfying the constitutive equations. The application of suitable matching conditions results in a set of simultaneous differential and algebraic equations for the amplitude coefficients and plastic region size. Using the example of a simply supported beam, the effect of varying the number of matching conditions on the accuracy of the solution is presented. 5 refs., 7 figs.

  15. Dynamical eikonal approximation in breakup reactions of {sup 11}Be

    SciTech Connect

    Goldstein, G.; Baye, D.

    2006-02-15

    The dynamical eikonal approximation is a quantal method unifying the semiclassical time-dependent and eikonal methods by taking into account interference effects. The principle of the calculation is described and expressions for different types of cross sections are established for two variants of the method, differing by a phase choice. The 'coherent' variant respects rotational symmetry around the beam axis and is therefore prefered. A good agreement is obtained with experimental differential and integrated cross sections for the elastic breakup of the {sup 11}Be halo nucleus on {sup 12}C and {sup 208}Pb near 70 MeV/nucleon, without any parameter adjustment. The dynamical approximation is compared with the traditional eikonal method. Differences are analyzed and the respective merits of both methods are discussed.

  16. Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model

    NASA Astrophysics Data System (ADS)

    Cheng, Qing; Yang, Xiaofeng; Shen, Jie

    2017-07-01

    In this paper, we consider numerical approximations of a hydro-dynamically coupled phase field diblock copolymer model, in which the free energy contains a kinetic potential, a gradient entropy, a Ginzburg-Landau double well potential, and a long range nonlocal type potential. We develop a set of second order time marching schemes for this system using the ;Invariant Energy Quadratization; approach for the double well potential, the projection method for the Navier-Stokes equation, and a subtle implicit-explicit treatment for the stress and convective term. The resulting schemes are linear and lead to symmetric positive definite systems at each time step, thus they can be efficiently solved. We further prove that these schemes are unconditionally energy stable. Various numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.

  17. A scheme for designing extreme multistable discrete dynamical systems

    NASA Astrophysics Data System (ADS)

    Chakraborty, Priyanka

    2017-09-01

    In this paper, we propose a scheme for designing discrete extreme multistable systems coupling two identical dynamical systems. Existence of infinitely many attractors in the system is obtained via partial synchronization between two systems for a given set of parameters. We give a conjecture that extreme multistable systems can be designed by coupling two m-dimensional dynamical systems in such a way that i (1 ≤ i≤ m-1) number of state variables of the two systems synchronize completely and (m-i) number of state variables keep constant difference. We demonstrate the applicability of our scheme in two-dimensional (2D) as well as three-dimensional (3D) discrete dynamical systems. In particular, we discuss our scheme taking coupled 2D Hénon maps, coupled 2D Duffing maps and coupled 3D Hénon maps. We have analytically shown the existence of fixed points and period-2 orbits in the coupled system with the variation of initial conditions. These analytically derived conditions matched very well with the numerical simulation results. Variation of the largest Lyapunov exponent with the initial conditions is shown to confirm the existence of extreme multistability in the model. Our scheme may be useful for designing physically, chemically and biologically useful multistable discrete dynamical systems.

  18. Jacob's ladder of approximations to paraxial dynamic electron scattering

    NASA Astrophysics Data System (ADS)

    Lubk, A.; Rusz, J.

    2015-12-01

    Dynamical scattering theory describes the dominant scattering process of beam electrons at targets in the transmission electron microscope (TEM). Hence, practically every quantitative TEM study has to consider its ramifications, typically by some approximate modeling. Here, we elaborate on a hierarchy within the various approximations focusing on the two principal approaches used in practice, Bloch wave and multislice. We reveal characteristic differences in the capability of these methods to reproduce the correct local propagation of the wave function, while convergent results are obtained over larger propagation distances. We investigate the dependency of local variations of the wave function on the atomic number of the atomic scatterers and discuss their significance for, e.g., inelastic scattering.

  19. Anderson Localization: Dynamical Cluster Approximation - Typical Medium Theory Perspective

    NASA Astrophysics Data System (ADS)

    Ekuma, Chinedu; Meng, Ziyang; Terletska, Hanna; Moreno, Juana; Jarrell, Mark; Dobrosavljevic, Vladimir

    2013-03-01

    Mean field theories like the coherent potential approximation (CPA) and its cluster extensions, including the dynamical cluster approximation (DCA), fail to describe the Anderson localization transition in disordered systems. This failure is intrinsic to these theories as the algebraically averaged quantities used in them always favor the metallic state, and hence cannot describe the localization transition. Here we extend the Typical Medium Theory (TMT), which replaces the average quantities with their corresponding typical (geometrically averaged) equivalents, to its cluster form such that non-local correlations can be incorporated systematically. We apply our method to study the localization phenomena in various dimensions. Such an approach opens a new avenue to study localization effect both in model and in real materials. This work was supported by the National Science Foundation (NSF) [Award No. LA-SiGMA EPS-1003897, DMR-1005751], Department of Energy, DOE-CMCSN

  20. Novel coupling scheme to control dynamics of coupled discrete systems

    NASA Astrophysics Data System (ADS)

    Shekatkar, Snehal M.; Ambika, G.

    2015-08-01

    We present a new coupling scheme to control spatio-temporal patterns and chimeras on 1-d and 2-d lattices and random networks of discrete dynamical systems. The scheme involves coupling with an external lattice or network of damped systems. When the system network and external network are set in a feedback loop, the system network can be controlled to a homogeneous steady state or synchronized periodic state with suppression of the chaotic dynamics of the individual units. The control scheme has the advantage that its design does not require any prior information about the system dynamics or its parameters and works effectively for a range of parameters of the control network. We analyze the stability of the controlled steady state or amplitude death state of lattices using the theory of circulant matrices and Routh-Hurwitz criterion for discrete systems and this helps to isolate regions of effective control in the relevant parameter planes. The conditions thus obtained are found to agree well with those obtained from direct numerical simulations in the specific context of lattices with logistic map and Henon map as on-site system dynamics. We show how chimera states developed in an experimentally realizable 2-d lattice can be controlled using this scheme. We propose this mechanism can provide a phenomenological model for the control of spatio-temporal patterns in coupled neurons due to non-synaptic coupling with the extra cellular medium. We extend the control scheme to regulate dynamics on random networks and adapt the master stability function method to analyze the stability of the controlled state for various topologies and coupling strengths.

  1. Compressible bubble dynamic simulations with central-upwind schemes

    NASA Astrophysics Data System (ADS)

    Koukouvinis, P.; Gavaises, M.; Georgoulas, A.; Marengo, M.

    2015-12-01

    This paper discusses the implementation of an explicit density-based solver, based on the central-upwind schemes originally suggested by Kurganov, for the simulation of cavitating bubble dynamic flows. Explicit density based solvers are suited for highly dynamic, violent flows, involving large density ratios, as is rather common in cavitating flows. Moreover, the central-upwind schemes have the advantage of avoiding direct evaluation of the Jacobian matrix or estimation of the wave pattern emerging from Euler equations. Second order accuracy can be achieved with TVD MUSCL schemes. Basic comparison with the predicted wave pattern of the central-upwind schemes is performed with the exact solution of the Riemann problem showing an excellent agreement. Then several different bubble configurations were tested, similar to the work of Lauer et al. (2012). The central-upwind schemes prove to be able to handle the large pressure and density ratios appearing in cavitating flows, giving similar predictions in the evolution of the bubble shape.

  2. Exponential discontinuous numerical scheme for electron transport in the continuous slowing down approximation

    SciTech Connect

    Prinja, A.K.; Lorence, L.J.

    1997-06-01

    A nonlinear discretization scheme in space and energy, based on the recently developed exponential discontinuous method, is applied to continuous slowing down dominated electron transport (i.e., in the absence of scattering.) Numerical results for dose and charge deposition are obtained and compared against results from the ONELD and ONEBFP codes, and against exact results from an adjoint Monte Carlo code. It is found that although the exponential discontinuous scheme yields strictly positive and monotonic solutions, the dose profile is considerably straggled when compared to results from the linear codes. On the other hand, the linear schemes produce negative results which, furthermore, do not damp effectively in some cases. A general conclusion is that while yielding strictly positive solutions, the exponential discontinuous method does not show the crude cell accuracy for charged particle transport as was apparent for neutral particle transport problems.

  3. Stochastic Approximation of Dynamical Exponent at Quantum Critical Point

    NASA Astrophysics Data System (ADS)

    Suwa, Hidemaro; Yasuda, Shinya; Todo, Synge

    We have developed a unified finite-size scaling method for quantum phase transitions that requires no prior knowledge of the dynamical exponent z. During a quantum Monte Carlo simulation, the temperature is automatically tuned by the Robbins-Monro stochastic approximation method, being proportional to the lowest gap of the finite-size system. The dynamical exponent is estimated in a straightforward way from the system-size dependence of the temperature. As a demonstration of our novel method, the two-dimensional S = 1 / 2 quantum XY model, or equivalently the hard-core boson system, in uniform and staggered magnetic fields is investigated in the combination of the world-line quantum Monte Carlo worm algorithm. In the absence of a uniform magnetic field, we obtain the fully consistent result with the Lorentz invariance at the quantum critical point, z = 1 . Under a finite uniform magnetic field, on the other hand, the dynamical exponent becomes two, and the mean-field universality with effective dimension (2+2) governs the quantum phase transition. We will discuss also the system with random magnetic fields, or the dirty boson system, bearing a non-trivial dynamical exponent.Reference: S. Yasuda, H. Suwa, and S. Todo Phys. Rev. B 92, 104411 (2015); arXiv:1506.04837

  4. F -Discrepancy for Efficient Sampling in Approximate Dynamic Programming.

    PubMed

    Cervellera, Cristiano; Maccio, Danilo

    2016-07-01

    In this paper, we address the problem of generating efficient state sample points for the solution of continuous-state finite-horizon Markovian decision problems through approximate dynamic programming. It is known that the selection of sampling points at which the value function is observed is a key factor when such function is approximated by a model based on a finite number of evaluations. A standard approach consists in generating these points through a random or deterministic procedure, aiming at a balanced covering of the state space. Yet, this solution may not be efficient if the state trajectories are not uniformly distributed. Here, we propose to exploit F -discrepancy, a quantity that measures how closely a set of random points represents a probability distribution, and introduce an example of an algorithm based on such concept to automatically select point sets that are efficient with respect to the underlying Markovian process. An error analysis of the approximate solution is provided, showing how the proposed algorithm enables convergence under suitable regularity hypotheses. Then, simulation results are provided concerning an inventory forecasting test problem. The tests confirm in general the important role of F -discrepancy, and show how the proposed algorithm is able to yield better results than uniform sampling, using sets even 50 times smaller.

  5. Trojan dynamics well approximated by a new Hamiltonian normal form

    NASA Astrophysics Data System (ADS)

    Páez, Rocío Isabel; Locatelli, Ugo

    2015-10-01

    We revisit a classical perturbative approach to the Hamiltonian related to the motions of Trojan bodies, in the framework of the planar circular restricted three-body problem, by introducing a number of key new ideas in the formulation. In some sense, we adapt the approach of Garfinkel to the context of the normal form theory and its modern techniques. First, we make use of Delaunay variables for a physically accurate representation of the system. Therefore, we introduce a novel manipulation of the variables so as to respect the natural behaviour of the model. We develop a normalization procedure over the fast angle which exploits the fact that singularities in this model are essentially related to the slow angle. Thus, we produce a new normal form, i.e. an integrable approximation to the Hamiltonian. We emphasize some practical examples of the applicability of our normalizing scheme, e.g. the estimation of the stable libration region. Finally, we compare the level curves produced by our normal form with surfaces of section provided by the integration of the non-normalized Hamiltonian, with very good agreement. Further precision tests are also provided. In addition, we give a step-by-step description of the algorithm, allowing for extensions to more complicated models.

  6. Electron-nucleus cusp correction scheme for the relativistic zeroth-order regular approximation quantum Monte Carlo method.

    PubMed

    Nakatsuka, Yutaka; Nakajima, Takahito; Hirao, Kimihiko

    2010-05-07

    A cusp correction scheme for the relativistic zeroth-order regular approximation (ZORA) quantum Monte Carlo method is proposed by extending the nonrelativistic cusp correction scheme of Ma et al. [J. Chem. Phys. 122, 224322 (2005)]. In this scheme, molecular orbitals that appear in Slater-Jastrow type wave functions are replaced with the exponential-type correction functions within a correction radius. Analysis of the behavior of the ZORA local energy in electron-nucleus collisions reveals that the Kato's cusp condition is not applicable to the ZORA QMC method. The divergence of the electron-nucleus Coulomb potential term in the ZORA local energy is remedied by adding a new logarithmic correction term. This method is shown to be useful for improving the numerical stability of the ZORA-QMC calculations using both Gaussian and Slater basis functions.

  7. Stochastic approximation of dynamical exponent at quantum critical point

    NASA Astrophysics Data System (ADS)

    Yasuda, Shinya; Suwa, Hidemaro; Todo, Synge

    2015-09-01

    We have developed a unified finite-size scaling method for quantum phase transitions that requires no prior knowledge of the dynamical exponent z . During a quantum Monte Carlo simulation, the temperature is automatically tuned by the Robbins-Monro stochastic approximation method, being proportional to the lowest gap of the finite-size system. The dynamical exponent is estimated in a straightforward way from the system-size dependence of the temperature. As a demonstration of our novel method, the two-dimensional S =1 /2 quantum X Y model in uniform and staggered magnetic fields is investigated in the combination of the world-line quantum Monte Carlo worm algorithm. In the absence of a uniform magnetic field, we obtain the fully consistent result with the Lorentz invariance at the quantum critical point, z =1 , i.e., the three-dimensional classical X Y universality class. Under a finite uniform magnetic field, on the other hand, the dynamical exponent becomes two, and the mean-field universality with effective dimension (2 +2 ) governs the quantum phase transition.

  8. Simple finite element methods for approximating predator-prey dynamics in two dimensions using MATLAB.

    PubMed

    Garvie, Marcus R; Burkardt, John; Morgan, Jeff

    2015-03-01

    We describe simple finite element schemes for approximating spatially extended predator-prey dynamics with the Holling type II functional response and logistic growth of the prey. The finite element schemes generalize 'Scheme 1' in the paper by Garvie (Bull Math Biol 69(3):931-956, 2007). We present user-friendly, open-source MATLAB code for implementing the finite element methods on arbitrary-shaped two-dimensional domains with Dirichlet, Neumann, Robin, mixed Robin-Neumann, mixed Dirichlet-Neumann, and Periodic boundary conditions. Users can download, edit, and run the codes from http://www.uoguelph.ca/~mgarvie/ . In addition to discussing the well posedness of the model equations, the results of numerical experiments are presented and demonstrate the crucial role that habitat shape, initial data, and the boundary conditions play in determining the spatiotemporal dynamics of predator-prey interactions. As most previous works on this problem have focussed on square domains with standard boundary conditions, our paper makes a significant contribution to the area.

  9. Path integral molecular dynamics method based on a pair density matrix approximation: An algorithm for distinguishable and identical particle systems

    NASA Astrophysics Data System (ADS)

    Miura, Shinichi; Okazaki, Susumu

    2001-09-01

    In this paper, the path integral molecular dynamics (PIMD) method has been extended to employ an efficient approximation of the path action referred to as the pair density matrix approximation. Configurations of the isomorphic classical systems were dynamically sampled by introducing fictitious momenta as in the PIMD based on the standard primitive approximation. The indistinguishability of the particles was handled by a pseudopotential of particle permutation that is an extension of our previous one [J. Chem. Phys. 112, 10 116 (2000)]. As a test of our methodology for Boltzmann statistics, calculations have been performed for liquid helium-4 at 4 K. We found that the PIMD with the pair density matrix approximation dramatically reduced the computational cost to obtain the structural as well as dynamical (using the centroid molecular dynamics approximation) properties at the same level of accuracy as that with the primitive approximation. With respect to the identical particles, we performed the calculation of a bosonic triatomic cluster. Unlike the primitive approximation, the pseudopotential scheme based on the pair density matrix approximation described well the bosonic correlation among the interacting atoms. Convergence with a small number of discretization of the path achieved by this approximation enables us to construct a method of avoiding the problem of the vanishing pseudopotential encountered in the calculations by the primitive approximation.

  10. Novel discretization schemes for the numerical simulation of membrane dynamics

    NASA Astrophysics Data System (ADS)

    Kolsti, Kyle F.

    Motivated by the demands of simulating flapping wings of Micro Air Vehicles, novel numerical methods were developed and evaluated for the dynamic simulation of membranes. For linear membranes, a mixed-form time-continuous Galerkin method was employed using trilinear space-time elements. Rather than time-marching, the entire space-time domain was discretized and solved simultaneously. Second-order rates of convergence in both space and time were observed in numerical studies. Slight high-frequency noise was filtered during post-processing. For geometrically nonlinear membranes, the model incorporated two new schemes that were independently developed and evaluated. Time marching was performed using quintic Hermite polynomials uniquely determined by end-point jerk constraints. The single-step, implicit scheme was significantly more accurate than the most common Newmark schemes. For a simple harmonic oscillator, the scheme was found to be symplectic, frequency-preserving, and conditionally stable. Time step size was limited by accuracy requirements rather than stability. The spatial discretization scheme employed a staggered grid, grouping of nonlinear terms, and polygon shape functions in a strong-form point collocation formulation. The observed rate of convergence was two for both displacement and strain. Validation against existing experimental data showed the method to be accurate until hyperelastic effects dominate.

  11. Stability and dynamical properties of Rosenau-Hyman compactons using Padé approximants.

    PubMed

    Mihaila, Bogdan; Cardenas, Andres; Cooper, Fred; Saxena, Avadh

    2010-05-01

    We present a systematic approach for calculating higher-order derivatives of smooth functions on a uniform grid using Padé approximants. We illustrate our findings by deriving higher-order approximations using traditional second-order finite-difference formulas as our starting point. We employ these schemes to study the stability and dynamical properties of K(2,2) Rosenau-Hyman compactons including the collision of two compactons and resultant shock formation. Our approach uses a differencing scheme involving only nearest and next-to-nearest neighbors on a uniform spatial grid. The partial differential equation for the compactons involves first, second, and third partial derivatives in the spatial coordinate and we concentrate on four different fourth-order methods which differ in the possibility of increasing the degree of accuracy (or not) of one of the spatial derivatives to sixth order. A method designed to reduce round-off errors was found to be the most accurate approximation in stability studies of single solitary waves even though all derivates are accurate only to fourth order. Simulating compacton scattering requires the addition of fourth derivatives related to artificial viscosity. For those problems the different choices lead to different amounts of "spurious" radiation and we compare the virtues of the different choices.

  12. Decentralized Bayesian search using approximate dynamic programming methods.

    PubMed

    Zhao, Yijia; Patek, Stephen D; Beling, Peter A

    2008-08-01

    We consider decentralized Bayesian search problems that involve a team of multiple autonomous agents searching for targets on a network of search points operating under the following constraints: 1) interagent communication is limited; 2) the agents do not have the opportunity to agree in advance on how to resolve equivalent but incompatible strategies; and 3) each agent lacks the ability to control or predict with certainty the actions of the other agents. We formulate the multiagent search-path-planning problem as a decentralized optimal control problem and introduce approximate dynamic heuristics that can be implemented in a decentralized fashion. After establishing some analytical properties of the heuristics, we present computational results for a search problem involving two agents on a 5 x 5 grid.

  13. Analytic Coulomb approximations for dynamic multipole polarizabilities and dispersion forces

    NASA Astrophysics Data System (ADS)

    Lamm, Gene; Szabo, Attila

    1980-03-01

    This paper presents a comprehensive and unified treatment of atomic multipole oscillator strengths, dynamic multipole polarizabilities, and dispersion force constants in a variety of Coulomb-like approximations. A theoretically and computationally superior modification of the original Bates-Damgaard (BD) procedure, referred to here simply as the Coulomb approximation (CA), is introduced. An analytic expression for the dynamic multipole polarizability is found which contains as special cases this quantity within the CA, the extended Coulomb approximation (ECA) of Adelman and Szabo, and the quantum defect orbital (QDO) method of Simons. This expression contains model-dependent parameters determined from ground and excited state ionization potentials and is derived using a powerful approach based on the sturmian representation of a generalized Coulomb Green's function. In addition, this result is obtained within the ECA and QDO models through an extension of the novel algebraic procedure previously used in obtaining the static polarizability within the ECA, thus demonstrating the equivalence of the two approaches. Static quadrupole and scalar and tensor dipole polarizabilities for a variety of mono and divalent ground and excited state systems within the CA, ECA, and QDO models are compared, when possible, with recent experimental and accurate theoretical work. Except for quadrupole polarizabilities of light divalent systems, agreement for all models is very good. For ground state systems, best accuracy is obtained using the ECA. Illustrative calculation for the dynamic dipole polarizability at real and imaginary frequencies for the He 11S and 21S systems within the ECA is presented and compared with the definitive results of Glover and Weinhold (GW). For He 11S, despite an 8% error in the predicted static polarizability, scaling the dynamic polarizability to the GW static value shows the frequency dependence to be accurately represented. The analytic nature of the

  14. Dynamic MTW: a dynamic bandwidth distribution scheme in EPON

    NASA Astrophysics Data System (ADS)

    Chen, Hong; Ge, Liangwei; Zeng, Lieguang

    2002-08-01

    An algorithm to improve the bandwidth utilization for EPON by using dynamic bandwidth distribution is put forward. System performance, such as queuing delay under self-similar traffic, is simulated by using OPNET.

  15. Interlaced coarse-graining for the dynamical cluster approximation

    NASA Astrophysics Data System (ADS)

    Haehner, Urs; Staar, Peter; Jiang, Mi; Maier, Thomas; Schulthess, Thomas

    The negative sign problem remains a challenging limiting factor in quantum Monte Carlo simulations of strongly correlated fermionic many-body systems. The dynamical cluster approximation (DCA) makes this problem less severe by coarse-graining the momentum space to map the bulk lattice to a cluster embedded in a dynamical mean-field host. Here, we introduce a new form of an interlaced coarse-graining and compare it with the traditional coarse-graining. We show that it leads to more controlled results with weaker cluster shape and smoother cluster size dependence, which with increasing cluster size converge to the results obtained using the standard coarse-graining. In addition, the new coarse-graining reduces the severity of the fermionic sign problem. Therefore, it enables calculations on much larger clusters and can allow the evaluation of the exact infinite cluster size result via finite size scaling. To demonstrate this, we study the hole-doped two-dimensional Hubbard model and show that the interlaced coarse-graining in combination with the DCA+ algorithm permits the determination of the superconducting Tc on cluster sizes, for which the results can be fitted with the Kosterlitz-Thouless scaling law. This research used resources of the Oak Ridge Leadership Computing Facility (OLCF) awarded by the INCITE program, and of the Swiss National Supercomputing Center. OLCF is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725.

  16. Approximating the maximum weight clique using replicator dynamics.

    PubMed

    Bomze, I R; Pelillo, M; Stix, V

    2000-01-01

    Given an undirected graph with weights on the vertices, the maximum weight clique problem (MWCP) is to find a subset of mutually adjacent vertices (i.e., a clique) having the largest total weight. This is a generalization of the classical problem of finding the maximum cardinality clique of an unweighted graph, which arises as a special case of the MWCP when all the weights associated to the vertices are equal. The problem is known to be NP-hard for arbitrary graphs and, according to recent theoretical results, so is the problem of approximating it within a constant factor. Although there has recently been much interest around neural-network algorithms for the unweighted maximum clique problem, no effort has been directed so far toward its weighted counterpart. In this paper, we present a parallel, distributed heuristic for approximating the MWCP based on dynamics principles developed and studied in various branches of mathematical biology. The proposed framework centers around a recently introduced continuous characterization of the MWCP which generalizes an earlier remarkable result by Motzkin and Straus. This allows us to formulate the MWCP (a purely combinatorial problem) in terms of a continuous quadratic programming problem. One drawback associated with this formulation, however, is the presence of "spurious" solutions, and we present characterizations of these solutions. To avoid them we introduce a new regularized continuous formulation of the MWCP inspired by previous works on the unweighted problem, and show how this approach completely solves the problem. The continuous formulation of the MWCP naturally maps onto a parallel, distributed computational network whose dynamical behavior is governed by the so-called replicator equations. These are dynamical systems introduced in evolutionary game theory and population genetics to model evolutionary processes on a macroscopic scale.We present theoretical results which guarantee that the solutions provided by

  17. Approximate pole-placement controller using inverse plant dynamics for floor vibration control

    NASA Astrophysics Data System (ADS)

    Nyawako, Donald S.; Reynolds, Paul; Hudson, Malcolm J.

    2013-04-01

    Past research and field trials have demonstrated the viability of active vibration control (AVC) technologies for the mitigation of human induced vibrations in problematic floors. They make use of smaller units than their passive counterparts, provide quicker and more efficient control, can tackle multiple modes of vibration simultaneously and adaptability can be introduced to enhance their robustness. Predominantly single-input-single-output (SISO) and multi- SISO collocated sensor and actuator pairs have been utilized in direct output feedback schemes, for example, with direct velocity feedback (DVF). On-going studies have extended such past works to include model-based control approaches, for example, pole-placement (PP), which demonstrate increased flexibility of achieving desired vibration mitigation performances but for which stability issues must be adequately addressed. The work presented here is an extension to the pole-placement controller design using an algebraic approach that has been investigated in past studies. An approximate pole-placement controller formulated via the inversion of the floor dynamics, considered as minimum phase, is designed to achieve target closed-loop performances. Analytical studies and experimental tests are based on a laboratory structure and comparisons in vibration mitigation performances are made with a typical DVF control scheme with inner loop actuator compensation. It is shown that with minimal compensation, primarily in the form of notch filters and gain adjustment, the approximate pole-placement controller scheme is easily formulated and implemented and offers good vibration mitigation performance as well as the potential for isolation and control of specific target modes of vibration. Predicted attenuations of 22dB and 12dB in both the first and second vibration modes of the laboratory structure were also realized in the experimental studies for DVF and the approximate PP controller.

  18. A Dynamical Initialization Scheme for Binary Tropical Cyclones

    NASA Astrophysics Data System (ADS)

    Liu, H.; Tan, Z. M.

    2015-12-01

    A dynamic initialization (DI) scheme for binary vortices (BVDI) is proposed to improve the initial conditions for the simulations of binary tropical cyclones (TCs) using the Weather Research and Forecasting (WRF) model. This BVDI scheme is based on a new hurricane/typhoon DI (HTDI) formulated for the single TC, which is a modification of the DI developed by Cha and Wang (2013) while further introduces the adjustment of initial vortex size and wet bogus vortex. Two TC cases, i.e., Super Typhoon Saomai (2006) and Tropical Storm Bopha (2006) in Western North Pacific, have been selected as a sample of binary TCs to test the performance of different DI schemes. The adjustment of initial vortex scale in HTDI makes improvements to the evolution of intensity and structure of Saomai. Moreover, the introduced wet bogus vortex ensures the spinning-up of Bopha's initial vortex. In addition, BVDI not only has the merits of HTDI, but also shows its advantage in reflecting the impact of the interaction on this pair of binary TCs within the initial condition. With that the tracks, intensities and structures as well as their evolutions (e.g. rapid intensification and concentric eyewall) of both Saomai and Bopha could be successfully captured comparing with the observations, which is advantage than other DI schemes. The results indicate that it is necessary to improve the representation of two TCs in the initial conditions and include their interactions in the binary TCs forecast.

  19. A skinning prediction scheme for dynamic 3D mesh compression

    NASA Astrophysics Data System (ADS)

    Mamou, Khaled; Zaharia, Titus; Prêteux, Françoise

    2006-08-01

    This paper presents a new prediction-based compression technique for dynamic 3D meshes with constant connectivity and time-varying geometry. The core of the proposed algorithm is a skinning model used for motion compensation. The mesh is first partitioned within vertex clusters that can be described by a single affine motion model. The proposed segmentation technique automatically determines the number of clusters and relays on a decimation strategy privileging the simplification of vertices exhibiting the same affine motion over the whole animation sequence. The residual prediction errors are finally compressed using a temporal-DCT representation. The performances of our encoder are objectively evaluated on a data set of eight animation sequences with various sizes, geometries and topologies, and exhibiting both rigid and elastic motions. The experimental evaluation shows that the proposed compression scheme outperforms state of the art techniques such as MPEG-4/AFX, Dynapack, RT, GV, MCGV, TDCT, PCA and RT compression schemes.

  20. Dynamical mass generation in QED 3 beyond the instantaneous approximation

    NASA Astrophysics Data System (ADS)

    Xiao, Hai-Xiao; Li, Jian-Feng; Wei, Wei; Yin, Pei-Lin; Zong, Hong-Shi

    2017-07-01

    In this paper, we investigate dynamical mass generation in (2+1)-dimensional quantum electrodynamics at finite temperature. Many studies are carried out within the instantaneous-exchange approximation, which ignores all but the zero-frequency component of the boson propagator and fermion self-energy function. We extend these studies by taking the retardation effects into consideration. In this paper, we get the explicit frequency n and momentum p dependence of the fermion self-energy function and identify the critical temperature for different fermion flavors in the chiral limit. Also, the phase diagram for spontaneous symmetry breaking in the theory is presented in T c-N f space. The results show that the chiral condensate is just one-tenth of the scale of previous results, and the chiral symmetry is restored at a smaller critical temperature. Supported by National Natural Science Foundation of China (11475085, 11535005, 11690030), Natural Science Foundation of Jiangsu Province (BK20130387) and Jiangsu Planned Projects for Postdoctoral Research Funds (1501035B)

  1. Dynamic Obstacle Avoidance Using Bayesian Occupancy Filter and Approximate Inference

    PubMed Central

    Llamazares, Ángel; Ivan, Vladimir; Molinos, Eduardo; Ocaña, Manuel; Vijayakumar, Sethu

    2013-01-01

    The goal of this paper is to solve the problem of dynamic obstacle avoidance for a mobile platform by using the stochastic optimal control framework to compute paths that are optimal in terms of safety and energy efficiency under constraints. We propose a three-dimensional extension of the Bayesian Occupancy Filter (BOF) (Coué et al. Int. J. Rob. Res. 2006, 25, 19–30) to deal with the noise in the sensor data, improving the perception stage. We reduce the computational cost of the perception stage by estimating the velocity of each obstacle using optical flow tracking and blob filtering. While several obstacle avoidance systems have been presented in the literature addressing safety and optimality of the robot motion separately, we have applied the approximate inference framework to this problem to combine multiple goals, constraints and priors in a structured way. It is important to remark that the problem involves obstacles that can be moving, therefore classical techniques based on reactive control are not optimal from the point of view of energy consumption. Some experimental results, including comparisons against classical algorithms that highlight the advantages are presented. PMID:23529117

  2. Secure Dynamic access control scheme of PHR in cloud computing.

    PubMed

    Chen, Tzer-Shyong; Liu, Chia-Hui; Chen, Tzer-Long; Chen, Chin-Sheng; Bau, Jian-Guo; Lin, Tzu-Ching

    2012-12-01

    With the development of information technology and medical technology, medical information has been developed from traditional paper records into electronic medical records, which have now been widely applied. The new-style medical information exchange system "personal health records (PHR)" is gradually developed. PHR is a kind of health records maintained and recorded by individuals. An ideal personal health record could integrate personal medical information from different sources and provide complete and correct personal health and medical summary through the Internet or portable media under the requirements of security and privacy. A lot of personal health records are being utilized. The patient-centered PHR information exchange system allows the public autonomously maintain and manage personal health records. Such management is convenient for storing, accessing, and sharing personal medical records. With the emergence of Cloud computing, PHR service has been transferred to storing data into Cloud servers that the resources could be flexibly utilized and the operation cost can be reduced. Nevertheless, patients would face privacy problem when storing PHR data into Cloud. Besides, it requires a secure protection scheme to encrypt the medical records of each patient for storing PHR into Cloud server. In the encryption process, it would be a challenge to achieve accurately accessing to medical records and corresponding to flexibility and efficiency. A new PHR access control scheme under Cloud computing environments is proposed in this study. With Lagrange interpolation polynomial to establish a secure and effective PHR information access scheme, it allows to accurately access to PHR with security and is suitable for enormous multi-users. Moreover, this scheme also dynamically supports multi-users in Cloud computing environments with personal privacy and offers legal authorities to access to PHR. From security and effectiveness analyses, the proposed PHR access

  3. Exact and approximate many-body dynamics with stochastic one-body density matrix evolution

    SciTech Connect

    Lacroix, Denis

    2005-06-01

    We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, D{sub ab}= vertical bar {phi}{sub a}><{phi}{sub b} vertical bar, where each state evolves according to the stochastic Schroedinger equation given by O. Juillet and Ph. Chomaz [Phys. Rev. Lett. 88, 142503 (2002)]. A stochastic Liouville-von Neumann equation is derived as well as the associated. Bogolyubov-Born-Green-Kirwood-Yvon hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean-field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean-field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended time-dependent Hartree-Fock scheme. In this stochastic mean-field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.

  4. A Dynamical Unification Scheme from General Conservation Laws

    NASA Astrophysics Data System (ADS)

    Basini, Giuseppe; Capozziello, Salvatore

    2003-12-01

    The aim of this work is to present an unification scheme of fundamental interactions based on a well defined dynamics, the non-introduction of ad hoc hypotheses and the consideration of the minimal necessary number of free parameters and dimensions. A dynamical unification scheme of fundamental interactions can be achieved assuming a 5D space where conservation laws are always and absolutely valid, i.e. never violated. This approach gives rise to an induced-matter theory in the usual 4D space-time through a process of embedding and dimensional reduction by which masses, spins and charges of particles naturally spring out, and also the the hierarchy problem can be successfully faced thanks to the mass spectrum. The emergence of asymptotic freedom also for gravitational interaction, the existence of two time arrows together with the possibility of closed time-like paths are intrinsic results of such a theory, leading to a recovering of the causality principle and to a formal, dynamical explanation of several paradoxes and questioning problems of modern physics e.g. entanglement of EPR-type quantum states, quantum teleportation, gamma ray bursts origin, black hole singularities and cosmic primary antimatter absence.

  5. Reconstruction of time-dependent coefficients: A check of approximation schemes for non-Markovian convolutionless dissipative generators

    SciTech Connect

    Bellomo, Bruno; De Pasquale, Antonella; Gualdi, Giulia; Marzolino, Ugo

    2010-12-15

    We propose a procedure to fully reconstruct the time-dependent coefficients of convolutionless non-Markovian dissipative generators via a finite number of experimental measurements. By combining a tomography-based approach with a proper data sampling, our proposal allows to relate the time-dependent coefficients governing the dissipative evolution of a quantum system to experimentally accessible quantities. The proposed scheme not only provides a way to retrieve the full information about potentially unknown dissipative coefficients, but also, most valuably, can be employed as a reliable consistency test for the approximations involved in the theoretical derivation of a given non-Markovian convolutionless master equation.

  6. Improvement of the recursive projection method for linear iterative scheme stabilization based on an approximate eigenvalue problem

    NASA Astrophysics Data System (ADS)

    Renac, Florent

    2011-06-01

    An algorithm for stabilizing linear iterative schemes is developed in this study. The recursive projection method is applied in order to stabilize divergent numerical algorithms. A criterion for selecting the divergent subspace of the iteration matrix with an approximate eigenvalue problem is introduced. The performance of the present algorithm is investigated in terms of storage requirements and CPU costs and is compared to the original Krylov criterion. Theoretical results on the divergent subspace selection accuracy are established. The method is then applied to the resolution of the linear advection-diffusion equation and to a sensitivity analysis for a turbulent transonic flow in the context of aerodynamic shape optimization. Numerical experiments demonstrate better robustness and faster convergence properties of the stabilization algorithm with the new criterion based on the approximate eigenvalue problem. This criterion requires only slight additional operations and memory which vanish in the limit of large linear systems.

  7. Multiple time scale based reduction scheme for nonlinear chemical dynamics

    NASA Astrophysics Data System (ADS)

    Das, D.; Ray, D. S.

    2013-07-01

    A chemical reaction is often characterized by multiple time scales governing the kinetics of reactants, products and intermediates. We eliminate the fast relaxing intermediates in autocatalytic reaction by transforming the original system into a new one in which the linearized part is diagonal. This allows us to reduce the dynamical system by identifying the associated time scales and subsequent adiabatic elimination of the fast modes. It has been shown that the reduced system sustains the robust qualitative signatures of the original system and at times the generic form of the return map for the chaotic system from which complex dynamics stems out in the original system can be identified. We illustrate the scheme for a three-variable cubic autocatalytic reaction and four-variable peroxidase-oxidase reaction.

  8. A novel dynamical community detection algorithm based on weighting scheme

    NASA Astrophysics Data System (ADS)

    Li, Ju; Yu, Kai; Hu, Ke

    2015-12-01

    Network dynamics plays an important role in analyzing the correlation between the function properties and the topological structure. In this paper, we propose a novel dynamical iteration (DI) algorithm, which incorporates the iterative process of membership vector with weighting scheme, i.e. weighting W and tightness T. These new elements can be used to adjust the link strength and the node compactness for improving the speed and accuracy of community structure detection. To estimate the optimal stop time of iteration, we utilize a new stability measure which is defined as the Markov random walk auto-covariance. We do not need to specify the number of communities in advance. It naturally supports the overlapping communities by associating each node with a membership vector describing the node's involvement in each community. Theoretical analysis and experiments show that the algorithm can uncover communities effectively and efficiently.

  9. Conformational modes in biomolecules: Dynamics and approximate invariance

    NASA Astrophysics Data System (ADS)

    Potapov, Alex; Stepanova, Maria

    2012-02-01

    Understanding the physical mechanisms behind the folding and conformational dynamics of biomolecules is one of the major unsolved challenges of soft matter theory. In this contribution, a theoretical framework for biomolecular dynamics is introduced, employing selected aspects of statistical mechanics, dimensionality reduction, the perturbation theory, and the theory of matrices. Biomolecular dynamics is represented by time-dependent orthogonal conformational modes, the dynamics of the modes is investigated, and invariant properties that persist are identified. As an example, the dynamics of a human prion protein is considered. The theory provides a rigorous background for assessing the stable dynamical properties of biomolecules, such as their coarse-grained structure, through a multiscale approach using short subnanosecond segments of molecular dynamics trajectories. Furthermore, the paper offers a theoretical platform for models of conformational changes in macromolecules, which may allow complementing molecular dynamics simulations.

  10. Equivalence Between Approximate Dynamic Inversion and Proportional-Integral Control

    DTIC Science & Technology

    2008-09-29

    systems that renders the closed-loop error dynamics independent of the reference model dynamics. The equivalent PI controller will be derived and both of...integral control, PI control . I. INTRODUCTION DYNAMIC inversion (DI) or feedback linearization isa popular control design method that is well suited for...Proportional-Integral (PI) model reference controller realiza- tion. The key characteristic of the equivalent PI controller is that it is largely independent

  11. Approximate but accurate quantum dynamics from the Mori formalism. II. Equilibrium time correlation functions

    NASA Astrophysics Data System (ADS)

    Montoya-Castillo, Andrés; Reichman, David R.

    2017-02-01

    The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. 144, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function Cz z(t ) =Re ⟨σz(0 ) σz(t ) ⟩ , we show that the current scheme affords remarkable boosts in accuracy and efficiency over bare Ehrenfest dynamics. We further explore the sensitivity of the resulting dynamics to the choice of kernel closures and the accuracy of the initial canonical density operator.

  12. Approximate but accurate quantum dynamics from the Mori formalism. II. Equilibrium time correlation functions.

    PubMed

    Montoya-Castillo, Andrés; Reichman, David R

    2017-02-28

    The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. 144, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function Czz(t)=Re⟨σz(0)σz(t)⟩, we show that the current scheme affords remarkable boosts in accuracy and efficiency over bare Ehrenfest dynamics. We further explore the sensitivity of the resulting dynamics to the choice of kernel closures and the accuracy of the initial canonical density operator.

  13. New literal approximations for the longitudinal dynamic characteristics of flexible flight vehicles

    NASA Technical Reports Server (NTRS)

    Livneh, Rafael; Schmidt, David K.

    1992-01-01

    The goal of the literal approximation method is to obtain simple literal (analytical) approximations for key dynamic characteristics of flexible flight vehicles. A basic question regarding the method is its usefulness as an additional design tool for existing design and simulation procedures. Two aspects of this question are: (1) ease of derivation and use of the literal approximations, and (2) the suitability of one set of literal approximations to describe the dynamics of a large set of significantly different vehicles. These issues are addressed by incorporating symbolic manipulation software into the literal approximation method for the analysis of a fifth order model of the longitudinal dynamics of a flexible flight vehicle. The automated literal approximation generated in this fashion reduces the manual derivation time by an approximate factor of four. A single set of literal approximations is shown to provide adequate approximations for the dynamics of significantly different flight vehicles configurations, such as an aircraft, a missile, and a hypersonic vehicle.

  14. A frequency independent approximation and a sliding mode control scheme for a system of a micro-cantilever beam.

    PubMed

    Vagia, Marialena

    2012-03-01

    In the present article, a sliding mode controller is proposed for a micro-cantilever beam (μCB) with fringing and squeezed film damping effects. The narrow micro-cantilever beam can move via the application of an external electrically induced force. The introduction of the squeezed film parameters results in a frequency-dependent nonlinear system. Particular attention, has been paid, in order to approximate the frequency dependent μCB model, with a valid, frequency independent one, that would be incorporated in the design of a robust sliding mode controller. The suggested control technique enables compact realization of a robust controller tolerant in device characteristics' variations, nonlinearities and types of inherent instabilities. Robustness of the proposed control scheme against disturbances is proved by Lyapunov's second method. In addition, bifurcation analysis is carried on the beam's nonlinear model, and numerous simulation test cases are presented in order to test the suggested modeling and control techniques.

  15. Interpolation schemes in the control of systems with unknown dynamics

    NASA Technical Reports Server (NTRS)

    Youcef-Toumi, K.; Mcmahon, E. H., II

    1990-01-01

    Time-delay control for systems with unknown dynamics involves estimations. In its present form, these estimations include not only the interpolation of a time-varying function but also its derivative between data points. Presently, the control law is reformulated, taking into account the computation delay. A window-shifting scheme is then devised to view n data points as they are sampled in order to perform the function estimation. At each new sampling time, the window shifts to include the new data point as well as the last n-1 points. Several interpolation methods are considered. These methods use data points from a sampled function to construct a polynomial estimate of the function. The control system performance was experimentally tested using a servosystem. The results show that a Newtonian interpolation provided best results when the computation time was 0.4 times the sampling period.

  16. Approximate and exact numerical integration of the gas dynamic equations

    NASA Technical Reports Server (NTRS)

    Lewis, T. S.; Sirovich, L.

    1979-01-01

    A highly accurate approximation and a rapidly convergent numerical procedure are developed for two dimensional steady supersonic flow over an airfoil. Examples are given for a symmetric airfoil over a range of Mach numbers. Several interesting features are found in the calculation of the tail shock and the flow behind the airfoil.

  17. Exact and approximate gas dynamics using the tangent gas

    NASA Technical Reports Server (NTRS)

    Daripa, P. K.; Sirovich, L.

    1986-01-01

    For the determination of aerodynamic characteristics such as lift, drag, and moment coefficients, it is crucial to compute the properties of steady flow past an airfoil. This investigation provides a set of flow dependent grid systems and initial flowfield guesses which substantially improve convergence rates when applied to the Euler equations for flows past an airfoil. The basic equations are examined, taking into account nonlinear equations which are difficult to solve. A good approximation to these equations under certain conditions can be obtained by introducing the so-called 'tangent gas approximation' considered by Woods (1961), in which the isentropic relation between rho and p is replaced by a tangent to a curve. Attention is given to the solution procedure, the analysis (direct) problem, and a comparison of the tangent gas solution with the converged Euler solution.

  18. Dynamical observer for a flexible beam via finite element approximations

    NASA Technical Reports Server (NTRS)

    Manitius, Andre; Xia, Hong-Xing

    1994-01-01

    The purpose of this view-graph presentation is a computational investigation of the closed-loop output feedback control of a Euler-Bernoulli beam based on finite element approximation. The observer is part of the classical observer plus state feedback control, but it is finite-dimensional. In the theoretical work on the subject it is assumed (and sometimes proved) that increasing the number of finite elements will improve accuracy of the control. In applications, this may be difficult to achieve because of numerical problems. The main difficulty in computing the observer and simulating its work is the presence of high frequency eigenvalues in the finite-element model and poor numerical conditioning of some of the system matrices (e.g. poor observability properties) when the dimension of the approximating system increases. This work dealt with some of these difficulties.

  19. Kernel-Based Approximate Dynamic Programming Using Bellman Residual Elimination

    DTIC Science & Technology

    2010-02-01

    framework is the ability to utilize stochastic system models, thereby allowing the system to make sound decisions even if there is randomness in the system ...approximate policy when a system model is unavailable. We present theoretical analysis of all BRE algorithms proving convergence to the optimal policy in...policies based on MDPs is that there may be parameters of the system model that are poorly known and/or vary with time as the system operates. System

  20. Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method.

    PubMed

    Zhang, Huaguang; Cui, Lili; Zhang, Xin; Luo, Yanhong

    2011-12-01

    In this paper, a novel data-driven robust approximate optimal tracking control scheme is proposed for unknown general nonlinear systems by using the adaptive dynamic programming (ADP) method. In the design of the controller, only available input-output data is required instead of known system dynamics. A data-driven model is established by a recurrent neural network (NN) to reconstruct the unknown system dynamics using available input-output data. By adding a novel adjustable term related to the modeling error, the resultant modeling error is first guaranteed to converge to zero. Then, based on the obtained data-driven model, the ADP method is utilized to design the approximate optimal tracking controller, which consists of the steady-state controller and the optimal feedback controller. Further, a robustifying term is developed to compensate for the NN approximation errors introduced by implementing the ADP method. Based on Lyapunov approach, stability analysis of the closed-loop system is performed to show that the proposed controller guarantees the system state asymptotically tracking the desired trajectory. Additionally, the obtained control input is proven to be close to the optimal control input within a small bound. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed control scheme.

  1. Dynamic multicast routing scheme in WDM optical network

    NASA Astrophysics Data System (ADS)

    Zhu, Yonghua; Dong, Zhiling; Yao, Hong; Yang, Jianyong; Liu, Yibin

    2007-11-01

    During the information era, the Internet and the service of World Wide Web develop rapidly. Therefore, the wider and wider bandwidth is required with the lower and lower cost. The demand of operation turns out to be diversified. Data, images, videos and other special transmission demands share the challenge and opportunity with the service providers. Simultaneously, the electrical equipment has approached their limit. So the optical communication based on the wavelength division multiplexing (WDM) and the optical cross-connects (OXCs) shows great potentials and brilliant future to build an optical network based on the unique technical advantage and multi-wavelength characteristic. In this paper, we propose a multi-layered graph model with inter-path between layers to solve the problem of multicast routing wavelength assignment (RWA) contemporarily by employing an efficient graph theoretic formulation. And at the same time, an efficient dynamic multicast algorithm named Distributed Message Copying Multicast (DMCM) mechanism is also proposed. The multicast tree with minimum hops can be constructed dynamically according to this proposed scheme.

  2. On a class of TVD schemes for gas dynamic calculations. [Total Variation Diminishing

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Warming, R. F.; Harten, A.

    1985-01-01

    The purpose of this paper is to review a class of explicit and implicit second-order accurate Total Variation Diminishing (TVD) schemes and to show by numerical experiments, the performance of these schemes to the Euler equations of gas dynamics. The method of constructing these second-order accurate TVD schemes is sometimes known as the modified flux approach.

  3. Delving Into Dissipative Quantum Dynamics: From Approximate to Numerically Exact Approaches

    NASA Astrophysics Data System (ADS)

    Chen, Hsing-Ta

    In this thesis, I explore dissipative quantum dynamics of several prototypical model systems via various approaches, ranging from approximate to numerically exact schemes. In particular, in the realm of the approximate I explore the accuracy of Pade-resummed master equations and the fewest switches surface hopping (FSSH) algorithm for the spin-boson model, and non-crossing approximations (NCA) for the Anderson-Holstein model. Next, I develop new and exact Monte Carlo approaches and test them on the spin-boson model. I propose well-defined criteria for assessing the accuracy of Pade-resummed quantum master equations, which correctly demarcate the regions of parameter space where the Pade approximation is reliable. I continue the investigation of spin-boson dynamics by benchmark comparisons of the semiclassical FSSH algorithm to exact dynamics over a wide range of parameters. Despite small deviations from golden-rule scaling in the Marcus regime, standard surface hopping algorithm is found to be accurate over a large portion of parameter space. The inclusion of decoherence corrections via the augmented FSSH algorithm improves the accuracy of dynamical behavior compared to exact simulations, but the effects are generally not dramatic for the cases I consider. Next, I introduce new methods for numerically exact real-time simulation based on real-time diagrammatic Quantum Monte Carlo (dQMC) and the inchworm algorithm. These methods optimally recycle Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. In the context of the spin-boson model, I formulate the inchworm expansion in two distinct ways: the first with respect to an expansion in the system-bath coupling and the second as an expansion in the diabatic coupling. In addition, a cumulant version of the inchworm Monte Carlo method is motivated by the latter expansion, which allows for further suppression of the growth of the sign error. I provide a comprehensive comparison of the

  4. Approximate photochemical dynamics of azobenzene with reactive force fields

    NASA Astrophysics Data System (ADS)

    Li, Yan; Hartke, Bernd

    2013-12-01

    We have fitted reactive force fields of the ReaxFF type to the ground and first excited electronic states of azobenzene, using global parameter optimization by genetic algorithms. Upon coupling with a simple energy-gap transition probability model, this setup allows for completely force-field-based simulations of photochemical cis→trans- and trans→cis-isomerizations of azobenzene, with qualitatively acceptable quantum yields. This paves the way towards large-scale dynamics simulations of molecular machines, including bond breaking and formation (via the reactive force field) as well as photochemical engines (presented in this work).

  5. Approximate photochemical dynamics of azobenzene with reactive force fields

    SciTech Connect

    Li, Yan; Hartke, Bernd

    2013-12-14

    We have fitted reactive force fields of the ReaxFF type to the ground and first excited electronic states of azobenzene, using global parameter optimization by genetic algorithms. Upon coupling with a simple energy-gap transition probability model, this setup allows for completely force-field-based simulations of photochemical cis→trans- and trans→cis-isomerizations of azobenzene, with qualitatively acceptable quantum yields. This paves the way towards large-scale dynamics simulations of molecular machines, including bond breaking and formation (via the reactive force field) as well as photochemical engines (presented in this work)

  6. Approximate maximum-entropy moment closures for gas dynamics

    NASA Astrophysics Data System (ADS)

    McDonald, James G.

    2016-11-01

    Accurate prediction of flows that exist between the traditional continuum regime and the free-molecular regime have proven difficult to obtain. Current methods are either inaccurate in this regime or prohibitively expensive for practical problems. Moment closures have long held the promise of providing new, affordable, accurate methods in this regime. The maximum-entropy hierarchy of closures seems to offer particularly attractive physical and mathematical properties. Unfortunately, several difficulties render the practical implementation of maximum-entropy closures very difficult. This work examines the use of simple approximations to these maximum-entropy closures and shows that physical accuracy that is vastly improved over continuum methods can be obtained without a significant increase in computational cost. Initially the technique is demonstrated for a simple one-dimensional gas. It is then extended to the full three-dimensional setting. The resulting moment equations are used for the numerical solution of shock-wave profiles with promising results.

  7. Dynamic remedial action scheme using online transient stability analysis

    NASA Astrophysics Data System (ADS)

    Shrestha, Arun

    Economic pressure and environmental factors have forced the modern power systems to operate closer to their stability limits. However, maintaining transient stability is a fundamental requirement for the operation of interconnected power systems. In North America, power systems are planned and operated to withstand the loss of any single or multiple elements without violating North American Electric Reliability Corporation (NERC) system performance criteria. For a contingency resulting in the loss of multiple elements (Category C), emergency transient stability controls may be necessary to stabilize the power system. Emergency control is designed to sense abnormal conditions and subsequently take pre-determined remedial actions to prevent instability. Commonly known as either Remedial Action Schemes (RAS) or as Special/System Protection Schemes (SPS), these emergency control approaches have been extensively adopted by utilities. RAS are designed to address specific problems, e.g. to increase power transfer, to provide reactive support, to address generator instability, to limit thermal overloads, etc. Possible remedial actions include generator tripping, load shedding, capacitor and reactor switching, static VAR control, etc. Among various RAS types, generation shedding is the most effective and widely used emergency control means for maintaining system stability. In this dissertation, an optimal power flow (OPF)-based generation-shedding RAS is proposed. This scheme uses online transient stability calculation and generator cost function to determine appropriate remedial actions. For transient stability calculation, SIngle Machine Equivalent (SIME) technique is used, which reduces the multimachine power system model to a One-Machine Infinite Bus (OMIB) equivalent and identifies critical machines. Unlike conventional RAS, which are designed using offline simulations, online stability calculations make the proposed RAS dynamic and adapting to any power system

  8. Dynamic-local-field approximation for the quantum solids

    NASA Technical Reports Server (NTRS)

    Etters, R. D.; Danilowicz, R. L.

    1974-01-01

    A local-molecular-field description for the ground-state properties of the quantum solids is presented. The dynamical behavior of atoms contributing to the local field, which acts on an arbitrary pair of test particles, is incorporated by decoupling the pair correlations between these field atoms. The energy, pressure, compressibility, single-particle-distribution function, and the rms atomic deviations about the equilibrium lattice sites are calculated for H2, He-3, and He-4 over the volume range from 5 to 24.5 cu cm/mole. The results are in close agreement with existing Monte Carlo calculations wherever comparisons are possible. At very high pressure, the results agree with simplified descriptions which depend on negligible overlap of the system wave function between neighboring lattice sites.

  9. Wave packet dynamics in the optimal superadiabatic approximation

    NASA Astrophysics Data System (ADS)

    Betz, V.; Goddard, B. D.; Manthe, U.

    2016-06-01

    We explain the concept of superadiabatic representations and show how in the context of electronically non-adiabatic transitions they lead to an explicit formula that can be used to predict transitions at avoided crossings. Based on this formula, we present a simple method for computing wave packet dynamics across avoided crossings. Only knowledge of the adiabatic potential energy surfaces near the avoided crossing is required for the computation. In particular, this means that no diabatization procedure is necessary, the adiabatic electronic energies can be computed on the fly, and they only need to be computed to higher accuracy when an avoided crossing is detected. We test the quality of our method on the paradigmatic example of photo-dissociation of NaI, finding very good agreement with results of exact wave packet calculations.

  10. Development of new flux splitting schemes. [computational fluid dynamics algorithms

    NASA Technical Reports Server (NTRS)

    Liou, Meng-Sing; Steffen, Christopher J., Jr.

    1992-01-01

    Maximizing both accuracy and efficiency has been the primary objective in designing a numerical algorithm for computational fluid dynamics (CFD). This is especially important for solutions of complex three dimensional systems of Navier-Stokes equations which often include turbulence modeling and chemistry effects. Recently, upwind schemes have been well received for their capability in resolving discontinuities. With this in mind, presented are two new flux splitting techniques for upwind differencing. The first method is based on High-Order Polynomial Expansions (HOPE) of the mass flux vector. The second new flux splitting is based on the Advection Upwind Splitting Method (AUSM). The calculation of the hypersonic conical flow demonstrates the accuracy of the splitting in resolving the flow in the presence of strong gradients. A second series of tests involving the two dimensional inviscid flow over a NACA 0012 airfoil demonstrates the ability of the AUSM to resolve the shock discontinuity at transonic speed. A third case calculates a series of supersonic flows over a circular cylinder. Finally, the fourth case deals with tests of a two dimensional shock wave/boundary layer interaction.

  11. Physically motivated Galerkin approximations in Geophysical Fluid Dynamics

    NASA Astrophysics Data System (ADS)

    Gluhovsky, Alexander; Tong, Christopher

    2001-11-01

    Finite-dimensional approximations of the Navier-Stokes equations (low-order models (LOMs)) are commonly derived by the Galerkin method. Its traditional implementation sometimes results in LOMs lacking energy conservation (in the absence of forcing and dissipation) and exhibiting unphysical behavior, e.g., trajectories diverging to infinity. An enhancement of the Galerkin method by the development of LOMs in the form of coupled Volterra gyrostats (Gluhovsky and Tong, Phys. Fluids, 1999) ensured energy conservation. In the present study, it is demonstrated that coupled gyrostats are instrumental in reducing the order of the model while keeping enough modes to describe the effect of interest and also in retaining the Hamiltonian structure of the original equations. Examples include LOMs for quasi-geostrophic atmospheric circulation with topography and for Rayleigh-Bénard convection. In particular, a LOM for three-dimensional Rayleigh-Bénard convection (Das et al. Phys. Rev. E, 2000) possessing trajectories diverging to infinity is first modified to a system in the form of coupled gyrostats (thereby eliminating such pathology), then altered to a Hamiltonian LOM. This research was supported by NSF grant ATM-9909009.

  12. Improved dynamic ID-based authentication scheme for telecare medical information systems.

    PubMed

    Cao, Tianjie; Zhai, Jingxuan

    2013-04-01

    In order to protect users' identity privacy, Chen et al. proposed an efficient dynamic ID-based authentication scheme for telecare medical information systems. However, Chen et al.'s scheme has some weaknesses. In Chen et al.'s scheme, an attacker can track a user by a linkability attack or an off-line identity guessing attack. Chen et al.'s scheme is also vulnerable to an off-line password guessing attack and an undetectable on-line password guessing attack when user's smart card is stolen. In server side, Chen et al.'s scheme needs large computational load to authentication a legal user or reject an illegal user. To remedy the weaknesses in Chen et al.'s scheme, we propose an improved smart card based password authentication scheme. Our analysis shows that the improved scheme can overcome the weaknesses in Chen et al.'s scheme.

  13. Stress stiffening and approximate equations in flexible multibody dynamics

    NASA Technical Reports Server (NTRS)

    Padilla, Carlos E.; Vonflotow, Andreas H.

    1993-01-01

    A useful model for open chains of flexible bodies undergoing large rigid body motions, but small elastic deformations, is one in which the equations of motion are linearized in the small elastic deformations and deformation rates. For slow rigid body motions, the correctly linearized, or consistent, set of equations can be compared to prematurely linearized, or inconsistent, equations and to 'oversimplified,' or ruthless, equations through the use of open loop dynamic simulations. It has been shown that the inconsistent model should never be used, while the ruthless model should be used whenever possible. The consistent and inconsistent models differ by stress stiffening terms. These are due to zeroth-order stresses effecting virtual work via nonlinear strain-displacement terms. In this paper we examine in detail the nature of these stress stiffening terms and conclude that they are significant only when the associated zeroth-order stresses approach 'buckling' stresses. Finally it is emphasized that when the stress stiffening terms are negligible the ruthlessly linearized equations should be used.

  14. COMPARISON OF IMPLICIT SCHEMES TO SOLVE EQUATIONS OF RADIATION HYDRODYNAMICS WITH A FLUX-LIMITED DIFFUSION APPROXIMATION: NEWTON–RAPHSON, OPERATOR SPLITTING, AND LINEARIZATION

    SciTech Connect

    Tetsu, Hiroyuki; Nakamoto, Taishi

    2016-03-15

    Radiation is an important process of energy transport, a force, and a basis for synthetic observations, so radiation hydrodynamics (RHD) calculations have occupied an important place in astrophysics. However, although the progress in computational technology is remarkable, their high numerical cost is still a persistent problem. In this work, we compare the following schemes used to solve the nonlinear simultaneous equations of an RHD algorithm with the flux-limited diffusion approximation: the Newton–Raphson (NR) method, operator splitting, and linearization (LIN), from the perspective of the computational cost involved. For operator splitting, in addition to the traditional simple operator splitting (SOS) scheme, we examined the scheme developed by Douglas and Rachford (DROS). We solve three test problems (the thermal relaxation mode, the relaxation and the propagation of linear waves, and radiating shock) using these schemes and then compare their dependence on the time step size. As a result, we find the conditions of the time step size necessary for adopting each scheme. The LIN scheme is superior to other schemes if the ratio of radiation pressure to gas pressure is sufficiently low. On the other hand, DROS can be the most efficient scheme if the ratio is high. Although the NR scheme can be adopted independently of the regime, especially in a problem that involves optically thin regions, the convergence tends to be worse. In all cases, SOS is not practical.

  15. Comparison of Implicit Schemes to Solve Equations of Radiation Hydrodynamics with a Flux-limited Diffusion Approximation: Newton--Raphson, Operator Splitting, and Linearization

    NASA Astrophysics Data System (ADS)

    Tetsu, Hiroyuki; Nakamoto, Taishi

    2016-03-01

    Radiation is an important process of energy transport, a force, and a basis for synthetic observations, so radiation hydrodynamics (RHD) calculations have occupied an important place in astrophysics. However, although the progress in computational technology is remarkable, their high numerical cost is still a persistent problem. In this work, we compare the following schemes used to solve the nonlinear simultaneous equations of an RHD algorithm with the flux-limited diffusion approximation: the Newton-Raphson (NR) method, operator splitting, and linearization (LIN), from the perspective of the computational cost involved. For operator splitting, in addition to the traditional simple operator splitting (SOS) scheme, we examined the scheme developed by Douglas & Rachford (DROS). We solve three test problems (the thermal relaxation mode, the relaxation and the propagation of linear waves, and radiating shock) using these schemes and then compare their dependence on the time step size. As a result, we find the conditions of the time step size necessary for adopting each scheme. The LIN scheme is superior to other schemes if the ratio of radiation pressure to gas pressure is sufficiently low. On the other hand, DROS can be the most efficient scheme if the ratio is high. Although the NR scheme can be adopted independently of the regime, especially in a problem that involves optically thin regions, the convergence tends to be worse. In all cases, SOS is not practical.

  16. Reinforcement learning control with approximation of time-dependent agent dynamics

    NASA Astrophysics Data System (ADS)

    Kirkpatrick, Kenton Conrad

    Reinforcement Learning has received a lot of attention over the years for systems ranging from static game playing to dynamic system control. Using Reinforcement Learning for control of dynamical systems provides the benefit of learning a control policy without needing a model of the dynamics. This opens the possibility of controlling systems for which the dynamics are unknown, but Reinforcement Learning methods like Q-learning do not explicitly account for time. In dynamical systems, time-dependent characteristics can have a significant effect on the control of the system, so it is necessary to account for system time dynamics while not having to rely on a predetermined model for the system. In this dissertation, algorithms are investigated for expanding the Q-learning algorithm to account for the learning of sampling rates and dynamics approximations. For determining a proper sampling rate, it is desired to find the largest sample time that still allows the learning agent to control the system to goal achievement. An algorithm called Sampled-Data Q-learning is introduced for determining both this sample time and the control policy associated with that sampling rate. Results show that the algorithm is capable of achieving a desired sampling rate that allows for system control while not sampling "as fast as possible". Determining an approximation of an agent's dynamics can be beneficial for the control of hierarchical multiagent systems by allowing a high-level supervisor to use the dynamics approximations for task allocation decisions. To this end, algorithms are investigated for learning first- and second-order dynamics approximations. These algorithms are respectively called First-Order Dynamics Learning and Second-Order Dynamics Learning. The dynamics learning algorithms are evaluated on several examples that show their capability to learn accurate approximations of state dynamics. All of these algorithms are then evaluated on hierarchical multiagent systems

  17. Design and analysis of a dynamic mobility management scheme for wireless mesh network.

    PubMed

    Majumder, Abhishek; Roy, Sudipta

    2013-01-01

    Seamless mobility management of the mesh clients (MCs) in wireless mesh network (WMN) has drawn a lot of attention from the research community. A number of mobility management schemes such as mesh network with mobility management (MEMO), mesh mobility management (M(3)), and wireless mesh mobility management (WMM) have been proposed. The common problem with these schemes is that they impose uniform criteria on all the MCs for sending route update message irrespective of their distinct characteristics. This paper proposes a session-to-mobility ratio (SMR) based dynamic mobility management scheme for handling both internet and intranet traffic. To reduce the total communication cost, this scheme considers each MC's session and mobility characteristics by dynamically determining optimal threshold SMR value for each MC. A numerical analysis of the proposed scheme has been carried out. Comparison with other schemes shows that the proposed scheme outperforms MEMO, M(3), and WMM with respect to total cost.

  18. Design and Analysis of a Dynamic Mobility Management Scheme for Wireless Mesh Network

    PubMed Central

    Roy, Sudipta

    2013-01-01

    Seamless mobility management of the mesh clients (MCs) in wireless mesh network (WMN) has drawn a lot of attention from the research community. A number of mobility management schemes such as mesh network with mobility management (MEMO), mesh mobility management (M3), and wireless mesh mobility management (WMM) have been proposed. The common problem with these schemes is that they impose uniform criteria on all the MCs for sending route update message irrespective of their distinct characteristics. This paper proposes a session-to-mobility ratio (SMR) based dynamic mobility management scheme for handling both internet and intranet traffic. To reduce the total communication cost, this scheme considers each MC's session and mobility characteristics by dynamically determining optimal threshold SMR value for each MC. A numerical analysis of the proposed scheme has been carried out. Comparison with other schemes shows that the proposed scheme outperforms MEMO, M3, and WMM with respect to total cost. PMID:24311982

  19. A dynamic identity based authentication scheme using chaotic maps for telecare medicine information systems.

    PubMed

    Wang, Zhiheng; Huo, Zhanqiang; Shi, Wenbo

    2015-01-01

    With rapid development of computer technology and wide use of mobile devices, the telecare medicine information system has become universal in the field of medical care. To protect patients' privacy and medial data's security, many authentication schemes for the telecare medicine information system have been proposed. Due to its better performance, chaotic maps have been used in the design of authentication schemes for the telecare medicine information system. However, most of them cannot provide user's anonymity. Recently, Lin proposed a dynamic identity based authentication scheme using chaotic maps for the telecare medicine information system and claimed that their scheme was secure against existential active attacks. In this paper, we will demonstrate that their scheme cannot provide user anonymity and is vulnerable to the impersonation attack. Further, we propose an improved scheme to fix security flaws in Lin's scheme and demonstrate the proposed scheme could withstand various attacks.

  20. An optimal implicit staggered-grid finite-difference scheme based on the modified Taylor-series expansion with minimax approximation method for elastic modeling

    NASA Astrophysics Data System (ADS)

    Yang, Lei; Yan, Hongyong; Liu, Hong

    2017-03-01

    Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.

  1. 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

  2. Solving the dynamic ambulance relocation and dispatching problem using approximate dynamic programming.

    PubMed

    Schmid, Verena

    2012-06-16

    Emergency service providers are supposed to locate ambulances such that in case of emergency patients can be reached in a time-efficient manner. Two fundamental decisions and choices need to be made real-time. First of all immediately after a request emerges an appropriate vehicle needs to be dispatched and send to the requests' site. After having served a request the vehicle needs to be relocated to its next waiting location. We are going to propose a model and solve the underlying optimization problem using approximate dynamic programming (ADP), an emerging and powerful tool for solving stochastic and dynamic problems typically arising in the field of operations research. Empirical tests based on real data from the city of Vienna indicate that by deviating from the classical dispatching rules the average response time can be decreased from 4.60 to 4.01 minutes, which corresponds to an improvement of 12.89%. Furthermore we are going to show that it is essential to consider time-dependent information such as travel times and changes with respect to the request volume explicitly. Ignoring the current time and its consequences thereafter during the stage of modeling and optimization leads to suboptimal decisions.

  3. Solving the dynamic ambulance relocation and dispatching problem using approximate dynamic programming

    PubMed Central

    Schmid, Verena

    2012-01-01

    Emergency service providers are supposed to locate ambulances such that in case of emergency patients can be reached in a time-efficient manner. Two fundamental decisions and choices need to be made real-time. First of all immediately after a request emerges an appropriate vehicle needs to be dispatched and send to the requests’ site. After having served a request the vehicle needs to be relocated to its next waiting location. We are going to propose a model and solve the underlying optimization problem using approximate dynamic programming (ADP), an emerging and powerful tool for solving stochastic and dynamic problems typically arising in the field of operations research. Empirical tests based on real data from the city of Vienna indicate that by deviating from the classical dispatching rules the average response time can be decreased from 4.60 to 4.01 minutes, which corresponds to an improvement of 12.89%. Furthermore we are going to show that it is essential to consider time-dependent information such as travel times and changes with respect to the request volume explicitly. Ignoring the current time and its consequences thereafter during the stage of modeling and optimization leads to suboptimal decisions. PMID:25540476

  4. Parallelization of Implicit Finite Difference Schemes in Computational Fluid Dynamics

    DTIC Science & Technology

    1990-08-01

    number, respectively. 3 The metric terms can be obtained by chain rule from the definitions of , ’ and C. The curvilinear derivatives in terms of the...have attempted to show, by analysis and experimentation, the extent to which CFD applications based on implicit scheme can be paralelized . A specific

  5. Optical properties of solids within the independent-quasiparticle approximation: Dynamical effects

    NASA Astrophysics Data System (ADS)

    del Sole, R.; Girlanda, Raffaello

    1996-11-01

    The independent-quasiparticle approximation to calculating the optical properties of solids is extended to account for dynamical effects, namely, the energy dependence of the GW self-energy. We use a simple but realistic model of such energy dependence. We find that the inclusion of dynamical effects reduces considerably the calculated absorption spectrum and makes the agreement with experiment worse.

  6. The Retrospective Iterated Analysis Scheme for Nonlinear Chaotic Dynamics

    NASA Technical Reports Server (NTRS)

    Todling, Ricardo

    2002-01-01

    Atmospheric data assimilation is the name scientists give to the techniques of blending atmospheric observations with atmospheric model results to obtain an accurate idea of what the atmosphere looks like at any given time. Because two pieces of information are used, observations and model results, the outcomes of data assimilation procedure should be better than what one would get by using one of these two pieces of information alone. There is a number of different mathematical techniques that fall under the data assimilation jargon. In theory most these techniques accomplish about the same thing. In practice, however, slight differences in the approaches amount to faster algorithms in some cases, more economical algorithms in other cases, and even give better overall results in yet some other cases because of practical uncertainties not accounted for by theory. Therefore, the key is to find the most adequate data assimilation procedure for the problem in hand. In our Data Assimilation group we have been doing extensive research to try and find just such data assimilation procedure. One promising possibility is what we call retrospective iterated analysis (RIA) scheme. This procedure has recently been implemented and studied in the context of a very large data assimilation system built to help predict and study weather and climate. Although the results from that study suggest that the RIA scheme produces quite reasonable results, a complete evaluation of the scheme is very difficult due to the complexity of that problem. The present work steps back a little bit and studies the behavior of the RIA scheme in the context of a small problem. The problem is small enough to allow full assessment of the quality of the RIA scheme, but it still has some of the complexity found in nature, namely, its chaotic-type behavior. We find that the RIA performs very well for this small but still complex problem which is a result that seconds the results of our early studies.

  7. Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

    NASA Astrophysics Data System (ADS)

    Pathak, Harshavardhana S.; Shukla, Ratnesh K.

    2016-08-01

    A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of

  8. Approximated Stable Inversion for Nonlinear Systems with Nonhyperbolic Internal Dynamics. Revised

    NASA Technical Reports Server (NTRS)

    Devasia, Santosh

    1999-01-01

    A technique to achieve output tracking for nonminimum phase nonlinear systems with non- hyperbolic internal dynamics is presented. The present paper integrates stable inversion techniques (that achieve exact-tracking) with approximation techniques (that modify the internal dynamics) to circumvent the nonhyperbolicity of the internal dynamics - this nonhyperbolicity is an obstruction to applying presently available stable inversion techniques. The theory is developed for nonlinear systems and the method is applied to a two-cart with inverted-pendulum example.

  9. Optimal staggered-grid finite-difference schemes by combining Taylor-series expansion and sampling approximation for wave equation modeling

    NASA Astrophysics Data System (ADS)

    Yan, Hongyong; Yang, Lei; Li, Xiang-Yang

    2016-12-01

    High-order staggered-grid finite-difference (SFD) schemes have been universally used to improve the accuracy of wave equation modeling. However, the high-order SFD coefficients on spatial derivatives are usually determined by the Taylor-series expansion (TE) method, which just leads to great accuracy at small wavenumbers for wave equation modeling. Some conventional optimization methods can achieve high accuracy at large wavenumbers, but they hardly guarantee the small numerical dispersion error at small wavenumbers. In this paper, we develop new optimal explicit SFD (ESFD) and implicit SFD (ISFD) schemes for wave equation modeling. We first derive the optimal ESFD and ISFD coefficients for the first-order spatial derivatives by applying the combination of the TE and the sampling approximation to the dispersion relation, and then analyze their numerical accuracy. Finally, we perform elastic wave modeling with the ESFD and ISFD schemes based on the TE method and the optimal method, respectively. When the appropriate number and interval for the sampling points are chosen, these optimal schemes have extremely high accuracy at small wavenumbers, and can also guarantee small numerical dispersion error at large wavenumbers. Numerical accuracy analyses and modeling results demonstrate the optimal ESFD and ISFD schemes can efficiently suppress the numerical dispersion and significantly improve the modeling accuracy compared to the TE-based ESFD and ISFD schemes.

  10. Dependence of the structure and dynamics of liquid silicon on the choice of density functional approximation

    NASA Astrophysics Data System (ADS)

    Remsing, Richard C.; Klein, Michael L.; Sun, Jianwei

    2017-07-01

    In addition to its technological relevance, silicon poses a challenge for first principles simulations because it undergoes a semiconductor-to-metal transition upon melting. Moreover, the resulting metallic liquid contains a mixture of metallic and covalent bonding. This coexistence of fundamentally different interactions is difficult to describe within approximate density functional methods, which oftentimes cannot accurately describe these two extremes simultaneously. We report an investigation of the structure, dynamics, and thermodynamics of liquid silicon using ab initio molecular dynamics simulations with three density functional approximations: the local density approximation, the Perdew-Burke-Ernzerhof generalized gradient approximation, and the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation. We demonstrate that SCAN describes this liquid with better accuracy than the other often-used functionals because it can simultaneously capture covalent and metallic bonding with similar high accuracy.

  11. Dynamical opacity-sampling models of Mira variables - I. Modelling description and analysis of approximations

    NASA Astrophysics Data System (ADS)

    Ireland, M. J.; Scholz, M.; Wood, P. R.

    2008-12-01

    We describe the Cool Opacity-sampling Dynamic EXtended (CODEX) atmosphere models of Mira variable stars, and examine in detail the physical and numerical approximations that go in-to the model creation. The CODEX atmospheric models are obtained by computing the temperature and the chemical and radiative states of the atmospheric layers, assuming gas pressure and velocity profiles from Mira pulsation models, which extend from near the H-burning shell to the outer layers of the atmosphere. Although the code uses the approximation of Local Thermodynamic Equilibrium (LTE) and a grey approximation in the dynamical atmosphere code, many key observable quantities, such as infrared diameters and low-resolution spectra, are predicted robustly in spite of these approximations. We show that in visible light, radiation from Mira variables is dominated by fluorescence scattering processes, and that the LTE approximation likely underpredicts visible-band fluxes by a factor of 2.

  12. A Numerical Homogenization Scheme for Glass Particle-Toughened Polymers Under Dynamic Loading

    NASA Astrophysics Data System (ADS)

    Karamnejad, Amin; Ahmed, Awais; Sluys, Lambertus Johannes

    A numerical homogenization scheme is presented to model glass particle-toughened polymer materials under dynamic loading. A constitutive law is developed for the polymer material and validated by comparing the results to experimental test data. A similar constitutive law as that of the polymer material with unknown material parameters is assumed for the glass particle-toughened polymer. A homogenization scheme is used to determine the unknown material parameters from the boundary value problem (BVP) of a representative volume element. Unlike the standard computational homogenization scheme, the proposed numerical homogenization scheme can be used after localization occurs in the material. The proposed multiscale model is then verified against direct numerical simulation.

  13. RIMBAY - a multi-approximation 3D ice-dynamics model for comprehensive applications: model description and examples

    NASA Astrophysics Data System (ADS)

    Thoma, M.; Grosfeld, K.; Barbi, D.; Determann, J.; Goeller, S.; Mayer, C.; Pattyn, F.

    2014-01-01

    Glaciers and ice caps exhibit currently the largest cryospheric contributions to sea level rise. Modelling the dynamics and mass balance of the major ice sheets is therefore an important issue to investigate the current state and the future response of the cryosphere in response to changing environmental conditions, namely global warming. This requires a powerful, easy-to-use, versatile multi-approximation ice dynamics model. Based on the well-known and established ice sheet model of Pattyn (2003) we develop the modular multi-approximation thermomechanic ice model RIMBAY, in which we improve the original version in several aspects like a shallow ice-shallow shelf coupler and a full 3D-grounding-line migration scheme based on Schoof's (2007) heuristic analytical approach. We summarise the full Stokes equations and several approximations implemented within this model and we describe the different numerical discretisations. The results are cross-validated against previous publications dealing with ice modelling, and some additional artificial set-ups demonstrate the robustness of the different solvers and their internal coupling. RIMBAY is designed for an easy adaption to new scientific issues. Hence, we demonstrate in very different set-ups the applicability and functionality of RIMBAY in Earth system science in general and ice modelling in particular.

  14. A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems

    SciTech Connect

    Smith, Kyle K. G.; Poulsen, Jens Aage Nyman, Gunnar; Rossky, Peter J.

    2015-06-28

    We develop two classes of quasi-classical dynamics that are shown to conserve the initial quantum ensemble when used in combination with the Feynman-Kleinert approximation of the density operator. These dynamics are used to improve the Feynman-Kleinert implementation of the classical Wigner approximation for the evaluation of quantum time correlation functions known as Feynman-Kleinert linearized path-integral. As shown, both classes of dynamics are able to recover the exact classical and high temperature limits of the quantum time correlation function, while a subset is able to recover the exact harmonic limit. A comparison of the approximate quantum time correlation functions obtained from both classes of dynamics is made with the exact results for the challenging model problems of the quartic and double-well potentials. It is found that these dynamics provide a great improvement over the classical Wigner approximation, in which purely classical dynamics are used. In a special case, our first method becomes identical to centroid molecular dynamics.

  15. A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems.

    PubMed

    Smith, Kyle K G; Poulsen, Jens Aage; Nyman, Gunnar; Rossky, Peter J

    2015-06-28

    We develop two classes of quasi-classical dynamics that are shown to conserve the initial quantum ensemble when used in combination with the Feynman-Kleinert approximation of the density operator. These dynamics are used to improve the Feynman-Kleinert implementation of the classical Wigner approximation for the evaluation of quantum time correlation functions known as Feynman-Kleinert linearized path-integral. As shown, both classes of dynamics are able to recover the exact classical and high temperature limits of the quantum time correlation function, while a subset is able to recover the exact harmonic limit. A comparison of the approximate quantum time correlation functions obtained from both classes of dynamics is made with the exact results for the challenging model problems of the quartic and double-well potentials. It is found that these dynamics provide a great improvement over the classical Wigner approximation, in which purely classical dynamics are used. In a special case, our first method becomes identical to centroid molecular dynamics.

  16. Application of approximate entropy on dynamic characteristics of epileptic absence seizure☆

    PubMed Central

    Zhou, Yi; Huang, Ruimei; Chen, Ziyi; Chang, Xin; Chen, Jialong; Xie, Lingli

    2012-01-01

    Electroencephalogram signals are time-varying complex electrophysiological signals. Existing studies show that approximate entropy, which is a nonlinear dynamics index, is not an ideal method for electroencephalogram analysis. Clinical electroencephalogram measurements usually contain electrical interference signals, creating additional challenges in terms of maintaining robustness of the analytic methods. There is an urgent need for a novel method of nonlinear dynamical analysis of the electroencephalogram that can characterize seizure-related changes in cerebral dynamics. The aim of this paper was to study the fluctuations of approximate entropy in preictal, ictal, and postictal electroencephalogram signals from a patient with absence seizures, and to improve the algorithm used to calculate the approximate entropy. The approximate entropy algorithm, especially our modified version, could accurately describe the dynamical changes of the brain during absence seizures. We could also demonstrate that the complexity of the brain was greater in the normal state than in the ictal state. The fluctuations of the approximate entropy before epileptic seizures observed in this study can form a good basis for further study on the prediction of seizures with nonlinear dynamics. PMID:25745446

  17. Dynamic approximate entropy electroanatomic maps detect rotors in a simulated atrial fibrillation model.

    PubMed

    Ugarte, Juan P; Orozco-Duque, Andrés; Tobón, Catalina; Kremen, Vaclav; Novak, Daniel; Saiz, Javier; Oesterlein, Tobias; Schmitt, Clauss; Luik, Armin; Bustamante, John

    2014-01-01

    There is evidence that rotors could be drivers that maintain atrial fibrillation. Complex fractionated atrial electrograms have been located in rotor tip areas. However, the concept of electrogram fractionation, defined using time intervals, is still controversial as a tool for locating target sites for ablation. We hypothesize that the fractionation phenomenon is better described using non-linear dynamic measures, such as approximate entropy, and that this tool could be used for locating the rotor tip. The aim of this work has been to determine the relationship between approximate entropy and fractionated electrograms, and to develop a new tool for rotor mapping based on fractionation levels. Two episodes of chronic atrial fibrillation were simulated in a 3D human atrial model, in which rotors were observed. Dynamic approximate entropy maps were calculated using unipolar electrogram signals generated over the whole surface of the 3D atrial model. In addition, we optimized the approximate entropy calculation using two real multi-center databases of fractionated electrogram signals, labeled in 4 levels of fractionation. We found that the values of approximate entropy and the levels of fractionation are positively correlated. This allows the dynamic approximate entropy maps to localize the tips from stable and meandering rotors. Furthermore, we assessed the optimized approximate entropy using bipolar electrograms generated over a vicinity enclosing a rotor, achieving rotor detection. Our results suggest that high approximate entropy values are able to detect a high level of fractionation and to locate rotor tips in simulated atrial fibrillation episodes. We suggest that dynamic approximate entropy maps could become a tool for atrial fibrillation rotor mapping.

  18. A Flexible Distributed Scheduling Scheme for Dynamic ESG Environments

    DTIC Science & Technology

    2006-06-01

    Branke, and H. Abbass, “Multi-objective opti- mization for dynamic environments”, The Artificial Life and Adaptive Robotics Laboratory ALAR Technical...Report Series TR- ALAR -200504007, Northcott Drive, Campbell, Canberra, Aus- tralia, 2005. [27] K. Yamasaki, “Dynamic Pareto optimum GA against the changing

  19. Finite Dimensional Markov Process Approximation for Time-Delayed Stochastic Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Sun, Jian-Qiao

    This paper presents a method of finite dimensional Markov process (FDMP) approximation for stochastic dynamical systems with time delay. The FDMP method preserves the standard state space format of the system, and allows us to apply all the existing methods and theories for analysis and control of stochastic dynamical systems. The paper presents the theoretical framework for stochastic dynamical systems with time delay based on the FDMP method, including the FPK equation, backward Kolmogorov equation, and reliability formulation. The work of this paper opens a door to various studies of stochastic dynamical systems with time delay.

  20. Finite dimensional Markov process approximation for stochastic time-delayed dynamical systems

    NASA Astrophysics Data System (ADS)

    Sun, Jian-Qiao

    2009-05-01

    This paper presents a method of finite dimensional Markov process (FDMP) approximation for stochastic dynamical systems with time delay. The FDMP method preserves the standard state space format of the system, and allows us to apply all the existing methods and theories for analysis and control of stochastic dynamical systems. The paper presents the theoretical framework for stochastic dynamical systems with time delay based on the FDMP method, including the FPK equation, backward Kolmogorov equation, and reliability formulation. A simple one-dimensional stochastic system is used to demonstrate the method and the theory. The work of this paper opens a door to various studies of stochastic dynamical systems with time delay.

  1. A gray-box neural network-based model identification and fault estimation scheme for nonlinear dynamic systems.

    PubMed

    Cen, Zhaohui; Wei, Jiaolong; Jiang, Rui

    2013-12-01

    A novel gray-box neural network model (GBNNM), including multi-layer perception (MLP) neural network (NN) and integrators, is proposed for a model identification and fault estimation (MIFE) scheme. With the GBNNM, both the nonlinearity and dynamics of a class of nonlinear dynamic systems can be approximated. Unlike previous NN-based model identification methods, the GBNNM directly inherits system dynamics and separately models system nonlinearities. This model corresponds well with the object system and is easy to build. The GBNNM is embedded online as a normal model reference to obtain the quantitative residual between the object system output and the GBNNM output. This residual can accurately indicate the fault offset value, so it is suitable for differing fault severities. To further estimate the fault parameters (FPs), an improved extended state observer (ESO) using the same NNs (IESONN) from the GBNNM is proposed to avoid requiring the knowledge of ESO nonlinearity. Then, the proposed MIFE scheme is applied for reaction wheels (RW) in a satellite attitude control system (SACS). The scheme using the GBNNM is compared with other NNs in the same fault scenario, and several partial loss of effect (LOE) faults with different severities are considered to validate the effectiveness of the FP estimation and its superiority.

  2. Improved free-energy interpolation scheme for obtaining gas-phase reaction rates from ring-polymer molecular dynamics

    NASA Astrophysics Data System (ADS)

    Stecher, Thomas; Althorpe, Stuart C.

    2012-05-01

    Quantum reaction rates for bimolecular gas-phase reactions can be computed efficiently and to a realistic degree of approximation by applying ring-polymer molecular dynamics within a free-energy interpolation scheme [R. Collepardo-Guevara, Y.V. Suleimanov, and D.E. Manolopoulos, J. Chem. Phys. 130, 174713 (2009)]. Here, we present modifications to this scheme which simplify the implementation of the method, and have the advantage of yielding directly the free-energy as a function of the interpolation coordinate. We also take the opportunity to verify the benchmark results obtained for the H + H2 and Cl + HCl reactions by Collepardo-Guevara et al., obtaining excellent agreement for H + H2 and reasonable agreement for Cl + HCl.

  3. A novel data hiding scheme for block truncation coding compressed images using dynamic programming strategy

    NASA Astrophysics Data System (ADS)

    Chang, Ching-Chun; Liu, Yanjun; Nguyen, Son T.

    2015-03-01

    Data hiding is a technique that embeds information into digital cover data. This technique has been concentrated on the spatial uncompressed domain, and it is considered more challenging to perform in the compressed domain, i.e., vector quantization, JPEG, and block truncation coding (BTC). In this paper, we propose a new data hiding scheme for BTC-compressed images. In the proposed scheme, a dynamic programming strategy was used to search for the optimal solution of the bijective mapping function for LSB substitution. Then, according to the optimal solution, each mean value embeds three secret bits to obtain high hiding capacity with low distortion. The experimental results indicated that the proposed scheme obtained both higher hiding capacity and hiding efficiency than the other four existing schemes, while ensuring good visual quality of the stego-image. In addition, the proposed scheme achieved a low bit rate as original BTC algorithm.

  4. Dynamics of optical solitons in dual-core fibers via two integration schemes

    NASA Astrophysics Data System (ADS)

    Arnous, A. H.; Mahmood, S. A.; Younis, M.

    2017-06-01

    This article studies the dynamics of optical solitons in dual-core fibers with group velocity mismatch, group velocity dispersion and linear coupling coefficient under Kerr law nonlinearity via two integration schemes, namely, Q-function scheme and trial solution approach. The Q-function scheme extracts dark and singular 1-soliton solutions, along with the corresponding existence restriction. This scheme, however, fails to retrieve bright 1-soliton solution. Moreover, the trial solution approach extracts bright, dark and singular 1-soliton solutions. The constraint conditions, for the existence of the soliton solutions, are also listed. Additionally, a couple of other solutions known as singular periodic solutions, fall out as a by-product of this scheme. The obtained results have potential applications in the study of solitons based optical communication.

  5. Enhanced studies on a composite time integration scheme in linear and non-linear dynamics

    NASA Astrophysics Data System (ADS)

    Klarmann, S.; Wagner, W.

    2015-03-01

    In Bathe and Baig (Comput Struct 83:2513-2524, 2005), Bathe (Comput Struct 85:437-445, 2007), Bathe and Noh (Comput Struct 98-99:1-6, 2012) Bathe et al. have proposed a composite implicit time integration scheme for non-linear dynamic problems. This paper is aimed at the further investigation of the scheme's behaviour for use in case of linear and non-linear problems. Therefore, the examination of the amplification matrix of the scheme will be extended in order to get in addition the properties for linear calculations. Besides, it will be demonstrated that the integration scheme also has an impact on some of these properties when used for non-linear calculations. In conclusion, a recommendation for the only selectable parameter of the scheme will be given for application in case of geometrically non-linear calculations.

  6. Approximate-model based estimation method for dynamic response of forging processes

    NASA Astrophysics Data System (ADS)

    Lei, Jie; Lu, Xinjiang; Li, Yibo; Huang, Minghui; Zou, Wei

    2015-03-01

    Many high-quality forging productions require the large-sized hydraulic press machine (HPM) to have a desirable dynamic response. Since the forging process is complex under the low velocity, its response is difficult to estimate. And this often causes the desirable low-velocity forging condition difficult to obtain. So far little work has been found to estimate the dynamic response of the forging process under low velocity. In this paper, an approximate-model based estimation method is proposed to estimate the dynamic response of the forging process under low velocity. First, an approximate model is developed to represent the forging process of this complex HPM around the low-velocity working point. Under guaranteeing the modeling performance, the model may greatly ease the complexity of the subsequent estimation of the dynamic response because it has a good linear structure. On this basis, the dynamic response is estimated and the conditions for stability, vibration, and creep are derived according to the solution of the velocity. All these analytical results are further verified by both simulations and experiment. In the simulation verification for modeling, the original movement model and the derived approximate model always have the same dynamic responses with very small approximate error. The simulations and experiment finally demonstrate and test the effectiveness of the derived conditions for stability, vibration, and creep, and these conditions will benefit both the prediction of the dynamic response of the forging process and the design of the controller for the high-quality forging. The proposed method is an effective solution to achieve the desirable low-velocity forging condition.

  7. TVD scheme for stiff problems of wave dynamics of heterogeneous media of nonhyperbolic nonconservative type

    NASA Astrophysics Data System (ADS)

    Sadin, D. V.

    2016-12-01

    A finite-difference TVD scheme is presented for problems in nonequilibrium wave dynamics of heterogeneous media with different velocities and temperatures but with identical pressures of the phases. A nonlinear form of artificial viscosity depending on the phase relaxation time is proposed. The computed solutions are compared with exact self-similar ones for an equilibrium heterogeneous medium. The performance of the scheme is demonstrated by numerical simulation with varying particle diameters, grid sizes, and particle concentrations. It is shown that the scheme is efficient in terms of Fletcher's criterion as applied to stiff problems.

  8. New parallelizable schemes for integrating the Dissipative Particle Dynamics with Energy conservation.

    PubMed

    Homman, Ahmed-Amine; Maillet, Jean-Bernard; Roussel, Julien; Stoltz, Gabriel

    2016-01-14

    This work presents new parallelizable numerical schemes for the integration of dissipative particle dynamics with energy conservation. So far, no numerical scheme introduced in the literature is able to correctly preserve the energy over long times and give rise to small errors on average properties for moderately small time steps, while being straightforwardly parallelizable. We present in this article two new methods, both straightforwardly parallelizable, allowing to correctly preserve the total energy of the system. We illustrate the accuracy and performance of these new schemes both on equilibrium and nonequilibrium parallel simulations.

  9. Error estimates for approximate dynamic systems. [linear and nonlinear control systems of different dimensions

    NASA Technical Reports Server (NTRS)

    Gunderson, R. W.; George, J. H.

    1974-01-01

    Two approaches are investigated for obtaining estimates on the error between approximate and exact solutions of dynamic systems. The first method is primarily useful if the system is nonlinear and of low dimension. The second requires construction of a system of v-functions but is useful for higher dimensional systems, either linear or nonlinear.

  10. Error estimates for approximate dynamic systems. [linear and nonlinear control systems of different dimensions

    NASA Technical Reports Server (NTRS)

    Gunderson, R. W.; George, J. H.

    1974-01-01

    Two approaches are investigated for obtaining estimates on the error between approximate and exact solutions of dynamic systems. The first method is primarily useful if the system is nonlinear and of low dimension. The second requires construction of a system of v-functions but is useful for higher dimensional systems, either linear or nonlinear.

  11. Kinetic description of ionospheric dynamics in the three-fluid approximation

    NASA Technical Reports Server (NTRS)

    Comfort, R. H.

    1975-01-01

    Conservation equations are developed in the three-fluid approximation for general application problems of ionospheric dynamics in the altitude region 90 km to 800 km for all geographic locations. These equations are applied to a detailed study of auroral E region neutral winds and their relationship to ionospheric plasma motions.

  12. Hamilton-Jacobi-Bellman equations and approximate dynamic programming on time scales.

    PubMed

    Seiffertt, John; Sanyal, Suman; Wunsch, Donald C

    2008-08-01

    The time scales calculus is a key emerging area of mathematics due to its potential use in a wide variety of multidisciplinary applications. We extend this calculus to approximate dynamic programming (ADP). The core backward induction algorithm of dynamic programming is extended from its traditional discrete case to all isolated time scales. Hamilton-Jacobi-Bellman equations, the solution of which is the fundamental problem in the field of dynamic programming, are motivated and proven on time scales. By drawing together the calculus of time scales and the applied area of stochastic control via ADP, we have connected two major fields of research.

  13. Implicit - symplectic partitioned (IMSP) Runge-Kutta schemes for predator-prey dynamics

    NASA Astrophysics Data System (ADS)

    Diele, F.; Marangi, C.; Ragni, S.

    2012-09-01

    In the study of the effects of habitat fragmentation on biodiversity the role of spatial processes reveals of great interest since both the variation of size of the domains as well as their heterogeneity largely affects the dynamics of species. In order to begin a preliminary study about the effects of habitat fragmentation on wolf - wild boar pair populating the Italian "Alta Murgia" Natura 2000 site, object of interest for FP7 project BIOSOS, (BIOdiversity multi-SOurce Monitoring System: from Space TO Species), spatially explicit models described by reaction-diffusion partial differential equations are considered. Numerical methods based on partitioned Runge-Kutta schemes which use an implicit scheme for the stiff diffusive term and a partitioned symplectic scheme for the reaction function are here proposed. We are motivated by the classical results about Lotka-Volterra model described by ordinary differential equations to which the spatially explicit model reduces for diffusion coefficients tending to zero: for their accurate solution symplectic schemes have to be used for an optimal long run preservation of the dynamics invariant. Moreover, for models based on logistic growth and Holling type II functional predator response we verify the better performance of our schemes when compared with classical implicit-explicit (IMEX) schemes on chaotic dynamics given in literature.

  14. A quartic B-spline based explicit time integration scheme for structural dynamics with controllable numerical dissipation

    NASA Astrophysics Data System (ADS)

    Wen, W. B.; Duan, S. Y.; Yan, J.; Ma, Y. B.; Wei, K.; Fang, D. N.

    2017-03-01

    An explicit time integration scheme based on quartic B-splines is presented for solving linear structural dynamics problems. The scheme is of a one-parameter family of schemes where free algorithmic parameter controls stability, accuracy and numerical dispersion. The proposed scheme possesses at least second-order accuracy and at most third-order accuracy. A 2D wave problem is analyzed to demonstrate the effectiveness of the proposed scheme in reducing high-frequency modes and retaining low-frequency modes. Except for general structural dynamics, the proposed scheme can be used effectively for wave propagation problems in which numerical dissipation is needed to reduce spurious oscillations.

  15. A Dynamic Probabilistic Based Broadcasting Scheme for MANETs

    PubMed Central

    Shanmugam, Kannan; Subburathinam, Karthik; Velayuthampalayam Palanisamy, Arunachalam

    2016-01-01

    MANET is commonly known as Mobile Ad Hoc Network in which cluster of mobile nodes can communicate with each other without having any basic infrastructure. The basic characteristic of MANET is dynamic topology. Due to the dynamic behavior nature, the topology of the network changes very frequently, and this will lead to the failure of the valid route repeatedly. Thus, the process of finding the valid route leads to notable drop in the throughput of the network. To identify a new valid path to the targeted mobile node, available proactive routing protocols use simple broadcasting method known as simple flooding. The simple flooding method broadcasts the RREQ packet from the source to the rest of the nodes in mobile network. But the problem with this method is disproportionate repetitive retransmission of RREQ packet which could result in high contention on the available channel and packet collision due to extreme traffic in the network. A reasonable number of routing algorithms have been suggested for reducing the lethal impact of flooding the RREQ packets. However, most of the algorithms have resulted in considerable amount of complexity and deduce the throughput by depending on special hardware components and maintaining complex information which will be less frequently used. By considering routing complexity with the goal of increasing the throughput of the network, in this paper, we have introduced a new approach called Dynamic Probabilistic Route (DPR) discovery. The Node's Forwarding Probability (NFP) is dynamically calculated by the DPR mobile nodes using Probability Function (PF) which depends on density of local neighbor nodes and the cumulative number of its broadcast covered neighbors. PMID:27019868

  16. A Dynamic Probabilistic Based Broadcasting Scheme for MANETs.

    PubMed

    Shanmugam, Kannan; Subburathinam, Karthik; Palanisamy, Arunachalam Velayuthampalayam

    2016-01-01

    MANET is commonly known as Mobile Ad Hoc Network in which cluster of mobile nodes can communicate with each other without having any basic infrastructure. The basic characteristic of MANET is dynamic topology. Due to the dynamic behavior nature, the topology of the network changes very frequently, and this will lead to the failure of the valid route repeatedly. Thus, the process of finding the valid route leads to notable drop in the throughput of the network. To identify a new valid path to the targeted mobile node, available proactive routing protocols use simple broadcasting method known as simple flooding. The simple flooding method broadcasts the RREQ packet from the source to the rest of the nodes in mobile network. But the problem with this method is disproportionate repetitive retransmission of RREQ packet which could result in high contention on the available channel and packet collision due to extreme traffic in the network. A reasonable number of routing algorithms have been suggested for reducing the lethal impact of flooding the RREQ packets. However, most of the algorithms have resulted in considerable amount of complexity and deduce the throughput by depending on special hardware components and maintaining complex information which will be less frequently used. By considering routing complexity with the goal of increasing the throughput of the network, in this paper, we have introduced a new approach called Dynamic Probabilistic Route (DPR) discovery. The Node's Forwarding Probability (NFP) is dynamically calculated by the DPR mobile nodes using Probability Function (PF) which depends on density of local neighbor nodes and the cumulative number of its broadcast covered neighbors.

  17. The NSVZ scheme for N = 1 SQED with Nf flavors, regularized by the dimensional reduction, in the three-loop approximation

    NASA Astrophysics Data System (ADS)

    Aleshin, S. S.; Goriachuk, I. O.; Kataev, A. L.; Stepanyantz, K. V.

    2017-01-01

    At the three-loop level we analyze, how the NSVZ relation appears for N = 1 SQED regularized by the dimensional reduction. This is done by the method analogous to the one which was earlier used for the theories regularized by higher derivatives. Within the dimensional technique, the loop integrals cannot be written as integrals of double total derivatives. However, similar structures can be written in the considered approximation and are taken as a starting point. Then we demonstrate that, unlike the higher derivative regularization, the NSVZ relation is not valid for the renormalization group functions defined in terms of the bare coupling constant. However, for the renormalization group functions defined in terms of the renormalized coupling constant, it is possible to impose boundary conditions to the renormalization constants giving the NSVZ scheme in the three-loop order. They are similar to the all-loop ones defining the NSVZ scheme obtained with the higher derivative regularization, but are more complicated. The NSVZ schemes constructed with the dimensional reduction and with the higher derivative regularization are related by a finite renormalization in the considered approximation.

  18. Dislocation climb models from atomistic scheme to dislocation dynamics

    NASA Astrophysics Data System (ADS)

    Niu, Xiaohua; Luo, Tao; Lu, Jianfeng; Xiang, Yang

    2017-02-01

    We develop a mesoscopic dislocation dynamics model for vacancy-assisted dislocation climb by upscalings from a stochastic model on the atomistic scale. Our models incorporate microscopic mechanisms of (i) bulk diffusion of vacancies, (ii) vacancy exchange dynamics between bulk and dislocation core, (iii) vacancy pipe diffusion along the dislocation core, and (iv) vacancy attachment-detachment kinetics at jogs leading to the motion of jogs. Our mesoscopic model consists of the vacancy bulk diffusion equation and a dislocation climb velocity formula. The effects of these microscopic mechanisms are incorporated by a Robin boundary condition near the dislocations for the bulk diffusion equation and a new contribution in the dislocation climb velocity due to vacancy pipe diffusion driven by the stress variation along the dislocation. Our climb formulation is able to quantitatively describe the translation of prismatic loops at low temperatures when the bulk diffusion is negligible. Using this new formulation, we derive analytical formulas for the climb velocity of a straight edge dislocation and a prismatic circular loop. Our dislocation climb formulation can be implemented in dislocation dynamics simulations to incorporate all the above four microscopic mechanisms of dislocation climb.

  19. A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition

    NASA Astrophysics Data System (ADS)

    Williams, Matthew O.; Kevrekidis, Ioannis G.; Rowley, Clarence W.

    2015-12-01

    The Koopman operator is a linear but infinite-dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system and is a powerful tool for the analysis and decomposition of nonlinear dynamical systems. In this manuscript, we present a data-driven method for approximating the leading eigenvalues, eigenfunctions, and modes of the Koopman operator. The method requires a data set of snapshot pairs and a dictionary of scalar observables, but does not require explicit governing equations or interaction with a "black box" integrator. We will show that this approach is, in effect, an extension of dynamic mode decomposition (DMD), which has been used to approximate the Koopman eigenvalues and modes. Furthermore, if the data provided to the method are generated by a Markov process instead of a deterministic dynamical system, the algorithm approximates the eigenfunctions of the Kolmogorov backward equation, which could be considered as the "stochastic Koopman operator" (Mezic in Nonlinear Dynamics 41(1-3): 309-325, 2005). Finally, four illustrative examples are presented: two that highlight the quantitative performance of the method when presented with either deterministic or stochastic data and two that show potential applications of the Koopman eigenfunctions.

  20. Application of TVD schemes for the Euler equations of gas dynamics. [method of Total Variation Diminishing for shock wave computation

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Warming, R. F.; Harten, A.

    1985-01-01

    Highly accurate and yet stable shock-capturing finite difference schemes have been designed for the computation of the Euler equations of gas dynamics. Four different principles for the construction of high resolution total variation diminishing (TVD) schemes are available, including hybrid schemes, a second-order extension of Godunov's scheme by van Leer (1979), the modified flux approach of Harten (1983, 1984), and the numerical fluctuation approach of Roe (1985). The present paper has the objective to review the class of second-order TVD schemes via the modified flux approach. Attention is given to first-order TVD schemes, a second-order accurate explicit TVD scheme, the global order of accuracy of the second-order TVD scheme, extensions to systems and two-dimensional conservation laws, numerical experiments with a second-order explicit TVD scheme, implicit TVD schemes, and second-order implicit TVD schemes.

  1. An efficient and secure dynamic ID-based authentication scheme for telecare medical information systems.

    PubMed

    Chen, Hung-Ming; Lo, Jung-Wen; Yeh, Chang-Kuo

    2012-12-01

    The rapidly increased availability of always-on broadband telecommunication environments and lower-cost vital signs monitoring devices bring the advantages of telemedicine directly into the patient's home. Hence, the control of access to remote medical servers' resources has become a crucial challenge. A secure authentication scheme between the medical server and remote users is therefore needed to safeguard data integrity, confidentiality and to ensure availability. Recently, many authentication schemes that use low-cost mobile devices have been proposed to meet these requirements. In contrast to previous schemes, Khan et al. proposed a dynamic ID-based remote user authentication scheme that reduces computational complexity and includes features such as a provision for the revocation of lost or stolen smart cards and a time expiry check for the authentication process. However, Khan et al.'s scheme has some security drawbacks. To remedy theses, this study proposes an enhanced authentication scheme that overcomes the weaknesses inherent in Khan et al.'s scheme and demonstrated this scheme is more secure and robust for use in a telecare medical information system.

  2. Dynamical real-space renormalization group calculations with a highly connected clustering scheme on disordered networks.

    PubMed

    Balcan, D; Erzan, A

    2005-02-01

    We have defined a type of clustering scheme preserving the connectivity of the nodes in a network, ignored by the conventional Migdal-Kadanoff bond moving process. In high dimensions, our clustering scheme performs better for correlation length and dynamical critical exponents than the conventional Migdal-Kadanoff bond moving scheme. In two and three dimensions we find the dynamical critical exponents for the kinetic Ising model to be z=2.13 and z=2.09 , respectively, at the pure Ising fixed point. These values are in very good agreement with recent Monte Carlo results. We investigate the phase diagram and the critical behavior of randomly bond diluted lattices in d=2 and 3 in the light of this transformation. We also provide exact correlation exponent and dynamical critical exponent values on hierarchical lattices with power-law and Poissonian degree distributions.

  3. Ballistic-diffusive approximation for the thermal dynamics of metallic nanoparticles in nanocomposite materials

    SciTech Connect

    Shirdel-Havar, A. H. Masoudian Saadabad, R.

    2015-03-21

    Based on ballistic-diffusive approximation, a method is presented to model heat transfer in nanocomposites containing metal nanoparticles. This method provides analytical expression for the temperature dynamics of metallic nanoparticles embedded in a dielectric medium. In this study, nanoparticles are considered as spherical shells, so that Boltzmann equation is solved using ballistic-diffusive approximation to calculate the electron and lattice thermal dynamics in gold nanoparticles, while thermal exchange between the particles is taken into account. The model was used to investigate the influence of particle size and metal concentration of the medium on the electron and lattice thermal dynamics. It is shown that these two parameters are crucial in determining the nanocomposite thermal behavior. Our results showed that the heat transfer rate from nanoparticles to the matrix decreases as the nanoparticle size increases. On the other hand, increasing the metal concentration of the medium can also decrease the heat transfer rate.

  4. A novel dynamic wavelength bandwidth allocation scheme over OFDMA PONs

    NASA Astrophysics Data System (ADS)

    Yan, Bo; Guo, Wei; Jin, Yaohui; Hu, Weisheng

    2011-12-01

    With rapid growth of Internet applications, supporting differentiated service and enlarging system capacity have been new tasks for next generation access system. In recent years, research in OFDMA Passive Optical Networks (PON) has experienced extraordinary development as for its large capacity and flexibility in scheduling. Although much work has been done to solve hardware layer obstacles for OFDMA PON, scheduling algorithm on OFDMA PON system is still under primary discussion. In order to support QoS service on OFDMA PON system, a novel dynamic wavelength bandwidth allocation (DWBA) algorithm is proposed in this paper. Per-stream QoS service is supported in this algorithm. Through simulation, we proved our bandwidth allocation algorithm performs better in bandwidth utilization and differentiate service support.

  5. Approximate Inference for Time-Varying Interactions and Macroscopic Dynamics of Neural Populations

    PubMed Central

    Obermayer, Klaus

    2017-01-01

    The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or anesthetized animals. However, modeling activity of cortical circuitries of awake animals has been more challenging because both spike-rates and interactions can change according to sensory stimulation, behavior, or an internal state of the brain. Previous approaches modeling the dynamics of neural interactions suffer from computational cost; therefore, its application was limited to only a dozen neurons. Here by introducing multiple analytic approximation methods to a state-space model of neural population activity, we make it possible to estimate dynamic pairwise interactions of up to 60 neurons. More specifically, we applied the pseudolikelihood approximation to the state-space model, and combined it with the Bethe or TAP mean-field approximation to make the sequential Bayesian estimation of the model parameters possible. The large-scale analysis allows us to investigate dynamics of macroscopic properties of neural circuitries underlying stimulus processing and behavior. We show that the model accurately estimates dynamics of network properties such as sparseness, entropy, and heat capacity by simulated data, and demonstrate utilities of these measures by analyzing activity of monkey V4 neurons as well as a simulated balanced network of spiking neurons. PMID:28095421

  6. The effective medium and the average field approximations vis-à-vis the Hashin-Shtrikman bounds. I. The self-consistent scheme in matrix-based composites

    NASA Astrophysics Data System (ADS)

    Benveniste, Y.; Milton, G. W.

    2010-07-01

    The effective medium approximation (EMA) and the average field approximation (AFA) are two classical micromechanics models for the determination of effective properties of heterogeneous media. They are also known in the literature as 'self-consistent' approximations. In the AFA, the basic idea is to estimate the actual average field existing in a phase through a configuration in which a typical particle of that phase is embedded in the homogenized medium. In the EMA, on the other hand, one or more representative microstructural elements of the composite is embedded in the homogenized effective medium subjected to a uniform field, and the demand is made that the dominant part of the far-field disturbance vanishes. Both parts of this study are concerned with two-phase, matrix-based, effectively isotropic composites with an inclusion phase consisting of randomly oriented particles of arbitrary shape in general, and ellipsoidal shape in particular. The constituent phases are assumed to be isotropic. It is shown that in those systems the AFA and EMA give different predictions, with the distinction between them becoming especially striking regarding their standing vis-à-vis the Hashin-Shtrikman (HS-bounds). While due to its realizability property the EMA will always obey the bounds, we show that there are circumstances in which the AFA may violate the bounds. In the AFA for two-phase matrix-based composites, the embedded inclusion is a particle of the inclusion phase. If the particle is directly embedded in the effective medium, the method is called here the self-consistent scheme-average field approximation (SCS-AFA), and will obey the HS-bounds for an inclusion shape that is simply connected. If the embedded entity is a matrix-coated particle, then the method is called the generalized self-consistent scheme-average field approximation (GSCS-AFA), and may violate the HS-bounds. On the other hand, in the EMA for matrix-based composites with well-separated inclusions, we

  7. Dynamics of zonal flows: failure of wave-kinetic theory, and new geometrical optics approximations

    NASA Astrophysics Data System (ADS)

    Parker, Jeffrey B.

    2016-12-01

    The self-organisation of turbulence into regular zonal flows can be fruitfully investigated with quasi-linear methods and statistical descriptions. A wave-kinetic equation that assumes asymptotically large-scale zonal flows leads to ultraviolet divergence. From an exact description of quasi-linear dynamics emerges two better geometrical optics approximations. These involve not only the mean flow shear but also the second and third derivative of the mean flow. One approximation takes the form of a new wave-kinetic equation, but is only valid when the zonal flow is quasi-static and wave action is conserved.

  8. Excitonic Insulator State of the Extended Falicov-Kimball Model in the Cluster Dynamical Impurity Approximation

    NASA Astrophysics Data System (ADS)

    Hamada, Kosuke; Kaneko, Tatsuya; Miyakoshi, Shohei; Ohta, Yukinori

    2017-07-01

    We comparatively study the excitonic insulator state in the extended Falicov-Kimball model (EFKM, a spinless two-band model) on the two-dimensional square lattice using the variational cluster approximation (VCA) and the cluster dynamical impurity approximation (CDIA). In the latter, the particle-bath sites are included in the reference cluster to take into account the particle-number fluctuations in the correlation sites. We thus calculate the particle-number distribution, order parameter, ground-state phase diagram, anomalous Green's function, and pair coherence length, thereby demonstrating the usefulness of the CDIA in the discussion of the excitonic condensation in the EFKM.

  9. The truncated Wigner approximation for spin dynamics in systems of trapped ions, atoms & molecules

    NASA Astrophysics Data System (ADS)

    Schachenmayer, Johannes; Zhu, Bihui; Pikovski, Alexander; Hazzard, Kaden; Holland, Murray; Rey, Ana Maria

    2014-05-01

    Trapped ions and systems of cold atoms or molecules in optical lattices offer controlled environments to experimentally study non-equilibrium dynamics of many-body quantum spin-models with interactions of varying range. Theoretically calculating dynamics of observables for these experiments is a major challenge both analytically and numerically. While in one dimension, time-dependent density matrix renormalization group techniques (t-DMRG) allow for an efficient simulation of the dynamics as long as the time-dependent bi-partite entanglement growth remains moderate, a simulation for systems in two or three dimensions is more demanding. Here we present a numerical technique, which employs the truncated Wigner approximation (TWA) and which can be used to simulate Ramsey-dynamics for current experiments with trapped ions, alkaline earth atoms, polar molecules in optical lattices, or for systems with Rydberg atoms.

  10. Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics.

    PubMed

    Montoya-Castillo, Andrés; Reichman, David R

    2016-05-14

    We present a formalism that explicitly unifies the commonly used Nakajima-Zwanzig approach for reduced density matrix dynamics with the more versatile Mori theory in the context of nonequilibrium dynamics. Employing a Dyson-type expansion to circumvent the difficulty of projected dynamics, we obtain a self-consistent equation for the memory kernel which requires only knowledge of normally evolved auxiliary kernels. To illustrate the properties of the current approach, we focus on the spin-boson model and limit our attention to the use of a simple and inexpensive quasi-classical dynamics, given by the Ehrenfest method, for the calculation of the auxiliary kernels. For the first time, we provide a detailed analysis of the dependence of the properties of the memory kernels obtained via different projection operators, namely, the thermal (Redfield-type) and population based (NIBA-type) projection operators. We further elucidate the conditions that lead to short-lived memory kernels and the regions of parameter space to which this program is best suited. Via a thorough analysis of the different closures available for the auxiliary kernels and the convergence properties of the self-consistently extracted memory kernel, we identify the mechanisms whereby the current approach leads to a significant improvement over the direct usage of standard semi- and quasi-classical dynamics.

  11. Dynamic load balance scheme for the DSMC algorithm

    SciTech Connect

    Li, Jin; Geng, Xiangren; Jiang, Dingwu; Chen, Jianqiang

    2014-12-09

    The direct simulation Monte Carlo (DSMC) algorithm, devised by Bird, has been used over a wide range of various rarified flow problems in the past 40 years. While the DSMC is suitable for the parallel implementation on powerful multi-processor architecture, it also introduces a large load imbalance across the processor array, even for small examples. The load imposed on a processor by a DSMC calculation is determined to a large extent by the total of simulator particles upon it. Since most flows are impulsively started with initial distribution of particles which is surely quite different from the steady state, the total of simulator particles will change dramatically. The load balance based upon an initial distribution of particles will break down as the steady state of flow is reached. The load imbalance and huge computational cost of DSMC has limited its application to rarefied or simple transitional flows. In this paper, by taking advantage of METIS, a software for partitioning unstructured graphs, and taking the total of simulator particles in each cell as a weight information, the repartitioning based upon the principle that each processor handles approximately the equal total of simulator particles has been achieved. The computation must pause several times to renew the total of simulator particles in each processor and repartition the whole domain again. Thus the load balance across the processors array holds in the duration of computation. The parallel efficiency can be improved effectively. The benchmark solution of a cylinder submerged in hypersonic flow has been simulated numerically. Besides, hypersonic flow past around a complex wing-body configuration has also been simulated. The results have displayed that, for both of cases, the computational time can be reduced by about 50%.

  12. Assessing the influence of electrostatic schemes on molecular dynamics simulations of secondary structure forming peptides

    NASA Astrophysics Data System (ADS)

    Monticelli, Luca; Simões, Carlos; Belvisi, Laura; Colombo, Giorgio

    2006-04-01

    Electrostatic interactions play a fundamental role in determining the structure and dynamics of biomolecules in solution. However the accurate representation of electrostatics in classical mechanics based simulation approaches such as molecular dynamics (MD) is a challenging task. Given the growing importance that MD simulation methods are taking on in the study of protein folding, protein stability and dynamics, and in structure prediction and design projects, it is important to evaluate the influence that different electrostatic schemes have on the results of MD simulations. In this paper we performed long timescale simulations (500 ns) of two peptides, beta3 and RN24 forming different secondary structures, using for each peptide four different electrostatic schemes (namely PME, reaction field correction, and cut-off schemes with and without neutralizing counterions) for a total of eight 500 ns long MD runs. The structural and conformational features of each peptide under the different conditions were evaluated in terms of the time dependence of the flexibility, secondary structure evolution, hydrogen-bonding patterns, and several other structural parameters. The degree of sampling for each simulation as a function of the electrostatic scheme was also critically evaluated. Our results suggest that, while in the case of the short peptide RN24 the performances of the four methods are comparable, PME and RF schemes perform better in maintaining the structure close to the native one for the β-sheet peptide beta3, in which long range contacts are mostly responsible for the definition of the native structure.

  13. On the security of a dynamic ID-based authentication scheme for telecare medical information systems.

    PubMed

    Lin, Han-Yu

    2013-04-01

    Telecare medical information systems (TMISs) are increasingly popular technologies for healthcare applications. Using TMISs, physicians and caregivers can monitor the vital signs of patients remotely. Since the database of TMISs stores patients' electronic medical records (EMRs), only authorized users should be granted the access to this information for the privacy concern. To keep the user anonymity, recently, Chen et al. proposed a dynamic ID-based authentication scheme for telecare medical information system. They claimed that their scheme is more secure and robust for use in a TMIS. However, we will demonstrate that their scheme fails to satisfy the user anonymity due to the dictionary attacks. It is also possible to derive a user password in case of smart card loss attacks. Additionally, an improved scheme eliminating these weaknesses is also presented.

  14. Dynamic behaviors of approximately ellipsoidal microbubbles photothermally generated by a graphene oxide-microheater

    PubMed Central

    Xing, Xiaobo; Zheng, Jiapeng; Li, Fengjia; Sun, Chao; Cai, Xiang; Zhu, Debin; Lei, Liang; Wu, Ting; Zhou, Bin; Evans, Julian; Chen, Ziyi

    2014-01-01

    Thermal microbubbles generally grow directly from the heater and are spherical to minimize surface tension. We demonstrate a novel type of microbubble indirectly generated from a graphene oxide-microheater. Graphene oxide's photothermal properties allowed for efficient generation of a thermal gradient field on the microscale. A series of approximately ellipsoidal microbubbles were generated on the smooth microwire based on heterogeneous nucleation. Other dynamic behaviors induced by the microheater such as constant growth, directional transport and coalescence were also investigated experimentally and theoretically. The results are not only helpful for understanding the bubble dynamics but also useful for developing novel photothermal bubble-based devices. PMID:25124694

  15. Approximate Analysis of Dynamic Characteristics of Short Journal Bearings in Turbulent Micropolar Lubrication

    NASA Astrophysics Data System (ADS)

    Rana, N. K.; Gautam, S. S.; Samanta, S.

    2014-10-01

    An approximate analysis has been carried out for short journal bearing to determine the dynamic behavior under micropolar turbulent flow condition. In this analysis, the Constantinescu's turbulent shear coefficient has been considered, which was later proposed by Taylor and Dowson. For the calculation of dynamic pressures, the classical Reynolds equation has been modified to incorporate turbulence and micropolar fluid parameters. The analysis has been further extended to determine the mass and whirl parameters to analyze the stability of the bearing. The bearing is found to be more stable with increase in eccentricity with high speed and large Reynolds number.

  16. Action versus result-oriented schemes in a grassland agroecosystem: a dynamic modelling approach.

    PubMed

    Sabatier, Rodolphe; Doyen, Luc; Tichit, Muriel

    2012-01-01

    Effects of agri-environment schemes (AES) on biodiversity remain controversial. While most AES are action-oriented, result-oriented and habitat-oriented schemes have recently been proposed as a solution to improve AES efficiency. The objective of this study was to compare action-oriented, habitat-oriented and result-oriented schemes in terms of ecological and productive performance as well as in terms of management flexibility. We developed a dynamic modelling approach based on the viable control framework to carry out a long term assessment of the three schemes in a grassland agroecosystem. The model explicitly links grazed grassland dynamics to bird population dynamics. It is applied to lapwing conservation in wet grasslands in France. We ran the model to assess the three AES scenarios. The model revealed the grazing strategies respecting ecological and productive constraints specific to each scheme. Grazing strategies were assessed by both their ecological and productive performance. The viable control approach made it possible to obtain the whole set of viable grazing strategies and therefore to quantify the management flexibility of the grassland agroecosystem. Our results showed that habitat and result-oriented scenarios led to much higher ecological performance than the action-oriented one. Differences in both ecological and productive performance between the habitat and result-oriented scenarios were limited. Flexibility of the grassland agroecosystem in the result-oriented scenario was much higher than in that of habitat-oriented scenario. Our model confirms the higher flexibility as well as the better ecological and productive performance of result-oriented schemes. A larger use of result-oriented schemes in conservation may also allow farmers to adapt their management to local conditions and to climatic variations.

  17. Action versus Result-Oriented Schemes in a Grassland Agroecosystem: A Dynamic Modelling Approach

    PubMed Central

    Sabatier, Rodolphe; Doyen, Luc; Tichit, Muriel

    2012-01-01

    Effects of agri-environment schemes (AES) on biodiversity remain controversial. While most AES are action-oriented, result-oriented and habitat-oriented schemes have recently been proposed as a solution to improve AES efficiency. The objective of this study was to compare action-oriented, habitat-oriented and result-oriented schemes in terms of ecological and productive performance as well as in terms of management flexibility. We developed a dynamic modelling approach based on the viable control framework to carry out a long term assessment of the three schemes in a grassland agroecosystem. The model explicitly links grazed grassland dynamics to bird population dynamics. It is applied to lapwing conservation in wet grasslands in France. We ran the model to assess the three AES scenarios. The model revealed the grazing strategies respecting ecological and productive constraints specific to each scheme. Grazing strategies were assessed by both their ecological and productive performance. The viable control approach made it possible to obtain the whole set of viable grazing strategies and therefore to quantify the management flexibility of the grassland agroecosystem. Our results showed that habitat and result-oriented scenarios led to much higher ecological performance than the action-oriented one. Differences in both ecological and productive performance between the habitat and result-oriented scenarios were limited. Flexibility of the grassland agroecosystem in the result-oriented scenario was much higher than in that of habitat-oriented scenario. Our model confirms the higher flexibility as well as the better ecological and productive performance of result-oriented schemes. A larger use of result-oriented schemes in conservation may also allow farmers to adapt their management to local conditions and to climatic variations. PMID:22496746

  18. Dynamic demonstration of diffractive optic analog-to-digital converter scheme.

    PubMed

    Galt, Sheila; Magnusson, Anders; Hård, Sverker

    2003-01-10

    Dynamic behavior of an analog-to-digital converter (ADC) based on diffractive optical element(s) (DOE)(s) was studied and found to be in agreement with predictions. The analog signal was translated to an angular deflection of a laser beam by means of an acousto-optic (AO) cell. The number of bits in this experimental demonstration was three, using an eight-element DOE array. The maximum sample rate was found to be 2.5 MS/s, the limiting factor being the transit time for the acoustic wave across the width of the laser beam in the AO cell. The study is intended as a first dynamic demonstration of a proposed ADC scheme previously demonstrated in a quasi-static version. The full potential of the ADC scheme will require the use of a fast tunable diode laser to replace the AO deflection scheme used here.

  19. Study of multiband disordered systems using the typical medium dynamical cluster approximation

    DOE PAGES

    Zhang, Yi; Terletska, Hanna; Moore, C.; ...

    2015-11-06

    We generalize the typical medium dynamical cluster approximation to multiband disordered systems. Using our extended formalism, we perform a systematic study of the nonlocal correlation effects induced by disorder on the density of states and the mobility edge of the three-dimensional two-band Anderson model. We include interband and intraband hopping and an intraband disorder potential. Our results are consistent with those obtained by the transfer matrix and the kernel polynomial methods. We also apply the method to KxFe2-ySe2 with Fe vacancies. Despite the strong vacancy disorder and anisotropy, we find the material is not an Anderson insulator. Moreover our resultsmore » demonstrate the application of the typical medium dynamical cluster approximation method to study Anderson localization in real materials.« less

  20. Study of multiband disordered systems using the typical medium dynamical cluster approximation

    SciTech Connect

    Zhang, Yi; Terletska, Hanna; Moore, C.; Ekuma, Chinedu; Tam, Ka-Ming; Berlijn, Tom; Ku, Wei; Moreno, Juana; Jarrell, Mark

    2015-11-06

    We generalize the typical medium dynamical cluster approximation to multiband disordered systems. Using our extended formalism, we perform a systematic study of the nonlocal correlation effects induced by disorder on the density of states and the mobility edge of the three-dimensional two-band Anderson model. We include interband and intraband hopping and an intraband disorder potential. Our results are consistent with those obtained by the transfer matrix and the kernel polynomial methods. We also apply the method to KxFe2-ySe2 with Fe vacancies. Despite the strong vacancy disorder and anisotropy, we find the material is not an Anderson insulator. Moreover our results demonstrate the application of the typical medium dynamical cluster approximation method to study Anderson localization in real materials.

  1. Adaptive control schemes for improving dynamic performance of efficiency-optimized induction motor drives.

    PubMed

    Kumar, Navneet; Raj Chelliah, Thanga; Srivastava, S P

    2015-07-01

    Model Based Control (MBC) is one of the energy optimal controllers used in vector-controlled Induction Motor (IM) for controlling the excitation of motor in accordance with torque and speed. MBC offers energy conservation especially at part-load operation, but it creates ripples in torque and speed during load transition, leading to poor dynamic performance of the drive. This study investigates the opportunity for improving dynamic performance of a three-phase IM operating with MBC and proposes three control schemes: (i) MBC with a low pass filter (ii) torque producing current (iqs) injection in the output of speed controller (iii) Variable Structure Speed Controller (VSSC). The pre and post operation of MBC during load transition is also analyzed. The dynamic performance of a 1-hp, three-phase squirrel-cage IM with mine-hoist load diagram is tested. Test results are provided for the conventional field-oriented (constant flux) control and MBC (adjustable excitation) with proposed schemes. The effectiveness of proposed schemes is also illustrated for parametric variations. The test results and subsequent analysis confer that the motor dynamics improves significantly with all three proposed schemes in terms of overshoot/undershoot peak amplitude of torque and DC link power in addition to energy saving during load transitions. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

  2. Acceleration of the chemistry solver for modeling DI engine combustion using dynamic adaptive chemistry (DAC) schemes

    NASA Astrophysics Data System (ADS)

    Shi, Yu; Liang, Long; Ge, Hai-Wen; Reitz, Rolf D.

    2010-03-01

    Acceleration of the chemistry solver for engine combustion is of much interest due to the fact that in practical engine simulations extensive computational time is spent solving the fuel oxidation and emission formation chemistry. A dynamic adaptive chemistry (DAC) scheme based on a directed relation graph error propagation (DRGEP) method has been applied to study homogeneous charge compression ignition (HCCI) engine combustion with detailed chemistry (over 500 species) previously using an R-value-based breadth-first search (RBFS) algorithm, which significantly reduced computational times (by as much as 30-fold). The present paper extends the use of this on-the-fly kinetic mechanism reduction scheme to model combustion in direct-injection (DI) engines. It was found that the DAC scheme becomes less efficient when applied to DI engine simulations using a kinetic mechanism of relatively small size and the accuracy of the original DAC scheme decreases for conventional non-premixed combustion engine. The present study also focuses on determination of search-initiating species, involvement of the NOx chemistry, selection of a proper error tolerance, as well as treatment of the interaction of chemical heat release and the fuel spray. Both the DAC schemes were integrated into the ERC KIVA-3v2 code, and simulations were conducted to compare the two schemes. In general, the present DAC scheme has better efficiency and similar accuracy compared to the previous DAC scheme. The efficiency depends on the size of the chemical kinetics mechanism used and the engine operating conditions. For cases using a small n-heptane kinetic mechanism of 34 species, 30% of the computational time is saved, and 50% for a larger n-heptane kinetic mechanism of 61 species. The paper also demonstrates that by combining the present DAC scheme with an adaptive multi-grid chemistry (AMC) solver, it is feasible to simulate a direct-injection engine using a detailed n-heptane mechanism with 543 species

  3. The river routing scheme in Organising Carbon and Hydrology in Dynamic Ecosystems (ORCHIDEE) using high resolution data

    NASA Astrophysics Data System (ADS)

    Nguyen-Quang, Trung; Polcher, Jan; Ducharne, Agnès; Arsouze, Thomas

    2017-04-01

    This study presents an improved version of river routing scheme in the Organising Carbon and Hydrology in Dynamic Ecosystems (ORCHIDEE) land surface model. The routing scheme in ORCHIDEE is designed to be resolution independent. This is achieved by routing water through sub-grid hydrological transfer units. An approach which also allows to use refined residence times in each transfer unit which also depend on the nature of the water to be routed. In the proposed evolution, the Hydrological data and maps based on SHuttle Elevation Derivatives at multiple Scales (HydroSHEDS) is used to enhance both these aspects. As a seamless near-global hydrological data set, HydroSHEDS is a suitable database for improving the water transfer scheme in ORCHIDEE. The approximately 1 km resolution HydroSHEDS data enables the construction of more adequate transfer units in each LSM grid box. In addition, the slope factor of each transfer unit, which is calculated with new averaging algorithm, improves the time constant of the reservoirs. Moreover, the new routing scheme is designed to function on generalized grids to make it applicable in modern regional and global climate models. We will present an analysis of the optimal transfer unit size which ensures that the results of the routing scheme are independent of the grid at which ORCHIDEE operates. It is found that with transfer units of 10km2 the model results are optimal and numerically stable. For the validation of this enhanced version of the routing scheme, 35-year simulations (1979-2013) were carried out forced by three atmospheric datasets on horizontal resolution of 0.5o and 0.25o. These datasets are: the Watch Forcing ERA-Interim dataset with bias-corrected precipitation using the (1) CRU station based product; (2) GPCCv5 satellite based estimates and (3) the higher resolution version E2OFD. Investigating on monthly and daily timescale at 22 stations of 12 rivers which contribute freshwater to Mediterranean sea shows that the

  4. Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

    PubMed

    Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

    2017-03-02

    This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

  5. Dark-bright soliton dynamics beyond the mean-field approximation

    NASA Astrophysics Data System (ADS)

    Katsimiga, G. C.; Koutentakis, G. M.; Mistakidis, S. I.; Kevrekidis, P. G.; Schmelcher, P.

    2017-07-01

    The dynamics of dark-bright (DB) solitons beyond the mean-field approximation is investigated. We first examine the case of a single DB soliton and its oscillations within a parabolic trap. Subsequently, we move to the setting of collisions, comparing the mean-field approximation to that involving multiple orbitals in both the dark and the bright component. Fragmentation is present and significantly affects the dynamics, especially in the case of slower solitons and in that of lower atom numbers. It is shown that the presence of fragmentation allows for bipartite entanglement between the distinguishable species. Most importantly the interplay between fragmentation and entanglement leads to the splitting of each of the parent mean-field DB solitons, placed off-center within the parabolic trap, into a fast and a slow daughter solitary wave. The latter process is in direct contrast to the predictions of the mean-field approximation. A variety of excitations including DB solitons in multiple (concurrently populated) orbitals is observed. Dark-antidark states and domain-wall-bright soliton complexes can also be observed to arise spontaneously in the beyond mean-field dynamics.

  6. Dynamic load identification for stochastic structures based on Gegenbauer polynomial approximation and regularization method

    NASA Astrophysics Data System (ADS)

    Liu, Jie; Sun, Xingsheng; Han, Xu; Jiang, Chao; Yu, Dejie

    2015-05-01

    Based on the Gegenbauer polynomial expansion theory and regularization method, an analytical method is proposed to identify dynamic loads acting on stochastic structures. Dynamic loads are expressed as functions of time and random parameters in time domain and the forward model of dynamic load identification is established through the discretized convolution integral of loads and the corresponding unit-pulse response functions of system. Random parameters are approximated through the random variables with λ-probability density function (PDFs) or their derivative PDFs. For this kind of random variables, Gegenbauer polynomial expansion is the unique correct choice to transform the problem of load identification for a stochastic structure into its equivalent deterministic system. Just via its equivalent deterministic system, the load identification problem of a stochastic structure can be solved by any available deterministic methods. With measured responses containing noise, the improved regularization operator is adopted to overcome the ill-posedness of load reconstruction and to obtain the stable and approximate solutions of certain inverse problems and the valid assessments of the statistics of identified loads. Numerical simulations demonstrate that with regard to stochastic structures, the identification and assessment of dynamic loads are achieved steadily and effectively by the presented method.

  7. Approximate calculation of femtosecond pump-probe spectra monitoring nonadiabatic excited-state dynamics

    NASA Astrophysics Data System (ADS)

    Dilthey, Stefan; Hahn, Susanne; Stock, Gerhard

    2000-03-01

    An approximate theory of femtosecond spectroscopy of nonadiabatically coupled electronic states is developed. Neglecting the commutators of vibrational Hamiltonians pertaining to different diabatic electronic states, the formulation represents a generalization of the semiclassical Franck-Condon approximation to the case of nonadiabatic dynamics. Explicit expressions for various time- and frequency-resolved spectra are derived which allow for a simple interpretation of femtosecond spectroscopy of vibronically coupled molecular systems. Employing multidimensional model problems describing (i) the nonadiabatic cis-trans isomerization of an electronic two-state system, and (ii) the S2→S1 internal conversion of pyrazine, exact reference data are compared to approximate calculations of transient absorbance and emission as well as time-resolved photoelectron spectra. In all cases considered, the approximation is shown to be appropriate for probe-pulse durations that are shorter than the period of the fastest relevant vibrational mode of the molecular system. Reducing the numerical costs of pump-probe simulations to the costs of a standard time-dependent wave-packet propagation, the approximate theory leads to substantial computational savings.

  8. Novel gas-dynamic levitation scheme for noncontact coating of spherical ICF targets

    SciTech Connect

    Kim, K.; Feng, Q.

    1995-12-01

    A novel gas-dynamic levitation technique has been developed to facilitate noncontact coating of spherical ICF targets. Using this technique three metal balls 450 {mu}m, 650 {mu}m and 950 {mu}m in diameter were levitated very stably for several hours, with the balls rotating continuously. Unlike the conventional gas-dynamic levitation scheme in which a single gas-emitting fixture, placed below an object, lifts it up and contains it in a confined volume, the present scheme relies on two fixtures, one placed under and the other above the object. The bottom fixture, as is with the conventional scheme, is a gas emitter; however, the top one is a gas collector shaping the flow field around the object so as to confine the object near the axis of symmetry of the levitation system. As a result, the present system exhibits excellent stability and robustness, and is immune to such external disturbances as nonuniform temperature fields and air currents, and small changes in the levitation gas pressure. The apparatus is inexpensive to fabricate and simple to operate. The details of the apparatus and the preliminary data demonstrating the capability of the levitation scheme are presented. A target coating method, compatible with the present target levitation scheme and suitable for uniform coating of ICF targets, is indicated. 6 refs., 5 figs.

  9. Proposal of dynamic protection/restoration schemes for QoS support in labeled optical burst switching networks

    NASA Astrophysics Data System (ADS)

    Yin, Yawei; Chi, Shuli; Shi, Jindan; Wu, Jian; Hong, Xiaobin; Lin, Jintong

    2008-11-01

    In this paper, two novel protection and restoration schemes were proposed by using the BC and BR schemes which were originally designed to reduce the bursts loss probability due to contention in OBS network. The 1+1 protection scheme in LOBS can be easily carried out using the MPLS 1+1 protection scheme in the 2.5 layer and burst cloning scheme in the OBS layer. By introducing some new OSPF-TE opaque LSA messages, the burst retransmission scheme can be transplanted into the restoration scheme in LOBS network. Furthermore, the dynamic quality of resilience mechanism to inherit these two schemes according to the QoS requirement of the traffic was also investigated. Experimental study using a LOBS network test bed verified that the proposed schemes suited well in the LOBS network.

  10. Image communication scheme based on dynamic visual cryptography and computer generated holography

    NASA Astrophysics Data System (ADS)

    Palevicius, Paulius; Ragulskis, Minvydas

    2015-01-01

    Computer generated holograms are often exploited to implement optical encryption schemes. This paper proposes the integration of dynamic visual cryptography (an optical technique based on the interplay of visual cryptography and time-averaging geometric moiré) with Gerchberg-Saxton algorithm. A stochastic moiré grating is used to embed the secret into a single cover image. The secret can be visually decoded by a naked eye if only the amplitude of harmonic oscillations corresponds to an accurately preselected value. The proposed visual image encryption scheme is based on computer generated holography, optical time-averaging moiré and principles of dynamic visual cryptography. Dynamic visual cryptography is used both for the initial encryption of the secret image and for the final decryption. Phase data of the encrypted image are computed by using Gerchberg-Saxton algorithm. The optical image is decrypted using the computationally reconstructed field of amplitudes.

  11. Binary-State Dynamics on Complex Networks: Pair Approximation and Beyond

    NASA Astrophysics Data System (ADS)

    Gleeson, James P.

    2013-04-01

    A wide class of binary-state dynamics on networks—including, for example, the voter model, the Bass diffusion model, and threshold models—can be described in terms of transition rates (spin-flip probabilities) that depend on the number of nearest neighbors in each of the two possible states. High-accuracy approximations for the emergent dynamics of such models on uncorrelated, infinite networks are given by recently developed compartmental models or approximate master equations (AMEs). Pair approximations (PAs) and mean-field theories can be systematically derived from the AME. We show that PA and AME solutions can coincide under certain circumstances, and numerical simulations confirm that PA is highly accurate in these cases. For monotone dynamics (where transitions out of one nodal state are impossible, e.g., susceptible-infected disease spread or Bass diffusion), PA and the AME give identical results for the fraction of nodes in the infected (active) state for all time, provided that the rate of infection depends linearly on the number of infected neighbors. In the more general nonmonotone case, we derive a condition—that proves to be equivalent to a detailed balance condition on the dynamics—for PA and AME solutions to coincide in the limit t→∞. This equivalence permits bifurcation analysis, yielding explicit expressions for the critical (ferromagnetic or paramagnetic transition) point of such dynamics, that is closely analogous to the critical temperature of the Ising spin model. Finally, the AME for threshold models of propagation is shown to reduce to just two differential equations and to give excellent agreement with numerical simulations. As part of this work, the Octave or Matlab code for implementing and solving the differential-equation systems is made available for download.

  12. Discrete-time nonlinear HJB solution using approximate dynamic programming: convergence proof.

    PubMed

    Al-Tamimi, Asma; Lewis, Frank L; Abu-Khalaf, Murad

    2008-08-01

    Convergence of the value-iteration-based heuristic dynamic programming (HDP) algorithm is proven in the case of general nonlinear systems. That is, it is shown that HDP converges to the optimal control and the optimal value function that solves the Hamilton-Jacobi-Bellman equation appearing in infinite-horizon discrete-time (DT) nonlinear optimal control. It is assumed that, at each iteration, the value and action update equations can be exactly solved. The following two standard neural networks (NN) are used: a critic NN is used to approximate the value function, whereas an action network is used to approximate the optimal control policy. It is stressed that this approach allows the implementation of HDP without knowing the internal dynamics of the system. The exact solution assumption holds for some classes of nonlinear systems and, specifically, in the specific case of the DT linear quadratic regulator (LQR), where the action is linear and the value quadratic in the states and NNs have zero approximation error. It is stressed that, for the LQR, HDP may be implemented without knowing the system A matrix by using two NNs. This fact is not generally appreciated in the folklore of HDP for the DT LQR, where only one critic NN is generally used.

  13. Analytic approximation of periodic Ateb functions via elementary functions in nonlinear dynamics

    NASA Astrophysics Data System (ADS)

    Andrianov, I.; Olevskyi, V.; Olevska, Yu.

    2016-10-01

    We consider the problem of analytic approximation of periodic Ateb functions, which are widely used in nonlinear dynamics. Ateb functions are the result of the following procedure. Initial ordinary differential equation contains only the inertial and non-linear terms. Its integration leads to an implicit solution. To obtain explicit solutions one needs to invert incomplete Beta functions. As a result of this inversion we obtain the special Ateb functions. Their properties are well known, but the use of Ateb functions is difficult on practice. In this regard, the problem arises of approximation of Ateb functions with the help of smooth elementary functions. For this purpose in the present article the asymptotic method is used with a small parameter which is inverted to the exponent of nonlinearity. We also investigated the analytical approximation of Ateb functions' period. Comparison of simulation results, obtained by the approximate expression, with the results of numerical solution of the corresponding Cauchy problem shows their sufficient accuracy for practical purposes, even for the exponent of nonlinearity equal to unity.

  14. A uniform source-and-sink scheme for calculating thermal conductivity by nonequilibrium molecular dynamics.

    PubMed

    Cao, Bing-Yang; Li, Yuan-Wei

    2010-07-14

    A uniform source-and-sink (USS) scheme, which combines features of the reverse [F. Müller-Plathe, J. Chem. Phys. 106, 6082 (1997)] and improved relaxation [B. Y. Cao, J. Chem. Phys. 129, 074106 (2008)] methods, is developed to calculate the thermal conductivity by nonequilibrium molecular dynamics (NEMD). The uniform internal heat source and sink are realized by exchanging the velocity vectors of individual atoms in the right half and left half systems, and produce a periodically quadratic temperature profile throughout the system. The thermal conductivity can be easily extracted from the mean temperatures of the right and left half systems rather than by fitting the temperature profiles. In particular, this scheme greatly increases the relaxation of the exited localized phonon modes which often worsen the calculation accuracy and efficiency in most other NEMD methods. The calculation of the thermal conductivities of solid argon shows that the simple USS scheme gives accurate results with fast convergence.

  15. A uniform source-and-sink scheme for calculating thermal conductivity by nonequilibrium molecular dynamics

    NASA Astrophysics Data System (ADS)

    Cao, Bing-Yang; Li, Yuan-Wei

    2010-07-01

    A uniform source-and-sink (USS) scheme, which combines features of the reverse [F. Müller-Plathe, J. Chem. Phys. 106, 6082 (1997)] and improved relaxation [B. Y. Cao, J. Chem. Phys. 129, 074106 (2008)] methods, is developed to calculate the thermal conductivity by nonequilibrium molecular dynamics (NEMD). The uniform internal heat source and sink are realized by exchanging the velocity vectors of individual atoms in the right half and left half systems, and produce a periodically quadratic temperature profile throughout the system. The thermal conductivity can be easily extracted from the mean temperatures of the right and left half systems rather than by fitting the temperature profiles. In particular, this scheme greatly increases the relaxation of the exited localized phonon modes which often worsen the calculation accuracy and efficiency in most other NEMD methods. The calculation of the thermal conductivities of solid argon shows that the simple USS scheme gives accurate results with fast convergence.

  16. Cosmological dynamics: from the Eulerian to the Lagrangian frame. Part I. Newtonian approximation

    SciTech Connect

    Villa, Eleonora; Maino, Davide; Matarrese, Sabino E-mail: sabino.matarrese@pd.infn.it

    2014-06-01

    We analyse the non-linear gravitational dynamics of a pressure-less fluid in the Newtonian limit of General Relativity in both the Eulerian and Lagrangian pictures. Starting from the Newtonian metric in the Poisson gauge, we transform to the synchronous and comoving gauge and obtain the Lagrangian metric within the Newtonian approximation. Our approach is fully non-perturbative, which implies that if our quantities are expanded according to the rules of standard perturbation theory, all terms are exactly recovered at any order in perturbation theory, only provided they are Newtonian. We explicitly show this result up to second order and in both gauges. Our transformation clarifies the meaning of the change of spatial and time coordinates from the Eulerian to the Lagrangian frame in the Newtonian approximation.

  17. Single-random-valley approximation in vibration-transit theory of liquid dynamics

    SciTech Connect

    De Lorenzi-Venneri, Giulia; Wallace, Duane C.

    2007-10-15

    The first goal of vibration-transit theory is to be able to calculate from a tractable partition function and without adjustable parameters the thermodynamic properties of the elemental monatomic liquids. The key hypothesis is that the random class of potential energy valleys dominates the statistical mechanics of the liquid at temperatures above melting T > or approx. T{sub m} and that these valleys are macroscopically uniform in the thermodynamic limit. This allows us to use a single random valley to calculate the vibrational contribution to liquid properties, exactly in the thermodynamic limit, and as an approximation at finite number of particles N. This approximation is tested here for liquid Na with a physically realistic potential based on electronic structure theory. Steepest descent quenches were made from the molecular dynamics equilibrium liquid (N=500) at temperatures from 0.90T{sub m} to 3.31T{sub m}, and six potential parameters were calculated for each structure, namely, the potential energy and five principal moments of the vibrational frequency distribution. The results show temperature-independent means and small standard deviations for all potential parameters, consistent with random valley uniformity at N{yields}{infinity}, and with finite-N broadening at N=500. The expected error in the single random valley approximation for Na at N=500 and T(greater-or-similar sign)T{sub m} is 0.1% for the entropy and 0.5% for the internal energy, negligible in the current development of liquid dynamics theory. In related quench studies of recent years, the common finding of nearly temperature-independent means of structural potential energy properties at T > or approx. T{sub m} suggests that the single random valley approximation might also apply to systems more complicated than the elemental liquids.

  18. Comparison of binary collision approximation and molecular dynamics for displacement cascades in GaAs.

    SciTech Connect

    Foiles, Stephen Martin

    2011-10-01

    The predictions of binary collision approximation (BCA) and molecular dynamics (MD) simulations of displacement cascades in GaAs are compared. There are three issues addressed in this work. The first is the optimal choice of the effective displacement threshold to use in the BCA calculations to obtain the best agreement with MD results. Second, the spatial correlations of point defects are compared. This is related to the level of clustering that occurs for different types of radiation. Finally, the size and structure of amorphous zones seen in the MD simulations is summarized. BCA simulations are not able to predict the formation of amorphous material.

  19. Typical medium dynamical cluster approximation for the study of Anderson localization in three dimensions

    NASA Astrophysics Data System (ADS)

    Ekuma, C. E.; Terletska, H.; Tam, K.-M.; Meng, Z.-Y.; Moreno, J.; Jarrell, M.

    2014-02-01

    We develop a systematic typical medium dynamical cluster approximation that provides a proper description of the Anderson localization transition in three dimensions (3D). Our method successfully captures the localization phenomenon both in the low and large disorder regimes, and allows us to study the localization in different momenta cells, which renders the discovery that the Anderson localization transition occurs in a cell-selective fashion. As a function of cluster size, our method systematically recovers the reentrance behavior of the mobility edge and obtains the correct critical disorder strength for Anderson localization in 3D.

  20. Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows

    SciTech Connect

    Ueckermann, M.P.; Lermusiaux, P.F.J.; Sapsis, T.P.

    2013-01-15

    The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non-homogeneous fluid and ocean flows. The dynamically orthogonal (DO) field equations provide an adaptive methodology to predict the probability density functions of such flows. The present work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier-Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. Semi-implicit projection methods are developed for the mean and for the DO modes, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with new advection schemes based on total variation diminishing methods. Other results include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size instead of quadratic; (ii) symmetric advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. To verify our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel. Different Reynolds number and Grashof number regimes are employed to illustrate robustness. Optimal convergence under both time and space refinements is shown as well as the convergence of the probability density functions with the number of stochastic realizations.

  1. Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows

    NASA Astrophysics Data System (ADS)

    Ueckermann, M. P.; Lermusiaux, P. F. J.; Sapsis, T. P.

    2013-01-01

    The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non-homogeneous fluid and ocean flows. The dynamically orthogonal (DO) field equations provide an adaptive methodology to predict the probability density functions of such flows. The present work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier-Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. Semi-implicit projection methods are developed for the mean and for the DO modes, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with new advection schemes based on total variation diminishing methods. Other results include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size instead of quadratic; (ii) symmetric advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. To verify our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel. Different Reynolds number and Grashof number regimes are employed to illustrate robustness. Optimal convergence under both time and space refinements is shown as well as the convergence of the probability density functions with the number of stochastic realizations.

  2. Quantum dynamics of water dissociative chemisorption on rigid Ni(111): An approximate nine-dimensional treatment

    NASA Astrophysics Data System (ADS)

    Jiang, Bin; Song, Hongwei; Yang, Minghui; Guo, Hua

    2016-04-01

    The quantum dynamics of water dissociative chemisorption on the rigid Ni(111) surface is investigated using a recently developed nine-dimensional potential energy surface. The quantum dynamical model includes explicitly seven degrees of freedom of D2O at fixed surface sites, and the final results were obtained with a site-averaging model. The mode specificity in the site-specific results is reported and analyzed. Finally, the approximate sticking probabilities for various vibrationally excited states of D2O are obtained considering surface lattice effects and formally all nine degrees of freedom. The comparison with experiment reveals the inaccuracy of the density functional theory and suggests the need to improve the potential energy surface.

  3. Sparse approximation of long-term biomedical signals for classification via dynamic PCA.

    PubMed

    Xie, Shengkun; Jin, Feng; Krishnan, Sridhar

    2011-01-01

    Sparse approximation is a novel technique in applications of event detection problems to long-term complex biomedical signals. It involves simplifying the extent of resources required to describe a large set of data sufficiently for classification. In this paper, we propose a multivariate statistical approach using dynamic principal component analysis along with the non-overlapping moving window technique to extract feature information from univariate long-term observational signals. Within the dynamic PCA framework, a few principal components plus the energy measure of signals in principal component subspace are highly promising for applying event detection problems to both stationary and non-stationary signals. The proposed method has been first tested using synthetic databases which contain various representative signals. The effectiveness of the method is then verified with real EEG signals for the purpose of epilepsy diagnosis and epileptic seizure detection. This sparse method produces a 100% classification accuracy for both synthetic data and real single channel EEG data.

  4. A New Split-Weight Perturbative Scheme for Shear-Alfvén Dynamics

    NASA Astrophysics Data System (ADS)

    Manuilskiy, I.; Lee, W. W.; Lewandowski, J. L. V.

    2001-10-01

    A split-weight perturbative scheme for finite-β gyrokinetic particle simulation based on the generalized Ohm's law has been used successfully to produce shear-Alfven waves.(W. W. Lee, J. L. V. Lewandowski, T. S. Hahm and Z. Lin, Phys. Plasmas (to appear).) The scheme depends crucially on the calculation of ψ ≡ φ + (1/c) int (partial A_allel / partial t) dx_allel. To extend the scheme for general geometry, a new split-weight scheme utilizing the parallel canonical momentum in the direction of the external magnetic field, P_allel ≡ p_allel + (q/c) A_allel, is developed, where p_allel is the mechanical momentum and A_allel is the vector potential. The resulting electron distribution then becomes Fe = (1 + eψ / T_e) F_0e + δ h_e, where δ he can be followed dynamically using the usual perturbative gyrokinetic particle simulation methods.(W. W. Lee, J. Comput. Phys. 72), 243 (1987).^,(S. E. Parker and W. W. Lee, Phys. Fluids B 5), 77 (1993). The resulting field equations include the modified Poisson's equation and Ampere's law as well as the equations for partial φ / partial t and for partial A_allel / partial t. The last two equation require higher order velocity moments for closure. The applications of the scheme for finite-β modified microinstabilities with microtearing will be reported.

  5. A chaos detectable and time step-size adaptive numerical scheme for nonlinear dynamical systems

    NASA Astrophysics Data System (ADS)

    Chen, Yung-Wei; Liu, Chein-Shan; Chang, Jiang-Ren

    2007-02-01

    The first step in investigation the dynamics of a continuous time system described by ordinary differential equations is to integrate them to obtain trajectories. In this paper, we convert the group-preserving scheme (GPS) developed by Liu [International Journal of Non-Linear Mechanics 36 (2001) 1047-1068] to a time step-size adaptive scheme, x=x+hf(x,t), where x∈R is the system variables we are concerned with, and f(x,t)∈R is a time-varying vector field. The scheme has the form similar to the Euler scheme, x=x+Δtf(x,t), but our step-size h is adaptive automatically. Very interestingly, the ratio h/Δt, which we call the adaptive factor, can forecast the appearance of chaos if the considered dynamical system becomes chaotical. The numerical examples of the Duffing equation, the Lorenz equation and the Rossler equation, which may exhibit chaotic behaviors under certain parameters values, are used to demonstrate these phenomena. Two other non-chaotic examples are included to compare the performance of the GPS and the adaptive one.

  6. Taylor-Lagrange renormalization scheme: Application to light-front dynamics

    NASA Astrophysics Data System (ADS)

    Grangé, P.; Mathiot, J.-F.; Mutet, B.; Werner, E.

    2009-11-01

    The recently proposed renormalization scheme based on the definition of field operators as operator valued distributions acting on specific test functions is shown to be very convenient in explicit calculations of physical observables within the framework of light-front dynamics. We first recall the main properties of this procedure based on identities relating the test functions to their Taylor remainder of any order expressed in terms of Lagrange’s formulas, hence the name given to this scheme. We thus show how it naturally applies to the calculation of state vectors of physical systems in the covariant formulation of light-front dynamics. As an example, we consider the case of the Yukawa model in the simple two-body Fock state truncation.

  7. An Analog Gamma Correction Scheme for High Dynamic Range CMOS Logarithmic Image Sensors

    PubMed Central

    Cao, Yuan; Pan, Xiaofang; Zhao, Xiaojin; Wu, Huisi

    2014-01-01

    In this paper, a novel analog gamma correction scheme with a logarithmic image sensor dedicated to minimize the quantization noise of the high dynamic applications is presented. The proposed implementation exploits a non-linear voltage-controlled-oscillator (VCO) based analog-to-digital converter (ADC) to perform the gamma correction during the analog-to-digital conversion. As a result, the quantization noise does not increase while the same high dynamic range of logarithmic image sensor is preserved. Moreover, by combining the gamma correction with the analog-to-digital conversion, the silicon area and overall power consumption can be greatly reduced. The proposed gamma correction scheme is validated by the reported simulation results and the experimental results measured for our designed test structure, which is fabricated with 0.35 μm standard complementary-metal-oxide-semiconductor (CMOS) process. PMID:25517692

  8. Parallel Dynamics Simulation Using a Krylov-Schwarz Linear Solution Scheme

    SciTech Connect

    Abhyankar, Shrirang; Constantinescu, Emil M.; Smith, Barry F.; Flueck, Alexander J.; Maldonado, Daniel A.

    2016-11-07

    Fast dynamics simulation of large-scale power systems is a computational challenge because of the need to solve a large set of stiff, nonlinear differential-algebraic equations at every time step. The main bottleneck in dynamic simulations is the solution of a linear system during each nonlinear iteration of Newton’s method. In this paper, we present a parallel Krylov- Schwarz linear solution scheme that uses the Krylov subspacebased iterative linear solver GMRES with an overlapping restricted additive Schwarz preconditioner. As a result, performance tests of the proposed Krylov-Schwarz scheme for several large test cases ranging from 2,000 to 20,000 buses, including a real utility network, show good scalability on different computing architectures.

  9. Parallel Dynamics Simulation Using a Krylov-Schwarz Linear Solution Scheme

    DOE PAGES

    Abhyankar, Shrirang; Constantinescu, Emil M.; Smith, Barry F.; ...

    2016-11-07

    Fast dynamics simulation of large-scale power systems is a computational challenge because of the need to solve a large set of stiff, nonlinear differential-algebraic equations at every time step. The main bottleneck in dynamic simulations is the solution of a linear system during each nonlinear iteration of Newton’s method. In this paper, we present a parallel Krylov- Schwarz linear solution scheme that uses the Krylov subspacebased iterative linear solver GMRES with an overlapping restricted additive Schwarz preconditioner. As a result, performance tests of the proposed Krylov-Schwarz scheme for several large test cases ranging from 2,000 to 20,000 buses, including amore » real utility network, show good scalability on different computing architectures.« less

  10. Taylor-Lagrange renormalization scheme: Application to light-front dynamics

    SciTech Connect

    Grange, P.; Mutet, B.

    2009-11-15

    The recently proposed renormalization scheme based on the definition of field operators as operator valued distributions acting on specific test functions is shown to be very convenient in explicit calculations of physical observables within the framework of light-front dynamics. We first recall the main properties of this procedure based on identities relating the test functions to their Taylor remainder of any order expressed in terms of Lagrange's formulas, hence the name given to this scheme. We thus show how it naturally applies to the calculation of state vectors of physical systems in the covariant formulation of light-front dynamics. As an example, we consider the case of the Yukawa model in the simple two-body Fock state truncation.

  11. An analog gamma correction scheme for high dynamic range CMOS logarithmic image sensors.

    PubMed

    Cao, Yuan; Pan, Xiaofang; Zhao, Xiaojin; Wu, Huisi

    2014-12-15

    In this paper, a novel analog gamma correction scheme with a logarithmic image sensor dedicated to minimize the quantization noise of the high dynamic applications is presented. The proposed implementation exploits a non-linear voltage-controlled-oscillator (VCO) based analog-to-digital converter (ADC) to perform the gamma correction during the analog-to-digital conversion. As a result, the quantization noise does not increase while the same high dynamic range of logarithmic image sensor is preserved. Moreover, by combining the gamma correction with the analog-to-digital conversion, the silicon area and overall power consumption can be greatly reduced. The proposed gamma correction scheme is validated by the reported simulation results and the experimental results measured for our designed test structure, which is fabricated with 0.35 μm standard complementary-metal-oxide-semiconductor (CMOS) process.

  12. A proposed dynamic dosing scheme to secure the target plasma drug concentrations based on the precision of the AUC estimate.

    PubMed

    Tsuruta, Harukazu; Wada, Toyofumi

    2013-01-01

    To reduce the number of blood samples necessary to estimate the patient's AUC (the area under the plasma drug concentration time-curve), various limited sampling strategies (LSSs) have been developed. We proposed a new LSS for busulfan, in which a curve that best approximates the measured data was searched for from a set of pre-generated theoretical plasma drug concentration time-curves. We evaluated this LSS and proved that it had virtually no bias and better precision compared with conventional LSSs. However, further study revealed that the precision of our new accurate LSS was still insufficient to secure the target concentration. To solve this problem, we proposed a new dosing scheme, in which the amount of dose was adjusted dynamically according to the estimated precision of the AUC estimator.

  13. Polynomial scaling approximations and dynamic correlation corrections to doubly occupied configuration interaction wave functions.

    PubMed

    Van Raemdonck, Mario; Alcoba, Diego R; Poelmans, Ward; De Baerdemacker, Stijn; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E; Van Neck, Dimitri; Bultinck, Patrick

    2015-09-14

    A class of polynomial scaling methods that approximate Doubly Occupied Configuration Interaction (DOCI) wave functions and improve the description of dynamic correlation is introduced. The accuracy of the resulting wave functions is analysed by comparing energies and studying the overlap between the newly developed methods and full configuration interaction wave functions, showing that a low energy does not necessarily entail a good approximation of the exact wave function. Due to the dependence of DOCI wave functions on the single-particle basis chosen, several orbital optimisation algorithms are introduced. An energy-based algorithm using the simulated annealing method is used as a benchmark. As a computationally more affordable alternative, a seniority number minimising algorithm is developed and compared to the energy based one revealing that the seniority minimising orbital set performs well. Given a well-chosen orbital basis, it is shown that the newly developed DOCI based wave functions are especially suitable for the computationally efficient description of static correlation and to lesser extent dynamic correlation.

  14. A probability density function discretization and approximation method for the dynamic load identification of stochastic structures

    NASA Astrophysics Data System (ADS)

    Liu, Jie; Sun, Xingsheng; Li, Kun; Jiang, Chao; Han, Xu

    2015-11-01

    Aiming at structures containing random parameters with multi-peak probability density functions (PDFs) or great variable coefficients, an analytical method of probability density function discretization and approximation (PDFDA) is proposed for dynamic load identification. Dynamic loads are expressed as the functions of time and random parameters in time domain and the forward model is established through the discretized convolution integral of loads and the corresponding unit-pulse response functions. The PDF of each random parameter is discretized into several subintervals and in each subinterval the original PDF curve is approximated via uniform distribution PDF with equal probability value. Then the joint distribution model is built and hence the equivalent deterministic equations are solved to identify unknown loads. Inverse analysis is operated separately at each variable in the joint distribution model through regularization because of noise-contaminated measured responses. In order to assess the accuracy of identified results, PDF curves and statistical properties of loads are achieved based on the specially assumed distributions of identified loads. Numerical simulations demonstrate the efficiency and superiority of the presented method.

  15. Dynamic nuclear polarization via thermal mixing: Beyond the high temperature approximation

    NASA Astrophysics Data System (ADS)

    Wenckebach, W. Th.

    2017-04-01

    Dynamic Nuclear Polarization (DNP) via the mechanism of thermal mixing has proven itself most powerful for the orientation of nuclear spins in polarized targets and hyperpolarization for magnetic resonance imaging (MRI). Unfortunately, theoretical descriptions of this mechanism have been limited to using-at least partially-the high temperature approximation, in which Boltzmann factors are expanded linearly. However, the high nuclear spin polarization required and obtained for these applications does not justify such approximations. This article extends the description of thermal mixing beyond the high temperature approximation, so Boltzmann factors are not expanded. It applies for DNP in samples doped with paramagnetic centres, for which the electron spin resonance spectrum is mainly inhomogeneously broadened by g-value anisotropy. It verifies Provotorov's hypothesis that fast spectral diffusion leads to a density matrix containing two inverse spin temperatures: the inverse electron Zeeman temperature and the inverse electron non-Zeeman temperature, while thermal mixing equalizes the nuclear Zeeman temperature and the electron non-Zeeman temperature. Equations are derived for the evolution of these temperatures and the energy flows between the spins and the lattice. Solutions are given for DNP of proton spins in samples doped with the radical TEMPO.

  16. Dynamic nuclear polarization via thermal mixing: Beyond the high temperature approximation.

    PubMed

    Wenckebach, W Th

    2017-04-01

    Dynamic Nuclear Polarization (DNP) via the mechanism of thermal mixing has proven itself most powerful for the orientation of nuclear spins in polarized targets and hyperpolarization for magnetic resonance imaging (MRI). Unfortunately, theoretical descriptions of this mechanism have been limited to using-at least partially-the high temperature approximation, in which Boltzmann factors are expanded linearly. However, the high nuclear spin polarization required and obtained for these applications does not justify such approximations. This article extends the description of thermal mixing beyond the high temperature approximation, so Boltzmann factors are not expanded. It applies for DNP in samples doped with paramagnetic centres, for which the electron spin resonance spectrum is mainly inhomogeneously broadened by g-value anisotropy. It verifies Provotorov's hypothesis that fast spectral diffusion leads to a density matrix containing two inverse spin temperatures: the inverse electron Zeeman temperature and the inverse electron non-Zeeman temperature, while thermal mixing equalizes the nuclear Zeeman temperature and the electron non-Zeeman temperature. Equations are derived for the evolution of these temperatures and the energy flows between the spins and the lattice. Solutions are given for DNP of proton spins in samples doped with the radical TEMPO.

  17. Finite-approximation-error-based discrete-time iterative adaptive dynamic programming.

    PubMed

    Wei, Qinglai; Wang, Fei-Yue; Liu, Derong; Yang, Xiong

    2014-12-01

    In this paper, a new iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for infinite horizon discrete-time nonlinear systems with finite approximation errors. First, a new generalized value iteration algorithm of ADP is developed to make the iterative performance index function converge to the solution of the Hamilton-Jacobi-Bellman equation. The generalized value iteration algorithm permits an arbitrary positive semi-definite function to initialize it, which overcomes the disadvantage of traditional value iteration algorithms. When the iterative control law and iterative performance index function in each iteration cannot accurately be obtained, for the first time a new "design method of the convergence criteria" for the finite-approximation-error-based generalized value iteration algorithm is established. A suitable approximation error can be designed adaptively to make the iterative performance index function converge to a finite neighborhood of the optimal performance index function. Neural networks are used to implement the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the developed method.

  18. A total ordering protocol using a dynamic token-passing scheme

    NASA Astrophysics Data System (ADS)

    Kim, Jongsung; Kim, Cheeha

    1997-06-01

    Solutions to the total ordering problem can be used to maintain consistency in distributed system applications such as replicated databases. We propose a total ordering protocol based on a dynamic token-passing scheme which determines the next token holder dynamically, not in predetermined order. The proposed protocol provides fast stability time, uses a small buffer, and distributes evenly the load of ordering messages to accomplish a total message ordering. We present simulation results to illustrate that the performance of the proposed protocol is superior to that of existing token-based total ordering protocols.

  19. Autonomous Path-Following by Approximate Inverse Dynamics and Vector Field Prediction

    NASA Astrophysics Data System (ADS)

    Gerlach, Adam R.

    In this dissertation, we develop two general frameworks for the navigation and control of autonomous vehicles that must follow predefined paths. These frameworks are designed such that they inherently provide accurate navigation and control of a wide class of systems directly from a model of the vehicle's dynamics. The first framework introduced is the inverse dynamics by radial basis function (IDRBF) algorithm, which exploits the best approximation property of radial basis functions to accurately approximate the inverse dynamics of non-linear systems. This approximation is then used with the known, desired state of the system at a future time point to generate the system input that must be applied to reach the desired state in the specified time interval. The IDRBF algorithm is then tested on two non-linear dynamic systems, and accurate path-following is demonstrated. The second framework introduced is the predictive vector field (PVF) algorithm. The PVF algorithm uses the equations of motion and constraints of the system to predict a set of reachable states by sampling the system's configuration space. By finding and minimizing a continuous mapping between the system's configuration space and a cost space relating the reachable states of the system with a vector field (VF), one can determine the system inputs required to follow the VF. The PVF algorithm is then tested on the Dubin's vehicle and aircraft models, and accurate path-following is demonstrated. As the PVF algorithm's performance is dependent on the quality of the underlying system model and VF, algorithms are introduced for automatically generating VFs for constant altitude paths defined by a series of waypoints and for handling modeling uncertainties. Additionally, we provide a mathematical proof showing that this method can automatically produce VFs of the desired form. To handle modeling uncertainties, we enhance the PVF algorithm with the Gaussian process machine learning framework, enabling the

  20. DYNAMICAL SPIN SUSCEPTIBILITY IN THE TD-LDA AND QSGW APPROXIMATIONS

    SciTech Connect

    SCHILFGAARDE, MARK VAN; KOTANI, TAKAO

    2012-10-15

    Abstract. This project was aimed at building the transverse dynamical spin susceptibility with the TD-LDA and the recently-developed Quasparticle Self-Consisent Approximations, which determines an optimum quasiparticle picture in a self-consistent manner within the GW approximation. Our main results were published into two papers, (J. Phys. Cond. Matt. 20, 95214 (2008), and Phys. Rev. B83, 060404(R) (2011). In the first paper we present spin wave dispersions for MnO, NiO, and -MnAs based on quasiparticle self-consistent GW approximation (QSGW). For MnO and NiO, QSGW results are in rather good agreement with experiments, in contrast to the LDA and LDA+U descriptions. For -MnAs, we find a collinear ferromagnetic ground state in QSGW, while this phase is unstable in the LDA. In the second, we apply TD-LDA to the CaFeAs2 the first attempt the first ab initio calculation of dynamical susceptibililty in a system with complex electronic structure Magnetic excitations in the striped phase of CaFe2As2 are studied as a function of local moment amplitude. We find a new kind of excitation: sharp resonances of Stoner-like (itinerant) excitations at energies comparable to the ´eel temperature, originating largely from a narrow band of Fe d states near the Fermi level, and coexisting with more conventional (localized) spin waves. Both kinds of excitations can show multiple branches, highlighting the inadequacy of a description based on a localized spin model.

  1. Approximate scheme by the coupled-wave theory to efficiently analyze the influences of moiré phenomena in liquid-crystal devices.

    PubMed

    Ho, I-Lin; Wang, Tsang-Chi; Chang, Yia-Chung; Li, Wang-Yang

    2012-08-20

    This work studies an approximate scheme by coupled-wave theory to analyze quickly the large-scale moiré phenomena as seen in common liquid-crystal devices. The moiré phenomena are considered to be caused by two periodic structures (with lattice vectors γ[combininb arrow](1) and γ[combininb arrow](2) and show an interference pattern spanning over a length γ(m)=|γ[combininb arrow](1)|·|γ[combininb arrow](2)|/|γ[combininb arrow](1)-γ[combininb arrow](2)| (with γ[combininb arrow](1)=/~γ[combininb arrow](2)). With the coupled-wave theory, the complete analysis of the moiré optics includes at least 2γ(m)/λ (λ: wavelength in vacuum) Fourier components and presents an ineffective computation. This work applies a cos(τ) type approximation for the openings of unpatterned liquid-crystal pixels, and considers the first-order coupling between the Fourier components of pixels and other (periodic) optical structures. We hence arrive at an effective evaluation, including 4τ|γ[combininb arrow](1)|/λ (or 4τ|γ[combininb arrow](2)|/λ) Fourier components, and are able to go back to a complete analysis when considering higher-order couplings at an appropriate τ integer value.

  2. Impact of nonlocal correlations over different energy scales: A dynamical vertex approximation study

    NASA Astrophysics Data System (ADS)

    Rohringer, G.; Toschi, A.

    2016-09-01

    In this paper, we investigate how nonlocal correlations affect, selectively, the physics of correlated electrons over different energy scales, from the Fermi level to the band edges. This goal is achieved by applying a diagrammatic extension of dynamical mean field theory (DMFT), the dynamical vertex approximation (D Γ A ), to study several spectral and thermodynamic properties of the unfrustrated Hubbard model in two and three dimensions. Specifically, we focus first on the low-energy regime by computing the electronic scattering rate and the quasiparticle mass renormalization for decreasing temperatures at a fixed interaction strength. This way, we obtain a precise characterization of the several steps through which the Fermi-liquid physics is progressively destroyed by nonlocal correlations. Our study is then extended to a broader energy range, by analyzing the temperature behavior of the kinetic and potential energy, as well as of the corresponding energy distribution functions. Our findings allow us to identify a smooth but definite evolution of the nature of nonlocal correlations by increasing interaction: They either increase or decrease the kinetic energy w.r.t. DMFT depending on the interaction strength being weak or strong, respectively. This reflects the corresponding evolution of the ground state from a nesting-driven (Slater) to a superexchange-driven (Heisenberg) antiferromagnet (AF), whose fingerprints are, thus, recognizable in the spatial correlations of the paramagnetic phase. Finally, a critical analysis of our numerical results of the potential energy at the largest interaction allows us to identify possible procedures to improve the ladder-based algorithms adopted in the dynamical vertex approximation.

  3. Parallel implementation of 3D FFT with volumetric decomposition schemes for efficient molecular dynamics simulations

    NASA Astrophysics Data System (ADS)

    Jung, Jaewoon; Kobayashi, Chigusa; Imamura, Toshiyuki; Sugita, Yuji

    2016-03-01

    Three-dimensional Fast Fourier Transform (3D FFT) plays an important role in a wide variety of computer simulations and data analyses, including molecular dynamics (MD) simulations. In this study, we develop hybrid (MPI+OpenMP) parallelization schemes of 3D FFT based on two new volumetric decompositions, mainly for the particle mesh Ewald (PME) calculation in MD simulations. In one scheme, (1d_Alltoall), five all-to-all communications in one dimension are carried out, and in the other, (2d_Alltoall), one two-dimensional all-to-all communication is combined with two all-to-all communications in one dimension. 2d_Alltoall is similar to the conventional volumetric decomposition scheme. We performed benchmark tests of 3D FFT for the systems with different grid sizes using a large number of processors on the K computer in RIKEN AICS. The two schemes show comparable performances, and are better than existing 3D FFTs. The performances of 1d_Alltoall and 2d_Alltoall depend on the supercomputer network system and number of processors in each dimension. There is enough leeway for users to optimize performance for their conditions. In the PME method, short-range real-space interactions as well as long-range reciprocal-space interactions are calculated. Our volumetric decomposition schemes are particularly useful when used in conjunction with the recently developed midpoint cell method for short-range interactions, due to the same decompositions of real and reciprocal spaces. The 1d_Alltoall scheme of 3D FFT takes 4.7 ms to simulate one MD cycle for a virus system containing more than 1 million atoms using 32,768 cores on the K computer.

  4. Polaron dynamics with off-diagonal coupling: beyond the Ehrenfest approximation.

    PubMed

    Huang, Zhongkai; Wang, Lu; Wu, Changqin; Chen, Lipeng; Grossmann, Frank; Zhao, Yang

    2017-01-04

    Treated traditionally by the Ehrenfest approximation, the dynamics of a one-dimensional molecular crystal model with off-diagonal exciton-phonon coupling is investigated in this work using the Dirac-Frenkel time-dependent variational principle with the multi-D2Ansatz. It is shown that the Ehrenfest method is equivalent to our variational method with the single D2Ansatz, and with the multi-D2Ansatz, the accuracy of our simulated dynamics is significantly enhanced in comparison with the semi-classical Ehrenfest dynamics. The multi-D2Ansatz is able to capture numerically accurate exciton momentum probability and help clarify the relation between the exciton momentum redistribution and the exciton energy relaxation. The results demonstrate that the exciton momentum distributions in the steady state are determined by a combination of the transfer integral and the off-diagonal coupling strength, independent of the excitonic initial conditions. We also probe the effect of the transfer integral and the off-diagonal coupling on exciton transport in both real and reciprocal space representations. Finally, the variational method with importance sampling is employed to investigate temperature effects on exciton transport using the multi-D2Ansatz, and it is demonstrated that the variational approach is valid in both low and high temperature regimes.

  5. Exact and approximate dynamics of the quantum mechanical O(N) model

    SciTech Connect

    Mihaila, Bogdan; Athan, Tara; Cooper, Fred; Dawson, John; Habib, Salman

    2000-12-15

    We study the dynamics of the quantum mechanical O(N) model as a specific example to investigate the systematics of a 1/N expansion. The closed time path formalism melded with an expansion in 1/N is used to derive time evolution equations valid to order 1/N (next-to-leading order). The effective potential is also obtained to this order and its properties are elucidated. In order to compare theoretical predictions against numerical solutions of the time-dependent Schro''dinger equation, we consider two initial conditions consistent with O(N) symmetry, one of them a quantum roll, the other a wave packet initially to one side of the potential minimum, whose center has all coordinates equal. For the case of the quantum roll we map out the domain of validity of the large-N expansion. We also discuss the existence of unitarity violation in this expansion, a well-known problem faced by moment truncation techniques. The 1/N results, both static and dynamic, are contrasted with those given by a Hartree variational ansatz at given values of N. A comparison against numerical results leads us to conclude that late-time dynamical behavior, where nonlinear effects are significant, is not well described by either approximation.

  6. A Simple, Approximate Method for Analysis of Kerr-Newman Black Hole Dynamics and Thermodynamics

    NASA Astrophysics Data System (ADS)

    Pankovic, V.; Ciganovic, S.; Glavatovic, R.

    2009-06-01

    In this work we present a simple approximate method for analysis of the basic dynamical and thermodynamical characteristics of Kerr-Newman black hole. Instead of the complete dynamics of the black hole self-interaction, we consider only the stable (stationary) dynamical situations determined by condition that the black hole (outer) horizon "circumference" holds the integer number of the reduced Compton wave lengths corresponding to mass spectrum of a small quantum system (representing the quantum of the black hole self-interaction). Then, we show that Kerr-Newman black hole entropy represents simply the ratio of the sum of static part and rotation part of the mass of black hole on one hand, and the ground mass of small quantum system on the other hand. Also we show that Kerr-Newman black hole temperature represents the negative value of the classical potential energy of gravitational interaction between a part of black hole with reduced mass and a small quantum system in the ground mass quantum state. Finally, we suggest a bosonic great canonical distribution of the statistical ensemble of given small quantum systems in the thermodynamical equilibrium with (macroscopic) black hole as thermal reservoir. We suggest that, practically, only the ground mass quantum state is significantly degenerate while all the other, excited mass quantum states, are non-degenerate. Kerr-Newman black hole entropy is practically equivalent to the ground mass quantum state degeneration. Given statistical distribution admits a rough (qualitative) but simple modeling of Hawking radiation of the black hole too.

  7. Approximate dynamic programming recurrence relations for a hybrid optimal control problem

    NASA Astrophysics Data System (ADS)

    Lu, W.; Ferrari, S.; Fierro, R.; Wettergren, T. A.

    2012-06-01

    This paper presents a hybrid approximate dynamic programming (ADP) method for a hybrid dynamic system (HDS) optimal control problem, that occurs in many complex unmanned systems which are implemented via a hybrid architecture, regarding robot modes or the complex environment. The HDS considered in this paper is characterized by a well-known three-layer hybrid framework, which includes a discrete event controller layer, a discrete-continuous interface layer, and a continuous state layer. The hybrid optimal control problem (HOCP) is to nd the optimal discrete event decisions and the optimal continuous controls subject to a deterministic minimization of a scalar function regarding the system state and control over time. Due to the uncertainty of environment and complexity of the HOCP, the cost-to-go cannot be evaluated before the HDS explores the entire system state space; as a result, the optimal control, neither continuous nor discrete, is not available ahead of time. Therefore, ADP is adopted to learn the optimal control while the HDS is exploring the environment, because of the online advantage of ADP method. Furthermore, ADP can break the curses of dimensionality which other optimizing methods, such as dynamic programming (DP) and Markov decision process (MDP), are facing due to the high dimensions of HOCP.

  8. Nonequilibrium dynamical cluster approximation study of the Falicov-Kimball model

    NASA Astrophysics Data System (ADS)

    Herrmann, Andreas J.; Tsuji, Naoto; Eckstein, Martin; Werner, Philipp

    2016-12-01

    We use a nonequilibrium implementation of the dynamical cluster approximation (DCA) to study the effect of short-range correlations on the dynamics of the two-dimensional Falicov-Kimball model after an interaction quench. As in the case of single-site dynamical mean-field theory, thermalization is absent in DCA simulations, and for quenches across the metal-insulator boundary, nearest-neighbor charge correlations in the nonthermal steady state are found to be larger than in the thermal state with identical energy. We investigate to what extent it is possible to define an effective temperature of the trapped state after a quench. Based on the ratio between the lesser and retarded Green's function, we conclude that a roughly thermal distribution is reached within the energy intervals corresponding to the momentum-patch dependent subbands of the spectral function. The effectively different chemical potentials of these distributions, however, lead to a very hot, or even negative, effective temperature in the energy intervals between these subbands.

  9. How to approximate viscoelastic dynamic topographies of stagnant lid planetary bodies?

    NASA Astrophysics Data System (ADS)

    Dumoulin, Caroline; Čadek, Ondřej; Choblet, Gaël

    2013-04-01

    Planetary mantles are viscoelastic media. However, since numerical models of thermal convection in a viscoelastic spherical shell are still very challenging, most of the studies concerning dynamic topography of planetary surfaces generated by mantle convection use one of the following simplified rheological set-up: i) IVF (instantaneous viscous flow), ii) viscous body with a free surface, or iii) hybrid methods combining viscous deformation and elastic filtering of the topography. Justifications for the use of such approximations instead of a fully viscoelastic rheology have been made on the basis of simple tests with step-like viscosity structures, with small to moderate viscosity contrasts. However, because the rheology of planetary materials is thermally activated, the radial stratification of viscosity is more likely to be a continuous function of depth, and global viscosity contrasts might be very large. In our study, we systematically compare viscoelastic dynamic topography induced by an internal load to topographies generated by the three different simplified approaches listed above using a realistic viscosity profile for a stagnant lid associated to the lithosphere of a one plate planete. To this purpose, we compute response functions of surface topography and geoid using three different semi-spectral models that all include self-gravitation: a) a linear Maxwell body with a pseudo free upper surface, b) a viscous body with a pseudo free upper surface, and c) a viscous body with a free-slip condition at the surface. Results obtained with this last model (IVF) can then be filtered using the elastic thin shell approximation: the effective elastic thickness then corresponds to the elastic thickness that is needed to fit the viscoelastic topography with an elastic filtering of the IVF topography. We show that the effective elastic thickness varies strongly with the degree of the load, with the depth of the load, and with the duration of the loading. These

  10. Dynamic Contention Window Control Scheme in IEEE 802.11e EDCA-Based Wireless LANs

    NASA Astrophysics Data System (ADS)

    Abeysekera, B. A. Hirantha Sithira; Matsuda, Takahiro; Takine, Tetsuya

    In the IEEE 802.11 MAC protocol, access points (APs) are given the same priority as wireless terminals in terms of acquiring the wireless link, even though they aggregate several downlink flows. This feature leads to a serious throughput degradation of downlink flows, compared with uplink flows. In this paper, we propose a dynamic contention window control scheme for the IEEE 802.11e EDCA-based wireless LANs, in order to achieve fairness between uplink and downlink TCP flows while guaranteeing QoS requirements for real-time traffic. The proposed scheme first determines the minimum contention window size in the best-effort access category at APs, based on the number of TCP flows. It then determines the minimum and maximum contention window sizes in higher priority access categories, such as voice and video, so as to guarantee QoS requirements for these real-time traffic. Note that the proposed scheme does not require any modification to the MAC protocol at wireless terminals. Through simulation experiments, we show the effectiveness of the proposed scheme.

  11. Dynamic and balanced capacity allocation scheme with uniform bandwidth for OFDM-PON systems

    NASA Astrophysics Data System (ADS)

    Lei, Cheng; Chen, Hongwei; Chen, Minghua; Yu, Ying; Guo, Qiang; Yang, Sigang; Xie, Shizhong

    2015-03-01

    As the bitrate of orthogonal frequency division multiplexing passive optical network (OFDM-PON) system is continuously increasing, how to effectively allocate the system bandwidth among the huge number of optical network units (ONUs) is one of the key problems before OFDM-PON can be practical deployed. Unlike traditional bandwidth allocation scheme, in this paper, the transmission performance of single ONU is for the first time taken into consideration and optimized. To reduce the manufacturing complexity and fully utilize the processing ability of the receivers, the system bandwidth is equally distributed to the ONUs. Bit loading is used to allocate the total transmission capacity, and power loading is used to guarantee the ONUs have balanced transmission performance even if they operate at different bitrate. In this way, a dynamic and balanced capacity allocation scheme with uniform bandwidth for OFDM-PON systems can be realized. At last, an experimental system is established to verify the feasibility of the proposed scheme, and the influence that the scheme brings to the whole system is also analyzed.

  12. Dynamical passage to approximate equilibrium shapes for spinning, gravitating rubble asteroids

    NASA Astrophysics Data System (ADS)

    Sharma, Ishan; Jenkins, James T.; Burns, Joseph A.

    2009-03-01

    Many asteroids are thought to be particle aggregates held together principally by self-gravity. Here we study — for static and dynamical situations — the equilibrium shapes of spinning asteroids that are permitted for rubble piles. As in the case of spinning fluid masses, not all shapes are compatible with a granular rheology. We take the asteroid to always be an ellipsoid with an interior modeled as a rigid-plastic, cohesion-less material with a Drucker-Prager yield criterion. Using an approximate volume-averaged procedure, based on the classical method of moments, we investigate the dynamical process by which such objects may achieve equilibrium. We first collapse our dynamical approach to its statical limit to derive regions in spin-shape parameter space that allow equilibrium solutions to exist. At present, only a graphical illustration of these solutions for a prolate ellipsoid following the Drucker-Prager failure law is available [Sharma, I., Jenkins, J.T., Burns, J.A., 2005a. Bull. Am. Astron. Soc. 37, 643; Sharma, I., Jenkins, J.T., Burns, J.A., 2005b. Equilibrium shapes of ellipsoidal soil asteroids. In: García-Rojo, R., Hermann, H.J., McNamara, S. (Eds.), Proceedings of the 5th International Conference on Micromechanics of Granular Media, vol. 1. A.A. Balkema, UK; Holsapple, K.A., 2007. Icarus 187, 500-509]. Here, we obtain the equilibrium landscapes for general triaxial ellipsoids, as well as provide the requisite governing formulae. In addition, we demonstrate that it may be possible to better interpret the results of Richardson et al. [Richardson, D.C., Elankumaran, P., Sanderson, R.E., 2005. Icarus 173, 349-361] within the context of a Drucker-Prager material. The graphical result for prolate ellipsoids in the static limit is the same as those of Holsapple [Holsapple, K.A., 2007. Icarus 187, 500-509] because, when worked out, his final equations will match ours. This is because, though the formalisms to reach these expressions differ, in statics

  13. Dynamics and control of foot-and-mouth disease in endemic countries: a pair approximation model.

    PubMed

    Ringa, N; Bauch, C T

    2014-09-21

    Previous mathematical models of spatial farm-to-farm transmission of foot and mouth disease (FMD) have explored the impacts of control measures such as culling and vaccination during a single outbreak in a country normally free of FMD. As a result, these models do not include factors that are relevant to countries where FMD is endemic in some regions, like long-term waning natural and vaccine immunity, use of prophylactic vaccination and disease re-importations. These factors may have implications for disease dynamics and control, yet few models have been developed for FMD-endemic settings. Here we develop and study an SEIRV (susceptible-exposed-infectious-recovered-vaccinated) pair approximation model of FMD. We focus on long term dynamics by exploring characteristics of repeated outbreaks of FMD and their dependence on disease re-importation, loss of natural immunity, and vaccine waning. We find that the effectiveness of ring and prophylactic vaccination strongly depends on duration of natural immunity, rate of vaccine waning, and disease re-introduction rate. However, the number and magnitude of FMD outbreaks are generally more sensitive to the duration of natural immunity than the duration of vaccine immunity. If loss of natural immunity and/or vaccine waning happen rapidly, then multiple epidemic outbreaks result, making it difficult to eliminate the disease. Prophylactic vaccination is more effective than ring vaccination, at the same per capita vaccination rate. Finally, more frequent disease re-importation causes a higher cumulative number of infections, although a lower average epidemic peak. Our analysis demonstrates significant differences between dynamics in FMD-free settings versus FMD-endemic settings, and that dynamics in FMD-endemic settings can vary widely depending on factors such as the duration of natural and vaccine immunity and the rate of disease re-importations. We conclude that more mathematical models tailored to FMD-endemic countries

  14. GC-based dynamic QoS priority handoff scheme in multimedia cellular systems

    NASA Astrophysics Data System (ADS)

    Chen, Huan; Kumar, Sunil; Kuo, C.-C. Jay

    2001-03-01

    A dynamic call admission control (CAC) and its associated resource reservation (RR) schemes are proposed in this research based on the guard channel (GC) concept for a wireless cellular system supporting multiple QoS classes. A comprehensive service model is developed, which includes not only mobile terminals' bandwidth requirements but also their different levels of priorities, rate adaptivity and mobility. The proposed CAC policy selects the resource access thresold according to the estimated number of incoming call requests of different QoS classes. The amount of resources to be reserved is dynamically adjusted by considering neighboring-cell higher-priority calls which are likely to handoff. The handoff interaction between adjacent cells is estimated by using radio propagation in terms of the signal-to-noise ratio (SNR) and the distance of each active call in neighboring cells. Experiments are conducted by using the OPNET simulator to study the performance of the proposed scheme under various traffic conditions. It is shown that better QoS guarantees can be provided by the proposed CAC and RR schemes.

  15. Efficient massively parallel simulation of dynamic channel assignment schemes for wireless cellular communications

    NASA Technical Reports Server (NTRS)

    Greenberg, Albert G.; Lubachevsky, Boris D.; Nicol, David M.; Wright, Paul E.

    1994-01-01

    Fast, efficient parallel algorithms are presented for discrete event simulations of dynamic channel assignment schemes for wireless cellular communication networks. The driving events are call arrivals and departures, in continuous time, to cells geographically distributed across the service area. A dynamic channel assignment scheme decides which call arrivals to accept, and which channels to allocate to the accepted calls, attempting to minimize call blocking while ensuring co-channel interference is tolerably low. Specifically, the scheme ensures that the same channel is used concurrently at different cells only if the pairwise distances between those cells are sufficiently large. Much of the complexity of the system comes from ensuring this separation. The network is modeled as a system of interacting continuous time automata, each corresponding to a cell. To simulate the model, conservative methods are used; i.e., methods in which no errors occur in the course of the simulation and so no rollback or relaxation is needed. Implemented on a 16K processor MasPar MP-1, an elegant and simple technique provides speedups of about 15 times over an optimized serial simulation running on a high speed workstation. A drawback of this technique, typical of conservative methods, is that processor utilization is rather low. To overcome this, new methods were developed that exploit slackness in event dependencies over short intervals of time, thereby raising the utilization to above 50 percent and the speedup over the optimized serial code to about 120 times.

  16. Analysis of Coulomb breakup experiments of B8 with a dynamical eikonal approximation

    NASA Astrophysics Data System (ADS)

    Goldstein, G.; Capel, P.; Baye, D.

    2007-08-01

    Various measurements of the Coulomb breakup of B8 are analyzed within the dynamical eikonal approximation using a single description of B8. We obtain a good agreement with experiment for different observables measured between 40 and 80 MeV/nucleon. A simple Be7-p potential model description of B8 seems sufficient to describe all observables. In particular, the asymmetry in parallel-momentum distributions due to E1-E2 interferences is well reproduced without any scaling. The projectile-target nuclear interactions seem negligible if data are selected at forward angles. On the contrary, like in previous analyses we observe a significant influence of higher-order effects. The accuracy of astrophysical S factors for the Be7(p,γ)B8 reaction at stellar energies extracted from breakup measurements therefore seems difficult to evaluate.

  17. An approximate model of the dynamics and heat transfer of an impact cylindrical ideal liquid jet

    NASA Astrophysics Data System (ADS)

    Uryukov, B. A.; Belik, V. D.; Tkachenko, G. V.

    2012-03-01

    A jet model based on approximations of velocities, satisfying the continuity equation, and on the integral momentum equation is presented. The solution for the jet dynamics turned out to be nonmonotonic: as an obstacle recedes over a distance larger than a certain critical one, the jet escapes from the receiver nozzle rectilinearly and remains unchanged until the distance to the obstacle becomes equal to the critical one, whereupon the jet begins to spread. The heat transfer law has been determined on the basis of the momentum and boundary layer energy equations written in an integral form. They were solved by the Squire method. It is shown that with decrease in the distance to the obstacle, if it is smaller than the critical one, the Nusselt number at the stagnation point increases.

  18. Analysis of Coulomb breakup experiments of {sup 8}B with a dynamical eikonal approximation

    SciTech Connect

    Goldstein, G.; Capel, P.; Baye, D.

    2007-08-15

    Various measurements of the Coulomb breakup of {sup 8}B are analyzed within the dynamical eikonal approximation using a single description of {sup 8}B. We obtain a good agreement with experiment for different observables measured between 40 and 80 MeV/nucleon. A simple {sup 7}Be-p potential model description of {sup 8}B seems sufficient to describe all observables. In particular, the asymmetry in parallel-momentum distributions due to E1-E2 interferences is well reproduced without any scaling. The projectile-target nuclear interactions seem negligible if data are selected at forward angles. On the contrary, like in previous analyses we observe a significant influence of higher-order effects. The accuracy of astrophysical S factors for the {sup 7}Be(p,{gamma}){sup 8}B reaction at stellar energies extracted from breakup measurements therefore seems difficult to evaluate.

  19. Sequentially Optimized Meshfree Approximation as a New Computational Fluid Dynamics Solver

    NASA Astrophysics Data System (ADS)

    Wilkinson, Matthew

    This thesis presents the Sequentially Optimized Meshfree Approximation (SOMA) method, a new and powerful Computational Fluid Dynamics (CFD) solver. While standard computational methods can be faster and cheaper that physical experimentation, both in cost and work time, these methods do have some time and user interaction overhead which SOMA eliminates. As a meshfree method which could use adaptive domain refinement methods, SOMA avoids the need for user generated and/or analyzed grids, volumes, and meshes. Incremental building of a feed-forward artificial neural network through machine learning to solve the flow problem significantly reduces user interaction and reduces computational cost. This is done by avoiding the creation and inversion of possibly dense block diagonal matrices and by focusing computational work on regions where the flow changes and ignoring regions where no changes occur.

  20. Approximating high-dimensional dynamics by barycentric coordinates with linear programming

    SciTech Connect

    Hirata, Yoshito Aihara, Kazuyuki; Suzuki, Hideyuki; Shiro, Masanori; Takahashi, Nozomu; Mas, Paloma

    2015-01-15

    The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.

  1. Approximating high-dimensional dynamics by barycentric coordinates with linear programming.

    PubMed

    Hirata, Yoshito; Shiro, Masanori; Takahashi, Nozomu; Aihara, Kazuyuki; Suzuki, Hideyuki; Mas, Paloma

    2015-01-01

    The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.

  2. Dynamics of a spinning particle in a linear in spin Hamiltonian approximation

    NASA Astrophysics Data System (ADS)

    Lukes-Gerakopoulos, Georgios; Katsanikas, Matthaios; Patsis, Panos A.; Seyrich, Jonathan

    2016-07-01

    We investigate for order and chaos the dynamical system of a spinning test particle of mass m moving in the spacetime background of a Kerr black hole of mass M . This system is approximated in our investigation by the linear in spin Hamiltonian function [E. Barausse and A. Buonanno, Phys. Rev. D 81, 084024 (2010)]. We study the corresponding phase space by using 2D projections on a surface of section and the method of color and rotation on a 4D Poincaré section. Various topological structures coming from the nonintegrability of the linear in spin Hamiltonian are found and discussed. Moreover, an interesting result is that from the value of the dimensionless spin S /(m M )=10-4 of the particle and below, the impact of the nonintegrability of the system on the motion of the particle seems to be negligible.

  3. Calculation of two-particle quantities in the typical medium dynamical cluster approximation

    NASA Astrophysics Data System (ADS)

    Zhang, Y.; Zhang, Y. F.; Yang, S. X.; Tam, K.-M.; Vidhyadhiraja, N. S.; Jarrell, M.

    2017-04-01

    The mean-field theory for disordered electron systems without interaction is widely and successfully used to describe equilibrium properties of materials over the whole range of disorder strengths. However, it fails to take into account the effects of quantum coherence and information of localization. Vertex corrections due to multiple backscatterings may drive the electrical conductivity to zero and make expansions around the mean field in strong disorder problematic. Here, we present a method for the calculation of two-particle quantities which enables us to characterize the metal-insulator transitions in disordered electron systems by using the typical medium dynamical cluster approximation. We show how to include vertex corrections and information about the mobility edge in the typical mean-field theory. We successfully demonstrate the application of the developed method by showing that the conductivity formulated in this way properly characterizes the metal-insulator transition in disordered systems.

  4. Estimating wildlife disease dynamics in complex systems using an Approximate Bayesian Computation framework.

    PubMed

    Kosmala, Margaret; Miller, Philip; Ferreira, Sam; Funston, Paul; Keet, Dewald; Packer, Craig

    2016-01-01

    Emerging infectious diseases of wildlife are of increasing concern to managers and conservation policy makers, but are often difficult to study and predict due to the complexity of host-disease systems and a paucity of empirical data. We demonstrate the use of an Approximate Bayesian Computation statistical framework to reconstruct the disease dynamics of bovine tuberculosis in Kruger National Park's lion population, despite limited empirical data on the disease's effects in lions. The modeling results suggest that, while a large proportion of the lion population will become infected with bovine tuberculosis, lions are a spillover host and long disease latency is common. In the absence of future aggravating factors, bovine tuberculosis is projected to cause a lion population decline of ~3% over the next 50 years, with the population stabilizing at this new equilibrium. The Approximate Bayesian Computation framework is a new tool for wildlife managers. It allows emerging infectious diseases to be modeled in complex systems by incorporating disparate knowledge about host demographics, behavior, and heterogeneous disease transmission, while allowing inference of unknown system parameters.

  5. Quantum speed limits in open systems: Non-Markovian dynamics without rotating-wave approximation

    PubMed Central

    Sun, Zhe; Liu, Jing; Ma, Jian; Wang, Xiaoguang

    2015-01-01

    We derive an easily computable quantum speed limit (QSL) time bound for open systems whose initial states can be chosen as either pure or mixed states. Moreover, this QSL time is applicable to either Markovian or non-Markovian dynamics. By using of a hierarchy equation method, we numerically study the QSL time bound in a qubit system interacting with a single broadened cavity mode without rotating-wave, Born and Markovian approximation. By comparing with rotating-wave approximation (RWA) results, we show that the counter-rotating terms are helpful to increase evolution speed. The problem of non-Markovianity is also considered. We find that for non-RWA cases, increasing system-bath coupling can not always enhance the non-Markovianity, which is qualitatively different from the results with RWA. When considering the relation between QSL and non-Markovianity, we find that for small broadening widths of the cavity mode, non-Markovianity can increase the evolution speed in either RWA or non-RWA cases, while, for larger broadening widths, it is not true for non-RWA cases. PMID:25676589

  6. Correlated Fluctuations and Intraband Dynamics of J-Aggregates Revealed by Combination of 2DES Schemes

    PubMed Central

    2016-01-01

    The intraband exciton dynamics of molecular aggregates is a crucial initial step to determine the possibly coherent nature of energy transfer and its implications for the ensuing interband relaxation pathways in strongly coupled excitonic systems. In this work, we fully characterize the intraband dynamics in linear J-aggregates of porphyrins, good model systems for multichromophoric assemblies in biological antenna complexes. Using different 2D electronic spectroscopy schemes together with Raman spectroscopy and theoretical modeling, we provide a full characterization of the inner structure of the main one-exciton band of the porphyrin aggregates. We find that the redistribution of population within the band occurs with a characteristic time of 280 fs and dominates the modulation of an electronic coherence. While we do not find that the coupling to vibrations significantly affects the dynamics of excitonic coherence, our results suggest that exciton fluctuations are nevertheless highly correlated. PMID:27973862

  7. Towards an ab-initio treatment of nonlocal electronic correlations with dynamical vertex approximation

    NASA Astrophysics Data System (ADS)

    Galler, Anna; Gunacker, Patrik; Tomczak, Jan; Thunström, Patrik; Held, Karsten

    Recently, approaches such as the dynamical vertex approximation (D ΓA) or the dual-fermion method have been developed. These diagrammatic approaches are going beyond dynamical mean field theory (DMFT) by including nonlocal electronic correlations on all length scales as well as the local DMFT correlations. Here we present our efforts to extend the D ΓA methodology to ab-initio materials calculations (ab-initio D ΓA). Our approach is a unifying framework which includes both GW and DMFT-type of diagrams, but also important nonlocal correlations beyond, e.g. nonlocal spin fluctuations. In our multi-band implementation we are using a worm sampling technique within continuous-time quantum Monte Carlo in the hybridization expansion to obtain the DMFT vertex, from which we construct the reducible vertex function using the two particle-hole ladders. As a first application we show results for transition metal oxides. Support by the ERC project AbinitioDGA (306447) is acknowledged.

  8. A correlated-polaron electronic propagator: Open electronic dynamics beyond the Born-Oppenheimer approximation

    NASA Astrophysics Data System (ADS)

    Parkhill, John A.; Markovich, Thomas; Tempel, David G.; Aspuru-Guzik, Alan

    2012-12-01

    In this work, we develop an approach to treat correlated many-electron dynamics, dressed by the presence of a finite-temperature harmonic bath. Our theory combines a small polaron transformation with the second-order time-convolutionless master equation and includes both electronic and system-bath correlations on equal footing. Our theory is based on the ab initio Hamiltonian, and is thus well-defined apart from any phenomenological choice of basis states or electronic system-bath coupling model. The equation-of-motion for the density matrix we derive includes non-Markovian and non-perturbative bath effects and can be used to simulate environmentally broadened electronic spectra and dissipative dynamics, which are subjects of recent interest. The theory also goes beyond the adiabatic Born-Oppenheimer approximation, but with computational cost scaling such as the Born-Oppenheimer approach. Example propagations with a developmental code are performed, demonstrating the treatment of electron-correlation in absorption spectra, vibronic structure, and decay in an open system. An untransformed version of the theory is also presented to treat more general baths and larger systems.

  9. Backstepping-Based Lyapunov Function Construction Using Approximate Dynamic Programming and Sum of Square Techniques.

    PubMed

    Wang, Zheng; Liu, Xiaoping; Liu, Kefu; Li, Shuai; Wang, Huanqing

    2016-06-20

    In this paper, backstepping for a class of block strict-feedback nonlinear systems is considered. Since the input function could be zero for each backstepping step, the backstepping technique cannot be applied directly. Based on the assumption that nonlinear systems are polynomials, for each backstepping step, Lypunov function can be constructed in a polynomial form by sum of square (SOS) technique. The virtual control can be obtained by the Sontag feedback formula, which is equivalent to an optimal control-the solution of a Hamilton-Jacobi-Bellman equation. Thus, approximate dynamic programming (ADP) could be used to estimate value functions (Lyapunov functions) instead of SOS. Through backstepping technique, the control Lyapunov function (CLF) of the full system is constructed finally making use of the strict-feedback structure and a stabilizable controller can be obtained through the constructed CLF. The contributions of the proposed method are twofold. On one hand, introducing ADP into backstepping can broaden the application of the backstepping technique. A class of block strict-feedback systems can be dealt by the proposed method and the requirement of nonzero input function for each backstepping step can be relaxed. On the other hand, backstepping with surface dynamic control actually reduces the computation complexity of ADP through constructing one part of the CLF by solving semidefinite programming using SOS. Simulation results verify contributions of the proposed method.

  10. A correlated-polaron electronic propagator: open electronic dynamics beyond the Born-Oppenheimer approximation.

    PubMed

    Parkhill, John A; Markovich, Thomas; Tempel, David G; Aspuru-Guzik, Alan

    2012-12-14

    In this work, we develop an approach to treat correlated many-electron dynamics, dressed by the presence of a finite-temperature harmonic bath. Our theory combines a small polaron transformation with the second-order time-convolutionless master equation and includes both electronic and system-bath correlations on equal footing. Our theory is based on the ab initio Hamiltonian, and is thus well-defined apart from any phenomenological choice of basis states or electronic system-bath coupling model. The equation-of-motion for the density matrix we derive includes non-markovian and non-perturbative bath effects and can be used to simulate environmentally broadened electronic spectra and dissipative dynamics, which are subjects of recent interest. The theory also goes beyond the adiabatic Born-Oppenheimer approximation, but with computational cost scaling such as the Born-Oppenheimer approach. Example propagations with a developmental code are performed, demonstrating the treatment of electron-correlation in absorption spectra, vibronic structure, and decay in an open system. An untransformed version of the theory is also presented to treat more general baths and larger systems.

  11. Elucidating the spatio-temporal dynamics of an emerging wildlife pathogen using approximate Bayesian computation.

    PubMed

    Rey, Olivier; Fourtune, Lisa; Paz-Vinas, Ivan; Loot, Géraldine; Veyssière, Charlotte; Roche, Benjamin; Blanchet, Simon

    2015-11-01

    Emerging pathogens constitute a severe threat for human health and biodiversity. Determining the status (native or non-native) of emerging pathogens, and tracing back their spatio-temporal dynamics, is crucial to understand the eco-evolutionary factors promoting their emergence, to control their spread and mitigate their impacts. However, tracing back the spatio-temporal dynamics of emerging wildlife pathogens is challenging because (i) they are often neglected until they become sufficiently abundant and pose socio-economical concerns and (ii) their geographical range is often little known. Here, we combined classical population genetics tools and approximate Bayesian computation (i.e. ABC) to retrace the dynamics of Tracheliastes polycolpus, a poorly documented pathogenic ectoparasite emerging in Western Europe that threatens several freshwater fish species. Our results strongly suggest that populations of T. polycolpus in France emerged from individuals originating from a unique genetic pool that were most likely introduced in the 1920s in central France. From this initial population, three waves of colonization occurred into peripheral watersheds within the next two decades. We further demonstrated that populations remained at low densities, and hence undetectable, during 10 years before a major demographic expansion occurred, and before its official detection in France. These findings corroborate and expand the few historical records available for this emerging pathogen. More generally, our study demonstrates how ABC can be used to determine the status, reconstruct the colonization history and infer key evolutionary parameters of emerging wildlife pathogens with low data availability, and for which samples from the putative native area are inaccessible.

  12. Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation.

    PubMed

    Huo, Pengfei; Coker, David F

    2012-12-14

    Powerful approximate methods for propagating the density matrix of complex systems that are conveniently described in terms of electronic subsystem states and nuclear degrees of freedom have recently been developed that involve linearizing the density matrix propagator in the difference between the forward and backward paths of the nuclear degrees of freedom while keeping the interference effects between the different forward and backward paths of the electronic subsystem described in terms of the mapping Hamiltonian formalism and semi-classical mechanics. Here we demonstrate that different approaches to developing the linearized approximation to the density matrix propagator can yield a mean-field like approximate propagator in which the nuclear variables evolve classically subject to Ehrenfest-like forces that involve an average over quantum subsystem states, and by adopting an alternative approach to linearizing we obtain an algorithm that involves classical like nuclear dynamics influenced by a quantum subsystem state dependent force reminiscent of trajectory surface hopping methods. We show how these different short time approximations can be implemented iteratively to achieve accurate, stable long time propagation and explore their implementation in different representations. The merits of the different approximate quantum dynamics methods that are thus consistently derived from the density matrix propagator starting point and different partial linearization approximations are explored in various model system studies of multi-state scattering problems and dissipative non-adiabatic relaxation in condensed phase environments that demonstrate the capabilities of these different types of approximations for treating non-adiabatic electronic relaxation, bifurcation of nuclear distributions, and the passage from nonequilibrium coherent dynamics at short times to long time thermal equilibration in the presence of a model dissipative environment.

  13. The particle-particle random phase approximation and beyond - insight from the superconductive Gorkov perspective and implications of an efficient truncation scheme

    NASA Astrophysics Data System (ADS)

    Zhang, Du; Yang, Weitao; Weitao Yang Group Team

    As an excited-state electronic structure method, the particle-particle random phase approximation (ppRPA) satisfactorily resolves many challenges for the time-dependent density functional theory (TDDFT)/particle-hole (ph) RPA, e.g. absence of double excitations, diradicals, singlet-to-triplet instability, etc. Given that the ppRPA equation has been derived from the pairing potential linear response, we derive it using the propagator approach using the superconductive Gorkov formalism. Systematic higher-order contributions are added to the ppRPA, yielding the pp Bethe-Salpeter equation (BSE). This development can be combined with our recently proposed truncation scheme, which makes typical ppRPA calculations up to 100 times faster than the Davidson's algorithm. Since the electron correlation is important in yielding good excitation energies for the ppRPA (the superiority of DFT reference states over Hartree-Fock ones, esp. for large systems), combining the two developments allows us to add the electron correlation into the ppRPA calculation at a modest formal scaling of O(N4), pushing the excitation energy calculations towards both larger systems and higher accuracy.

  14. Conditional Moment Closure Schemes for Studying Stochastic Dynamics of Genetic Circuits.

    PubMed

    Soltani, Mohammad; Vargas-Garcia, Cesar Augusto; Singh, Abhyudai

    2015-08-01

    Inside individual cells, stochastic expression drives random fluctuations in gene product copy numbers, which corrupts functioning of both natural and synthetic genetic circuits. Dynamic models of genetic circuits are formulated stochastically using the chemical master equation framework. Since obtaining probability distributions can be computationally expensive in these models, noise is typically investigated through lower-order statistical moments (mean, variance, correlation, skewness, etc.) of mRNA/proteins levels. However, due to the nonlinearities in genetic circuits, this moment dynamics is typically not closed, in the sense that the time derivative of the lower-order statistical moments depends on high-order moments. Moment equations are closed by expressing higher-order moments as nonlinear functions of lower-order moments, a technique commonly referred to as moment closure. We provide a new moment closure scheme for studying stochastic dynamics of genetic circuits, where genes randomly toggle between transcriptionally active and inactive states. The method is based on conditioning protein levels on active states of genes and then expressing higher-order moments as functions of lower-order conditional moments. The conditional closure scheme is illustrated on different circuit motifs and found to outperform existing closure techniques. Rapid computation of stochasticity through closure methods will enable improved characterization and design of synthetic circuits that exhibit robust performance in spite of noisy expression of underlying genes.

  15. Robust low-dose dynamic cerebral perfusion CT image restoration via coupled dictionary learning scheme.

    PubMed

    Tian, Xiumei; Zeng, Dong; Zhang, Shanli; Huang, Jing; Zhang, Hua; He, Ji; Lu, Lijun; Xi, Weiwen; Ma, Jianhua; Bian, Zhaoying

    2016-11-22

    Dynamic cerebral perfusion x-ray computed tomography (PCT) imaging has been advocated to quantitatively and qualitatively assess hemodynamic parameters in the diagnosis of acute stroke or chronic cerebrovascular diseases. However, the associated radiation dose is a significant concern to patients due to its dynamic scan protocol. To address this issue, in this paper we propose an image restoration method by utilizing coupled dictionary learning (CDL) scheme to yield clinically acceptable PCT images with low-dose data acquisition. Specifically, in the present CDL scheme, the 2D background information from the average of the baseline time frames of low-dose unenhanced CT images and the 3D enhancement information from normal-dose sequential cerebral PCT images are exploited to train the dictionary atoms respectively. After getting the two trained dictionaries, we couple them to represent the desired PCT images as spatio-temporal prior in objective function construction. Finally, the low-dose dynamic cerebral PCT images are restored by using a general DL image processing. To get a robust solution, the objective function is solved by using a modified dictionary learning based image restoration algorithm. The experimental results on clinical data show that the present method can yield more accurate kinetic enhanced details and diagnostic hemodynamic parameter maps than the state-of-the-art methods.

  16. A Secure Dynamic Identity and Chaotic Maps Based User Authentication and Key Agreement Scheme for e-Healthcare Systems.

    PubMed

    Li, Chun-Ta; Lee, Cheng-Chi; Weng, Chi-Yao; Chen, Song-Jhih

    2016-11-01

    Secure user authentication schemes in many e-Healthcare applications try to prevent unauthorized users from intruding the e-Healthcare systems and a remote user and a medical server can establish session keys for securing the subsequent communications. However, many schemes does not mask the users' identity information while constructing a login session between two or more parties, even though personal privacy of users is a significant topic for e-Healthcare systems. In order to preserve personal privacy of users, dynamic identity based authentication schemes are hiding user's real identity during the process of network communications and only the medical server knows login user's identity. In addition, most of the existing dynamic identity based authentication schemes ignore the inputs verification during login condition and this flaw may subject to inefficiency in the case of incorrect inputs in the login phase. Regarding the use of secure authentication mechanisms for e-Healthcare systems, this paper presents a new dynamic identity and chaotic maps based authentication scheme and a secure data protection approach is employed in every session to prevent illegal intrusions. The proposed scheme can not only quickly detect incorrect inputs during the phases of login and password change but also can invalidate the future use of a lost/stolen smart card. Compared the functionality and efficiency with other authentication schemes recently, the proposed scheme satisfies desirable security attributes and maintains acceptable efficiency in terms of the computational overheads for e-Healthcare systems.

  17. Vectorization of a Monte Carlo simulation scheme for nonequilibrium gas dynamics

    NASA Technical Reports Server (NTRS)

    Boyd, Iain D.

    1991-01-01

    Significant improvement has been obtained in the numerical performance of a Monte Carlo scheme for the analysis of nonequilibrium gas dynamics through an implementation of the algorithm which takes advantage of vector hardware, as presently demonstrated through application to three different problems. These are (1) a 1D standing-shock wave; (2) the flow of an expanding gas through an axisymmetric nozzle; and (3) the hypersonic flow of Ar gas over a 3D wedge. Problem (3) is illustrative of the greatly increased number of molecules which the simulation may involve, thanks to improved algorithm performance.

  18. A convergent scheme for a non-local coupled system modelling dislocations densities dynamics

    NASA Astrophysics Data System (ADS)

    Hajj, A. El; Forcadel, N.

    2008-06-01

    In this paper, we study a non-local coupled system that arises in the theory of dislocations densities dynamics. Within the framework of viscosity solutions, we prove a long time existence and uniqueness result for the solution of this model. We also propose a convergent numerical scheme and we prove a Crandall-Lions type error estimate between the continuous solution and the numerical one. As far as we know, this is the first error estimate of Crandall-Lions type for Hamilton-Jacobi systems. We also provide some numerical simulations.

  19. Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics

    PubMed Central

    Kreula, J. M.; Clark, S. R.; Jaksch, D.

    2016-01-01

    We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case. PMID:27609673

  20. Dynamic adaptive chemistry with operator splitting schemes for reactive flow simulations

    NASA Astrophysics Data System (ADS)

    Ren, Zhuyin; Xu, Chao; Lu, Tianfeng; Singer, Michael A.

    2014-04-01

    A numerical technique that uses dynamic adaptive chemistry (DAC) with operator splitting schemes to solve the equations governing reactive flows is developed and demonstrated. Strang-based splitting schemes are used to separate the governing equations into transport fractional substeps and chemical reaction fractional substeps. The DAC method expedites the numerical integration of reaction fractional substeps by using locally valid skeletal mechanisms that are obtained using the directed relation graph (DRG) reduction method to eliminate unimportant species and reactions from the full mechanism. Second-order temporal accuracy of the Strang-based splitting schemes with DAC is demonstrated on one-dimensional, unsteady, freely-propagating, premixed methane/air laminar flames with detailed chemical kinetics and realistic transport. The use of DAC dramatically reduces the CPU time required to perform the simulation, and there is minimal impact on solution accuracy. It is shown that with DAC the starting species and resulting skeletal mechanisms strongly depend on the local composition in the flames. In addition, the number of retained species may be significant only near the flame front region where chemical reactions are significant. For the one-dimensional methane/air flame considered, speed-up factors of three and five are achieved over the entire simulation for GRI-Mech 3.0 and USC-Mech II, respectively. Greater speed-up factors are expected for larger chemical kinetics mechanisms.

  1. A new time-marching scheme that suppresses spurious oscillations in the dynamic rupture problem of the spectral element method: the weighted velocity Newmark scheme

    NASA Astrophysics Data System (ADS)

    Zhou, Hong; Jiang, Han

    2015-11-01

    For dynamic rupture problems, numerical simulation methods, such as the finite-difference method, the finite-element method and the boundary integral element method, usually produce spurious high-frequency oscillations that are mainly generated by discontinuities in the friction law and poor resolution of the breakdown zone. Techniques have been developed to reduce the oscillations; for example, the application of a damping coefficient, the introduction of a Green's function with higher accuracy and the use of a high-frequency filter. Presently, the spectral element method (SEM) is an important method used to simulate strong ground motion because of its high precision in calculations and flexibility in gridding media. Its greatest advantage is that it applies the orthogonal property of Gauss-Lobatto-Legendre points to form a diagonal mass matrix and is thus suitable for parallel computation that greatly reduces the computational time. However, comparisons made in the SCEC/USGS Spontaneous Rupture Code Verification Project show that the SEM has larger high-frequency oscillations than some other numerical methods for dynamic rupture problems. In this paper, we propose a new time-marching scheme of the SEM that has the frequency response of suppressing high-frequency oscillations for the slip-weakening friction law. Computation in rupture problem illustrates that the scheme greatly reduces spurious high-frequency oscillations. Furthermore, in the Appendix of the paper we provide some formula derivation to distinguish our scheme from generalized velocity schemes.

  2. An Adaptive Scheme for Robot Localization and Mapping with Dynamically Configurable Inter-Beacon Range Measurements

    PubMed Central

    Torres-González, Arturo; Martinez-de Dios, Jose Ramiro; Ollero, Anibal

    2014-01-01

    This work is motivated by robot-sensor network cooperation techniques where sensor nodes (beacons) are used as landmarks for range-only (RO) simultaneous localization and mapping (SLAM). This paper presents a RO-SLAM scheme that actuates over the measurement gathering process using mechanisms that dynamically modify the rate and variety of measurements that are integrated in the SLAM filter. It includes a measurement gathering module that can be configured to collect direct robot-beacon and inter-beacon measurements with different inter-beacon depth levels and at different rates. It also includes a supervision module that monitors the SLAM performance and dynamically selects the measurement gathering configuration balancing SLAM accuracy and resource consumption. The proposed scheme has been applied to an extended Kalman filter SLAM with auxiliary particle filters for beacon initialization (PF-EKF SLAM) and validated with experiments performed in the CONET Integrated Testbed. It achieved lower map and robot errors (34% and 14%, respectively) than traditional methods with a lower computational burden (16%) and similar beacon energy consumption. PMID:24776938

  3. An adaptive scheme for robot localization and mapping with dynamically configurable inter-beacon range measurements.

    PubMed

    Torres-González, Arturo; Martinez-de Dios, Jose Ramiro; Ollero, Anibal

    2014-04-25

    This work is motivated by robot-sensor network cooperation techniques where sensor nodes (beacons) are used as landmarks for range-only (RO) simultaneous localization and mapping (SLAM). This paper presents a RO-SLAM scheme that actuates over the measurement gathering process using mechanisms that dynamically modify the rate and variety of measurements that are integrated in the SLAM filter. It includes a measurement gathering module that can be configured to collect direct robot-beacon and inter-beacon measurements with different inter-beacon depth levels and at different rates. It also includes a supervision module that monitors the SLAM performance and dynamically selects the measurement gathering configuration balancing SLAM accuracy and resource consumption. The proposed scheme has been applied to an extended Kalman filter SLAM with auxiliary particle filters for beacon initialization (PF-EKF SLAM) and validated with experiments performed in the CONET Integrated Testbed. It achieved lower map and robot errors (34% and 14%, respectively) than traditional methods with a lower computational burden (16%) and similar beacon energy consumption.

  4. Girsanov's transformation based variance reduced Monte Carlo simulation schemes for reliability estimation in nonlinear stochastic dynamics

    NASA Astrophysics Data System (ADS)

    Kanjilal, Oindrila; Manohar, C. S.

    2017-07-01

    The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations.

  5. Switching dynamics of doped CoFeB trilayers and a comparison to the quasistatic approximation

    NASA Astrophysics Data System (ADS)

    Forrester, Michael; Kusmartsev, Feodor; Kovács, Endre

    2013-05-01

    The investigation of the switching times of the magnetization reversal of two interacting CoFeB nanomagnets, with dimensions small enough to maintain a single-domain structure, has been carried out. A quasistatic approximation is shown to give valid results and to compare well to the damped dynamical solutions of the Landau-Lifshitz-Gilbert equations. The characteristics of the switching are shown in the associated hysteresis loops and we build a complete phase diagram of the various parallel, antiparallel, and scissoring states of the magnetization in terms of the coupling energy between the nanomagnets, magnetic anisotropy, and the interaction with an applied magnetic field. The phase diagram summarizes the different kinds of hysteresis associated with the magnetization reversal phenomena. The switching fields and times are estimated and the vulnerabilities of the magnetic phases to thermally induced magnetic field variations are examined. The stability of the phases is a fine balance between intrinsic and extrinsic magnetism and we examine its precarious nature. Our work identifies the structures that have the most robust magnetization states and hence a design ethic for creating nanomagnetic heterostructures with outstanding magnetoresistance properties based upon the two magnetic elements.

  6. Generalized multiband typical medium dynamical cluster approximation: Application to (Ga,Mn)N

    DOE PAGES

    Zhang, Yi; Nelson, R.; Siddiqui, Elisha; ...

    2016-12-29

    Here, we generalize the multiband typical medium dynamical cluster approximation and the formalism introduced by Blackman, Esterling, and Berk so that it can deal with localization in multiband disordered systems with both diagonal and off-diagonal disorder with complicated potentials. We also introduce an ansatz for the momentum-resolved typical density of states that greatly improves the numerical stability of the method while preserving the independence of scattering events at different frequencies. Starting from the first-principles effective Hamiltonian, we also apply this method to the diluted magnetic semiconductor Ga 1 - x Mn x N , and find the impurity band ismore » completely localized for Mn concentrations x < 0.03 , while for 0.03 < x < 0.10 the impurity band has delocalized states but the chemical potential resides at or above the mobility edge. So, the system is always insulating within the experimental compositional limit ( x ≈ 0.10 ) due to Anderson localization. But, for 0.03 < x < 0.10 hole doping could make the system metallic, allowing double-exchange mediated, or enhanced, ferromagnetism. The developed method is expected to have a large impact on first-principles studies of Anderson localization.« less

  7. Generalized multiband typical medium dynamical cluster approximation: Application to (Ga,Mn)N

    SciTech Connect

    Zhang, Yi; Nelson, R.; Siddiqui, Elisha; Tam, K. -M.; Yu, U.; Berlijn, T.; Ku, W.; Vidhyadhiraja, N. S.; Moreno, J.; Jarrell, M.

    2016-12-29

    Here, we generalize the multiband typical medium dynamical cluster approximation and the formalism introduced by Blackman, Esterling, and Berk so that it can deal with localization in multiband disordered systems with both diagonal and off-diagonal disorder with complicated potentials. We also introduce an ansatz for the momentum-resolved typical density of states that greatly improves the numerical stability of the method while preserving the independence of scattering events at different frequencies. Starting from the first-principles effective Hamiltonian, we also apply this method to the diluted magnetic semiconductor Ga 1 - x Mn x N , and find the impurity band is completely localized for Mn concentrations x < 0.03 , while for 0.03 < x < 0.10 the impurity band has delocalized states but the chemical potential resides at or above the mobility edge. So, the system is always insulating within the experimental compositional limit ( x ≈ 0.10 ) due to Anderson localization. But, for 0.03 < x < 0.10 hole doping could make the system metallic, allowing double-exchange mediated, or enhanced, ferromagnetism. The developed method is expected to have a large impact on first-principles studies of Anderson localization.

  8. Generalized multiband typical medium dynamical cluster approximation: Application to (Ga,Mn)N

    DOE PAGES

    Zhang, Yi; Nelson, R.; Siddiqui, Elisha; ...

    2016-12-29

    We generalize the multiband typical medium dynamical cluster approximation and the formalism introduced by Blackman, Esterling, and Berk so that it can deal with localization in multiband disordered systems with both diagonal and off-diagonal disorder with complicated potentials. We also introduce an ansatz for the momentum-resolved typical density of states that greatly improves the numerical stability of the method while preserving the independence of scattering events at different frequencies. Starting from the first-principles effective Hamiltonian, we apply this method to the diluted magnetic semiconductor Ga 1 - x Mn x N , and find the impurity band is completely localizedmore » for Mn concentrations x < 0.03 , while for 0.03 < x < 0.10 the impurity band has delocalized states but the chemical potential resides at or above the mobility edge. So, the system is always insulating within the experimental compositional limit ( x ≈ 0.10 ) due to Anderson localization. But, for 0.03 < x < 0.10 hole doping could make the system metallic, allowing double-exchange mediated, or enhanced, ferromagnetism. Finally, this developed method is expected to have a large impact on first-principles studies of Anderson localization.« less

  9. Generalized multiband typical medium dynamical cluster approximation: Application to (Ga,Mn)N

    NASA Astrophysics Data System (ADS)

    Zhang, Yi; Nelson, R.; Siddiqui, Elisha; Tam, K.-M.; Yu, U.; Berlijn, T.; Ku, W.; Vidhyadhiraja, N. S.; Moreno, J.; Jarrell, M.

    2016-12-01

    We generalize the multiband typical medium dynamical cluster approximation and the formalism introduced by Blackman, Esterling, and Berk so that it can deal with localization in multiband disordered systems with both diagonal and off-diagonal disorder with complicated potentials. We also introduce an ansatz for the momentum-resolved typical density of states that greatly improves the numerical stability of the method while preserving the independence of scattering events at different frequencies. Starting from the first-principles effective Hamiltonian, we apply this method to the diluted magnetic semiconductor Ga1 -xMnxN , and find the impurity band is completely localized for Mn concentrations x <0.03 , while for 0.03

  10. Generalized multiband typical medium dynamical cluster approximation: Application to (Ga,Mn)N

    SciTech Connect

    Zhang, Yi; Nelson, R.; Siddiqui, Elisha; Tam, K. -M.; Yu, U.; Berlijn, T.; Ku, W.; Vidhyadhiraja, N. S.; Moreno, J.; Jarrell, M.

    2016-12-29

    We generalize the multiband typical medium dynamical cluster approximation and the formalism introduced by Blackman, Esterling, and Berk so that it can deal with localization in multiband disordered systems with both diagonal and off-diagonal disorder with complicated potentials. We also introduce an ansatz for the momentum-resolved typical density of states that greatly improves the numerical stability of the method while preserving the independence of scattering events at different frequencies. Starting from the first-principles effective Hamiltonian, we apply this method to the diluted magnetic semiconductor Ga 1 - x Mn x N , and find the impurity band is completely localized for Mn concentrations x < 0.03 , while for 0.03 < x < 0.10 the impurity band has delocalized states but the chemical potential resides at or above the mobility edge. So, the system is always insulating within the experimental compositional limit ( x ≈ 0.10 ) due to Anderson localization. But, for 0.03 < x < 0.10 hole doping could make the system metallic, allowing double-exchange mediated, or enhanced, ferromagnetism. Finally, this developed method is expected to have a large impact on first-principles studies of Anderson localization.

  11. Dynamics of a planar vortex filament under the quantum local induction approximation

    PubMed Central

    Van Gorder, Robert A.

    2014-01-01

    The Hasimoto planar vortex filament is one of the rare exact solutions to the classical local induction approximation (LIA). This solution persists in the absence of friction or other disturbances, and it maintains its form over time. As such, the dynamics of such a filament have not been extended to more complicated physical situations. We consider the planar vortex filament under the quantum LIA, which accounts for mutual friction and the velocity of a normal fluid impinging on the filament. We show that, for most interesting situations, a filament which is planar in the absence of mutual friction at zero temperature will gradually deform owing to friction effects and the normal fluid flow corresponding to warmer temperatures. The influence of friction is to induce torsion, so the filaments bend as they rotate. Furthermore, the flow of a normal fluid along the vortex filament length will result in a growth in space of the initial planar perturbations of a line filament. For warmer temperatures, these effects increase in magnitude, since the growth in space scales with the mutual friction coefficient. A number of nice qualitative results are analytical in nature, and these results are verified numerically for physically interesting cases. PMID:25484602

  12. A new multi-tracer transport scheme for the dynamical core of NCAR's Community Atmosphere Model

    NASA Astrophysics Data System (ADS)

    Erath, C.

    2012-04-01

    The integration of a conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) in NCAR's High-Order Method Modeling Environment (HOMME) is considered here. HOMME is a highly scalable atmospheric modeling framework, and its current horizontal discretization relies on spectral element (SE) and/or discontinuous Galerkin (DG) methods on the cubed-sphere. It is one dynamical core of NCAR's Community Atmosphere Model (CAM). The main advantage of CSLAM is that the upstream cell (trajectories) information and computation of weights of integrals can be reused for each additional tracer. This makes CSLAM particularly interesting for global atmospheric modeling with growing number of tracers, e.g. more than 100 tracers for the chemistry version of CAM. An algorithm specifically designed for multiple processors and on the cubed-sphere grid for CSLAM in HOMME is a challenging task. HOMME is running on an element ansatz on the six cube faces. Inside these elements we create an Eulerian finite volume grid of equiangular gnomonic type, which represents the arrival grid in the scheme. But CSLAM relies on backward trajectories, which entails a departure grid. That means departure and arrival grid don't necessary have to be on the same element and certainly not on the same cube face. Also the reconstruction for higher order modeling needs a patch of tracer values which extend the element. Here we consider a third order reconstruction method. Therefore, we introduce a halo for the tracer values in the cell centers of a cube-element. The size of this halo depends on the Courant number (CFL condition) and the reconstruction type. Note that for a third order scheme and CFL number < 1 we need at least a halo size four (four values in the halo in one direction). But the communication can be limited to one per time step. This data structure allows us to consider an element with its halo as one task where we have to be extra carful for elements which share a cube edge due to

  13. A Fast and Accurate Scheme for Sea Ice Dynamics with a Stochastic Subgrid Model

    NASA Astrophysics Data System (ADS)

    Seinen, C.; Khouider, B.

    2016-12-01

    Sea ice physics is a very complex process occurring over a wide range of scales; such as local melting or large scale drift. At the current grid resolution of Global Climate Models (GCMs), we are able to resolve large scale sea ice dynamics but uncertainty remains due to subgrid physics and potential dynamic feedback, especially due to the formation of melt ponds. Recent work in atmospheric science has shown success of Markov Jump stochastic subgrid models in the representation of clouds and convection and their feedback into the large scales. There has been a push to implement these methods in other parts of the Earth System and for the cryosphere in particular but in order to test these methods, efficient and accurate solvers are required for the resolved large scale sea-ice dynamics. We present a second order accurate scheme, in both time and space, for the sea ice momentum equation (SIME) with a Jacobian Free Newton Krylov (JFNK) solver. SIME is a highly nonlinear equation due to sea ice rheology terms appearing in the stress tensor. The most commonly accepted formulation, introduced by Hibler, allows sea-ice to resist significant stresses in compression but significantly less in tension. The relationship also leads to large changes in internal stresses from small changes in velocity fields. These non-linearities have resulted in the use of implicit methods for SIME and a JFNK solver was recently introduced and used to gain efficiency. However, the method used so far is only first order accurate in time. Here we expand the JFNK approach to a Crank-Nicholson discretization of SIME. This fully second order scheme is achieved with no increase in computational cost and will allow efficient testing and development of subgrid stochastic models of sea ice in the near future.

  14. Efficient systematic scheme to construct second-principles lattice dynamical models

    NASA Astrophysics Data System (ADS)

    Escorihuela-Sayalero, Carlos; Wojdeł, Jacek C.; Íñiguez, Jorge

    2017-03-01

    We start from the polynomial interatomic potentials introduced by Wojdeł et al. [J. Phys.: Condens. Matter 25, 305401 (2013), 10.1088/0953-8984/25/30/305401] and take advantage of one of their key features—namely, the linear dependence of the energy on the potential's adjustable parameters—to devise a scheme for the construction of first-principles-based (second-principles) models for large-scale lattice-dynamical simulations. Our method presents the following convenient features. The parameters of the model are computed in a very fast and efficient way, as it is possible to recast the fit to a training set of first-principles data into a simple matrix diagonalization problem. Our method selects automatically the interactions that are most relevant to reproduce the training-set data, by choosing from a pool that includes virtually all possible coupling terms, and produces a family of models of increasing complexity and accuracy. We work with practical and convenient cross-validation criteria linked to the physical properties that will be relevant in future simulations based on the new model, and which greatly facilitate the task of identifying a potential that is simultaneously simple (thus computationally light), very accurate, and predictive. We also discuss practical ways to guarantee that our energy models are bounded from below, with a minimal impact on their accuracy. Finally, we demonstrate our scheme with an application to ferroelastic perovskite SrTiO3, which features many nontrivial lattice-dynamical features (e.g., a phase transition driven by soft phonons, competing structural instabilities, highly anharmonic dynamics) and provides a very demanding test.

  15. Waste Heat Approximation for Understanding Dynamic Compression in Nature and Experiments

    NASA Astrophysics Data System (ADS)

    Jeanloz, R.

    2015-12-01

    Energy dissipated during dynamic compression quantifies the residual heat left in a planet due to impact and accretion, as well as the deviation of a loading path from an ideal isentrope. Waste heat ignores the difference between the pressure-volume isentrope and Hugoniot in approximating the dissipated energy as the area between the Rayleigh line and Hugoniot (assumed given by a linear dependence of shock velocity on particle velocity). Strength and phase transformations are ignored: justifiably, when considering sufficiently high dynamic pressures and reversible transformations. Waste heat mis-estimates the dissipated energy by less than 10-20 percent for volume compressions under 30-60 percent. Specific waste heat (energy per mass) reaches 0.2-0.3 c02 at impact velocities 2-4 times the zero-pressure bulk sound velocity (c0), its maximum possible value being 0.5 c02. As larger impact velocities are implied for typical orbital velocities of Earth-like planets, and c02 ≈ 2-30 MJ/kg for rock, the specific waste heat due to accretion corresponds to temperature rises of about 3-15 x 103 K for rock: melting accompanies accretion even with only 20-30 percent waste heat retained. Impact sterilization is similarly quantified in terms of waste heat relative to the energy required to vaporize H2O (impact velocity of 7-8 km/s, or 4.5-5 c0, is sufficient). Waste heat also clarifies the relationship between shock, multi-shock and ramp loading experiments, as well as the effect of (static) pre-compression. Breaking a shock into 2 steps significantly reduces the dissipated energy, with minimum waste heat achieved for two equal volume compressions in succession. Breaking a shock into as few as 4 steps reduces the waste heat to within a few percent of zero, documenting how multi-shock loading approaches an isentrope. Pre-compression, being less dissipative than an initial shock to the same strain, further reduces waste heat. Multi-shock (i.e., high strain-rate) loading of pre

  16. Scalable modeling and performance evaluation of dynamic RED router using fluid-flow approximation

    NASA Astrophysics Data System (ADS)

    Ohsaki, Hiroyuki; Yamamoto, Hideyuki; Imase, Makoto

    2005-10-01

    In recent years, AQM (Active Queue Management) mechanisms, which support the end-to-end congestion control mechanism of TCP (Transmission Control Protocol), have been widely studied in the literature. AQM mechanism is a congestion controller at a router for suppressing and stabilizing its queue length (i.e., the number of packets in the buffer) by actively discarding arriving packets. Although a number of AQM mechanisms have been proposed, behaviors of those AQM mechanisms other than RED (Random Early Detection) have not been fully investigated. In this paper, using fluid-flow approximation, we analyze steady state behavior of DRED (Dynamic RED), which is designed with a control theoretic approach. More specifically, we model several network components such as congestion control mechanism of TCP, DRED router, and link propagation delay as independent SISO (Single-Input Single-Output) continuous-time systems. By interconnecting those SISO models, we obtain a continuous-time model for the entire network. Unlike other fluid-based modeling approaches, our analytic approach is scalable; our analytic approach is scalable in terms of the number of TCP connections and DRED routers since both input and output of all continuous-time systems are uniformly defined as a packet transmission rate. By performing steady-state analysis, we derive TCP throughput, average queue length of DRED router, and packet loss probability. Through several numerical examples, we quantitatively show that DRED has an intrinsic problem in high-speed networks; i.e., DRED cannot stabilize its queue length when the bottleneck link bandwidth is high. We also validate accuracy of our analytic approach by comparing analytic results with simulation ones.

  17. Approximate dynamic programming based solutions for fixed-final-time optimal control and optimal switching

    NASA Astrophysics Data System (ADS)

    Heydari, Ali

    Optimal solutions with neural networks (NN) based on an approximate dynamic programming (ADP) framework for new classes of engineering and non-engineering problems and associated difficulties and challenges are investigated in this dissertation. In the enclosed eight papers, the ADP framework is utilized for solving fixed-final-time problems (also called terminal control problems) and problems with switching nature. An ADP based algorithm is proposed in Paper 1 for solving fixed-final-time problems with soft terminal constraint, in which, a single neural network with a single set of weights is utilized. Paper 2 investigates fixed-final-time problems with hard terminal constraints. The optimality analysis of the ADP based algorithm for fixed-final-time problems is the subject of Paper 3, in which, it is shown that the proposed algorithm leads to the global optimal solution providing certain conditions hold. Afterwards, the developments in Papers 1 to 3 are used to tackle a more challenging class of problems, namely, optimal control of switching systems. This class of problems is divided into problems with fixed mode sequence (Papers 4 and 5) and problems with free mode sequence (Papers 6 and 7). Each of these two classes is further divided into problems with autonomous subsystems (Papers 4 and 6) and problems with controlled subsystems (Papers 5 and 7). Different ADP-based algorithms are developed and proofs of convergence of the proposed iterative algorithms are presented. Moreover, an extension to the developments is provided for online learning of the optimal switching solution for problems with modeling uncertainty in Paper 8. Each of the theoretical developments is numerically analyzed using different real-world or benchmark problems.

  18. Improving the convergence of closed and open path integral molecular dynamics via higher order Trotter factorization schemes

    NASA Astrophysics Data System (ADS)

    Pérez, Alejandro; Tuckerman, Mark E.

    2011-08-01

    Higher order factorization schemes are developed for path integral molecular dynamics in order to improve the convergence of estimators for physical observables as a function of the Trotter number. The methods are based on the Takahashi-Imada and Susuki decompositions of the Boltzmann operator. The methods introduced improve the averages of the estimators by using the classical forces needed to carry out the dynamics to construct a posteriori weighting factors for standard path integral molecular dynamics. The new approaches are straightforward to implement in existing path integral codes and carry no significant overhead. The Suzuki higher order factorization was also used to improve the end-to-end distance estimator in open path integral molecular dynamics. The new schemes are tested in various model systems, including an ab initio path integral molecular dynamics calculation on the hydrogen molecule and a quantum water model. The proposed algorithms have potential utility for reducing the cost of path integral molecular dynamics calculations of bulk systems.

  19. Improving the convergence of closed and open path integral molecular dynamics via higher order Trotter factorization schemes.

    PubMed

    Pérez, Alejandro; Tuckerman, Mark E

    2011-08-14

    Higher order factorization schemes are developed for path integral molecular dynamics in order to improve the convergence of estimators for physical observables as a function of the Trotter number. The methods are based on the Takahashi-Imada and Susuki decompositions of the Boltzmann operator. The methods introduced improve the averages of the estimators by using the classical forces needed to carry out the dynamics to construct a posteriori weighting factors for standard path integral molecular dynamics. The new approaches are straightforward to implement in existing path integral codes and carry no significant overhead. The Suzuki higher order factorization was also used to improve the end-to-end distance estimator in open path integral molecular dynamics. The new schemes are tested in various model systems, including an ab initio path integral molecular dynamics calculation on the hydrogen molecule and a quantum water model. The proposed algorithms have potential utility for reducing the cost of path integral molecular dynamics calculations of bulk systems.

  20. Dynamic Online Bandwidth Adjustment Scheme Based on Kalai-Smorodinsky Bargaining Solution

    NASA Astrophysics Data System (ADS)

    Kim, Sungwook

    Virtual Private Network (VPN) is a cost effective method to provide integrated multimedia services. Usually heterogeneous multimedia data can be categorized into different types according to the required Quality of Service (QoS). Therefore, VPN should support the prioritization among different services. In order to support multiple types of services with different QoS requirements, efficient bandwidth management algorithms are important issues. In this paper, I employ the Kalai-Smorodinsky Bargaining Solution (KSBS) for the development of an adaptive bandwidth adjustment algorithm. In addition, to effectively manage the bandwidth in VPNs, the proposed control paradigm is realized in a dynamic online approach, which is practical for real network operations. The simulations show that the proposed scheme can significantly improve the system performances.

  1. On Constructing Dynamic and Forward Secure Authenticated Group Key Agreement Scheme from Multikey Encapsulation Mechanism

    PubMed Central

    Fathirad, Iraj; Devlin, John

    2015-01-01

    The approach of instantiating authenticated group key exchange (GAKE) protocol from the multikey encapsulation mechanism (mKEM) has an important advantage of achieving classical requirement of GAKE security in one communication round. In spite of the limitations of this approach, for example, lack of forward secrecy, it is very useful in group environments when maximum communication efficiency is desirable. To enrich this mKEM-based GAKE construction, we suggest an efficient solution to convert this static GAKE framework into a partially dynamic scheme. Furthermore, to address the associated lack of forward-secrecy, we propose two variants of this generic construction which can also provide a means of forward secrecy at the cost of extra communication round. In addition, concerning associated implementation cost of deploying this generic GAKE construction in elliptic curve cryptosystem, we compare the possible instantiations of this model from existing mKEM algorithms in terms of the number of elliptic curve scalar multiplications. PMID:26451388

  2. Fluid-dynamical scheme for equilibrium properties of two trapped fermion species with pairing interactions

    NASA Astrophysics Data System (ADS)

    Capuzzi, P.; Hernández, E. S.; Szybisz, L.

    2008-10-01

    We present a generalization of the fluid-dynamical scheme developed for nuclear physics to the case of two trapped fermion species with pairing interactions. To establish a macroscopic description of the mass and momentum conservation laws, we adopt a generalization of the usual Thomas-Fermi approach that includes the pairing energy. We analyze the equilibrium density and gap profiles for an equal population mixture of harmonically trapped Li6 atoms for different choices of the local equation of state. We examine slight departures from equilibrium within our formulation, finding that density oscillations can propagate as first sound coupled to pairing vibrations, that in a homogeneous fermion system exhibit a Bogoliubov-like quasiparticle spectrum. In this case, the dispersion relation for the coupled modes displays a rich scenario of stable, unstable, and damped regimes.

  3. A high performance communications and memory caching scheme for molecular dynamics on the CM-5

    SciTech Connect

    Beazley, D.M.; Lomdahl, P.S.; Gronbech-Jensen, N.; Tamayo, P.

    1993-09-15

    In this paper, we provide a brief overview of our general molecular dynamics algorithm and focus on several performance enhancements that have allowed us to achieve high performance on the CM-5. Our use of the CM-5 vector units (VUs) to calculate forces is described along with a memory caching scheme that speeds up the force calculation by as much as 50%. In addition, we discuss a method used to speed up the communication aspects of our algorithm by more than 35%. Lastly, recent timing and scaling results are presented. Our code has been implemented in ANSI C with explicit calls to the CMMD message-passing library. To use the VUs we have written our force calculation in CDPEAC (a C interface to the VU assembler language, DPEAC). We also assume that particles interact according to the Lennard-Jones 6--12 (LJ) potential.

  4. Long-term stable time integration scheme for dynamic analysis of planar geometrically exact Timoshenko beams

    NASA Astrophysics Data System (ADS)

    Nguyen, Tien Long; Sansour, Carlo; Hjiaj, Mohammed

    2017-05-01

    In this paper, an energy-momentum method for geometrically exact Timoshenko-type beam is proposed. The classical time integration schemes in dynamics are known to exhibit instability in the non-linear regime. The so-called Timoshenko-type beam with the use of rotational degree of freedom leads to simpler strain relations and simpler expressions of the inertial terms as compared to the well known Bernoulli-type model. The treatment of the Bernoulli-model has been recently addressed by the authors. In this present work, we extend our approach of using the strain rates to define the strain fields to in-plane geometrically exact Timoshenko-type beams. The large rotational degrees of freedom are exactly computed. The well-known enhanced strain method is used to avoid locking phenomena. Conservation of energy, momentum and angular momentum is proved formally and numerically. The excellent performance of the formulation will be demonstrated through a range of examples.

  5. Systematic renormalization scheme in light-front dynamics with Fock space truncation

    SciTech Connect

    Karmanov, V. A.; Smirnov, A. V.; Mathiot, J.-F.

    2008-04-15

    Within the framework of the covariant formulation of light-front dynamics, we develop a general nonperturbative renormalization scheme based on the Fock decomposition of the state vector and its truncation. The counterterms and bare parameters needed to renormalize the theory depend on the Fock sectors. We present a general strategy in order to calculate these quantities, as well as state vectors of physical systems, in a truncated Fock space. The explicit dependence of our formalism on the orientation of the light-front plane is essential in order to analyze the structure of the counterterms. We apply our formalism to the two-body (one fermion and one boson) truncation in the Yukawa model and in QED, and to the three-body truncation in a scalar model. In QED, we recover analytically, without any perturbative expansion, the renormalization of the electric charge, according to the requirements of the Ward identity.

  6. On numerical schemes for solving the Euler equations of gas dynamics

    NASA Astrophysics Data System (ADS)

    Dervieux, A.; Vijayasundaram, G.

    The first-order upwind schemes of Godunov-Van Leer, Steger-Warming, Godunov, Roe, Osher and Glimm; Godunov type scheme I; the second-order upwind schemes of Van Leer, Fromm-Van Leer, Hancock-Van Leer, and Moretti; and the second-order centered schemes of Richtmyer, Mac Cormack, Lerat-Peyrat, and Jameson are described. Their performances for the shock-tube problem proposed by Sod are compared. The schemes of Godunov-Van Leer, Glimm, Fromm-Van Leer, and Hancock-Van Leer produced the best results. All the First-order upwind schemes, the Glimm scheme, the Jameson scheme, and the Hancock-Van Leer scheme can be extended to two dimensions in the finite element setting.

  7. How well can the exponential-growth coalescent approximate constant-rate birth-death population dynamics?

    PubMed

    Stadler, Tanja; Vaughan, Timothy G; Gavryushkin, Alex; Guindon, Stephane; Kühnert, Denise; Leventhal, Gabriel E; Drummond, Alexei J

    2015-05-07

    One of the central objectives in the field of phylodynamics is the quantification of population dynamic processes using genetic sequence data or in some cases phenotypic data. Phylodynamics has been successfully applied to many different processes, such as the spread of infectious diseases, within-host evolution of a pathogen, macroevolution and even language evolution. Phylodynamic analysis requires a probability distribution on phylogenetic trees spanned by the genetic data. Because such a probability distribution is not available for many common stochastic population dynamic processes, coalescent-based approximations assuming deterministic population size changes are widely employed. Key to many population dynamic models, in particular epidemiological models, is a period of exponential population growth during the initial phase. Here, we show that the coalescent does not well approximate stochastic exponential population growth, which is typically modelled by a birth-death process. We demonstrate that introducing demographic stochasticity into the population size function of the coalescent improves the approximation for values of R0 close to 1, but substantial differences remain for large R0. In addition, the computational advantage of using an approximation over exact models vanishes when introducing such demographic stochasticity. These results highlight that we need to increase efforts to develop phylodynamic tools that correctly account for the stochasticity of population dynamic models for inference.

  8. Dynamic screening of an ion in a degenerate electron gas within the second-order Born approximation

    NASA Astrophysics Data System (ADS)

    Nersisyan, Hrachya B.; Fernández-Varea, José M.; Arista, Néstor R.

    2015-07-01

    The dynamic Friedel sum rule (FSR) is derived within the second-order Born (B2) approximation for an ion that moves in a fully degenerate electron gas and for an arbitrary spherically-symmetric electron-ion interaction potential. This results in an implicit equation for the dynamic B2 screening parameter which depends on the ion atomic number Z1 unlike the first-order Born (B1) dynamic screening parameter reported earlier by some authors. Furthermore, for typical metallic densities our analytical results for the Yukawa and hydrogenic potentials are compared, for both positive and negative ions, to the exact screening parameters calculated self-consistently by imposing the exact dynamic FSR requirement to the scattering phase shifts. The B1 and B2 screening parameters agree excellently with the exact values at large velocities, while at moderate and low velocities the B1 approximation deviates from the exact solution whereas the B2 approximation still remains close to it. In addition, a Padé approximant to the Born series yields a further improvement of the perturbative approach, showing an excellent agreement on the whole velocity range in the case of antiprotons.

  9. Comparison of different coupling schemes between counterions and charged nanoparticles in multiparticle collision dynamics.

    PubMed

    Dahirel, Vincent; Zhao, Xudong; Jardat, Marie

    2016-08-01

    We applied the multiparticle collision dynamics (MPC) simulation technique to highly asymmetric electrolytes in solution, i.e., charged nanoparticles and their counterions in a solvent. These systems belong to a domain of solute size which ranges between the electrolyte and the colloidal domains, where most analytical theories are expected to fail, and efficient simulation techniques are still missing. MPC is a mesoscopic simulation method which mimics hydrodynamics properties of a fluid, includes thermal fluctuations, and can be coupled to a molecular dynamics of solutes. We took advantage of the size asymmetry between nanoparticles and counterions to treat the coupling between solutes and the solvent bath within the MPC method. Counterions were coupled to the solvent bath during the collision step and nanoparticles either through a direct interaction force or with stochastic rotation rules which mimic stick boundary conditions. Moreover, we adapted the simulation procedure to address the issue of the strong electrostatic interactions between solutes of opposite charges. We show that the short-ranged repulsion between counterions and nanoparticles can be modeled by stochastic reflection rules. This simulation scheme is very efficient from a computational point of view. We have also computed the transport coefficients for various densities. The diffusion of counterions was found in one case to increase slightly with the volume fraction of nanoparticles. The deviation of the electric conductivity from the ideal behavior (solutes at infinite dilution without any direct interactions) is found to be strong.

  10. Comparison of different coupling schemes between counterions and charged nanoparticles in multiparticle collision dynamics

    NASA Astrophysics Data System (ADS)

    Dahirel, Vincent; Zhao, Xudong; Jardat, Marie

    2016-08-01

    We applied the multiparticle collision dynamics (MPC) simulation technique to highly asymmetric electrolytes in solution, i.e., charged nanoparticles and their counterions in a solvent. These systems belong to a domain of solute size which ranges between the electrolyte and the colloidal domains, where most analytical theories are expected to fail, and efficient simulation techniques are still missing. MPC is a mesoscopic simulation method which mimics hydrodynamics properties of a fluid, includes thermal fluctuations, and can be coupled to a molecular dynamics of solutes. We took advantage of the size asymmetry between nanoparticles and counterions to treat the coupling between solutes and the solvent bath within the MPC method. Counterions were coupled to the solvent bath during the collision step and nanoparticles either through a direct interaction force or with stochastic rotation rules which mimic stick boundary conditions. Moreover, we adapted the simulation procedure to address the issue of the strong electrostatic interactions between solutes of opposite charges. We show that the short-ranged repulsion between counterions and nanoparticles can be modeled by stochastic reflection rules. This simulation scheme is very efficient from a computational point of view. We have also computed the transport coefficients for various densities. The diffusion of counterions was found in one case to increase slightly with the volume fraction of nanoparticles. The deviation of the electric conductivity from the ideal behavior (solutes at infinite dilution without any direct interactions) is found to be strong.

  11. Analysis and design of numerical schemes for gas dynamics. 2: Artificial diffusion and discrete shock structure

    NASA Technical Reports Server (NTRS)

    Jameson, Antony

    1994-01-01

    The effect of artificial diffusion on discrete shock structures is examined for a family of schemes which includes scalar diffusion, convective upwind and split pressure (CUSP) schemes, and upwind schemes with characteristics splitting. The analysis leads to conditions on the diffusive flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets these conditions is a CUSP scheme in which the coefficients of the pressure differences is fully determined by the coefficient of convective diffusion. It is also shown how both the characteristic and CUSP schemes can be modified to preserve constant stagnation enthalpy in steady flow, leading to four variants, the E and H-characteristic schemes, and the E and H-CUSP schemes. Numerical results are presented which confirm the properties of these schemes.

  12. A new flux splitting scheme for Euler equations of gas dynamics

    SciTech Connect

    Li, Xindong; Hu, Zongmin; Jiang, Zonglin

    2015-03-10

    A new flux splitting method named K-CUSP scheme is proposed in the paper. The major difference between K-CUSP and two traditional CUSP schemes (H-CUSP and E-CUSP) is that all kinematic quantities and all thermodynamic quantities in total enthalpy will be separately split into convective term and pressure term. The present scheme adopts the cell-face Mach number splitting method of AUSM+ scheme and the interface flux of pressure term is given a new way in the subsonic regime. Numerical solutions demonstrate that the new scheme inherits the simplicity and robustness of FVS schemes, which overcomes the shortcomings of pressure overshoot of shock wave in H-CUSP and E-CUSP schemes, but also retains the high-resolution of FDS schemes, which achieves the high accuracy of contact discontinuity and shock discontinuity.

  13. A robust and novel dynamic-ID-based authentication scheme for care team collaboration with smart cards.

    PubMed

    Chang, Ya-Fen; Chen, Chia-Chen; Chang, Pei-Yu

    2013-04-01

    Nowadays, users/patients may gain desired medical services on-line because of the rapid development of computer network technologies. Conventional healthcare services are provided by a single server. However, care team collaboration by integrating services is the key to improve financial and clinical performance. How a user/patient accesses desired medical services provided by multiple servers becomes a challenge to realize care team collaboration. User authentication plays an important role to protect resources or services from being accessed by unauthorized users. In this paper, we first discuss the perceived security drawbacks of pervasive smart-card-based remote user authentication schemes. Then, we propose a novel dynamic-ID-based user authentication scheme based on elliptic curve cryptosystem (ECC) for multi-server environment with smart cards. The proposed scheme ensures user anonymity and computational efficiency and complies with essential requirements of a secure smart-card-based authentication scheme for multi-server environment to enable care team collaboration.

  14. Accurate schemes for calculation of thermodynamic properties of liquid mixtures from molecular dynamics simulations

    NASA Astrophysics Data System (ADS)

    Caro, Miguel A.; Laurila, Tomi; Lopez-Acevedo, Olga

    2016-12-01

    We explore different schemes for improved accuracy of entropy calculations in aqueous liquid mixtures from molecular dynamics (MD) simulations. We build upon the two-phase thermodynamic (2PT) model of Lin et al. [J. Chem. Phys. 119, 11792 (2003)] and explore new ways to obtain the partition between the gas-like and solid-like parts of the density of states, as well as the effect of the chosen ideal "combinatorial" entropy of mixing, both of which have a large impact on the results. We also propose a first-order correction to the issue of kinetic energy transfer between degrees of freedom (DoF). This problem arises when the effective temperatures of translational, rotational, and vibrational DoF are not equal, either due to poor equilibration or reduced system size/time sampling, which are typical problems for ab initio MD. The new scheme enables improved convergence of the results with respect to configurational sampling, by up to one order of magnitude, for short MD runs. To ensure a meaningful assessment, we perform MD simulations of liquid mixtures of water with several other molecules of varying sizes: methanol, acetonitrile, N, N-dimethylformamide, and n-butanol. Our analysis shows that results in excellent agreement with experiment can be obtained with little computational effort for some systems. However, the ability of the 2PT method to succeed in these calculations is strongly influenced by the choice of force field, the fluidicity (hard-sphere) formalism employed to obtain the solid/gas partition, and the assumed combinatorial entropy of mixing. We tested two popular force fields, GAFF and OPLS with SPC/E water. For the mixtures studied, the GAFF force field seems to perform as a slightly better "all-around" force field when compared to OPLS+SPC/E.

  15. Accurate schemes for calculation of thermodynamic properties of liquid mixtures from molecular dynamics simulations.

    PubMed

    Caro, Miguel A; Laurila, Tomi; Lopez-Acevedo, Olga

    2016-12-28

    We explore different schemes for improved accuracy of entropy calculations in aqueous liquid mixtures from molecular dynamics (MD) simulations. We build upon the two-phase thermodynamic (2PT) model of Lin et al. [J. Chem. Phys. 119, 11792 (2003)] and explore new ways to obtain the partition between the gas-like and solid-like parts of the density of states, as well as the effect of the chosen ideal "combinatorial" entropy of mixing, both of which have a large impact on the results. We also propose a first-order correction to the issue of kinetic energy transfer between degrees of freedom (DoF). This problem arises when the effective temperatures of translational, rotational, and vibrational DoF are not equal, either due to poor equilibration or reduced system size/time sampling, which are typical problems for ab initio MD. The new scheme enables improved convergence of the results with respect to configurational sampling, by up to one order of magnitude, for short MD runs. To ensure a meaningful assessment, we perform MD simulations of liquid mixtures of water with several other molecules of varying sizes: methanol, acetonitrile, N, N-dimethylformamide, and n-butanol. Our analysis shows that results in excellent agreement with experiment can be obtained with little computational effort for some systems. However, the ability of the 2PT method to succeed in these calculations is strongly influenced by the choice of force field, the fluidicity (hard-sphere) formalism employed to obtain the solid/gas partition, and the assumed combinatorial entropy of mixing. We tested two popular force fields, GAFF and OPLS with SPC/E water. For the mixtures studied, the GAFF force field seems to perform as a slightly better "all-around" force field when compared to OPLS+SPC/E.

  16. Multi-state trajectory approach to non-adiabatic dynamics: General formalism and the active state trajectory approximation

    NASA Astrophysics Data System (ADS)

    Tao, Guohua

    2017-07-01

    A general theoretical framework is derived for the recently developed multi-state trajectory (MST) approach from the time dependent Schrödinger equation, resulting in equations of motion for coupled nuclear-electronic dynamics equivalent to Hamilton dynamics or Heisenberg equation based on a new multistate Meyer-Miller (MM) model. The derived MST formalism incorporates both diabatic and adiabatic representations as limiting cases and reduces to Ehrenfest or Born-Oppenheimer dynamics in the mean-field or the single-state limits, respectively. In the general multistate formalism, nuclear dynamics is represented in terms of a set of individual state-specific trajectories, while in the active state trajectory (AST) approximation, only one single nuclear trajectory on the active state is propagated with its augmented images running on all other states. The AST approximation combines the advantages of consistent nuclear-coupled electronic dynamics in the MM model and the single nuclear trajectory in the trajectory surface hopping (TSH) treatment and therefore may provide a potential alternative to both Ehrenfest and TSH methods. The resulting algorithm features in a consistent description of coupled electronic-nuclear dynamics and excellent numerical stability. The implementation of the MST approach to several benchmark systems involving multiple nonadiabatic transitions and conical intersection shows reasonably good agreement with exact quantum calculations, and the results in both representations are similar in accuracy. The AST treatment also reproduces the exact results reasonably, sometimes even quantitatively well, with a better performance in the adiabatic representation.

  17. Ion dynamics in compacted clays: Derivation of a two-state diffusion-reaction scheme from the lattice Fokker-Planck equation

    NASA Astrophysics Data System (ADS)

    Rotenberg, B.; Dufrêche, J.-F.; Bagchi, B.; Giffaut, E.; Hansen, J.-P.; Turq, P.

    2006-04-01

    We show how a two-state diffusion-reaction description of the mobility of ions confined within compacted clays can be constructed from the microscopic dynamics of ions in an external field. The diffusion-reaction picture provides the usual interpretation of the reduced ionic mobility in clays, but the required partitioning coefficient Kd between trapped and mobile ions is generally an empirical parameter. We demonstrate that it is possible to obtain Kd from the microscopic dynamics of ions interacting with the clay surfaces by evaluating the ionic mobility using a novel lattice implementation of the Fokker-Planck equation. The resulting Kd allows a clear-cut characterization of the trapping sites on the clay surfaces and determines the adsorption/desorption rates. The results highlight the limitations of standard approximation schemes and pinpoint the crossover from jump to Brownian diffusion regimes.

  18. Performance Evaluation of Counter-Based Dynamic Load Balancing Schemes for Massive Contingency Analysis with Different Computing Environments

    SciTech Connect

    Chen, Yousu; Huang, Zhenyu; Chavarría-Miranda, Daniel

    2010-09-30

    Contingency analysis is a key function in the Energy Management System (EMS) to assess the impact of various combinations of power system component failures based on state estimation. Contingency analysis is also extensively used in power market operation for feasibility test of market solutions. High performance computing holds the promise of faster analysis of more contingency cases for the purpose of safe and reliable operation of today’s power grids with less operating margin and more intermittent renewable energy sources. This paper evaluates the performance of counter-based dynamic load balancing schemes for massive contingency analysis under different computing environments. Insights from the performance evaluation can be used as guidance for users to select suitable schemes in the application of massive contingency analysis. Case studies, as well as MATLAB simulations, of massive contingency cases using the Western Electricity Coordinating Council power grid model are presented to illustrate the application of high performance computing with counter-based dynamic load balancing schemes.

  19. Dynamics of helical worm-like chains. VIII. Higher-order subspace approximations to dielectric and magnetic relaxation and fluorescence depolarization for flexible chains

    NASA Astrophysics Data System (ADS)

    Yamakawa, Hiromi; Yoshizaki, Takenao; Fujii, Motoharu

    1986-04-01

    Following the general scheme developed in the preceding paper (paper VII), dielectric and magnetic relaxation and fluorescence depolarization for flexible chain polymers in dilute solution are reinvestigated on the basis of the discrete helical worm-like chain in the higher-order subspace approximation. A comparison of theory with experiment is made with respect to the dielectric correlation time τD, the spin-lattice relaxation time T1, the spin-spin relaxation time T2, the nuclear Overhauser enhancement (NOE), the fluorescence emission anisotropy r(t), the average fluorescence anisotropy r¯, and the fluorescence correlation time τF. It is found that there is agreement between the diameters of the chains determined from these dynamic properties and those from chemical structures, better than in the previous crude subspace approximation, indicating that the theory is remarkably improved in the present approximation. The magnetic correlation time τM is in general not an observable, and therefore an empirical equation to be used for its determination from the observed T1 is constructed. It is then found that there is good correlation between the dynamic chain stiffness τX/τ0X and the static chain stiffness λ-1, where τ0X is the correlation time of the isolated subbody (monomer unit) with X=D, M, and F; τX/τ0X is a monotonically increasing function of λ-1 nearly independent of X as far as perpendicular dipoles are concerned. An explanation of this result is given. However, the dependence of τX on temperature cannot be explained very satisfactorily.

  20. Approximating the head characteristics and characteristic surfaces of dynamic pumps by means of an exponential function

    NASA Astrophysics Data System (ADS)

    Shekun, G. D.

    2009-08-01

    Results obtained from statistical and experimental studies of the head characteristics of commercially available centrifugal and free-vortex pumps are presented. A regression equation in the form of an exponential function written in a reduced-relative system of coordinates for approximating the head characteristics of blade pumps is obtained.

  1. Galerkin approximations for dissipative magnetohydrodynamics

    NASA Technical Reports Server (NTRS)

    Chen, Hudong; Shan, Xiaowen; Montgomery, David

    1990-01-01

    A Galerkin approximation scheme is proposed for voltage-driven, dissipative magnetohydrodynamics. The trial functions are exact eigenfunctions of the linearized continuum equations and represent helical deformations of the axisymmetric, zero-flow, driven steady state. The lowest nontrivial truncation is explored: one axisymmetric trial function and one helical trial function each for the magnetic and velocity fields. The system resembles the Lorenz approximation to Benard convection, but in the region of believed applicability, its dynamical behavior is rather different, including relaxation to a helically deformed state similar to those that have emerged in the much higher resolution computations of Dahlburg et al.

  2. A Massive Parallel Variational Multiscale FEM Scheme Applied to Nonhydrostatic Atmospheric Dynamics

    NASA Astrophysics Data System (ADS)

    Vazquez, Mariano; Marras, Simone; Moragues, Margarida; Jorba, Oriol; Houzeaux, Guillaume; Aubry, Romain

    2010-05-01

    The solution of the fully compressible Euler equations of stratified flows is approached from the point of view of Computational Fluid Dynamics techniques. Specifically, the main aim of this contribution is the introduction of a Variational Multiscale Finite Element (CVMS-FE) approach to solve dry atmospheric dynamics effectively on massive parallel architectures with more than 1000 processors. The conservation form of the equations of motion is discretized in all directions with a Galerkin scheme with stabilization given by the compressible counterpart of the variational multiscale technique of Hughes [1] and Houzeaux et al. [2]. The justification of this effort is twofold: the search of optimal parallelization characteristics and linear scalability trends on petascale machines is one. The development of a numerical algorithm whose local nature helps maintaining minimal the communication among the processors implies, in fact, a large leap towards efficient parallel computing. Second, the rising trend to global models and models of higher spatial resolution naturally suggests the use of adaptive grids to only resolve zones of larger gradients while keeping the computational mesh properly coarse elsewhere (thus keeping the computational cost low). With these two hypotheses in mind, the finite element scheme presented here is an open option to the development of the next generation Numerical Weather Prediction (NWP) codes. This methodology is as new in Computational Fluid Dynamics for compressible flows at low Mach number as it is in Numerical Weather Prediction (NWP). We however mean to show its ability to maintain stability in the solution of thermal, gravity-driven flows in a stratified environment in the specific context of dry atmospheric dynamics. Standard two dimensional benchmarks are implemented and compared against the reference literature. In the context of thermal and gravity-driven flows in a neutral atmosphere, we present: (1) the density current

  3. Atomic dynamics of the α-(Al,Si)CuFe alloy: A crystalline approximant of a quasicrystal...

    NASA Astrophysics Data System (ADS)

    Parshin, P. P.; Zemlyanov, M. G.; Brand, R. A.; Pavlyuchkov, D.; Ollivier, J.

    2010-07-01

    The atomic dynamics of the Al0.550Si0.070Cu0.255Fe0.125 alloy with the structure that approximates the structure of an icosahedral quasicrystal with a similar chemical composition has been investigated using inelastic neutron scattering. The partial vibrational spectra of copper, iron, and aluminum atoms and the total spectrum of thermal vibrations of the compound have been directly reconstructed from the experimental data for the first time. A combined analysis of the results obtained and the data on the atomic dynamics of the i-AlCuFe icosahedral quasicrystal has been performed.

  4. Breakdown of the ponderomotive approximation as an acceleration mechanism in wave-particle nonlinear dynamics

    NASA Astrophysics Data System (ADS)

    Marini, S.; Peter, E.; de Oliveira, G. I.; Rizzato, F. B.

    2017-09-01

    In the present analysis, we study the dynamics of charged particles submitted to the action of slowly modulated electromagnetic carrier waves. While the velocity of the particles remains smaller than the carrier's phase-velocity, their dynamics is well described by a refined ponderomotive approach. The ponderomotive approach has its own validity limits well established, beyond which particles are resonantly trapped by the carrier waves. We show that under adequate conditions, the trapping mechanism places particles at an optimal relative phase with respect to the carrier for maximum acceleration. In addition to the analytical approach involved in the ponderomotive description, we use numerical simulations to validate the corresponding dynamics as well as to explore various features of the resonant trapping and acceleration.

  5. Phase of transmitted wave in dynamical theory and quasi-kinematical approximation

    NASA Astrophysics Data System (ADS)

    Gorobtsov, O. Yu.; Vartanyants, I. A.

    2016-05-01

    Variation of the phase of the beam transmitted through a crystalline material as a function of the rocking angle is a well-known dynamical effect in x-ray scattering. Unfortunately, it is not so easy to directly measure these phase variations in a conventional scattering experiment. It was recently suggested that the transmitted phase can be directly measured in ptychography experiments performed on nanocrystal samples. Results of such experiment for different crystal thickness, reflections, and incoming photon energies, in principle, can be fully described in the frame of dynamical theory. However, dynamical theory does not provide a simple analytical expression for the further analysis. Here we develop a quasi-kinematical theory approach that allows one to correctly describe the phase of the transmitted beam for the crystal thickness less than extinction length that is beyond applicability of the conventional kinematical theory.

  6. Dynamic emission and population control in a Λ-type excitation scheme of atomic potassium

    NASA Astrophysics Data System (ADS)

    Papademetriou, G.; Pentaris, D.; Efthimiopoulos, T.; Lyras, A.

    2017-06-01

    The nonlinear interaction of a four-level atomic configuration in potassium, with ns pump and coupling fields, is numerically investigated. The resonant pump acts on the two-photon transition | 4{{{S}}}{1/2}> ≤ftrightarrow | 6{{{S}}}{1/2}> causing internally generated emissions in two atomic paths: path-1, | 4{{{S}}}{1/2}> ≤ftrightarrow | 6{{{S}}}{1/2}> ≤ftrightarrow | 5{{{P}}}{3/2}> ≤ftrightarrow | 4{{{S}}}{1/2}> , and path-2, | 4{{{S}}}{1/2}> ≤ftrightarrow | 6{{{S}}}{1/2}> ≤ftrightarrow | 4{{{P}}}{3/2}> ≤ftrightarrow | 4{{{S}}}{1/2}> , respectively. The coupling laser resonantly excites the single-photon transition | 6{{{S}}}{1/2}> \\to | 4{{{P}}}{3/2}> in a Λ-type scheme. A controlled temporal shift and enhancement of the partially coherent cascade emissions of path-2 is obtained. The amplification without inversion mechanism is proposed to explain the lower path-2 emission. It is shown that when the coupling field is delayed from the pump, then an efficient dynamic effect is induced, based on an additional population interplay of states | 6{{{S}}}{1/2}> and | 4{{{P}}}{3/2}> . Finally, a novel coherent method for temporally controlling the quasi-stationary population dynamics in a saturated system is proposed, when the driving fields are also delayed. The importance of the present work is related to the fact that the induced coherence (polarisation or energy injection) of the coupling field can be temporally controlled in nonlinear gaseous media.

  7. Large-scale molecular dynamics verification of the Rayleigh-Plesset approximation for collapse of nanobubbles

    NASA Astrophysics Data System (ADS)

    Hołyst, Robert; Litniewski, Marek; Garstecki, Piotr

    2010-12-01

    We report large-scale ( 107 atoms in an 85-nm-wide container) molecular dynamics simulations of collapse of nanoscopic (5-12 nm in diameter) voids in liquid argon. During the collapse the pressure on the liquid side decreases, and this decrease propagates into liquid at the speed of sound. Despite the nonuniform profile of pressure in the liquid the solutions of the Rayleigh-Plesset equation compares well to the measured evolution of the radius of the void and the velocity of the interface. Evaporation of liquid into the void does not affect the dynamics appreciably.

  8. On some approximations of the resultant contact forces and their applications in rigid body dynamics

    NASA Astrophysics Data System (ADS)

    Kudra, Grzegorz; Szewc, Michał; Wojtunik, Igor; Awrejcewicz, Jan

    2016-10-01

    The work presents the possible applications and effectiveness of certain class of models of the resultant friction force and rolling resistance. The friction models are based on the integral model constructed under assumption of fully developed sliding on the plane contact area of general shape and any pressure distribution. Then the integral model of friction force and moment are approximated based on Padé approximants and their generalizations. These models are expected to be computationally effective in numerical simulations of rigid bodies with frictional contacts, such like billiard balls, Thompson top, the wobble stone and many others. In the present work two different examples of application of the developed contact models are presented and tested: a) a billiard ball rolling and sliding on the plane horizontal table; b) a full ellipsoid of revolution in contact with plane and horizontal base.

  9. Automatic selection of dynamic data partitioning schemes for distributed memory multicomputers

    NASA Technical Reports Server (NTRS)

    Palermo, Daniel J.; Banerjee, Prithviraj

    1995-01-01

    For distributed memory multicomputers such as the Intel Paragon, the IBM SP-2, the NCUBE/2, and the Thinking Machines CM-5, the quality of the data partitioning for a given application is crucial to obtaining high performance. This task has traditionally been the user's responsibility, but in recent years much effort has been directed to automating the selection of data partitioning schemes. Several researchers have proposed systems that are able to produce data distributions that remain in effect for the entire execution of an application. For complex programs, however, such static data distributions may be insufficient to obtain acceptable performance. The selection of distributions that dynamically change over the course of a program's execution adds another dimension to the data partitioning problem. In this paper, we present a technique that can be used to automatically determine which partitionings are most beneficial over specific sections of a program while taking into account the added overhead of performing redistribution. This system is being built as part of the PARADIGM (PARAllelizing compiler for DIstributed memory General-purpose Multicomputers) project at the University of Illinois. The complete system will provide a fully automated means to parallelize programs written in a serial programming model obtaining high performance on a wide range of distributed-memory multicomputers.

  10. General Force-Field Parametrization Scheme for Molecular Dynamics Simulations of Conjugated Materials in Solution

    PubMed Central

    2016-01-01

    We describe a general scheme to obtain force-field parameters for classical molecular dynamics simulations of conjugated polymers. We identify a computationally inexpensive methodology for calculation of accurate intermonomer dihedral potentials and partial charges. Our findings indicate that the use of a two-step methodology of geometry optimization and single-point energy calculations using DFT methods produces potentials which compare favorably to high level theory calculation. We also report the effects of varying the conjugated backbone length and alkyl side-chain lengths on the dihedral profiles and partial charge distributions and determine the existence of converged lengths above which convergence is achieved in the force-field parameter sets. We thus determine which calculations are required for accurate parametrization and the scope of a given parameter set for variations to a given molecule. We perform simulations of long oligomers of dioctylfluorene and hexylthiophene in explicit solvent and find peristence lengths and end-length distributions consistent with experimental values. PMID:27397762

  11. Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

    NASA Technical Reports Server (NTRS)

    Batina, John T.

    1990-01-01

    Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

  12. Investigation of uncertainties of establishment schemes in dynamic global vegetation models

    NASA Astrophysics Data System (ADS)

    Song, Xiang; Zeng, Xiaodong

    2014-01-01

    In Dynamic Global Vegetation Models (DGVMs), the establishment of woody vegetation refers to flowering, fertilization, seed production, germination, and the growth of tree seedlings. It determines not only the population densities but also other important ecosystem structural variables. In current DGVMs, establishments of woody plant functional types (PFTs) are assumed to be either the same in the same grid cell, or largely stochastic. We investigated the uncertainties in the competition of establishment among coexisting woody PFTs from three aspects: the dependence of PFT establishments on vegetation states; background establishment; and relative establishment potentials of different PFTs. Sensitivity experiments showed that the dependence of establishment rate on the fractional coverage of a PFT favored the dominant PFT by increasing its share in establishment. While a small background establishment rate had little impact on equilibrium states of the ecosystem, it did change the timescale required for the establishment of alien species in pre-existing forest due to their disadvantage in seed competition during the early stage of invasion. Meanwhile, establishment purely from background (the scheme commonly used in current DGVMs) led to inconsistent behavior in response to the change in PFT specification (e.g., number of PFTs and their specification). Furthermore, the results also indicated that trade-off between individual growth and reproduction/colonization has significant influences on the competition of establishment. Hence, further development of establishment parameterization in DGVMs is essential in reducing the uncertainties in simulations of both ecosystem structures and successions.

  13. Dynamics of high-risk nonvaccine human papillomavirus types after actual vaccination scheme.

    PubMed

    Peralta, Raúl; Vargas-De-León, Cruz; Cabrera, Augusto; Miramontes, Pedro

    2014-01-01

    Human papillomavirus (HPV) has been identified as the main etiological factor in the developing of cervical cancer (CC). This finding has propitiated the development of vaccines that help to prevent the HPVs 16 and 18 infection. Both genotypes are associated with 70% of CC worldwide. In the present study, we aimed to determine the emergence of high-risk nonvaccine HPV after actual vaccination scheme to estimate the impact of the current HPV vaccines. A SIR-type model was used to study the HPV dynamics after vaccination. According to the results, our model indicates that the application of the vaccine reduces infection by target or vaccine genotypes as expected. However, numerical simulations of the model suggest the presence of the phenomenon called vaccine-induced pathogen strain replacement. Here, we report the following replacement mechanism: if the effectiveness of cross-protective immunity is not larger than the effectiveness of the vaccine, then the high-risk nonvaccine genotypes emerge. In this scenario, further studies of infection dispersion by HPV are necessary to ascertain the real impact of the current vaccines, primarily because of the different high-risk HPV types that are found in CC.

  14. Dynamics of High-Risk Nonvaccine Human Papillomavirus Types after Actual Vaccination Scheme

    PubMed Central

    Peralta, Raúl; Vargas-De-León, Cruz; Cabrera, Augusto; Miramontes, Pedro

    2014-01-01

    Human papillomavirus (HPV) has been identified as the main etiological factor in the developing of cervical cancer (CC). This finding has propitiated the development of vaccines that help to prevent the HPVs 16 and 18 infection. Both genotypes are associated with 70% of CC worldwide. In the present study, we aimed to determine the emergence of high-risk nonvaccine HPV after actual vaccination scheme to estimate the impact of the current HPV vaccines. A SIR-type model was used to study the HPV dynamics after vaccination. According to the results, our model indicates that the application of the vaccine reduces infection by target or vaccine genotypes as expected. However, numerical simulations of the model suggest the presence of the phenomenon called vaccine—induced pathogen strain replacement. Here, we report the following replacement mechanism: if the effectiveness of cross-protective immunity is not larger than the effectiveness of the vaccine, then the high-risk nonvaccine genotypes emerge. In this scenario, further studies of infection dispersion by HPV are necessary to ascertain the real impact of the current vaccines, primarily because of the different high-risk HPV types that are found in CC. PMID:24803952

  15. A unified scheme for ab initio molecular orbital theory and path integral molecular dynamics

    NASA Astrophysics Data System (ADS)

    Shiga, Motoyuki; Tachikawa, Masanori; Miura, Shinichi

    2001-11-01

    We present a general approach for accurate calculation of chemical substances which treats both nuclei and electrons quantum mechanically, adopting ab initio molecular orbital theory for the electronic structure and path integral molecular dynamics for the nuclei. The present approach enables the evaluation of physical quantities dependent on the nuclear configuration as well as the electronic structure, within the framework of Born-Oppenheimer adiabatic approximation. As an application, we give the path integral formulation of electric response properties—dipole moment and polarizability, which characterize the changes both in electronic structure and nuclear configuration at a given temperature when uniform electrostatic field is present. We also demonstrate the calculation of a water molecule using the present approach and the result of temperature and isotope effects is discussed.

  16. Measuring nonadiabaticity of molecular quantum dynamics with quantum fidelity and with its efficient semiclassical approximation.

    PubMed

    Zimmermann, Tomáš; Vaníček, Jiří

    2012-03-07

    We propose to measure nonadiabaticity of molecular quantum dynamics rigorously with the quantum fidelity between the Born-Oppenheimer and fully nonadiabatic dynamics. It is shown that this measure of nonadiabaticity applies in situations where other criteria, such as the energy gap criterion or the extent of population transfer, fail. We further propose to estimate this quantum fidelity efficiently with a generalization of the dephasing representation to multiple surfaces. Two variants of the multiple-surface dephasing representation (MSDR) are introduced, in which the nuclei are propagated either with the fewest-switches surface hopping or with the locally mean field dynamics (LMFD). The LMFD can be interpreted as the Ehrenfest dynamics of an ensemble of nuclear trajectories, and has been used previously in the nonadiabatic semiclassical initial value representation. In addition to propagating an ensemble of classical trajectories, the MSDR requires evaluating nonadiabatic couplings and solving the Schrödinger (or more generally, the quantum Liouville-von Neumann) equation for a single discrete degree of freedom. The MSDR can be also used in the diabatic basis to measure the importance of the diabatic couplings. The method is tested on three model problems introduced by Tully and on a two-surface model of dissociation of NaI.

  17. A unified thermostat scheme for efficient configurational sampling for classical/quantum canonical ensembles via molecular dynamics

    NASA Astrophysics Data System (ADS)

    Zhang, Zhijun; Liu, Xinzijian; Chen, Zifei; Zheng, Haifeng; Yan, Kangyu; Liu, Jian

    2017-07-01

    We show a unified second-order scheme for constructing simple, robust, and accurate algorithms for typical thermostats for configurational sampling for the canonical ensemble. When Langevin dynamics is used, the scheme leads to the BAOAB algorithm that has been recently investigated. We show that the scheme is also useful for other types of thermostats, such as the Andersen thermostat and Nosé-Hoover chain, regardless of whether the thermostat is deterministic or stochastic. In addition to analytical analysis, two 1-dimensional models and three typical real molecular systems that range from the gas phase, clusters, to the condensed phase are used in numerical examples for demonstration. Accuracy may be increased by an order of magnitude for estimating coordinate-dependent properties in molecular dynamics (when the same time interval is used), irrespective of which type of thermostat is applied. The scheme is especially useful for path integral molecular dynamics because it consistently improves the efficiency for evaluating all thermodynamic properties for any type of thermostat.

  18. Beam dynamics design of an RFQ for a planned accelerator, which uses a direct plasma injection scheme

    NASA Astrophysics Data System (ADS)

    Zhang, Zhou-Li; Jameson, R. A.; Zhao, Hong-Wei; Liu, Yong; Zhang, Sheng-Hu; Zhang, Cong

    2008-07-01

    To meet the requirements of providing high-intensity heavy ion beams the direct plasma injection scheme (DPIS) was proposed by a RIKEN-CNS-TIT collaboration. In this scheme a radio frequency quadrupole (RFQ) was joined directly with the laser ion source (LIS) without a low-energy beam transport (LEBT) line. To find the best design of the RFQ that will have short length, high transmission efficiency and small emittance growth, beam dynamics designs with equipartitioning design strategy and with matched-only design strategy have been performed, and a comparison of their results has also been done. Impacts of the input beam parameters on transmission efficiency are presented, too.

  19. Non-Markovian dynamics for an open two-level system without rotating wave approximation: indivisibility versus backflow of information

    NASA Astrophysics Data System (ADS)

    Zeng, H. S.; Tang, N.; Zheng, Y. P.; Xu, T. T.

    2012-10-01

    By use of the recently presented two measures, the indivisibility and the backflow of information, we study the non-Markovianity of the dynamics for a two-level system interacting with a zero-temperature structured environment without using rotating wave approximation (RWA). In the limit of weak coupling between the system and its reservoir, and by expanding the time-convolutionless (TCL) generator to the forth order with respect to the coupling strength, the time-local non-Markovian master equation for the reduced state of the system is derived. Under the secular approximation, the exact analytic solution is obtained and the sufficient and necessary conditions for the indivisibility and the backflow of information for the system dynamics are presented. In the more general case, we investigate numerically the properties of the two measures for the case of Lorentzian reservoir. Our results show the importance of the counter-rotating terms to the short-time-scale non-Markovian behavior of the system dynamics, further expose the relation between the two measures and their rationality as non-Markovian measures. Finally, the complete positivity of the dynamics of the considered system is discussed.

  20. Kinematic and dynamic modeling and approximate analysis of a roller chain drive

    NASA Astrophysics Data System (ADS)

    Fuglede, Niels; Thomsen, Jon Juel

    2016-03-01

    A simple roller chain drive consisting of two sprockets connected by tight chain spans is investigated. First, a kinematic model is presented which include both spans and sprockets. An approach for calculating the chain wrapping length is presented, which also allows for the exact calculation of sprocket center positions for a given chain length. The kinematic analysis demonstrates that the total length of the chain wrapped around the sprockets generally varies during one tooth period. Analytical predictions for the wrapping length are compared to multibody simulation results and show very good agreement. It is thereby demonstrated that chain drives with tight chain spans must include compliant components to function. Second, a dynamic model is presented which includes the two spans and the driven sprocket. Assuming the presence of a stationary operating state, the presented dynamic model allows for analytical studies of the coupled motion of the chain spans and driven sprocket. Parametric excitation of the spans come from sprocket angular displacements, and the driven sprocket acts as a boundary which can be compliant in the axial direction. External transverse excitation of the spans comes from polygonal action, and is treated through kinematic forcing at the moving string boundaries. Perturbation analysis of the model is carried out using the method of multiple scales. Results show a multitude of internal and external resonance conditions, and some examples are presented of both decoupled and coupled motion. Together, the kinematic and dynamic model are aimed toward providing a framework for conducting and understanding both numerical, and experimental investigations of roller chain drive dynamics.

  1. Calculation of static and dynamic linear magnetic response in approximate time-dependent density functional theory.

    PubMed

    Krykunov, Mykhaylo; Autschbach, Jochen

    2007-01-14

    We report implementations and results of time-dependent density functional calculations (i) of the frequency-dependent magnetic dipole-magnetic dipole polarizability, (ii) of the (observable) translationally invariant linear magnetic response, and (iii) of a linear intensity differential (LID) which includes the dynamic dipole magnetizability. The density functional calculations utilized density fitting. For achieving gauge-origin independence we have employed time-periodic magnetic-field-dependent basis functions as well as the dipole velocity gauge, and have included explicit density-fit related derivatives of the Coulomb potential. We present the results of calculations of static and dynamic magnetic dipole-magnetic dipole polarizabilities for a set of small molecules, the LID for the SF6 molecule, and dispersion curves for M-hexahelicene of the origin invariant linear magnetic response as well as of three dynamic polarizabilities: magnetic dipole-magnetic dipole, electric dipole-electric dipole, and electric dipole-magnetic dipole. We have also performed comparison of the linear magnetic response and magnetic dipole-magnetic dipole polarizability over a wide range of frequencies for H2O and SF6.

  2. Quantum Dynamics of Dark and Dark-Bright Solitons beyond the Mean-Field Approximation

    NASA Astrophysics Data System (ADS)

    Krönke, Sven; Schmelcher, Peter

    2014-05-01

    Dark solitons are well-known excitations in one-dimensional repulsively interacting Bose-Einstein condensates, which feature a characteristical phase-jump across a density dip and form stability in the course of their dynamics. While these objects are stable within the celebrated Gross-Pitaevskii mean-field theory, the situation changes dramatically in the full many-body description: The condensate being initially in a dark soliton state dynamically depletes and the density notch fills up with depleted atoms. We analyze this process in detail with a particular focus on two-body correlations and the fate of grey solitons (dark solitons with finite density in the notch) and thereby complement the existing results in the literature. Moreover, we extend these studies to mixtures of two repulsively interacting bosonic species with a dark-bright soliton (dark soliton in one component filled with localized atoms of the other component) as the initial state. All these many-body quantum dynamics simulations are carried out with the recently developed multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB).

  3. Communication: On the consistency of approximate quantum dynamics simulation methods for vibrational spectra in the condensed phase

    NASA Astrophysics Data System (ADS)

    Rossi, Mariana; Liu, Hanchao; Paesani, Francesco; Bowman, Joel; Ceriotti, Michele

    2014-11-01

    Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here, we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer model and a mixed quantum-classical model as representatives of the first family of methods, and centroid molecular dynamics and thermostatted ring polymer molecular dynamics as examples of the latter. We use as benchmarks D2O doped with HOD and pure H2O at three distinct thermodynamic state points (ice Ih at 150 K, and the liquid at 300 K and 600 K), modeled with the simple q-TIP4P/F potential energy and dipole moment surfaces. With few exceptions the different techniques yield IR absorption frequencies that are consistent with one another within a few tens of cm-1. Comparison with classical molecular dynamics demonstrates the importance of nuclear quantum effects up to the highest temperature, and a detailed discussion of the discrepancies between the various methods let us draw some (circumstantial) conclusions about the impact of the very different approximations that underlie them. Such cross validation between radically different approaches could indicate a way forward to further improve the state of the art in simulations of condensed-phase quantum dynamics.

  4. Communication: On the consistency of approximate quantum dynamics simulation methods for vibrational spectra in the condensed phase.

    PubMed

    Rossi, Mariana; Liu, Hanchao; Paesani, Francesco; Bowman, Joel; Ceriotti, Michele

    2014-11-14

    Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here, we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer model and a mixed quantum-classical model as representatives of the first family of methods, and centroid molecular dynamics and thermostatted ring polymer molecular dynamics as examples of the latter. We use as benchmarks D2O doped with HOD and pure H2O at three distinct thermodynamic state points (ice Ih at 150 K, and the liquid at 300 K and 600 K), modeled with the simple q-TIP4P/F potential energy and dipole moment surfaces. With few exceptions the different techniques yield IR absorption frequencies that are consistent with one another within a few tens of cm(-1). Comparison with classical molecular dynamics demonstrates the importance of nuclear quantum effects up to the highest temperature, and a detailed discussion of the discrepancies between the various methods let us draw some (circumstantial) conclusions about the impact of the very different approximations that underlie them. Such cross validation between radically different approaches could indicate a way forward to further improve the state of the art in simulations of condensed-phase quantum dynamics.

  5. Communication: On the consistency of approximate quantum dynamics simulation methods for vibrational spectra in the condensed phase

    SciTech Connect

    Rossi, Mariana; Liu, Hanchao; Bowman, Joel; Paesani, Francesco; Ceriotti, Michele

    2014-11-14

    Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here, we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer model and a mixed quantum-classical model as representatives of the first family of methods, and centroid molecular dynamics and thermostatted ring polymer molecular dynamics as examples of the latter. We use as benchmarks D{sub 2}O doped with HOD and pure H{sub 2}O at three distinct thermodynamic state points (ice Ih at 150 K, and the liquid at 300 K and 600 K), modeled with the simple q-TIP4P/F potential energy and dipole moment surfaces. With few exceptions the different techniques yield IR absorption frequencies that are consistent with one another within a few tens of cm{sup −1}. Comparison with classical molecular dynamics demonstrates the importance of nuclear quantum effects up to the highest temperature, and a detailed discussion of the discrepancies between the various methods let us draw some (circumstantial) conclusions about the impact of the very different approximations that underlie them. Such cross validation between radically different approaches could indicate a way forward to further improve the state of the art in simulations of condensed-phase quantum dynamics.

  6. A scatter-corrected list-mode reconstruction and a practical scatter/random approximation technique for dynamic PET imaging

    NASA Astrophysics Data System (ADS)

    Cheng, Ju-Chieh Kevin; Rahmim, Arman; Blinder, Stephan; Camborde, Marie-Laure; Raywood, Kelvin; Sossi, Vesna

    2007-04-01

    We describe an ordinary Poisson list-mode expectation maximization (OP-LMEM) algorithm with a sinogram-based scatter correction method based on the single scatter simulation (SSS) technique and a random correction method based on the variance-reduced delayed-coincidence technique. We also describe a practical approximate scatter and random-estimation approach for dynamic PET studies based on a time-averaged scatter and random estimate followed by scaling according to the global numbers of true coincidences and randoms for each temporal frame. The quantitative accuracy achieved using OP-LMEM was compared to that obtained using the histogram-mode 3D ordinary Poisson ordered subset expectation maximization (3D-OP) algorithm with similar scatter and random correction methods, and they showed excellent agreement. The accuracy of the approximated scatter and random estimates was tested by comparing time activity curves (TACs) as well as the spatial scatter distribution from dynamic non-human primate studies obtained from the conventional (frame-based) approach and those obtained from the approximate approach. An excellent agreement was found, and the time required for the calculation of scatter and random estimates in the dynamic studies became much less dependent on the number of frames (we achieved a nearly four times faster performance on the scatter and random estimates by applying the proposed method). The precision of the scatter fraction was also demonstrated for the conventional and the approximate approach using phantom studies. This work was supported by the Canadian Institute of Health Research, a TRIUMF Life Science Grant, the Natural Sciences and Engineering Research Council of Canada UFA (V Sossi) and the Michael Smith Foundation for Health Research Scholarship (V Sossi).

  7. A Dynamically Computed Convective Time Scale for the Kain–Fritsch Convective Parameterization Scheme

    EPA Science Inventory

    Many convective parameterization schemes define a convective adjustment time scale τ as the time allowed for dissipation of convective available potential energy (CAPE). The Kain–Fritsch scheme defines τ based on an estimate of the advective time period for deep con...

  8. A Dynamically Computed Convective Time Scale for the Kain–Fritsch Convective Parameterization Scheme

    EPA Science Inventory

    Many convective parameterization schemes define a convective adjustment time scale τ as the time allowed for dissipation of convective available potential energy (CAPE). The Kain–Fritsch scheme defines τ based on an estimate of the advective time period for deep con...

  9. The spatiotemporal master equation: Approximation of reaction-diffusion dynamics via Markov state modeling

    NASA Astrophysics Data System (ADS)

    Winkelmann, Stefanie; Schütte, Christof

    2016-12-01

    Accurate modeling and numerical simulation of reaction kinetics is a topic of steady interest. We consider the spatiotemporal chemical master equation (ST-CME) as a model for stochastic reaction-diffusion systems that exhibit properties of metastability. The space of motion is decomposed into metastable compartments, and diffusive motion is approximated by jumps between these compartments. Treating these jumps as first-order reactions, simulation of the resulting stochastic system is possible by the Gillespie method. We present the theory of Markov state models as a theoretical foundation of this intuitive approach. By means of Markov state modeling, both the number and shape of compartments and the transition rates between them can be determined. We consider the ST-CME for two reaction-diffusion systems and compare it to more detailed models. Moreover, a rigorous formal justification of the ST-CME by Galerkin projection methods is presented.

  10. Barycentric approximation in financial decision making

    SciTech Connect

    Frauendorfer, K.

    1994-12-31

    We consider dynamic portfolio selection problems which are exposed to interest rate risk and credit risk caused by stochastic cash-flows and interest rates. For maximizing the expected net present value, we apply the barycentric approximation scheme of stochastic programming and discuss its features to be utilized in financial decision making. In particular, we focus on the martingale property, the term structure of interest rates, cash-flow dynamics, and correlations of the later two.

  11. Approximate analytical solutions to the double-stance dynamics of the lossy spring-loaded inverted pendulum.

    PubMed

    Shahbazi, Mohammad; Saranlı, Uluç; Babuška, Robert; Lopes, Gabriel A D

    2016-12-05

    This paper introduces approximate time-domain solutions to the otherwise non-integrable double-stance dynamics of the 'bipedal' spring-loaded inverted pendulum (B-SLIP) in the presence of non-negligible damping. We first introduce an auxiliary system whose behavior under certain conditions is approximately equivalent to the B-SLIP in double-stance. Then, we derive approximate solutions to the dynamics of the new system following two different methods: (i) updated-momentum approach that can deal with both the lossy and lossless B-SLIP models, and (ii) perturbation-based approach following which we only derive a solution to the lossless case. The prediction performance of each method is characterized via a comprehensive numerical analysis. The derived representations are computationally very efficient compared to numerical integrations, and, hence, are suitable for online planning, increasing the autonomy of walking robots. Two application examples of walking gait control are presented. The proposed solutions can serve as instrumental tools in various fields such as control in legged robotics and human motion understanding in biomechanics.

  12. The effect of rheological approximations on the dynamics and topography in 3D subduction-collision models

    NASA Astrophysics Data System (ADS)

    Pusok, Adina E.; Kaus, Boris J. P.; Popov, Anton A.

    2016-04-01

    Most of the major mountain belts and orogenic plateaus are found within the overlying plate of active or fossil subduction and/or collision zones. Moreover, they evolve differently from one another as the result of specific combinations of surface and mantle processes. These differences arise for several reasons, such as different rheological properties, different amounts of regional isostatic compensation, and different mechanisms by which forces are applied to the convergent plates. Previous 3D geodynamic models of subduction/collision processes have used various rheological approximations, making numerical results difficult to compare, since there is no clear image on the extent of these approximations on the dynamics. Here, we employ the code LaMEM to perform high-resolution long-term 3D simulations of subduction/continental collision in an integrated lithospheric and upper-mantle scale model. We test the effect of rheological approximations on mantle and lithosphere dynamics in a geometrically simplified model setup that resembles a tectonic map of the India-Asia collision zone. We use the "sticky-air" approach to allow for the development of topography and the dynamics of subduction and collision is entirely driven by slab-pull (i.e. "free subduction"). The models exhibit a wide range of behaviours depending on the rheological law employed: from linear to temperature-dependent visco-elasto-plastic rheology that takes into account both diffusion and dislocation creep. For example, we find that slab dynamics varies drastically between end member models: in viscous approximations, slab detachment is slow following a viscous thinning, while for a non-linear visco-elasto-plastic rheology, slab detachment is relatively fast, inducing strong mantle flow in the slab window. We also examine the stress states in the subducting and overriding plates and topography evolution in the upper plate, and we discuss the implications on lithosphere dynamics at convergent margins

  13. The effect of a dynamic soil scheme on the climate of the mid-Holocene and the Last Glacial Maximum

    NASA Astrophysics Data System (ADS)

    Stärz, M.; Lohmann, G.; Knorr, G.

    2016-01-01

    In order to account for coupled climate-soil processes, we have developed a soil scheme which is asynchronously coupled to a comprehensive climate model with dynamic vegetation. This scheme considers vegetation as the primary control of changes in physical soil characteristics. We test the scheme for a warmer (mid-Holocene) and colder (Last Glacial Maximum) climate relative to the preindustrial climate. We find that the computed changes in physical soil characteristics lead to significant amplification of global climate anomalies, representing a positive feedback. The inclusion of the soil feedback yields an extra surface warming of 0.24 °C for the mid-Holocene and an additional global cooling of 1.07 °C for the Last Glacial Maximum. Transition zones such as desert-savannah and taiga-tundra exhibit a pronounced response in the model version with dynamic soil properties. Energy balance model analyses reveal that our soil scheme amplifies the temperature anomalies in the mid-to-high northern latitudes via changes in the planetary albedo and the effective longwave emissivity. As a result of the modified soil treatment and the positive feedback to climate, part of the underestimated mid-Holocene temperature response to orbital forcing can be reconciled in the model.

  14. The effect of a dynamic soil scheme on the climate of the mid-Holocene and the Last Glacial Maximum

    NASA Astrophysics Data System (ADS)

    Stärz, Michael; Lohmann, Gerrit; Knorr, Gregor

    2016-04-01

    In order to account for coupled climate-soil processes, we have developed a soil scheme, which is asynchronously coupled to a comprehensive climate model with dynamic vegetation. This scheme considers vegetation as the primary control of changes in physical soil characteristics. We test the scheme for a warmer (mid-Holocene) and colder (Last Glacial Maximum) climate relative to the preindustrial climate. We find that the computed changes of physical soil characteristics lead to significant amplification of global climate anomalies, representing a positive feedback. The inclusion of the soil feedback yields an extra surface warming of 0.24°C for the mid-Holocene and an additional global cooling of 1.07°C for the Last Glacial Maximum. Transition zones such as desert/savannah and taiga/tundra exhibit a pronounced response in the model version with dynamic soil properties. Energy balance model analyses reveal that our soil scheme amplifies the temperature anomalies in the mid-to-high northern latitudes via changes in the planetary albedo and the effective longwave emissivity. As a result of the modified soil treatment and the positive feedback on climate, part of the underestimated mid-Holocene temperature response to orbital forcing can be reconciled in the model.

  15. Ordering and dynamics of the central tetrahedron in the 1/1 Zn6Sc periodic approximant to quasicrystal.

    PubMed

    Euchner, Holger; Yamada, Tsunetomo; Schober, Helmut; Rols, Stephane; Mihalkovič, Marek; Tamura, Ryuji; Ishimasa, Tsutomu; de Boissieu, Marc

    2012-10-17

    Periodic approximants to quasicrystals offer a unique opportunity to better understand the structure, physical properties and stabilizing mechanisms of their quasicrystal counterparts. We present a detailed study of the order-disorder phase transition occurring at about 160 K in the Zn(6)Sc cubic approximant to the icosahedral quasicrystal i-MgZnSc. This transition goes along with an anti-parallel ordering of the tetrahedra located at the centres of large atomic clusters, which are packed on a bcc lattice. Single crystal x-ray diffuse scattering shows that the tetrahedra display pre-transitional short range ordering above T(c) (Yamada et al 2012 in preparation). Using quasielastic neutron scattering (QENS) we clearly evidence this short range order to be dynamical in nature above T(c). The QENS data are consistent with a model of tetrahedra 'jumping' between almost equivalent positions, which is supported by molecular dynamics simulations. This demonstrates a unique dynamical flexibility of the Zn(6)Sc structure even at room temperature.

  16. Testing approximations for non-linear gravitational clustering

    NASA Technical Reports Server (NTRS)

    Coles, Peter; Melott, Adrian L.; Shandarin, Sergei F.

    1993-01-01

    The accuracy of various analytic approximations for following the evolution of cosmological density fluctuations into the nonlinear regime is investigated. The Zel'dovich approximation is found to be consistently the best approximation scheme. It is extremely accurate for power spectra characterized by n = -1 or less; when the approximation is 'enhanced' by truncating highly nonlinear Fourier modes the approximation is excellent even for n = +1. The performance of linear theory is less spectrum-dependent, but this approximation is less accurate than the Zel'dovich one for all cases because of the failure to treat dynamics. The lognormal approximation generally provides a very poor fit to the spatial pattern.

  17. [Approximation of Time Series of Paramecia caudatum Dynamics by Verhulst and Gompertz Models: Non-traditional Approach].

    PubMed

    Nedorezov, L V

    2015-01-01

    For approximation of some well-known time series of Paramecia caudatun population dynamics (G. F. Gause, The Struggle for Existence, 1934) Verhulst and Gompertz models were used. The parameters were estimated for each of the models in two different ways: with the least squares method (global fitting) and non-traditional approach (a method of extreme points). The results obtained were compared and also with those represented by G. F. Gause. Deviations of theoretical (model) trajectories from experimental time series were tested using various non-parametric statistical tests. It was shown that the least square method-estimations lead to the results which not always meet the requirements imposed for a "fine" model. But in some cases a small modification of the least square method-estimations is possible allowing for satisfactory representations of experimental data set for approximation.

  18. The effect of mass loss on the dynamical evolution of a stellar system - Analytic approximations

    NASA Astrophysics Data System (ADS)

    Hills, J. G.

    1980-02-01

    If half or more of the mass of a virialized system is lost in less than one dynamical crossing time, the system dissociates. If the mass loss occurs in a collapsing protosystem with uniform density, no angular momentum, and relatively little radiation of energy, the minimum fractional mass loss required for dissociation is reduced to ΔM/M0 = Rc/(2R0). Here Rc is the radius of the system when the mass loss occurs and R0 is the radius it would have attained after virialization if no mass loss had occurred. A situation of this type is expected in a protocluster that forms from a collapsing interstellar cloud. The stars form when the protocluster is near its point of maximum compression. Any newly formed OB stars produce an H II region whose expansion dissipates the residual gas in the protocluster before the system reaches dynamical equilibrium. The angular momentum of the protosystem and any radiative losses from it prior to star formation will tend to stabilize it against mass loss by limiting the compression factor 2R0/Rc. The angular momentum places a lower limit on the radius Rc, and the radiative losses reduce the final equilibrium radius R0. However, observed infantile clusters such as the Trapezium are sufficiently compressed at the present time that a loss of as little as 10% of their mass is sufficient to dissociate them. This may explain why most young stars are not located in gravitationally bound clusters. If the protocluster gas contains an appreciable magnetic field, the compression of this field in the collapsing cloud drains off some of the gravitational energy that otherwise would go into the kinetic energy of collapse. This increases the minimum mass loss required to dissociate the system, but it is still very small for most systems. The mean terminal expansion velocity of an association produced by the breakup of a protocluster is usually comparable to the velocity dispersion in an open cluster and cannot be larger than the expansion velocity of

  19. Numerical simulation of the debris flow dynamics with an upwind scheme and specific friction treatment

    NASA Astrophysics Data System (ADS)

    Sánchez Burillo, Guillermo; Beguería, Santiago; Latorre, Borja; Burguete, Javier

    2014-05-01

    Debris flows, snow and rock avalanches, mud and earth flows are often modeled by means of a particular realization of the so called shallow water equations (SWE). Indeed, a number of simulation models have been already developed [1], [2], [3], [4], [5], [6], [7]. Debris flow equations differ from shallow water equations in two main aspects. These are (a) strong bed gradient and (b) rheology friction terms that differ from the traditional SWE. A systematic analysis of the numerical solution of the hyperbolic system of equations rising from the shallow water equations with different rheological laws has not been done. Despite great efforts have been done to deal with friction expressions common in hydraulics (such as Manning friction), landslide rheologies are characterized by more complicated expressions that may deal to unphysical solutions if not treated carefully. In this work, a software that solves the time evolution of sliding masses over complex bed configurations is presented. The set of non- linear equations is treated by means of a first order upwind explicit scheme, and the friction contribution to the dynamics is treated with a suited numerical scheme [8]. In addition, the software incorporates various rheological models to accommodate for different flow types, such as the Voellmy frictional model [9] for rock and debris avalanches, or the Herschley-Bulkley model for debris and mud flows. The aim of this contribution is to release this code as a free, open source tool for the simulation of mass movements, and to encourage the scientific community to make use of it. The code uses as input data the friction coefficients and two input files: the topography of the bed and the initial (pre-failure) position of the sliding mass. In addition, another file with the final (post-event) position of the sliding mass, if desired, can be introduced to be compared with the simulation obtained result. If the deposited mass is given, an error estimation is computed by

  20. Speed of sound in solid molecular hydrogen-deuterium: Quantum Molecular Dynamics Approximation

    NASA Astrophysics Data System (ADS)

    Guerrero, Carlo Luis; Perlado, Jose Manuel

    2016-05-01

    Uniformity of the solid layer is one of the critical points for an efficient ignition of the Deuterium-Tritium (DT) target. During the compression process this layer, perturbations grow as the Rayleigh-Taylor instability. Knowing the mechanical properties of this layer and its thermo-mechanical limits is necessary if we want to control or to minimize these instabilities. In this work we have used a simplified approach, replacing the DT ice system with a mixture of hydrogen-deuterium (HD) because beta decay of tritium complicates the analysis in the former case. Through simulation with ab initio methods we have calculated the elastic constants, the bulk modulus and sound velocity for hydrogen isotopes in solid molecular state. In this work we present the results for hydrogen-deuterium mixtures 50%-50%, at 15 K and with a compression which covers the range of 1 to 15 GPa. This system is interesting for study the early stages of the dynamic compression and provides conditions that are close to the manufacture of DT target in inertial confinement fusion. Discontinuities in the curve that have been observed on pure hydrogen, which are associated with phase transitions and the phase hysteresis.

  1. Dynamic Key Management Schemes for Secure Group Access Control Using Hierarchical Clustering in Mobile Ad Hoc Networks

    NASA Astrophysics Data System (ADS)

    Tsaur, Woei-Jiunn; Pai, Haw-Tyng

    2008-11-01

    The applications of group computing and communication motivate the requirement to provide group access control in mobile ad hoc networks (MANETs). The operation in MANETs' groups performs a decentralized manner and accommodated membership dynamically. Moreover, due to lack of centralized control, MANETs' groups are inherently insecure and vulnerable to attacks from both within and outside the groups. Such features make access control more challenging in MANETs. Recently, several researchers have proposed group access control mechanisms in MANETs based on a variety of threshold signatures. However, these mechanisms cannot actually satisfy MANETs' dynamic environments. This is because the threshold-based mechanisms cannot be achieved when the number of members is not up to the threshold value. Hence, by combining the efficient elliptic curve cryptosystem, self-certified public key cryptosystem and secure filter technique, we construct dynamic key management schemes based on hierarchical clustering for securing group access control in MANETs. Specifically, the proposed schemes can constantly accomplish secure group access control only by renewing the secure filters of few cluster heads, when a cluster head joins or leaves a cross-cluster. In such a new way, we can find that the proposed group access control scheme can be very effective for securing practical applications in MANETs.

  2. Dynamical screening in correlated metals: Spectral properties of SrVO3 in the GW approximation and beyond

    NASA Astrophysics Data System (ADS)

    Gatti, Matteo; Guzzo, Matteo

    2013-04-01

    SrVO3 is a prototypical strongly correlated metal. Here we interpret the signatures of electronic correlation measured in photoemission spectroscopy by combining the many-body GW approximation of the self-energy with an exponential representation of the Green's function. We explain those correlation effects as the consequence of the dynamical screening of the Coulomb interaction and the coupling between elementary excitations in the solid. Moreover we address the issue of satellites for empty states and discuss the possibility of plasmon-satellite series above the Fermi energy EF. In good agreement with experiment, we obtain from first principles the renormalization of the V 3d quasiparticle bands and the satellites close to EF that so far have been interpreted on the basis of the Hubbard model. Finally, we identify incoherent features due to dynamical correlation also at the bottom of the O 2p bands, beyond the traditional three-band Hubbard-model description.

  3. A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator

    DOE PAGES

    Haut, T. S.; Babb, T.; Martinsson, P. G.; ...

    2015-06-16

    Our manuscript demonstrates a technique for efficiently solving the classical wave equation, the shallow water equations, and, more generally, equations of the form ∂u/∂t=Lu∂u/∂t=Lu, where LL is a skew-Hermitian differential operator. The idea is to explicitly construct an approximation to the time-evolution operator exp(τL)exp(τL) for a relatively large time-step ττ. Recently developed techniques for approximating oscillatory scalar functions by rational functions, and accelerated algorithms for computing functions of discretized differential operators are exploited. Principal advantages of the proposed method include: stability even for large time-steps, the possibility to parallelize in time over many characteristic wavelengths and large speed-ups over existingmore » methods in situations where simulation over long times are required. Numerical examples involving the 2D rotating shallow water equations and the 2D wave equation in an inhomogenous medium are presented, and the method is compared to the 4th order Runge–Kutta (RK4) method and to the use of Chebyshev polynomials. The new method achieved high accuracy over long-time intervals, and with speeds that are orders of magnitude faster than both RK4 and the use of Chebyshev polynomials.« less

  4. A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator

    SciTech Connect

    Haut, T. S.; Babb, T.; Martinsson, P. G.; Wingate, B. A.

    2015-06-16

    Our manuscript demonstrates a technique for efficiently solving the classical wave equation, the shallow water equations, and, more generally, equations of the form ∂u/∂t=Lu∂u/∂t=Lu, where LL is a skew-Hermitian differential operator. The idea is to explicitly construct an approximation to the time-evolution operator exp(τL)exp(τL) for a relatively large time-step ττ. Recently developed techniques for approximating oscillatory scalar functions by rational functions, and accelerated algorithms for computing functions of discretized differential operators are exploited. Principal advantages of the proposed method include: stability even for large time-steps, the possibility to parallelize in time over many characteristic wavelengths and large speed-ups over existing methods in situations where simulation over long times are required. Numerical examples involving the 2D rotating shallow water equations and the 2D wave equation in an inhomogenous medium are presented, and the method is compared to the 4th order Runge–Kutta (RK4) method and to the use of Chebyshev polynomials. The new method achieved high accuracy over long-time intervals, and with speeds that are orders of magnitude faster than both RK4 and the use of Chebyshev polynomials.

  5. A distributed scheme to manage the dynamic coexistence of IEEE 802.15.4-based health-monitoring WBANs.

    PubMed

    Deylami, Mohammad N; Jovanov, Emil

    2014-01-01

    The overlap of transmission ranges between wireless networks as a result of mobility is referred to as dynamic coexistence. The interference caused by coexistence may significantly affect the performance of wireless body area networks (WBANs) where reliability is particularly critical for health monitoring applications. In this paper, we analytically study the effects of dynamic coexistence on the operation of IEEE 802.15.4-based health monitoring WBANs. The current IEEE 802.15.4 standard lacks mechanisms for effectively managing the coexistence of mobile WBANs. Considering the specific characteristics and requirements of health monitoring WBANs, we propose the dynamic coexistence management (DCM) mechanism to make IEEE 802.15.4-based WBANs able to detect and mitigate the harmful effects of coexistence. We assess the effectiveness of this scheme using extensive OPNET simulations. Our results indicate that DCM improves the successful transmission rates of dynamically coexisting WBANs by 20%-25% for typical medical monitoring applications.

  6. Quantum dynamics of incoherently driven V-type systems: Analytic solutions beyond the secular approximation.

    PubMed

    Dodin, Amro; Tscherbul, Timur V; Brumer, Paul

    2016-06-28

    Closed-form analytic solutions to non-secular Bloch-Redfield master equations for quantum dynamics of a V-type system driven by weak coupling to a thermal bath, relevant to light harvesting processes, are obtained and discussed. We focus on noise-induced Fano coherences among the excited states induced by incoherent driving of the V-system initially in the ground state. For suddenly turned-on incoherent driving, the time evolution of the coherences is determined by the damping parameter ζ=12(γ1+γ2)/Δp, where γi are the radiative decay rates of the excited levels i = 1, 2, and Δp=Δ(2)+(1-p(2))γ1γ2 depends on the excited-state level splitting Δ > 0 and the angle between the transition dipole moments in the energy basis. The coherences oscillate as a function of time in the underdamped limit (ζ ≫ 1), approach a long-lived quasi-steady state in the overdamped limit (ζ ≪ 1), and display an intermediate behavior at critical damping (ζ = 1). The sudden incoherent turn-on is shown to generate a mixture of excited eigenstates |e1〉 and |e2〉 and their in-phase coherent superposition |ϕ+〉=1r1+r2(r1|e1〉+r2|e2〉), which is remarkably long-lived in the overdamped limit (where r1 and r2 are the incoherent pumping rates). Formation of this coherent superposition enhances the decay rate from the excited states to the ground state. In the strongly asymmetric V-system where the coupling strengths between the ground state and the excited states differ significantly, additional asymptotic quasistationary coherences are identified, which arise due to slow equilibration of one of the excited states. Finally, we demonstrate that noise-induced Fano coherences are maximized with respect to populations when r1 = r2 and the transition dipole moments are fully aligned.

  7. Quantum dynamics of incoherently driven V-type systems: Analytic solutions beyond the secular approximation

    NASA Astrophysics Data System (ADS)

    Dodin, Amro; Tscherbul, Timur V.; Brumer, Paul

    2016-06-01

    Closed-form analytic solutions to non-secular Bloch-Redfield master equations for quantum dynamics of a V-type system driven by weak coupling to a thermal bath, relevant to light harvesting processes, are obtained and discussed. We focus on noise-induced Fano coherences among the excited states induced by incoherent driving of the V-system initially in the ground state. For suddenly turned-on incoherent driving, the time evolution of the coherences is determined by the damping parameter ζ = /1 2 ( γ 1 + γ 2) / Δ p , where γi are the radiative decay rates of the excited levels i = 1, 2, and Δ p = √{ Δ 2 + ( 1 - p 2) γ 1 γ 2 } depends on the excited-state level splitting Δ > 0 and the angle between the transition dipole moments in the energy basis. The coherences oscillate as a function of time in the underdamped limit (ζ ≫ 1), approach a long-lived quasi-steady state in the overdamped limit (ζ ≪ 1), and display an intermediate behavior at critical damping (ζ = 1). The sudden incoherent turn-on is shown to generate a mixture of excited eigenstates |e1> and |e2> and their in-phase coherent superposition | ϕ + > = /1 √{ r 1 + r 2 } ( √{ r 1 } | e 1 > + √{ r 2 } | e 2 >) , which is remarkably long-lived in the overdamped limit (where r1 and r2 are the incoherent pumping rates). Formation of this coherent superposition enhances the decay rate from the excited states to the ground state. In the strongly asymmetric V-system where the coupling strengths between the ground state and the excited states differ significantly, additional asymptotic quasistationary coherences are identified, which arise due to slow equilibration of one of the excited states. Finally, we demonstrate that noise-induced Fano coherences are maximized with respect to populations when r1 = r2 and the transition dipole moments are fully aligned.

  8. CaMKII activation and dynamics are independent of the holoenzyme structure: an infinite subunit holoenzyme approximation

    NASA Astrophysics Data System (ADS)

    Michalski, P. J.; Loew, L. M.

    2012-06-01

    The combinatorial explosion produced by the multi-state, multi-subunit character of CaMKII has made analysis and modeling of this key signaling protein a significant challenge. Using rule-based and particle-based approaches, we construct exact models of CaMKII holoenzyme dynamics and study these models as a function of the number of subunits per holoenzyme, N. Without phosphatases the dynamics of activation are independent of the holoenzyme structure unless phosphorylation significantly alters the kinase activity of a subunit. With phosphatases the model is independent of holoenzyme size for N > 6. We introduce an infinite subunit holoenzyme approximation (ISHA), which simplifies the modeling by eliminating the combinatorial complexities encountered in any finite holoenzyme model. The ISHA is an excellent approximation to the full system over a broad range of physiologically relevant parameters. Finally, we demonstrate that the ISHA reproduces the behavior of exact models during synaptic plasticity protocols, which justifies its use as a module in large models of synaptic plasticity.

  9. Relativistic dynamics of interacting point particles: Central position of the Wheeler-Feynman scheme

    NASA Astrophysics Data System (ADS)

    Costa de Beauregard, O.

    1985-06-01

    The Wheeler-Feynman (WF) relativistic theory of interacting point particles, generalized by acceptance of an arbitrary spacelike interaction, is shown to possess a privileged status, reminiscent of the “central force” interactions occurring in Newtonian mechanics. This scheme is shown to be isomorphic to the classical one of the statics of interacting flexible current-carrying wires obeying the Ampère-Laplace (AL) formulas: to the tension T (T 2 =const) of the wire corresponds the momentum-energy pi (pipi=-c2m2) of the particle; to the Laplace linear force density -i H×dr corresponds the Lorentz force QHij drj; to the Laplace potential ir-1 dr corresponds the WF potential Qδ(r2) dri, etc. Among the differences, there is self-action in the AL scheme and no self-action in the WF scheme. A stationary energy principle in the AL scheme is isomorphic to Fokker's stationary action principle in the WF scheme.

  10. Computational fluid dynamics modelling of biomass fast pyrolysis in fluidised bed reactors, focusing different kinetic schemes.

    PubMed

    Ranganathan, Panneerselvam; Gu, Sai

    2016-08-01

    The present work concerns with CFD modelling of biomass fast pyrolysis in a fluidised bed reactor. Initially, a study was conducted to understand the hydrodynamics of the fluidised bed reactor by investigating the particle density and size, and gas velocity effect. With the basic understanding of hydrodynamics, the study was further extended to investigate the different kinetic schemes for biomass fast pyrolysis process. The Eulerian-Eulerian approach was used to model the complex multiphase flows in the reactor. The yield of the products from the simulation was compared with the experimental data. A good comparison was obtained between the literature results and CFD simulation. It is also found that CFD prediction with the advanced kinetic scheme is better when compared to other schemes. With the confidence obtained from the CFD models, a parametric study was carried out to study the effect of biomass particle type and size and temperature on the yield of the products.

  11. The effective medium and the average field approximations vis-à-vis the Hashin-Shtrikman bounds. II. The generalized self-consistent scheme in matrix-based composites

    NASA Astrophysics Data System (ADS)

    Benveniste, Y.; Milton, G. W.

    2010-07-01

    The present Part II of this two-part study is concerned with the average field approximation (AFA), and the effective medium approximation (EMA) in two-phase matrix-based dielectric composites through the use of an auxiliary configuration in which a particle of the inclusion phase is first surrounded by some matrix material, and then embedded in the effective medium. Those models will be referred as the generalized self-consistent scheme-average field approximation (GSCS-AFA), and the generalized self-consistent scheme-effective medium approximation (GSCS-EMA). We show that there are four types of the GSCS-AFA and a single type of the GSCS-EMA. In this paper the application of those models to dielectric composites with isotropic constituents and an inclusion phase that consists of randomly oriented ellipsoidal particles will be studied. The analytical solution of the auxiliary problem, which consists of an ellipsoidal particle confocally surrounded by a matrix shell and embedded in the effective medium, is achieved by means of ellipsoidal harmonics. Our results show that the effective property predictions of the GSCS-EMA and GSCS-AFA for the considered systems differ from each other, and more importantly, out of the four GSCS-AFA models, three of them violate the Hashin-Shtrikman bounds. The predictions of the GSCS-EMA obey the bounds. It is then shown that the version of the GSCS-AFA which obeys the Hashin-Shtrikman bounds for an inclusion phase with randomly oriented ellipsoids will violate them in the case of a particle shape which is not simply connected. Moreover, it turns out that the SCS-AFA studied in Part I also violates the Hashin-Shtrikman bounds in that case; the EMA, as expected, owing to its realizability property, continues to obey the bounds. Among the AFA and EMA in matrix-based composites, the GSCS-EMA therefore stands out as the method to be recommended.

  12. Dynamical downscaling of regional climate over eastern China using RSM with multiple physics scheme ensembles

    NASA Astrophysics Data System (ADS)

    Peishu, Zong; Jianping, Tang; Shuyu, Wang; Lingyun, Xie; Jianwei, Yu; Yunqian, Zhu; Xiaorui, Niu; Chao, Li

    2016-06-01

    The parameterization of physical processes is one of the critical elements to properly simulate the regional climate over eastern China. It is essential to conduct detailed analyses on the effect of physical parameterization schemes on regional climate simulation, to provide more reliable regional climate change information. In this paper, we evaluate the 25-year (1983-2007) summer monsoon climate characteristics of precipitation and surface air temperature by using the regional spectral model (RSM) with different physical schemes. The ensemble results using the reliability ensemble averaging (REA) method are also assessed. The result shows that the RSM model has the capacity to reproduce the spatial patterns, the variations, and the temporal tendency of surface air temperature and precipitation over eastern China. And it tends to predict better climatology characteristics over the Yangtze River basin and the South China. The impact of different physical schemes on RSM simulations is also investigated. Generally, the CLD3 cloud water prediction scheme tends to produce larger precipitation because of its overestimation of the low-level moisture. The systematic biases derived from the KF2 cumulus scheme are larger than those from the RAS scheme. The scale-selective bias correction (SSBC) method improves the simulation of the temporal and spatial characteristics of surface air temperature and precipitation and advances the circulation simulation capacity. The REA ensemble results show significant improvement in simulating temperature and precipitation distribution, which have much higher correlation coefficient and lower root mean square error. The REA result of selected experiments is better than that of nonselected experiments, indicating the necessity of choosing better ensemble samples for ensemble.

  13. Dynamical downscaling of regional climate over eastern China using RSM with multiple physics scheme ensembles

    NASA Astrophysics Data System (ADS)

    Peishu, Zong; Jianping, Tang; Shuyu, Wang; Lingyun, Xie; Jianwei, Yu; Yunqian, Zhu; Xiaorui, Niu; Chao, Li

    2017-08-01

    The parameterization of physical processes is one of the critical elements to properly simulate the regional climate over eastern China. It is essential to conduct detailed analyses on the effect of physical parameterization schemes on regional climate simulation, to provide more reliable regional climate change information. In this paper, we evaluate the 25-year (1983-2007) summer monsoon climate characteristics of precipitation and surface air temperature by using the regional spectral model (RSM) with different physical schemes. The ensemble results using the reliability ensemble averaging (REA) method are also assessed. The result shows that the RSM model has the capacity to reproduce the spatial patterns, the variations, and the temporal tendency of surface air temperature and precipitation over eastern China. And it tends to predict better climatology characteristics over the Yangtze River basin and the South China. The impact of different physical schemes on RSM simulations is also investigated. Generally, the CLD3 cloud water prediction scheme tends to produce larger precipitation because of its overestimation of the low-level moisture. The systematic biases derived from the KF2 cumulus scheme are larger than those from the RAS scheme. The scale-selective bias correction (SSBC) method improves the simulation of the temporal and spatial characteristics of surface air temperature and precipitation and advances the circulation simulation capacity. The REA ensemble results show significant improvement in simulating temperature and precipitation distribution, which have much higher correlation coefficient and lower root mean square error. The REA result of selected experiments is better than that of nonselected experiments, indicating the necessity of choosing better ensemble samples for ensemble.

  14. Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations. [in gas dynamics

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Warming, R. F.; Harten, A.

    1985-01-01

    The novel implicit and unconditionally stable, high resolution Total Variation Diminishing (TVD) scheme whose application to steady state calculations is presently examined is a member of a one-parameter family of implicit, second-order accurate systems developed by Harten (1983) for the computation of weak solutions for one-dimensional hyperbolic conservation laws. The scheme will not generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments for a quasi-one-dimensional nozzle problem show that the experimentally determined stability limit correlates exactly with the theoretical stability limit for the nonlinear scalar hyberbolic conservation laws.

  15. Assessment of physical approximations on simulating past and future dynamics of Haig Glacier in the Canadian Rockies

    NASA Astrophysics Data System (ADS)

    Adhikari, S.; Marshall, S. J.

    2011-12-01

    Over the past several decades, a number of numerical models with various degrees of complexity have been developed and applied to simulate the dynamics of valley glaciers. The Stokes model, which solves a complete set of elliptical diagnostic and hyperbolic prognostic equations, describes the most sophisticated treatment of glacier dynamics. In a three-dimensional Euclidean space, this full-system model simulates the ice flow according to a balance between the gravitational driving stress, τd, the basal drag, τb, the resistance due to longitudinal stress gradients, τlon, and the lateral drag, τlat. Other models deal with reduced physics; such as the plane-strain Stokes approximation (where τd is balanced by τb and τlon) and shear-deformational flow (where τd is solely balanced by τb). Considering each of the Stokes and reduced models, we reconstruct the past and project the future dynamics of Haig Glacier in the Canadian Rockies in order to analyze whether low-order models are good enough for such simulations. Furthermore, we assess how effectively the Stokes solutions can be achieved via low-order models with available ad-hoc parameterizations, e.g. the L-factor (Adhikari and Marshall, in press) and the cross-sectional valley shape factor (Nye, 1965).

  16. Incorporation of a radiation parameterization scheme into the Naval Research Laboratory limited area dynamical weather prediction model. Master's thesis

    SciTech Connect

    Stewart, P.C.

    1992-09-01

    This paper describes the incorporation of the Harshvardhan et al. (1987) radiation parameterization into the Naval Research Laboratory Limited Area Dynamical Weather Prediction Model. A comparison between model runs with the radiation scheme and runs without the scheme was made to examine three mesoscale phenomena along the west coast of the United States during the period 0000 UTC 02 May 1990 - 1200 UTC 03 %lay 1990: the land and sea breeze, the southerly surge and the Catalina eddy. In general the updated model with the radiation parameterization yielded a more accurate simulation of the layer temperatures, geopotential heights, cloud cover, and radiative processes as verified from synoptic, mesoscale: and satellite observations. Subsequently, the updated model also forecast a more realistic diurnal evolution of the sea and land breeze, the southerly surge and the Catalina eddy.

  17. On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. I - Nonstiff strongly dynamic problems

    NASA Technical Reports Server (NTRS)

    Harten, A.; Tal-Ezer, H.

    1981-01-01

    An implicit finite difference method of fourth order accuracy in space and time is introduced for the numerical solution of one-dimensional systems of hyperbolic conservation laws. The basic form of the method is a two-level scheme which is unconditionally stable and nondissipative. The scheme uses only three mesh points at level t and three mesh points at level t + delta t. The dissipative version of the basic method given is conditionally stable under the CFL (Courant-Friedrichs-Lewy) condition. This version is particularly useful for the numerical solution of problems with strong but nonstiff dynamic features, where the CFL restriction is reasonable on accuracy grounds. Numerical results are provided to illustrate properties of the proposed method.

  18. Network coding based joint signaling and dynamic bandwidth allocation scheme for inter optical network unit communication in passive optical networks

    NASA Astrophysics Data System (ADS)

    Wei, Pei; Gu, Rentao; Ji, Yuefeng

    2014-06-01

    As an innovative and promising technology, network coding has been introduced to passive optical networks (PON) in recent years to support inter optical network unit (ONU) communication, yet the signaling process and dynamic bandwidth allocation (DBA) in PON with network coding (NC-PON) still need further study. Thus, we propose a joint signaling and DBA scheme for efficiently supporting differentiated services of inter ONU communication in NC-PON. In the proposed joint scheme, the signaling process lays the foundation to fulfill network coding in PON, and it can not only avoid the potential threat to downstream security in previous schemes but also be suitable for the proposed hybrid dynamic bandwidth allocation (HDBA) scheme. In HDBA, a DBA cycle is divided into two sub-cycles for applying different coding, scheduling and bandwidth allocation strategies to differentiated classes of services. Besides, as network traffic load varies, the entire upstream transmission window for all REPORT messages slides accordingly, leaving the transmission time of one or two sub-cycles to overlap with the bandwidth allocation calculation time at the optical line terminal (the OLT), so that the upstream idle time can be efficiently eliminated. Performance evaluation results validate that compared with the existing two DBA algorithms deployed in NC-PON, HDBA demonstrates the best quality of service (QoS) support in terms of delay for all classes of services, especially guarantees the end-to-end delay bound of high class services. Specifically, HDBA can eliminate queuing delay and scheduling delay of high class services, reduce those of lower class services by at least 20%, and reduce the average end-to-end delay of all services over 50%. Moreover, HDBA also achieves the maximum delay fairness between coded and uncoded lower class services, and medium delay fairness for high class services.

  19. Approximate constants of motion for classically chaotic vibrational dynamics - Vague tori, semiclassical quantization, and classical intramolecular energy flow

    NASA Technical Reports Server (NTRS)

    Shirts, R. B.; Reinhardt, W. P.

    1982-01-01

    Substantial short time regularity, even in the chaotic regions of phase space, is found for what is seen as a large class of systems. This regularity manifests itself through the behavior of approximate constants of motion calculated by Pade summation of the Birkhoff-Gustavson normal form expansion; it is attributed to remnants of destroyed invariant tori in phase space. The remnant torus-like manifold structures are used to justify Einstein-Brillouin-Keller semiclassical quantization procedures for obtaining quantum energy levels, even in the absence of complete tori. They also provide a theoretical basis for the calculation of rate constants for intramolecular mode-mode energy transfer. These results are illustrated by means of a thorough analysis of the Henon-Heiles oscillator problem. Possible generality of the analysis is demonstrated by brief consideration of classical dynamics for the Barbanis Hamiltonian, Zeeman effect in hydrogen and recent results of Wolf and Hase (1980) for the H-C-C fragment.

  20. Approximate constants of motion for classically chaotic vibrational dynamics - Vague tori, semiclassical quantization, and classical intramolecular energy flow

    NASA Technical Reports Server (NTRS)

    Shirts, R. B.; Reinhardt, W. P.

    1982-01-01

    Substantial short time regularity, even in the chaotic regions of phase space, is found for what is seen as a large class of systems. This regularity manifests itself through the behavior of approximate constants of motion calculated by Pade summation of the Birkhoff-Gustavson normal form expansion; it is attributed to remnants of destroyed invariant tori in phase space. The remnant torus-like manifold structures are used to justify Einstein-Brillouin-Keller semiclassical quantization procedures for obtaining quantum energy levels, even in the absence of complete tori. They also provide a theoretical basis for the calculation of rate constants for intramolecular mode-mode energy transfer. These results are illustrated by means of a thorough analysis of the Henon-Heiles oscillator problem. Possible generality of the analysis is demonstrated by brief consideration of classical dynamics for the Barbanis Hamiltonian, Zeeman effect in hydrogen and recent results of Wolf and Hase (1980) for the H-C-C fragment.

  1. Electric Double-Layer Structure in Primitive Model Electrolytes. Comparing Molecular Dynamics with Local-Density Approximations

    DOE PAGES

    Giera, Brian; Lawrence Livermore National Lab.; Henson, Neil; ...

    2015-02-27

    We evaluate the accuracy of local-density approximations (LDAs) using explicit molecular dynamics simulations of binary electrolytes comprised of equisized ions in an implicit solvent. The Bikerman LDA, which considers ions to occupy a lattice, poorly captures excluded volume interactions between primitive model ions. Instead, LDAs based on the Carnahan–Starling (CS) hard-sphere equation of state capture simulated values of ideal and excess chemical potential profiles extremely well, as is the relationship between surface charge density and electrostatic potential. Excellent agreement between the EDL capacitances predicted by CS-LDAs and computed in molecular simulations is found even in systems where ion correlations drivemore » strong density and free charge oscillations within the EDL, despite the inability of LDAs to capture the oscillations in the detailed EDL profiles.« less

  2. Electric Double-Layer Structure in Primitive Model Electrolytes. Comparing Molecular Dynamics with Local-Density Approximations

    SciTech Connect

    Giera, Brian; Henson, Neil; Kober, Edward M.; Shell, M. Scott; Squires, Todd M.

    2015-02-27

    We evaluate the accuracy of local-density approximations (LDAs) using explicit molecular dynamics simulations of binary electrolytes comprised of equisized ions in an implicit solvent. The Bikerman LDA, which considers ions to occupy a lattice, poorly captures excluded volume interactions between primitive model ions. Instead, LDAs based on the Carnahan–Starling (CS) hard-sphere equation of state capture simulated values of ideal and excess chemical potential profiles extremely well, as is the relationship between surface charge density and electrostatic potential. Excellent agreement between the EDL capacitances predicted by CS-LDAs and computed in molecular simulations is found even in systems where ion correlations drive strong density and free charge oscillations within the EDL, despite the inability of LDAs to capture the oscillations in the detailed EDL profiles.

  3. Reduced quantum dynamics with arbitrary bath spectral densities: Hierarchical equations of motion based on several different bath decomposition schemes

    SciTech Connect

    Liu, Hao; Zhu, Lili; Bai, Shuming; Shi, Qiang

    2014-04-07

    We investigated applications of the hierarchical equation of motion (HEOM) method to perform high order perturbation calculations of reduced quantum dynamics for a harmonic bath with arbitrary spectral densities. Three different schemes are used to decompose the bath spectral density into analytical forms that are suitable to the HEOM treatment: (1) The multiple Lorentzian mode model that can be obtained by numerically fitting the model spectral density. (2) The combined Debye and oscillatory Debye modes model that can be constructed by fitting the corresponding classical bath correlation function. (3) A new method that uses undamped harmonic oscillator modes explicitly in the HEOM formalism. Methods to extract system-bath correlations were investigated for the above bath decomposition schemes. We also show that HEOM in the undamped harmonic oscillator modes can give detailed information on the partial Wigner transform of the total density operator. Theoretical analysis and numerical simulations of the spin-Boson dynamics and the absorption line shape of molecular dimers show that the HEOM formalism for high order perturbations can serve as an important tool in studying the quantum dissipative dynamics in the intermediate coupling regime.

  4. Reduced quantum dynamics with arbitrary bath spectral densities: hierarchical equations of motion based on several different bath decomposition schemes.

    PubMed

    Liu, Hao; Zhu, Lili; Bai, Shuming; Shi, Qiang

    2014-04-07

    We investigated applications of the hierarchical equation of motion (HEOM) method to perform high order perturbation calculations of reduced quantum dynamics for a harmonic bath with arbitrary spectral densities. Three different schemes are used to decompose the bath spectral density into analytical forms that are suitable to the HEOM treatment: (1) The multiple Lorentzian mode model that can be obtained by numerically fitting the model spectral density. (2) The combined Debye and oscillatory Debye modes model that can be constructed by fitting the corresponding classical bath correlation function. (3) A new method that uses undamped harmonic oscillator modes explicitly in the HEOM formalism. Methods to extract system-bath correlations were investigated for the above bath decomposition schemes. We also show that HEOM in the undamped harmonic oscillator modes can give detailed information on the partial Wigner transform of the total density operator. Theoretical analysis and numerical simulations of the spin-Boson dynamics and the absorption line shape of molecular dimers show that the HEOM formalism for high order perturbations can serve as an important tool in studying the quantum dissipative dynamics in the intermediate coupling regime.

  5. Control scheme of nonadiabatic transitions with the dynamical shift of potential curve crossing

    SciTech Connect

    Scheit, Simona; Arasaki, Yasuki Takatsuka, Kazuo

    2014-06-28

    We investigate how the nuclear dynamics at an avoided crossing is affected and can be controlled by the introduction of a laser field whose cycle is comparable to the time-scale of the nuclear dynamics. By introducing the concepts of light-induced effective potential energy curves and dynamical avoided crossing, we describe the laser controlled nuclear dynamics and present basic control scenarios, giving a detailed explanation of the underlying dynamical mechanisms. The scenarios presented allow for examples to understand from a different perspective the results of dynamic Stark control experiments. The proposed interpretation is applied to the laser-controlled nonadiabatic dynamics between the two lowest {sup 1}Σ{sup +} states of LiF, where the usefulness of the concepts developed is elucidated.

  6. On the construction and application of implicit factored schemes for conservation laws. [in computational fluid dynamics

    NASA Technical Reports Server (NTRS)

    Warming, R. F.; Beam, R. M.

    1978-01-01

    Efficient, noniterative, implicit finite difference algorithms are systematically developed for nonlinear conservation laws including purely hyperbolic systems and mixed hyperbolic parabolic systems. Utilization of a rational fraction or Pade time differencing formulas, yields a direct and natural derivation of an implicit scheme in a delta form. Attention is given to advantages of the delta formation and to various properties of one- and two-dimensional algorithms.

  7. Energy conserving schemes for the simulation of musical instrument contact dynamics

    NASA Astrophysics Data System (ADS)

    Chatziioannou, Vasileios; van Walstijn, Maarten

    2015-03-01

    Collisions are an innate part of the function of many musical instruments. Due to the nonlinear nature of contact forces, special care has to be taken in the construction of numerical schemes for simulation and sound synthesis. Finite difference schemes and other time-stepping algorithms used for musical instrument modelling purposes are normally arrived at by discretising a Newtonian description of the system. However because impact forces are non-analytic functions of the phase space variables, algorithm stability can rarely be established this way. This paper presents a systematic approach to deriving energy conserving schemes for frictionless impact modelling. The proposed numerical formulations follow from discretising Hamilton's equations of motion, generally leading to an implicit system of nonlinear equations that can be solved with Newton's method. The approach is first outlined for point mass collisions and then extended to distributed settings, such as vibrating strings and beams colliding with rigid obstacles. Stability and other relevant properties of the proposed approach are discussed and further demonstrated with simulation examples. The methodology is exemplified through a case study on tanpura string vibration, with the results confirming the main findings of previous studies on the role of the bridge in sound generation with this type of string instrument.

  8. Hybrid dynamic modeling of Escherichia coli central metabolic network combining Michaelis-Menten and approximate kinetic equations.

    PubMed

    Costa, Rafael S; Machado, Daniel; Rocha, Isabel; Ferreira, Eugénio C

    2010-05-01

    The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis-Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action, convenience kinetics, lin-log and power-law). Using the mechanistic model for Escherichia coli central carbon metabolism as a benchmark, we investigate the alternative modeling approaches through comparative simulations analyses. The good dynamic behavior and the powerful predictive capabilities obtained using the hybrid model composed of Michaelis-Menten and the approximate lin-log kinetics indicate that this is a possible suitable approach to model complex large-scale networks where the exact rate laws are unknown.

  9. Coarse-graining scheme for simulating uniaxial stress-strain response of glassy polymers through molecular dynamics

    NASA Astrophysics Data System (ADS)

    Majumder, Manoj K.; Ramkumar, S.; Mahajan, Dhiraj K.; Basu, Sumit

    2010-01-01

    Simulation of the deformation of polymers below their glass transition through molecular dynamics provides an useful route to correlate their molecular architecture to deformation behavior. However, present computational capabilities severely restrict the time and length scales that can be simulated when detailed models of these macromolecules are used. Coarse-graining techniques for macromolecular structures intend to make bigger and longer simulations possible by grouping atoms into superatoms and devising ways of determining reasonable force fields for the superatoms in a manner that retains essential macromolecular features relevant to the process under study but jettisons unnecessary details. In this work we systematically develop a coarse-graining scheme aimed at simulating uniaxial stress-strain behavior of polymers below their glass transition. The scheme involves a two step process of obtaining the coarse grained force field parameters above glass transition. This seems to be enough to obtain “faithful” stress-strain responses after quenching to below the glass transition temperature. We apply the scheme developed to a commercially important polymer polystyrene, derive its complete force field parameters and thus demonstrate the effectiveness of the technique.

  10. Coarse-graining scheme for simulating uniaxial stress-strain response of glassy polymers through molecular dynamics.

    PubMed

    Majumder, Manoj K; S, Ramkumar; Mahajan, Dhiraj K; Basu, Sumit

    2010-01-01

    Simulation of the deformation of polymers below their glass transition through molecular dynamics provides an useful route to correlate their molecular architecture to deformation behavior. However, present computational capabilities severely restrict the time and length scales that can be simulated when detailed models of these macromolecules are used. Coarse-graining techniques for macromolecular structures intend to make bigger and longer simulations possible by grouping atoms into superatoms and devising ways of determining reasonable force fields for the superatoms in a manner that retains essential macromolecular features relevant to the process under study but jettisons unnecessary details. In this work we systematically develop a coarse-graining scheme aimed at simulating uniaxial stress-strain behavior of polymers below their glass transition. The scheme involves a two step process of obtaining the coarse grained force field parameters above glass transition. This seems to be enough to obtain "faithful" stress-strain responses after quenching to below the glass transition temperature. We apply the scheme developed to a commercially important polymer polystyrene, derive its complete force field parameters and thus demonstrate the effectiveness of the technique.

  11. Full Stokes or shallow ice approximation? Comparing the ice flow dynamics at the Shirase Drainage Basin, Antarctica

    NASA Astrophysics Data System (ADS)

    Seddik, H.; Greve, R.; Zwinger, T.; Sugiyama, S.

    2012-12-01

    Covering an area of 2 x 105 km2, the Shirase Drainage Basin is located in East Antarctica (37-50° E, 70-78° S). The basin is characterized by the convergence of the ice flow towards the Shirase glacier, one of the fastest flowing glacier in Antarctica. The Shirase glacier flows at a speed of 2.3 km a-1 at the grounding line (Rignot, 2002; Pattyn and Derauw, 2002; Nakamura and others, 2008) and drains about 10 Gt a-1 of ice through a narrow outlet into the Lützow-Holm Bay (Fujii, 1981). With nearly 90% of total ice discharge from the basin being calved by the glacier, the fast flowing nature of the Shirase glacier is important for the investigation of the ice sheet mass budget in this region. The dynamics of the Shirase glacier is investigated by means of the full Stokes equations and the shallow ice approximation. The model Elmer/Ice (http://elmerice.elmerfem.com) is applied to the Shirase Drainage Basin and employs the finite element method to solve the full Stokes equations, the temperature evolution equation and the evolution equation of the free surface. The shallow ice approximation is also implemented into Elmer/Ice so that both the full Stokes and the shallow ice approximation are computed on the same mesh. Data for the present geometry (surface and basal topographies with no shelf) are obtained from the Community Ice Sheet Model, based on the DEM of Bamber and others (2009) and Griggs and Bamber (2009), and on the BEDMAP1-Plus ice sheet basal topography. A mesh of the computational domain is created using an initial footprint which contains elements from 15 km to 500 m horizontal resolution. The footprint is vertically extruded to form a 3D mesh of 240720 elements with 21 equidistant, terrain-following layers. The approach taken in this study is to compare the response of the glacier to dynamical and climate forcings when separately the full Stokes and the shallow ice approximation are employed. The sensitivity experiments are modeled after the Sea

  12. Robust master-slave synchronization for general uncertain delayed dynamical model based on adaptive control scheme.

    PubMed

    Wang, Tianbo; Zhou, Wuneng; Zhao, Shouwei; Yu, Weiqin

    2014-03-01

    In this paper, the robust exponential synchronization problem for a class of uncertain delayed master-slave dynamical system is investigated by using the adaptive control method. Different from some existing master-slave models, the considered master-slave system includes bounded unmodeled dynamics. In order to compensate the effect of unmodeled dynamics and effectively achieve synchronization, a novel adaptive controller with simple updated laws is proposed. Moreover, the results are given in terms of LMIs, which can be easily solved by LMI Toolbox in Matlab. A numerical example is given to illustrate the effectiveness of the method.

  13. Approximations and Implementations of Nonlinear Filtering Schemes.

    DTIC Science & Technology

    1988-02-01

    systems. At any rate, 103 KS the modelers dream is to come up with a mathematical model, which is suitably small in order to allow computable predictions of...in the presence of noise, C), we understand the reduction of the given system (A, leading to the EQG balanced realizations. An interpre - B, C) to a

  14. A study of design approach of spreading schemes for viral marketing based on human dynamics

    NASA Astrophysics Data System (ADS)

    Yang, Jianmei; Zhuang, Dong; Xie, Weicong; Chen, Guangrong

    2013-12-01

    Before launching a real viral marketing campaign, it is needed to design a spreading scheme by simulations. Based on a categorization of spreading patterns in real world and models, we point out that the existing research (especially Yang et al. (2010) Ref. [16]) implicitly assume that if a user decides to post a received message (is activated), he/she will take the reposting action promptly (Prompt Action After Activation, or PAAA). After a careful analysis on a real dataset however, it is found that the observed time differences between action and activation exhibit a heavy-tailed distribution. A simulation model for heavy-tailed pattern is then proposed and performed. Similarities and differences of spreading processes between the heavy-tailed and PAAA patterns are analyzed. Consequently, a more practical design approach of spreading scheme for viral marketing on QQ platform is proposed. The design approach can be extended and applied to the contexts of non-heavy-tailed pattern, and viral marketing on other instant messaging platforms.

  15. Filtering schemes in the quantum-classical Liouville approach to nonadiabatic dynamics.

    PubMed

    Uken, Daniel A; Sergi, Alessandro; Petruccione, Francesco

    2013-09-01

    We study a number of filtering schemes for the reduction of the statistical error in nonadiabatic calculations by means of the quantum-classical Liouville equation. In particular, we focus on a scheme based on setting a threshold value on the sampling weights, so that when the threshold is overcome the value of the weight is reset, and on another approach which prunes the ensemble of the allowed nonadiabatic transitions according to a generalized sampling probability. Both methods have advantages and drawbacks, however, their combination drastically improves the performance of an algorithm known as the sequential short-time step propagation [MacKernan et al., J. Phys: Condens. Matter 14, 9069 (2002)], which is derived from a simple first order expansion of the quantum-classical propagator. Such an algorithm together with the combined filtering procedures produce results that compare very well with those obtained by means of numerically accurate path integral quantum calculations for the spin-boson model, even for intermediate and strong coupling regimes.

  16. Grid integration and smart grid implementation of emerging technologies in electric power systems through approximate dynamic programming

    NASA Astrophysics Data System (ADS)

    Xiao, Jingjie

    A key hurdle for implementing real-time pricing of electricity is a lack of consumers' responses. Solutions to overcome the hurdle include the energy management system that automatically optimizes household appliance usage such as plug-in hybrid electric vehicle charging (and discharging with vehicle-to-grid) via a two-way communication with the grid. Real-time pricing, combined with household automation devices, has a potential to accommodate an increasing penetration of plug-in hybrid electric vehicles. In addition, the intelligent energy controller on the consumer-side can help increase the utilization rate of the intermittent renewable resource, as the demand can be managed to match the output profile of renewables, thus making the intermittent resource such as wind and solar more economically competitive in the long run. One of the main goals of this dissertation is to present how real-time retail pricing, aided by control automation devices, can be integrated into the wholesale electricity market under various uncertainties through approximate dynamic programming. What distinguishes this study from the existing work in the literature is that whole- sale electricity prices are endogenously determined as we solve a system operator's economic dispatch problem on an hourly basis over the entire optimization horizon. This modeling and algorithm framework will allow a feedback loop between electricity prices and electricity consumption to be fully captured. While we are interested in a near-optimal solution using approximate dynamic programming; deterministic linear programming benchmarks are use to demonstrate the quality of our solutions. The other goal of the dissertation is to use this framework to provide numerical evidence to the debate on whether real-time pricing is superior than the current flat rate structure in terms of both economic and environmental impacts. For this purpose, the modeling and algorithm framework is tested on a large-scale test case

  17. Efficient implementation of weighted ENO schemes

    NASA Technical Reports Server (NTRS)

    Jiang, Guang-Shan; Shu, Chi-Wang

    1995-01-01

    In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially non-oscillatory) finite difference schemes of Liu, Osher and Chan. It was shown by Liu et al. that WENO schemes constructed from the r-th order (in L1 norm) ENO schemes are (r+1)-th order accurate. We propose a new way of measuring the smoothness of a numerical solution, emulating the idea of minimizing the total variation of the approximation, which results in a 5-th order WENO scheme for the case r = 3, instead of the 4-th order with the original smoothness measurement by Liu et al. This 5-th order WENO scheme is as fast as the 4-th order WENO scheme of Liu et al., and both schemes are about twice as fast as the 4-th order ENO schemes on vector supercomputers and as fast on serial and parallel computers. For Euler systems of gas dynamics, we suggest computing the weights from pressure and entropy instead of the characteristic values to simplify the costly characteristic procedure. The resulting WENO schemes are about twice as fast as the WENO schemes using the characteristic decompositions to compute weights, and work well for problems which do not contain strong shocks or strong reflected waves. We also prove that, for conservation laws with smooth solutions, all WENO schemes are convergent. Many numerical tests, including the 1D steady state nozzle flow problem and 2D shock entropy wave interaction problem, are presented to demonstrate the remarkable capability of the WENO schemes, especially the WENO scheme using the new smoothness measurement, in resolving complicated shock and flow structures. We have also applied Yang's artificial compression method to the WENO schemes to sharpen contact discontinuities.

  18. Tetrahedron dynamics in the icosahedral quasicrystals i-ZnMgSc and i-ZnAgSc and the cubic 1/1-approximant Zn6Sc.

    PubMed

    Euchner, H; Yamada, T; Rols, S; Ishimasa, T; Kaneko, Y; Ollivier, J; Schober, H; Mihalkovic, M; de Boissieu, M

    2013-03-20

    A comparison of periodic approximants and their quasicrystalline counterparts offers the opportunity to better understand the structure, physical properties and stabilizing mechanisms of these complex phases. We present a combined experimental and molecular dynamics study of the lattice dynamics of the icosahedral quasicrystals i-ZnMgSc and i-ZnAgSc and compare it to recently published results obtained for the cubic 1/1-approximant Zn(6)Sc. Both phases, quasicrystal and approximant, are built up from large atomic clusters which contain a tetrahedral shell at the cluster centre and are packed either quasiperiodically or on a bcc lattice. Using quasielastic neutron scattering and atomic scale simulations, we show that in the quasicrystal the tetrahedra display a dynamics similar to that observed in the 1/1-approximant: the tetrahedra behave as a 'single molecule' and reorient dynamically on a timescale of the order of a few ps. The tetrahedra reorientation is accompanied by a large distortion of the surrounding cluster shells which provide a unique dynamical flexibility to the quasicrystal. However, whereas in the 1/1-approximant the tetrahedron reorientation is observed down to T(c) = 160 K, where a phase transition takes place, in the quasicrystal the tetrahedron dynamics is gradually freezing from 550 to 300 K, similarly to a glassy system.

  19. BWM*: A Novel, Provable, Ensemble-based Dynamic Programming Algorithm for Sparse Approximations of Computational Protein Design.

    PubMed

    Jou, Jonathan D; Jain, Swati; Georgiev, Ivelin S; Donald, Bruce R

    2016-06-01

    Sparse energy functions that ignore long range interactions between residue pairs are frequently used by protein design algorithms to reduce computational cost. Current dynamic programming algorithms that fully exploit the optimal substructure produced by these energy functions only compute the GMEC. This disproportionately favors the sequence of a single, static conformation and overlooks better binding sequences with multiple low-energy conformations. Provable, ensemble-based algorithms such as A* avoid this problem, but A* cannot guarantee better performance than exhaustive enumeration. We propose a novel, provable, dynamic programming algorithm called Branch-Width Minimization* (BWM*) to enumerate a gap-free ensemble of conformations in order of increasing energy. Given a branch-decomposition of branch-width w for an n-residue protein design with at most q discrete side-chain conformations per residue, BWM* returns the sparse GMEC in O([Formula: see text]) time and enumerates each additional conformation in merely O([Formula: see text]) time. We define a new measure, Total Effective Search Space (TESS), which can be computed efficiently a priori before BWM* or A* is run. We ran BWM* on 67 protein design problems and found that TESS discriminated between BWM*-efficient and A*-efficient cases with 100% accuracy. As predicted by TESS and validated experimentally, BWM* outperforms A* in 73% of the cases and computes the full ensemble or a close approximation faster than A*, enumerating each additional conformation in milliseconds. Unlike A*, the performance of BWM* can be predicted in polynomial time before running the algorithm, which gives protein designers the power to choose the most efficient algorithm for their particular design problem.

  20. The dynamics of Soil Organic Carbon fractions defined by alternative fractionation schemes

    NASA Astrophysics Data System (ADS)

    Sohi, Saran; Stack, Philip; Dondini, Marta; McNamara, Niall; Rowe, Rebecca

    2014-05-01

    A change in (1) soil carbon input or (2) rate of stabilisation of new inputs, results in a trajectory for soil organic carbon (SOC) towards a new equilibrium level. The ultimate change in SOC may become statistically significant over decades, but is not easily detected within 1-10 years. Pool-based soil carbon models suggest that larger changes should occur in the distribution of carbon between fractions that differ in turnover rate. These effects may be measurable, indicative of change and potentially diagnostic. Alternative schemes exist for isolating sets of contrasting SOC fractions. In the Ecosystem Land Use Modelling & Soil Carbon GHG Flux Trial (ELUM) project, two schemes have been applied to soils from 20 sites in transitions from pasture and/or arable to different types of short rotation forestry (biomass energy crops). Both schemes target carbon fractions of intermediate stability that should show proportional changes. These fractions should decline with higher decomposition and increase with greater soil inputs. In this work we show the relationship between fractions obtained using "sand plus aggregate protected SOC" (Zimmerman et al., 2007) and "intra-aggregate SOC" (Sohi et al., 2001). The correlation is first made for soils continuing in historical land use at each site, as well as adjacent soils changed to one or more types of forestry. The variable of interest here is the quantitative comparability of the fractions, as well as the effect of site specific factors (notably soil texture and land-use). This is shown as a proportion of SOC as well as amount of SOC. Secondly, we compare the status of the alternate fractions in transition. A different relationship relative to soils at equilibrium could suggest they are characterised by a different reactivity in the soil (turnover rate, mapping to modelled SOC pools), or that they are affected differently by soil texture, initial total SOC, etc. This reveals information on the fractions' likely use as

  1. Performance of a Dynamic Initialization Scheme in the Coupled Ocean-Atmosphere Mesoscale Prediction System for Tropical Cyclones (COAMPS-TC)

    DTIC Science & Technology

    2011-10-01

    Performance of a Dynamic Initialization Scheme in the Coupled Ocean –Atmosphere Mesoscale Prediction System for Tropical Cyclones (COAMPS-TC) ERIC A...initialization scheme was tested on multiple tropical cyclones during 2008 and 2009 in the North Atlantic and western North Pacific Ocean basins using the...Naval Research Laboratory’s tropical cyclone version of the Coupled Ocean –Atmosphere Mesoscale Prediction System (COAMPS-TC). The use of this

  2. Explicit dynamic analysis of elasto-plastic laminated composite shells: implementation of non-iterative stress update schemes for the HOFFMAN yield criterion

    NASA Astrophysics Data System (ADS)

    Koh, C. G.; Owen, D. R. J.; Perić, D.

    1995-08-01

    The dynamic analysis of composite shell structures is carried out by an explicit finite element code employing 4-node one-point quadrature elements. The anisotropic Hoffman yield criterion is adopted to model the laminates. The formulation for stress update using a backward Euler scheme is presented in the plane stress subspace. Several numerical examples are presented. The issue of implementing single-iteration schemes for stress update is also investigated.

  3. Adiabatic-impulse approximation for avoided level crossings: From phase-transition dynamics to Landau-Zener evolutions and back again

    SciTech Connect

    Damski, Bogdan; Zurek, Wojciech H.

    2006-06-15

    We show that a simple approximation based on concepts underlying the Kibble-Zurek theory of second order phase-transition dynamics can be used to treat avoided level crossing problems. The approach discussed in this paper provides an intuitive insight into quantum dynamics of two-level systems, and may serve as a link between the theory of dynamics of classical and quantum phase transitions. To illustrate these ideas we analyze dynamics of a paramagnet-ferromagnet quantum phase transition in the Ising model. We also present exact unpublished solutions of the Landau-Zener-like problems.

  4. Resonance in the dynamics of chemical systems simulated by the implicit midpoint scheme

    NASA Astrophysics Data System (ADS)

    Mandziuk, Margaret; Schlick, Tamar

    1995-05-01

    The numerical behavior of the symplectic, implicit midpoint method with a wide range of integration timesteps is examined through an application to a diatomic molecule governed by a Morse potential. Our oscillator with a 12.6 fs period exhibits notable, integrator induced, timestep- ( Δt) dependent resonances and we predict approximate values of Δt where they will occur. The particular case of a third-order resonance ( Δt ≈ 7 fs here) leads to instability, and higher-order resonances ( n = 4, 5) to large energetic fluctuations and/or corrupted phase diagrams. Significantly, for Δt > 10 fs the energy errors remain bound.

  5. Convergence of a class of semi-implicit time-stepping schemes for nonsmooth rigid multibody dynamics.

    SciTech Connect

    Gavrea, B. I.; Anitescu, M.; Potra, F. A.; Mathematics and Computer Science; Univ. of Pennsylvania; Univ. of Maryland

    2008-01-01

    In this work we present a framework for the convergence analysis in a measure differential inclusion sense of a class of time-stepping schemes for multibody dynamics with contacts, joints, and friction. This class of methods solves one linear complementarity problem per step and contains the semi-implicit Euler method, as well as trapezoidal-like methods for which second-order convergence was recently proved under certain conditions. By using the concept of a reduced friction cone, the analysis includes, for the first time, a convergence result for the case that includes joints. An unexpected intermediary result is that we are able to define a discrete velocity function of bounded variation, although the natural discrete velocity function produced by our algorithm may have unbounded variation.

  6. Convergence of a Time-Stepping Scheme for Rigid-Body Dynamics and Resolution of Painlevé's Problem

    NASA Astrophysics Data System (ADS)

    Stewart, David E.

    This paper gives convergence theory for a new implicit time-stepping scheme for general rigid-body dynamics with Coulomb friction and purely inelastic collisions and shocks. An important consequence of this work is the proof of existence of solutions of rigid-body problems which include the famous counterexamples of Painlevé. The mathematical basis for this work is the formulation of the rigid-body problem in terms of measure differential inclusions of Moreau and Monteiro Marques. The implicit time-stepping method is based on complementarity problems, and is essentially a particular case of the algorithm described in Anitescu & Potra [2], which in turn is based on the formulation in Stewart & Trinkle [47].

  7. Dissipative Particle Dynamics Simulations for Phospholipid Membranes Based on a Four-To-One Coarse-Grained Mapping Scheme

    PubMed Central

    Li, Xiaoxu; Gao, Lianghui; Fang, Weihai

    2016-01-01

    In this article, a new set of parameters compatible with the dissipative particle dynamics (DPD) force field is developed for phospholipids. The coarse-grained (CG) models of these molecules are constructed by mapping four heavy atoms and their attached hydrogen atoms to one bead. The beads are divided into types distinguished by charge type, polarizability, and hydrogen-bonding capacity. First, we derive the relationship between the DPD repulsive force and Flory-Huggins χ-parameters based on this four-to-one CG mapping scheme. Then, we optimize the DPD force parameters for phospholipids. The feasibility of this model is demonstrated by simulating the structural and thermodynamic properties of lipid bilayer membranes, including the membrane thickness, the area per lipid, the lipid tail orientation, the bending rigidity, the rupture behavior, and the potential of mean force for lipid flip-flop. PMID:27137463

  8. Cascade structures of fault-tolerant control schemes with the static and dynamic output controllers

    NASA Astrophysics Data System (ADS)

    Krokavec, Dušan; Filasová, Anna

    2017-01-01

    An enhanced approach to fault-tolerant control design is proposed in the paper for linear systems subject to cascade control strategy, while static and dynamic output controllers are employed to maintain the stability of the overall interconnected control structure. The controller gains are solved simultaneously using two-step linear matrix inequality formulation, conditioned by linear matrix equalities. A simulation example, subject to a system matrix parameter fault, demonstrates the effiectiveness of the proposed method of design and cascade control technique.

  9. Dynamic inversion method based on the time-staggered stereo-modeling scheme and its acceleration

    NASA Astrophysics Data System (ADS)

    Jing, Hao; Yang, Dinghui; Wu, Hao

    2016-12-01

    A set of second-order differential equations describing the space-time behaviour of derivatives of displacement with respect to model parameters (i.e. waveform sensitivities) is obtained via taking the derivative of the original wave equations. The dynamic inversion method obtains sensitivities of the seismic displacement field with respect to earth properties directly by solving differential equations for them instead of constructing sensitivities from the displacement field itself. In this study, we have taken a new perspective on the dynamic inversion method and used acceleration approaches to reduce the computational time and memory usage to improve its ability of performing high-resolution imaging. The dynamic inversion method, which can simultaneously use different waves and multicomponent observation data, is appropriate for directly inverting elastic parameters, medium density or wave velocities. Full wavefield information is utilized as much as possible at the expense of a larger amount of calculations. To mitigate the computational burden, two ways are proposed to accelerate the method from a computer-implementation point of view. One is source encoding which uses a linear combination of all shots, and the other is to reduce the amount of calculations on forward modeling. We applied a new finite-difference (FD) method to the dynamic inversion to improve the computational accuracy and speed up the performance. Numerical experiments indicated that the new FD method can effectively suppress the numerical dispersion caused by the discretization of wave equations, resulting in enhanced computational efficiency with less memory cost for seismic modeling and inversion based on the full wave equations. We present some inversion results to demonstrate the validity of this method through both checkerboard and Marmousi models. It shows that this method is also convergent even with big deviations for the initial model. Besides, parallel calculations can be easily

  10. Adaptive lag synchronization based topology identification scheme of uncertain general complex dynamical networks

    NASA Astrophysics Data System (ADS)

    Che, Y.; Li, R. X.; Han, C. X.; Wang, J.; Cui, S. G.; Deng, B.; Wei, X.

    2012-08-01

    This paper presents an adaptive lag synchronization based method for simultaneous identification of topology and parameters of uncertain general complex dynamical networks with and without time delays. Based on Lyapunov stability theorem and LaSalle's invariance principle, an adaptive controller is designed to realize lag synchronization between drive and response systems, meanwhile, identification criteria of network topology and system parameters are obtained. Numerical simulations illustrate the effectiveness of the proposed method.

  11. Lattice dynamics of the icosahedral quasicrystals i-ZnMgSc and i-ZnAgSc and the cubic 1/1-approximant Zn6Sc.

    PubMed

    Euchner, H; Yamada, T; Rols, S; Ishimasa, T; Ollivier, J; Schober, H; Mihalkovic, M; de Boissieu, M

    2014-02-05

    A comparison of periodic approximants and their quasicrystalline counterparts offers the opportunity to better understand the structure, physical properties and stabilizing mechanisms of these complex phases. We present a combined experimental and computational study of the lattice dynamics of the icosahedral quasicrystals i-ZnMgSc and i-ZnAgSc and compare these to the lattice dynamics of the cubic 1/1-approximant Zn6Sc. The two phases, quasicrystal and approximant, are built up from the same atomic clusters, which are packed either quasiperiodically or on a body centered cubic lattice, respectively. Using inelastic neutron scattering and atomic scale simulations, we show that the vibrational spectra of these three systems are very similar, however, they contain a clear signature of the increasing structural complexity from approximant to quasicrystal.

  12. Inference for optimal dynamic treatment regimes using an adaptive m-out-of-n bootstrap scheme.

    PubMed

    Chakraborty, Bibhas; Laber, Eric B; Zhao, Yingqi

    2013-09-01

    A dynamic treatment regime consists of a set of decision rules that dictate how to individualize treatment to patients based on available treatment and covariate history. A common method for estimating an optimal dynamic treatment regime from data is Q-learning which involves nonsmooth operations of the data. This nonsmoothness causes standard asymptotic approaches for inference like the bootstrap or Taylor series arguments to breakdown if applied without correction. Here, we consider the m-out-of-n bootstrap for constructing confidence intervals for the parameters indexing the optimal dynamic regime. We propose an adaptive choice of m and show that it produces asymptotically correct confidence sets under fixed alternatives. Furthermore, the proposed method has the advantage of being conceptually and computationally much simple than competing methods possessing this same theoretical property. We provide an extensive simulation study to compare the proposed method with currently available inference procedures. The results suggest that the proposed method delivers nominal coverage while being less conservative than alternatives. The proposed methods are implemented in the qLearn R-package and have been made available on the Comprehensive R-Archive Network (http://cran.r-project.org/). Analysis of the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) study is used as an illustrative example. © 2013, The International Biometric Society.

  13. Inference for Optimal Dynamic Treatment Regimes using an Adaptive m-out-of-n Bootstrap Scheme

    PubMed Central

    Chakraborty, Bibhas; Laber, Eric B.; Zhao, Yingqi

    2013-01-01

    Summary A dynamic treatment regime consists of a set of decision rules that dictate how to individualize treatment to patients based on available treatment and covariate history. A common method for estimating an optimal dynamic treatment regime from data is Q-learning which involves nonsmooth operations of the data. This nonsmoothness causes standard asymptotic approaches for inference like the bootstrap or Taylor series arguments to breakdown if applied without correction. Here, we consider the m-out-of-n bootstrap for constructing confidence intervals for the parameters indexing the optimal dynamic regime. We propose an adaptive choice of m and show that it produces asymptotically correct confidence sets under fixed alternatives. Furthermore, the proposed method has the advantage of being conceptually and computationally much more simple than competing methods possessing this same theoretical property. We provide an extensive simulation study to compare the proposed method with currently available inference procedures. The results suggest that the proposed method delivers nominal coverage while being less conservative than alternatives. The proposed methods are implemented in the qLearn R-package and have been made available on the Comprehensive R-Archive Network (http://cran.r-project.org/). Analysis of the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) study is used as an illustrative example. PMID:23845276

  14. Energy landscape scheme for an intuitive understanding of complex domain dynamics in ferroelectric thin films.

    PubMed

    Kim, Tae Heon; Yoon, Jong-Gul; Baek, Seung Hyub; Park, Woong-kyu; Yang, Sang Mo; Yup Jang, Seung; Min, Taeyuun; Chung, Jin-Seok; Eom, Chang-Beom; Noh, Tae Won

    2015-07-01

    Fundamental understanding of domain dynamics in ferroic materials has been a longstanding issue because of its relevance to many systems and to the design of nanoscale domain-wall devices. Despite many theoretical and experimental studies, a full understanding of domain dynamics still remains incomplete, partly due to complex interactions between domain-walls and disorder. We report domain-shape-preserving deterministic domain-wall motion, which directly confirms microscopic return point memory, by observing domain-wall breathing motion in ferroelectric BiFeO3 thin film using stroboscopic piezoresponse force microscopy. Spatial energy landscape that provides new insights into domain dynamics is also mapped based on the breathing motion of domain walls. The evolution of complex domain structure can be understood by the process of occupying the lowest available energy states of polarization in the energy landscape which is determined by defect-induced internal fields. Our result highlights a pathway for the novel design of ferroelectric domain-wall devices through the engineering of energy landscape using defect-induced internal fields such as flexoelectric fields.

  15. Primary damage in tungsten using the binary collision approximation, molecular dynamic simulations and the density functional theory

    NASA Astrophysics Data System (ADS)

    De Backer, A.; Sand, A.; Ortiz, C. J.; Domain, C.; Olsson, P.; Berthod, E.; Becquart, C. S.

    2016-02-01

    The damage produced by primary knock-on atoms (PKA) in W has been investigated from the threshold displacement energy (TDE) where it produces one self interstitial atom-vacancy pair to larger energies, up to 100 keV, where a large molten volume is formed. The TDE has been determined in different crystal directions using the Born-Oppenheimer density functional molecular dynamics (DFT-MD). A significant difference has been observed without and with the semi-core electrons. Classical MD has been used with two different empirical potentials characterized as ‘soft’ and ‘hard’ to obtain statistics on TDEs. Cascades of larger energy have been calculated, with these potentials, using a model that accounts for electronic losses (Sand et al 2013 Europhys. Lett. 103 46003). Two other sets of cascades have been produced using the binary collision approximation (BCA): a Monte Carlo BCA using SDTrimSP (Eckstein et al 2011 SDTrimSP: Version 5.00. Report IPP 12/8) (similar to SRIM www.srim.org) and MARLOWE (RSICC Home Page. (https://rsicc.ornl.gov/codes/psr/psr1/psr-137.html) (accessed May, 2014)). The comparison of these sets of cascades gave a recombination distance equal to 12 Å which is significantly larger from the one we reported in Hou et al (2010 J. Nucl. Mater. 403 89) because, here, we used bulk cascades rather than surface cascades which produce more defects (Stoller 2002 J. Nucl. Mater. 307 935, Nordlund et al 1999 Nature 398 49). Investigations on the defect clustering aspect showed that the difference between BCA and MD cascades is considerably reduced after the annealing of the cascade debris at 473 K using our Object Kinetic Monte Carlo model, LAKIMOCA (Domain et al 2004 J. Nucl. Mater. 335 121).

  16. Nonlinear dynamics of a two-level system of a single spin driven beyond the rotating-wave approximation

    NASA Astrophysics Data System (ADS)

    Rao, K. Rama Koteswara; Suter, Dieter

    2017-05-01

    Quantum systems driven by strong oscillating fields are the source of many interesting physical phenomena. In this work, we experimentally study the dynamics of a two-level system of a single spin driven in the strong-driving regime where the rotating-wave approximation is not valid. This two-level system is a subsystem of a single nitrogen-vacancy (NV) center in diamond coupled to a first-shell 13C nuclear spin at a level anticrossing point. This near degeneracy occurs in the ms=±1 manifold of the electron spin when the energy level splitting between the ms=-1 and +1 states due to the static magnetic field is ≈127 MHz and thus equal to the splitting due to the 13C hyperfine interaction. The transition frequency of this electron spin two-level system in a static magnetic field of 28.9 G is 1.7 MHz and it can be driven only by the component of the radio-frequency (RF) field along the NV symmetry axis. Electron spin Rabi frequencies in this system can reach tens of MHz even for moderate RF powers. The simple sinusoidal Rabi oscillations that occur when the amplitude of the driving field is small compared to the transition frequency evolve into complex patterns when the driving field amplitude is comparable to or greater than the energy level splitting. We observe that the system oscillates faster than the amplitude of the driving field and the response of the system shows multiple frequencies.

  17. Deterministic global optimization algorithm based on outer approximation for the parameter estimation of nonlinear dynamic biological systems

    PubMed Central

    2012-01-01

    Background The estimation of parameter values for mathematical models of biological systems is an optimization problem that is particularly challenging due to the nonlinearities involved. One major difficulty is the existence of multiple minima in which standard optimization methods may fall during the search. Deterministic global optimization methods overcome this limitation, ensuring convergence to the global optimum within a desired tolerance. Global optimization techniques are usually classified into stochastic and deterministic. The former typically lead to lower CPU times but offer no guarantee of convergence to the global minimum in a finite number of iterations. In contrast, deterministic methods provide solutions of a given quality (i.e., optimality gap), but tend to lead to large computational burdens. Results This work presents a deterministic outer approximation-based algorithm for the global optimization of dynamic problems arising in the parameter estimation of models of biological systems. Our approach, which offers a theoretical guarantee of convergence to global minimum, is based on reformulating the set of ordinary differential equations into an equivalent set of algebraic equations through the use of orthogonal collocation methods, giving rise to a nonconvex nonlinear programming (NLP) problem. This nonconvex NLP is decomposed into two hierarchical levels: a master mixed-integer linear programming problem (MILP) that provides a rigorous lower bound on the optimal solution, and a reduced-space slave NLP that yields an upper bound. The algorithm iterates between these two levels until a termination criterion is satisfied. Conclusion The capabilities of our approach were tested in two benchmark problems, in which the performance of our algorithm was compared with that of the commercial global optimization package BARON. The proposed strategy produced near optimal solutions (i.e., within a desired tolerance) in a fraction of the CPU time required by

  18. Deterministic global optimization algorithm based on outer approximation for the parameter estimation of nonlinear dynamic biological systems.

    PubMed

    Miró, Anton; Pozo, Carlos; Guillén-Gosálbez, Gonzalo; Egea, Jose A; Jiménez, Laureano

    2012-05-10

    The estimation of parameter values for mathematical models of biological systems is an optimization problem that is particularly challenging due to the nonlinearities involved. One major difficulty is the existence of multiple minima in which standard optimization methods may fall during the search. Deterministic global optimization methods overcome this limitation, ensuring convergence to the global optimum within a desired tolerance. Global optimization techniques are usually classified into stochastic and deterministic. The former typically lead to lower CPU times but offer no guarantee of convergence to the global minimum in a finite number of iterations. In contrast, deterministic methods provide solutions of a given quality (i.e., optimality gap), but tend to lead to large computational burdens. This work presents a deterministic outer approximation-based algorithm for the global optimization of dynamic problems arising in the parameter estimation of models of biological systems. Our approach, which offers a theoretical guarantee of convergence to global minimum, is based on reformulating the set of ordinary differential equations into an equivalent set of algebraic equations through the use of orthogonal collocation methods, giving rise to a nonconvex nonlinear programming (NLP) problem. This nonconvex NLP is decomposed into two hierarchical levels: a master mixed-integer linear programming problem (MILP) that provides a rigorous lower bound on the optimal solution, and a reduced-space slave NLP that yields an upper bound. The algorithm iterates between these two levels until a termination criterion is satisfied. The capabilities of our approach were tested in two benchmark problems, in which the performance of our algorithm was compared with that of the commercial global optimization package BARON. The proposed strategy produced near optimal solutions (i.e., within a desired tolerance) in a fraction of the CPU time required by BARON.

  19. Spatiotemporal dynamics of immature culicines (subfamily Culicinae) and their larval habitats in Mwea Rice Scheme, Kenya.

    PubMed

    Muturi, Ephantus J; Mwangangi, Joseph M; Jacob, Benjamin G; Shililu, Josephat I; Mbogo, Charles M; Githure, John I; Novak, Robert J

    2009-03-01

    An ecological study was conducted at three study sites in Mwea Rice Scheme, Kenya to identify the diverse aquatic habitats in which culicine mosquitoes thrived and to explore the best strategies for mosquito control in the area. During the 11-month study period, ten habitat categories and 11 culicine species mainly dominated by Culex quinquefasciatus (72.0%) and Culex annulioris (17.9%) were identified from pupae and late instars larval samples. Two of the 11 culicine species, Ficalbia (Mimomyia) plumosa and Uranotaenia spp., have not been reported previously in the study area. Rurumi had more habitat types than either of the other study sites but the least number of mosquito species. In contrast, Karima had the least number of habitat types but significantly higher density of early instars than the other study sites. The relative abundance of late instars and pupae did not vary significantly among study sites. The contribution of different habitat types to larval production varied markedly between seasons and among study sites. Paddies and canals were perennial contributors of culicine mosquito larvae while the other habitat types were important mainly during the wet season. Some habitat types such as ditches, seeps, marshes, and fishpond were absent in some study sites but of great significance in other study sites. C. quinquefasciatus was positively associated with turbidity at all study sites and also negatively associated with emergent vegetation and distance to the nearest homestead in Karima, emergent vegetation in Kiuria, and other aquatic invertebrates in Rurumi. C. annulioris was positively associated with emergent vegetation at all study sites and also with depth in Kiuria. These findings indicate that besides rice fields and associated habitats, a diversity of other aquatic habitats contribute to culicine adult mosquito production in the study area and that environmental factors that determine the occurrence of a particular mosquito species may vary

  20. Quantum fluctuations beyond the Gutzwiller approximation

    NASA Astrophysics Data System (ADS)

    Fabrizio, Michele

    2017-02-01

    We present a simple scheme to evaluate linear response functions including quantum fluctuation corrections on top of the Gutzwiller approximation. The method is derived for a generic multiband lattice Hamiltonian without any assumption about the dynamics of the variational correlation parameters that define the Gutzwiller wave function, and which thus behave as genuine dynamical degrees of freedom that add on those of the variational uncorrelated Slater determinant. We apply the method to the standard half-filled single-band Hubbard model. We are able to recover known results, but, as a by-product, we also obtain a few other results. In particular, we show that quantum fluctuations can reproduce, almost quantitatively, the behavior of the uniform magnetic susceptibility uncovered by dynamical mean-field theory, which, though enhanced by correlations, is found to be smooth across the paramagnetic Mott transition. By contrast, the simple Gutzwiller approximation predicts that susceptibility to diverge at the transition.

  1. Exploration of a Dynamic Merging Scheme for Precipitation Estimation over a Small Urban Catchment

    NASA Astrophysics Data System (ADS)

    Al-Azerji, Sherien; Rico-Ramirez, Miguel, ,, Dr.; Han, Dawei, ,, Prof.

    2016-04-01

    The accuracy of quantitative precipitation estimation is of significant importance for urban areas due to the potentially damaging consequences that can result from pluvial flooding. Improved accuracy could be accomplished by merging rain gauge measurements with weather radar data through different merging methods. Several factors may affect the accuracy of the merged data, and the gauge density used for merging is one of the most important. However, if there are no gauges inside the research area, then a gauge network outside the research area can be used for the merging. Generally speaking, the denser the rain gauge network is, the better the merging results that can be achieved. However, in practice, the rain gauge network around the research area is fixed, and the research question is about the optimal merging area. The hypothesis is that if the merging area is too small, there are fewer gauges for merging and thus the result would be poor. If the merging area is too large, gauges far away from the research area can be included in merging. However, due to their large distances, those gauges far away from the research area provide little relevant information to the study and may even introduce noise in merging. Therefore, an optimal merging area that produces the best merged rainfall estimation in the research area could exist. To test this hypothesis, the distance from the centre of the research area and the number of merging gauges around the research area were gradually increased and merging with a new domain of radar data was then performed. The performance of the new merging scheme was compared with a gridded interpolated rainfall from four experimental rain gauges installed inside the research area for validation. The result of this analysis shows that there is indeed an optimum distance from the centre of research area and consequently an optimum number of rain gauges that produce the best merged rainfall data inside the research area. This study is of

  2. Parallel Adaptive Mesh Refinement for High-Order Finite-Volume Schemes in Computational Fluid Dynamics

    NASA Astrophysics Data System (ADS)

    Schwing, Alan Michael

    For computational fluid dynamics, the governing equations are solved on a discretized domain of nodes, faces, and cells. The quality of the grid or mesh can be a driving source for error in the results. While refinement studies can help guide the creation of a mesh, grid quality is largely determined by user expertise and understanding of the flow physics. Adaptive mesh refinement is a technique for enriching the mesh during a simulation based on metrics for error, impact on important parameters, or location of important flow features. This can offload from the user some of the difficult and ambiguous decisions necessary when discretizing the domain. This work explores the implementation of adaptive mesh refinement in an implicit, unstructured, finite-volume solver. Consideration is made for applying modern computational techniques in the presence of hanging nodes and refined cells. The approach is developed to be independent of the flow solver in order to provide a path for augmenting existing codes. It is designed to be applicable for unsteady simulations and refinement and coarsening of the grid does not impact the conservatism of the underlying numerics. The effect on high-order numerical fluxes of fourth- and sixth-order are explored. Provided the criteria for refinement is appropriately selected, solutions obtained using adapted meshes have no additional error when compared to results obtained on traditional, unadapted meshes. In order to leverage large-scale computational resources common today, the methods are parallelized using MPI. Parallel performance is considered for several test problems in order to assess scalability of both adapted and unadapted grids. Dynamic repartitioning of the mesh during refinement is crucial for load balancing an evolving grid. Development of the methods outlined here depend on a dual-memory approach that is described in detail. Validation of the solver developed here against a number of motivating problems shows favorable

  3. Langevin spin dynamics based on ab initio calculations: numerical schemes and applications.

    PubMed

    Rózsa, L; Udvardi, L; Szunyogh, L

    2014-05-28

    A method is proposed to study the finite-temperature behaviour of small magnetic clusters based on solving the stochastic Landau-Lifshitz-Gilbert equations, where the effective magnetic field is calculated directly during the solution of the dynamical equations from first principles instead of relying on an effective spin Hamiltonian. Different numerical solvers are discussed in the case of a one-dimensional Heisenberg chain with nearest-neighbour interactions. We performed detailed investigations for a monatomic chain of ten Co atoms on top of a Au(0 0 1) surface. We found a spiral-like ground state of the spins due to Dzyaloshinsky-Moriya interactions, while the finite-temperature magnetic behaviour of the system was well described by a nearest-neighbour Heisenberg model including easy-axis anisotropy.

  4. Compact internal representation as a protocognitive scheme for robots in dynamic environments

    NASA Astrophysics Data System (ADS)

    Villacorta-Atienza, Jose A.; Salas, Luis; Alba, Luis; Velarde, Manuel G.; Makarov, Valeri A.

    2011-05-01

    Animals for surviving have developed cognitive abilities allowing them an abstract representation of the environment. This Internal Representation (IR) could contain a huge amount of information concerning the evolution and interactions of the elements in their surroundings. The complexity of this information should be enough to ensure the maximum fidelity in the representation of those aspects of the environment critical for the agent, but not so high to prevent the management of the IR in terms of neural processes, i.e. storing, retrieving, etc. One of the most subtle points is the inclusion of temporal information, necessary in IRs of dynamic environments. This temporal information basically introduces the environmental information for each moment, so the information required to generate the IR would eventually be increased dramatically. The inclusion of this temporal information in biological neural processes remains an open question. In this work we propose a new IR, the Compact Internal Representation (CIR), based on the compaction of spatiotemporal information into only space, leading to a stable structure (with no temporal dimension) suitable to be the base for complex cognitive processes, as memory or learning. The Compact Internal Representation is especially appropriate for be implemented in autonomous robots because it provides global strategies for the interaction with real environments (roving robots, manipulators, etc.). This paper presents the mathematical basis of CIR hardware implementation in the context of navigation in dynamic environments. The aim of such implementation is the obtaining of free-collision trajectories under the requirements of an optimal performance by means of a fast and accurate process.

  5. Mapping and controlling ultrafast dynamics of highly excited H2 molecules by VUV-IR pump-probe schemes

    DOE PAGES

    Sturm, F. P.; Tong, X. M.; Palacios, A.; ...

    2017-01-09

    Here, we used ultrashort femtosecond vacuum ultraviolet (VUV) and infrared (IR) pulses in a pump-probe scheme to map the dynamics and nonequilibrium dissociation channels of excited neutral H2 molecules. A nuclear wave packet is created in the B1Σmore » $$+\\atop{u}$$ state of the neutral H2 molecule by absorption of the ninth harmonic of the driving infrared laser field. Due to the large stretching amplitude of the molecule excited in the B1Σ$$+\\atop{u}$$ electronic state, the effective H2+ ionization potential changes significantly as the nuclear wave packet vibrates in the bound, highly electronically and vibrationally excited B potential-energy curve. We probed such dynamics by ionizing the excited neutral molecule using time-delayed VUV-or-IR radiation. We identified the nonequilibrium dissociation channels by utilizing three-dimensional momentum imaging of the ion fragments. We also found that different dissociation channels can be controlled, to some extent, by changing the IR laser intensity and by choosing the wavelength of the probe laser light. Furthermore, we concluded that even in a benchmark molecular system such as H2*, the interpretation of the nonequilibrium multiphoton and multicolor ionization processes is still a challenging task, requiring intricate theoretical analysis.« less

  6. An evolution-based DNA-binding residue predictor using a dynamic query-driven learning scheme.

    PubMed

    Chai, H; Zhang, J; Yang, G; Ma, Z

    2016-11-15

    DNA-binding proteins play a pivotal role in various biological activities. Identification of DNA-binding residues (DBRs) is of great importance for understanding the mechanism of gene regulations and chromatin remodeling. Most traditional computational methods usually construct their predictors on static non-redundant datasets. They excluded many homologous DNA-binding proteins so as to guarantee the generalization capability of their models. However, those ignored samples may potentially provide useful clues when studying protein-DNA interactions, which have not obtained enough attention. In view of this, we propose a novel method, namely DQPred-DBR, to fill the gap of DBR predictions. First, a large-scale extensible sample pool was compiled. Second, evolution-based features in the form of a relative position specific score matrix and covariant evolutionary conservation descriptors were used to encode the feature space. Third, a dynamic query-driven learning scheme was designed to make more use of proteins with known structure and functions. In comparison with a traditional static model, the introduction of dynamic models could obviously improve the prediction performance. Experimental results from the benchmark and independent datasets proved that our DQPred-DBR had promising generalization capability. It was capable of producing decent predictions and outperforms many state-of-the-art methods. For the convenience of academic use, our proposed method was also implemented as a web server at .

  7. Mapping and controlling ultrafast dynamics of highly excited H2 molecules by VUV-IR pump-probe schemes

    NASA Astrophysics Data System (ADS)

    Sturm, F. P.; Tong, X. M.; Palacios, A.; Wright, T. W.; Zalyubovskaya, I.; Ray, D.; Shivaram, N.; Martín, F.; Belkacem, A.; Ranitovic, P.; Weber, Th.

    2017-01-01

    We used ultrashort femtosecond vacuum ultraviolet (VUV) and infrared (IR) pulses in a pump-probe scheme to map the dynamics and nonequilibrium dissociation channels of excited neutral H2 molecules. A nuclear wave packet is created in the B Σ+1u state of the neutral H2 molecule by absorption of the ninth harmonic of the driving infrared laser field. Due to the large stretching amplitude of the molecule excited in the B Σ+1u electronic state, the effective H2+ ionization potential changes significantly as the nuclear wave packet vibrates in the bound, highly electronically and vibrationally excited B potential-energy curve. We probed such dynamics by ionizing the excited neutral molecule using time-delayed VUV-or-IR radiation. We identified the nonequilibrium dissociation channels by utilizing three-dimensional momentum imaging of the ion fragments. We found that different dissociation channels can be controlled, to some extent, by changing the IR laser intensity and by choosing the wavelength of the probe laser light. Furthermore, we concluded that even in a benchmark molecular system such as H2*, the interpretation of the nonequilibrium multiphoton and multicolor ionization processes is still a challenging task, requiring intricate theoretical analysis.

  8. Understanding Ion Binding Affinity and Selectivity in β-Parvalbumin Using Molecular Dynamics and Mean Spherical Approximation Theory.

    PubMed

    Kucharski, Amir N; Scott, Caitlin E; Davis, Jonathan P; Kekenes-Huskey, Peter M

    2016-08-25

    Parvalbumin (PV) is a globular calcium (Ca(2+))-selective protein expressed in a variety of biological tissues. Our computational studies of the rat β-parvalbumin (β-PV) isoform seek to elucidate the molecular thermodynamics of Ca(2+) versus magnesium (Mg(2+)) binding at the protein's two EF-hand motifs. Specifically, we have utilized molecular dynamics (MD) simulations and a mean-field electrolyte model (mean spherical approximation (MSA) theory) to delineate how the EF-hand scaffold controls the "local" thermodynamics of Ca(2+) binding selectivity over Mg(2+). Our MD simulations provide the probability density of metal-chelating oxygens within the EF-hand scaffolds for both Ca(2+) and Mg(2+), as well the conformational strain induced by Mg(2+) relative to Ca(2+) binding. MSA theory utilizes the binding domain oxygen and charge distributions to predict the chemical potential of ion binding, as well as their corresponding concentrations within the binding domain. We find that the electrostatic and steric contributions toward ion binding were similar for Mg(2+) and Ca(2+), yet the latter was 5.5 kcal/mol lower in enthalpy when internal strain within the EF hand was considered. We therefore speculate that beyond differences in dehydration energies for the Ca(2+) versus Mg(2+), strain induced in the β-PV EF hand by cation binding significantly contributes to the nearly 10,000-fold difference in binding affinity reported in the literature. We further complemented our analyses of local factors governing cation binding selectivity with whole-protein (global) contributions, such as interhelical residue-residue contacts and solvent exposure of hydrophobic surface. These contributions were found to be comparable for both Ca(2+)- and Mg(2+)-bound β-PV, which may implicate local factors, EF-hand strain, and dehydration, in providing the primary means of selectivity. We anticipate these methods could be used to estimate metal binding thermodynamics across a broad range of

  9. Extended application of Kohn-Sham first-principles molecular dynamics method with plane wave approximation at high energy—From cold materials to hot dense plasmas

    NASA Astrophysics Data System (ADS)

    Zhang, Shen; Wang, Hongwei; Kang, Wei; Zhang, Ping; He, X. T.

    2016-04-01

    An extended first-principles molecular dynamics (FPMD) method based on Kohn-Sham scheme is proposed to elevate the temperature limit of the FPMD method in the calculation of dense plasmas. The extended method treats the wave functions of high energy electrons as plane waves analytically and thus expands the application of the FPMD method to the region of hot dense plasmas without suffering from the formidable computational costs. In addition, the extended method inherits the high accuracy of the Kohn-Sham scheme and keeps the information of electronic structures. This gives an edge to the extended method in the calculation of mixtures of plasmas composed of heterogeneous ions, high-Z dense plasmas, lowering of ionization potentials, X-ray absorption/emission spectra, and opacities, which are of particular interest to astrophysics, inertial confinement fusion engineering, and laboratory astrophysics.

  10. Extended application of Kohn-Sham first-principles molecular dynamics method with plane wave approximation at high energy—From cold materials to hot dense plasmas

    SciTech Connect

    Zhang, Shen; Kang, Wei; Wang, Hongwei; Zhang, Ping; He, X. T.

    2016-04-15

    An extended first-principles molecular dynamics (FPMD) method based on Kohn-Sham scheme is proposed to elevate the temperature limit of the FPMD method in the calculation of dense plasmas. The extended method treats the wave functions of high energy electrons as plane waves analytically and thus expands the application of the FPMD method to the region of hot dense plasmas without suffering from the formidable computational costs. In addition, the extended method inherits the high accuracy of the Kohn-Sham scheme and keeps the information of electronic structures. This gives an edge to the extended method in the calculation of mixtures of plasmas composed of heterogeneous ions, high-Z dense plasmas, lowering of ionization potentials, X-ray absorption/emission spectra, and opacities, which are of particular interest to astrophysics, inertial confinement fusion engineering, and laboratory astrophysics.

  11. Molecular dynamics scheme for precise estimation of electrostatic interaction via zero-dipole summation principle

    NASA Astrophysics Data System (ADS)

    Fukuda, Ikuo; Yonezawa, Yasushige; Nakamura, Haruki

    2011-04-01

    We propose a novel idea, zero-dipole summation, for evaluating the electrostatic energy of a classical particle system, and have composed an algorithm for effectively utilizing the idea for molecular dynamics. It conceptually prevents the nonzero-charge and nonzero-dipole states artificially generated by a simple cutoff truncation. The resulting energy formula is nevertheless represented by a simple pairwise function sum, which enables facile application to high-performance computation. By following a heuristic approach to derive the current electrostatic energy formula, we developed an axiomatic approach to construct the method consistently. Explorations of the theoretical details of our method revealed the structure of the generated error, and we analyzed it by comparisons with other methods. A numerical simulation using liquid sodium chloride confirmed that the current method with a small damping factor yielded sufficient accuracy with a practical cutoff distance region. The current energy function also conducts stable numerical integration in a liquid MD simulation. Our method is an extension of the charge neutralized summation developed by Wolf et al. [J. Chem. Phys. 110, 8254 (1999)]. Furthermore, we found that the current method becomes a generalization of the preaveraged potential method proposed by Yakub and Ronchi [J. Chem. Phys. 119, 11556 (2003)], which is based on a viewpoint different from the neutrality. The current study presents these relationships and suggests possibilities for their further applications.

  12. Scheme for Launching and Observing Dynamics of Cold Atoms in Rydberg States

    NASA Astrophysics Data System (ADS)

    Goodsell, Anne; Weidner, Erik; Fitzpatrick, Mattias

    2013-05-01

    We are assembling a source of laser-cooled Rb atoms that can be launched at slow, controlled velocities and excited into Rydberg states. We assess the feasibility of detecting the motion of cold Rydberg atoms around a macroscopic charged wire. The capture and ionization of cold ground-state atoms in a 1 / r -electric field has been observed previously, using a nanowire to ensure that captured atoms could move in free space at small radial distances before impacting the wire or field-ionizing near the surface. Using highly-excited atoms instead, we suggest that a macroscopic wire offers a robust system with magnified effects. The capture cross-section increases for incident atoms in high- n states. For a 20-micron-diameter wire charged to +300 V, the critical impact parameter for atoms traveling at 2 m/s with n = 50 is 30 μm, 10 times larger than for ground-state atoms. We propose that aspects of this model can be realized experimentally. Using an estimated lifetime of 40 ns for the n = 50 state, we calculate that excitation must occur at r=100 μm, significantly beyond the wire's surface. In this way, we are preparing to promote launched atoms into high- n states and study their dynamics.

  13. Time-optimal path planning in dynamic flows using level set equations: theory and schemes

    NASA Astrophysics Data System (ADS)

    Lolla, Tapovan; Lermusiaux, Pierre F. J.; Ueckermann, Mattheus P.; Haley, Patrick J.

    2014-10-01

    We develop an accurate partial differential equation-based methodology that predicts the time-optimal paths of autonomous vehicles navigating in any continuous, strong, and dynamic ocean currents, obviating the need for heuristics. The goal is to predict a sequence of steering directions so that vehicles can best utilize or avoid currents to minimize their travel time. Inspired by the level set method, we derive and demonstrate that a modified level set equation governs the time-optimal path in any continuous flow. We show that our algorithm is computationally efficient and apply it to a number of experiments. First, we validate our approach through a simple benchmark application in a Rankine vortex flow for which an analytical solution is available. Next, we apply our methodology to more complex, simulated flow fields such as unsteady double-gyre flows driven by wind stress and flows behind a circular island. These examples show that time-optimal paths for multiple vehicles can be planned even in the presence of complex flows in domains with obstacles. Finally, we present and support through illustrations several remarks that describe specific features of our methodology.

  14. Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

    NASA Technical Reports Server (NTRS)

    Batina, John T.

    1990-01-01

    Improved algorithms for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration shceme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. The paper presents a description of the Euler solvers along with results and comparisons which assess the capability.

  15. Dynamic Construction Scheme for Virtualization Security Service in Software-Defined Networks.

    PubMed

    Lin, Zhaowen; Tao, Dan; Wang, Zhenji

    2017-04-21

    For a Software Defined Network (SDN), security is an important factor affecting its large-scale deployment. The existing security solutions for SDN mainly focus on the controller itself, which has to handle all the security protection tasks by using the programmability of the network. This will undoubtedly involve a heavy burden for the controller. More devastatingly, once the controller itself is attacked, the entire network will be paralyzed. Motivated by this, this paper proposes a novel security protection architecture for SDN. We design a security service orchestration center in the control plane of SDN, and this center physically decouples from the SDN controller and constructs SDN security services. We adopt virtualization technology to construct a security meta-function library, and propose a dynamic security service composition construction algorithm based on web service composition technology. The rule-combining method is used to combine security meta-functions to construct security services which meet the requirements of users. Moreover, the RETE algorithm is introduced to improve the efficiency of the rule-combining method. We evaluate our solutions in a realistic scenario based on OpenStack. Substantial experimental results demonstrate the effectiveness of our solutions that contribute to achieve the effective security protection with a small burden of the SDN controller.

  16. Dynamic Construction Scheme for Virtualization Security Service in Software-Defined Networks

    PubMed Central

    Lin, Zhaowen; Tao, Dan; Wang, Zhenji

    2017-01-01

    For a Software Defined Network (SDN), security is an important factor affecting its large-scale deployment. The existing security solutions for SDN mainly focus on the controller itself, which has to handle all the security protection tasks by using the programmability of the network. This will undoubtedly involve a heavy burden for the controller. More devastatingly, once the controller itself is attacked, the entire network will be paralyzed. Motivated by this, this paper proposes a novel security protection architecture for SDN. We design a security service orchestration center in the control plane of SDN, and this center physically decouples from the SDN controller and constructs SDN security services. We adopt virtualization technology to construct a security meta-function library, and propose a dynamic security service composition construction algorithm based on web service composition technology. The rule-combining method is used to combine security meta-functions to construct security services which meet the requirements of users. Moreover, the RETE algorithm is introduced to improve the efficiency of the rule-combining method. We evaluate our solutions in a realistic scenario based on OpenStack. Substantial experimental results demonstrate the effectiveness of our solutions that contribute to achieve the effective security protection with a small burden of the SDN controller. PMID:28430155

  17. Developing a computationally efficient dynamic multilevel hybrid optimization scheme using multifidelity model interactions.

    SciTech Connect

    Hough, Patricia Diane (Sandia National Laboratories, Livermore, CA); Gray, Genetha Anne (Sandia National Laboratories, Livermore, CA); Castro, Joseph Pete Jr.; Giunta, Anthony Andrew

    2006-01-01

    Many engineering application problems use optimization algorithms in conjunction with numerical simulators to search for solutions. The formulation of relevant objective functions and constraints dictate possible optimization algorithms. Often, a gradient based approach is not possible since objective functions and constraints can be nonlinear, nonconvex, non-differentiable, or even discontinuous and the simulations involved can be computationally expensive. Moreover, computational efficiency and accuracy are desirable and also influence the choice of solution method. With the advent and increasing availability of massively parallel computers, computational speed has increased tremendously. Unfortunately, the numerical and model complexities of many problems still demand significant computational resources. Moreover, in optimization, these expenses can be a limiting factor since obtaining solutions often requires the completion of numerous computationally intensive simulations. Therefore, we propose a multifidelity optimization algorithm (MFO) designed to improve the computational efficiency of an optimization method for a wide range of applications. In developing the MFO algorithm, we take advantage of the interactions between multi fidelity models to develop a dynamic and computational time saving optimization algorithm. First, a direct search method is applied to the high fidelity model over a reduced design space. In conjunction with this search, a specialized oracle is employed to map the design space of this high fidelity model to that of a computationally cheaper low fidelity model using space mapping techniques. Then, in the low fidelity space, an optimum is obtained using gradient or non-gradient based optimization, and it is mapped back to the high fidelity space. In this paper, we describe the theory and implementation details of our MFO algorithm. We also demonstrate our MFO method on some example problems and on two applications: earth penetrators and

  18. Approximate probabilistic cellular automata for the dynamics of single-species populations under discrete logisticlike growth with and without weak Allee effects

    NASA Astrophysics Data System (ADS)

    Mendonça, J. Ricardo G.; Gevorgyan, Yeva

    2017-05-01

    We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with nonoverlapping generations. Beginning with a general six-parameter model, we find constraints on the transition probabilities of the PCA that guarantee that the ensuing approximations make sense in terms of population dynamics and classify the valid combinations thereof. Several possible models display a negative cubic term that can be interpreted as a weak Allee factor. We also investigate the conditions under which a one-parameter PCA derived from the more general six-parameter model can generate valid population growth dynamics. Numerical simulations illustrate the behavior of some of the PCA found.

  19. Approximate probabilistic cellular automata for the dynamics of single-species populations under discrete logisticlike growth with and without weak Allee effects.

    PubMed

    Mendonça, J Ricardo G; Gevorgyan, Yeva

    2017-05-01

    We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with nonoverlapping generations. Beginning with a general six-parameter model, we find constraints on the transition probabilities of the PCA that guarantee that the ensuing approximations make sense in terms of population dynamics and classify the valid combinations thereof. Several possible models display a negative cubic term that can be interpreted as a weak Allee factor. We also investigate the conditions under which a one-parameter PCA derived from the more general six-parameter model can generate valid population growth dynamics. Numerical simulations illustrate the behavior of some of the PCA found.

  20. A minimalistic approach to static and dynamic electron correlations: Amending generalized valence bond method with extended random phase approximation correlation correction

    NASA Astrophysics Data System (ADS)

    Chatterjee, Koushik; Pastorczak, Ewa; Jawulski, Konrad; Pernal, Katarzyna

    2016-06-01

    A perfect-pairing generalized valence bond (GVB) approximation is known to be one of the simplest approximations, which allows one to capture the essence of static correlation in molecular systems. In spite of its attractive feature of being relatively computationally efficient, this approximation misses a large portion of dynamic correlation and does not offer sufficient accuracy to be generally useful for studying electronic structure of molecules. We propose to correct the GVB model and alleviate some of its deficiencies by amending it with the correlation energy correction derived from the recently formulated extended random phase approximation (ERPA). On the examples of systems of diverse electronic structures, we show that the resulting ERPA-GVB method greatly improves upon the GVB model. ERPA-GVB recovers most of the electron correlation and it yields energy barrier heights of excellent accuracy. Thanks to a balanced treatment of static and dynamic correlation, ERPA-GVB stays reliable when one moves from systems dominated by dynamic electron correlation to those for which the static correlation comes into play.

  1. Convergence of the standard RLS method and UDUT factorisation of covariance matrix for solving the algebraic Riccati equation of the DLQR via heuristic approximate dynamic programming

    NASA Astrophysics Data System (ADS)

    Moraes Rêgo, Patrícia Helena; Viana da Fonseca Neto, João; Ferreira, Ernesto M.

    2015-08-01

    The main focus of this article is to present a proposal to solve, via UDUT factorisation, the convergence and numerical stability problems that are related to the covariance matrix ill-conditioning of the recursive least squares (RLS) approach for online approximations of the algebraic Riccati equation (ARE) solution associated with the discrete linear quadratic regulator (DLQR) problem formulated in the actor-critic reinforcement learning and approximate dynamic programming context. The parameterisations of the Bellman equation, utility function and dynamic system as well as the algebra of Kronecker product assemble a framework for the solution of the DLQR problem. The condition number and the positivity parameter of the covariance matrix are associated with statistical metrics for evaluating the approximation performance of the ARE solution via RLS-based estimators. The performance of RLS approximators is also evaluated in terms of consistence and polarisation when associated with reinforcement learning methods. The used methodology contemplates realisations of online designs for DLQR controllers that is evaluated in a multivariable dynamic system model.

  2. A minimalistic approach to static and dynamic electron correlations: Amending generalized valence bond method with extended random phase approximation correlation correction.

    PubMed

    Chatterjee, Koushik; Pastorczak, Ewa; Jawulski, Konrad; Pernal, Katarzyna

    2016-06-28

    A perfect-pairing generalized valence bond (GVB) approximation is known to be one of the simplest approximations, which allows one to capture the essence of static correlation in molecular systems. In spite of its attractive feature of being relatively computationally efficient, this approximation misses a large portion of dynamic correlation and does not offer sufficient accuracy to be generally useful for studying electronic structure of molecules. We propose to correct the GVB model and alleviate some of its deficiencies by amending it with the correlation energy correction derived from the recently formulated extended random phase approximation (ERPA). On the examples of systems of diverse electronic structures, we show that the resulting ERPA-GVB method greatly improves upon the GVB model. ERPA-GVB recovers most of the electron correlation and it yields energy barrier heights of excellent accuracy. Thanks to a balanced treatment of static and dynamic correlation, ERPA-GVB stays reliable when one moves from systems dominated by dynamic electron correlation to those for which the static correlation comes into play.

  3. Dynamic MTF improvement scheme and its validation for CCD operating in TDI mode for Earth imaging applications

    NASA Astrophysics Data System (ADS)

    Dubey, Neeraj; Banerjee, Arup

    2016-05-01

    The paper presents the scheme for improving the image contrast in the remote sensing images and highlights the novelty in hardware & software design in the test system developed for measuring image contrast function. Modulation transfer function (MTF) is the most critical quality element of the high-resolution imaging payloads for earth observation consisting of TDI-CCD (Time Delayed Integration Charge Coupled Device) image. From the mathematical model for MTF Smear MTF of 65% (35% degradation) is observed. Then a operating method for TDI-CCD is developed, using which 96% of Motion Smear MTF will occur within the imaging operation. As a major part of the validation, indigenously designed and developed a test system for measuring the dynamic MTF of TDI Sensors which consists of the optical scanning system, TDI-CCD camera drive & video processing electronics, thermal control system and telecentric uniform illumination system. The experimental results confirm that image quality improvement can be achieved by this method. This method is now implemented in the flight model hardware of the remote sensing payload.

  4. Rational molecular dynamics scheme for predicting optimum concentration loading of nano-additive in phase change materials

    NASA Astrophysics Data System (ADS)

    Rastogi, Monisha; Vaish, Rahul; Madhar, Niyaz Ahamad; Shaikh, Hamid; Al-Zahrani, S. M.

    2015-10-01

    The present study deals with the diffusion and phase transition behaviour of paraffin reinforced with carbon nano-additives namely graphene oxide (GO) and surface functionalized single walled carbon nanotubes (SWCNT). Bulk disordered systems of paraffin hydrocarbons impregnated with carbon nano-additives have been generated in realistic equilibrium conformations for potential application as latent heat storage systems. Ab initio molecular dynamics(MD) in conjugation with COMPASS forcefield has been implemented using periodic boundary conditions. The proposed scheme allows determination of optimum nano-additive loading for improving thermo-physical properties through analysis of mass, thermal and transport properties; and assists in determination of composite behaviour and related performance from microscopic point of view. It was observed that nanocomposites containing 7.8 % surface functionalised SWCNT and 55% GO loading corresponds to best latent heat storage system. The propounded methodology could serve as a by-pass route for economically taxing and iterative experimental procedures required to attain the optimum composition for best performance. The results also hint at the large unexplored potential of ab-initio classical MD techniques for predicting performance of new nanocomposites for potential phase change material applications.

  5. Application of TVD schemes for the Euler equations of gas dynamics. [total variation diminishing for nonlinear hyperbolic systems

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Warming, R. F.; Harten, A.

    1985-01-01

    First-order, second-order, and implicit total variation diminishing (TVD) schemes are reviewed using the modified flux approach. Some transient and steady-state calculations are then carried out to illustrate the applicability of these schemes to the Euler equations. It is shown that the second-order explicit TVD schemes generate good shock resolution for both transient and steady-state one-dimensional and two-dimensional problems. Numerical experiments for a quasi-one-dimensional nozzle problem show that the second-order implicit TVD scheme produces a fairly rapid convergence rate and remains stable even when running with a Courant number of 10 to the 6th.

  6. Lattice dynamics and thermophysical properties of h.c.p. Os and Ru from the quasi-harmonic approximation

    NASA Astrophysics Data System (ADS)

    Palumbo, Mauro; Dal Corso, Andrea

    2017-10-01

    We report first-principles phonon frequencies and anharmonic thermodynamic properties of h.c.p. Os and Ru calculated within the quasi-harmonic approximation, including Grüneisen parameters, temperature-dependent lattice parameters, thermal expansion, and isobaric heat capacity. We discuss the differences between a full treatment of anisotropy and a simplified approach with a constant c/a ratio. The results are systematically compared with the available theoretical and experimental data and an overall satisfactory agreement is obtained.

  7. Lattice dynamics and thermophysical properties of h.c.p. Os and Ru from the quasi-harmonic approximation.

    PubMed

    Palumbo, Mauro; Dal Corso, Andrea

    2017-10-04

    We report first-principles phonon frequencies and anharmonic thermodynamic properties of h.c.p. Os and Ru calculated within the quasi-harmonic approximation, including Grüneisen parameters, temperature-dependent lattice parameters, thermal expansion, and isobaric heat capacity. We discuss the differences between a full treatment of anisotropy and a simplified approach with a constant [Formula: see text] ratio. The results are systematically compared with the available theoretical and experimental data and an overall satisfactory agreement is obtained.

  8. Optimal approximation of harmonic growth clusters by orthogonal polynomials

    SciTech Connect

    Teodorescu, Razvan

    2008-01-01

    Interface dynamics in two-dimensional systems with a maximal number of conservation laws gives an accurate theoreticaI model for many physical processes, from the hydrodynamics of immiscible, viscous flows (zero surface-tension limit of Hele-Shaw flows), to the granular dynamics of hard spheres, and even diffusion-limited aggregation. Although a complete solution for the continuum case exists, efficient approximations of the boundary evolution are very useful due to their practical applications. In this article, the approximation scheme based on orthogonal polynomials with a deformed Gaussian kernel is discussed, as well as relations to potential theory.

  9. Diverse Eruptions at Approximately 2,200 Years B.P. on the Great Rift, Idaho: Inferences for Magma Dynamics Along Volcanic Rift Zones

    NASA Technical Reports Server (NTRS)

    Hughes, S. S.; Nawotniak, S. E. Kobs; Borg, C.; Mallonee, H. C.; Purcell, S.; Neish, C.; Garry, W. B.; Haberle, C. W.; Lim, D. S. S.; Heldmann, J. L.

    2016-01-01

    Compositionally and morphologically diverse lava flows erupted on the Great Rift of Idaho approximately 2.2 ka (kilo-annum, 1000 years ago) during a volcanic "flare-up" of activity following an approximately 2 ky (kiloyear, 1000 years) hiatus in eruptions. Volcanism at Craters of the Moon (COTM), Wapi and Kings Bowl lava fields around this time included primitive and evolved compositions, separated over 75 kilometers along the approximately 85 kilometers-long rift, with striking variability in lava flow emplacement mechanisms and surface morphologies. Although the temporal associations may be coincidental, the system provides a planetary analog to better understand magma dynamics along rift systems, including that associated with lunar floor-fractured craters. This study aims to help bridge the knowledge gap between ancient rift volcanism evident on the Moon and other terrestrial planets, and active rift volcanism, e.g., at Hawai'i and Iceland.

  10. A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics

    SciTech Connect

    M. D. Landon; R. W. Johnson

    1999-07-01

    The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve complex curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.

  11. A B-Spline-Based Colocation Method to Approximate the Solutions to the Equations of Fluid Dynamics

    SciTech Connect

    Johnson, Richard Wayne; Landon, Mark Dee

    1999-07-01

    The potential of a B-spline collocation method for numerically solving the equations of fluid dynamics is discussed. It is known that B-splines can resolve curves with drastically fewer data than can their standard shape function counterparts. This feature promises to allow much faster numerical simulations of fluid flow than standard finite volume/finite element methods without sacrificing accuracy. An example channel flow problem is solved using the method.

  12. Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications. [computational fluid dynamics

    NASA Technical Reports Server (NTRS)

    Taylor, Arthur C., III; Hou, Gene W.

    1992-01-01

    Fundamental equations of aerodynamic sensitivity analysis and approximate analysis for the two dimensional thin layer Navier-Stokes equations are reviewed, and special boundary condition considerations necessary to apply these equations to isolated lifting airfoils on 'C' and 'O' meshes are discussed in detail. An efficient strategy which is based on the finite element method and an elastic membrane representation of the computational domain is successfully tested, which circumvents the costly 'brute force' method of obtaining grid sensitivity derivatives, and is also useful in mesh regeneration. The issue of turbulence modeling is addressed in a preliminary study. Aerodynamic shape sensitivity derivatives are efficiently calculated, and their accuracy is validated on two viscous test problems, including: (1) internal flow through a double throat nozzle, and (2) external flow over a NACA 4-digit airfoil. An automated aerodynamic design optimization strategy is outlined which includes the use of a design optimization program, an aerodynamic flow analysis code, an aerodynamic sensitivity and approximate analysis code, and a mesh regeneration and grid sensitivity analysis code. Application of the optimization methodology to the two test problems in each case resulted in a new design having a significantly improved performance in the aerodynamic response of interest.

  13. High resolution TVD schemes using flux limiters. [method of Total Variation Diminishing for rarefied gas dynamics calculations

    NASA Technical Reports Server (NTRS)

    Sweby, P. K.

    1985-01-01

    Roe (1981, 1985) has utilized flux limiters to obtain second order monotonicity preserving schemes. In the present paper, the foundation for flux limiters in the formulation of first order three-point schemes are discussed, and a systematic outline is provided of the method of using flux limiters to obtain second order accurate TVD schemes. Attention is given to Phi limiters, the Van Leer limiter, the Chakravarthy-Osher limiter, the linear advection equation and square wave data, the inviscid Burger's equation, and the extension of flux limiters to irregular grids, systems of equations, and implicit calculations.

  14. Dynamic knee stability estimated by finite helical axis methods during functional performance approximately twenty years after anterior cruciate ligament injury.

    PubMed

    Grip, Helena; Tengman, Eva; Häger, Charlotte K

    2015-07-16

    Finite helical axis (FHA) measures of the knee joint during weight-bearing tasks may capture dynamic knee stability following Anterior Cruciate Ligament (ACL) injury. The aim was to investigate dynamic knee stability during two-leg squat (TLS) and one-leg side hop (SH) in a long-term follow-up of ACL injury, and to examine correlations with knee laxity (KT-1000), osteoarthritis (OA, Kellgren-Lawrence) and knee function (Lysholm score). Participants were injured 17-28 years ago and then treated with surgery (n=33, ACLR) or physiotherapy only (n=37, ACLPT) and healthy-knee controls (n=33) were tested. Movements were registered with an optical motion capture system. We computed three FHA inclination angles, its' Anterior-Posterior (A-P) position, and an index quantifying directional changes (DI), during stepwise knee flexion intervals of ∼15°. Injured knees were less stable compared to healthy controls' and to contralateral non-injured knees, regardless of treatment: the A-P intersection was more anterior (indicating a more anterior positioning of tibia relative to femur) positively correlating with high laxity/low knee function, and during SH, the FHA was more inclined relative to the flexion-extension axis, possibly due to reduced rotational stability. During the TLS, A-P intersection was more anterior in the non-injured knee than the injured, and DI was higher, probably related to higher load on the non-injured knee. ACLR had less anterior A-P intersection than ACLPT, suggesting that surgery enhanced stability, although rotational stability may remain reduced. More anterior A-P intersection and greater inclination between the FHA and the knee flexion-extension axis best revealed reduced dynamic stability ∼23 years post-injury.

  15. Scale-free memory model for multiagent reinforcement learning. Mean field approximation and rock-paper-scissors dynamics

    NASA Astrophysics Data System (ADS)

    Lubashevsky, I.; Kanemoto, S.

    2010-07-01

    A continuous time model for multiagent systems governed by reinforcement learning with scale-free memory is developed. The agents are assumed to act independently of one another in optimizing their choice of possible actions via trial-and-error search. To gain awareness about the action value the agents accumulate in their memory the rewards obtained from taking a specific action at each moment of time. The contribution of the rewards in the past to the agent current perception of action value is described by an integral operator with a power-law kernel. Finally a fractional differential equation governing the system dynamics is obtained. The agents are considered to interact with one another implicitly via the reward of one agent depending on the choice of the other agents. The pairwise interaction model is adopted to describe this effect. As a specific example of systems with non-transitive interactions, a two agent and three agent systems of the rock-paper-scissors type are analyzed in detail, including the stability analysis and numerical simulation. Scale-free memory is demonstrated to cause complex dynamics of the systems at hand. In particular, it is shown that there can be simultaneously two modes of the system instability undergoing subcritical and supercritical bifurcation, with the latter one exhibiting anomalous oscillations with the amplitude and period growing with time. Besides, the instability onset via this supercritical mode may be regarded as “altruism self-organization”. For the three agent system the instability dynamics is found to be rather irregular and can be composed of alternate fragments of oscillations different in their properties.

  16. Effective Estimation of Dynamic Metabolic Fluxes Using 13C Labeling and Piecewise Affine Approximation: From Theory to Practical Applicability

    PubMed Central

    Schumacher, Robin; Wahl, S. Aljoscha

    2015-01-01

    The design of microbial production processes relies on rational choices for metabolic engineering of the production host and the process conditions. These require a systematic and quantitative understanding of cellular regulation. Therefore, a novel method for dynamic flux identification using quantitative metabolomics and 13C labeling to identify piecewise-affine (PWA) flux functions has been described recently. Obtaining flux estimates nevertheless still required frequent manual reinitalization to obtain a good reproduction of the experimental data and, moreover, did not optimize on all observables simultaneously (metabolites and isotopomer concentrations). In our contribution we focus on measures to achieve faster and robust dynamic flux estimation which leads to a high dimensional parameter estimation problem. Specifically, we address the following challenges within the PWA problem formulation: (1) Fast selection of sufficient domains for the PWA flux functions, (2) Control of over-fitting in the concentration space using shape-prescriptive modeling and (3) robust and efficient implementation of the parameter estimation using the hybrid implicit filtering algorithm. With the improvements we significantly speed up the convergence by efficiently exploiting that the optimization problem is partly linear. This allows application to larger-scale metabolic networks and demonstrates that the proposed approach is not purely theoretical, but also applicable in practice. PMID:26690237

  17. Dynamic design, numerical solution and effective verification of acceleration-level obstacle-avoidance scheme for robot manipulators

    NASA Astrophysics Data System (ADS)

    Xiao, Lin; Zhang, Yunong

    2016-03-01

    For avoiding obstacles and joint physical constraints of robot manipulators, this paper proposes and investigates a novel obstacle avoidance scheme (termed the acceleration-level obstacle-avoidance scheme). The scheme is based on a new obstacle-avoidance criterion that is designed by using the gradient neural network approach for the first time. In addition, joint physical constraints such as joint-angle limits, joint-velocity limits and joint-acceleration limits are incorporated into such a scheme, which is further reformulated as a quadratic programming (QP). Two important 'bridge' theorems are established so that such a QP can be converted equivalently to a linear variational inequality and then equivalently to a piecewise-linear projection equation (PLPE). A numerical algorithm based on a PLPE is thus developed and applied for an online solution of the resultant QP. Four path-tracking tasks based on the PA10 robot in the presence of point and window-shaped obstacles demonstrate and verify the effectiveness and accuracy of the acceleration-level obstacle-avoidance scheme. Besides, the comparisons between the non-obstacle-avoidance and obstacle-avoidance results further validate the superiority of the proposed scheme.

  18. Wavelet Approximation in Data Assimilation

    NASA Technical Reports Server (NTRS)

    Tangborn, Andrew; Atlas, Robert (Technical Monitor)

    2002-01-01

    Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.

  19. Approximation algorithms

    PubMed Central

    Schulz, Andreas S.; Shmoys, David B.; Williamson, David P.

    1997-01-01

    Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science. PMID:9370525

  20. Approximate optimal guidance for the advanced launch system

    NASA Technical Reports Server (NTRS)

    Feeley, T. S.; Speyer, J. L.

    1993-01-01

    A real-time guidance scheme for the problem of maximizing the payload into orbit subject to the equations of motion for a rocket over a spherical, non-rotating earth is presented. An approximate optimal launch guidance law is developed based upon an asymptotic expansion of the Hamilton - Jacobi - Bellman or dynamic programming equation. The expansion is performed in terms of a small parameter, which is used to separate the dynamics of the problem into primary and perturbation dynamics. For the zeroth-order problem the small parameter is set to zero and a closed-form solution to the zeroth-order expansion term of Hamilton - Jacobi - Bellman equation is obtained. Higher-order terms of the expansion include the effects of the neglected perturbation dynamics. These higher-order terms are determined from the solution of first-order linear partial differential equations requiring only the evaluation of quadratures. This technique is preferred as a real-time, on-line guidance scheme to alternative numerical iterative optimization schemes because of the unreliable convergence properties of these iterative guidance schemes and because the quadratures needed for the approximate optimal guidance law can be performed rapidly and by parallel processing. Even if the approximate solution is not nearly optimal, when using this technique the zeroth-order solution always provides a path which satisfies the terminal constraints. Results for two-degree-of-freedom simulations are presented for the simplified problem of flight in the equatorial plane and compared to the guidance scheme generated by the shooting method which is an iterative second-order technique.

  1. A new multi-frequency approach based on Padé approximants for the treatment of transient dynamics problems with the variational theory of complex rays

    NASA Astrophysics Data System (ADS)

    Rouzaud, C.; Gatuingt, F.; Hervé, G.; Dorival, O.

    2017-03-01

    Frequency-based methods were set up in order to circumvent the limits of classical finite element methods in fast dynamic simulations due to discretizations. In this approach the dynamic loading was shifted in the frequency domain by FFT, then treated by the Variational Theory of Complex Rays, and then the time response was reconstructed through an IFFT. This strategy proved to be very efficient due to the CPU VTCR very low cost. However in the case of a large loading spectrum this frequency-by-frequency approach could seriously degrade the computational performances of the strategy. This paper addresses this point by proposing the use of Padé approximants in order to limit the number of frequencies at which the response should be calculated. Padé approximation is applied to the overall VTCR system based on its frequency dependency. Finally, as simulations on a simple academic case and on a civil engineering structure show, this method is found to be very efficient for interpolating the frequency response functions of a complex structure. This is a key point to preserve the efficiency of the complete VTCR strategy for transient dynamic problems.

  2. Asymmetric pendulum effect and transparency change of P T -symmetric photonic crystals under dynamical Bragg diffraction beyond the paraxial approximation

    NASA Astrophysics Data System (ADS)

    Bushuev, V. A.; Dergacheva, L. V.; Mantsyzov, B. I.

    2017-03-01

    Light propagating in P T -symmetric photonic crystals (PhCs) under Bragg diffraction in the Laue geometry has been studied theoretically using the spectral method. The P T -symmetric solutions describing propagating modes have been found in the PhCs with gain and loss beyond paraxial approximation. We described the pendulum effect—the periodical spatial localization of the total field intensity in a PhC—near the P T -symmetry-breaking point. It is shown that, due to P T -symmetric properties of the medium, an asymmetric change in the amplitudes of the diffracted waves in PhCs is observed when the sign of the Bragg incidence angle is changed from positive to negative. Thus, the intensity of a spatially periodic field in a medium radically alters under the pendulum effect. Moreover, when the sign of the Bragg incidence angle changes, a PhC of a certain thickness is turned from an absorbing structure into an amplifying one, also a PhC of any thickness evolves from completely transparent into amplifying in the vicinity of the P T -symmetry-breaking point. Under a small change of the imaginary part of permittivity, the light switching from a transmitted wave into a gain or loss diffracted wave is possible in a diffraction-thick PhC.

  3. Upwind and symmetric shock-capturing schemes

    NASA Technical Reports Server (NTRS)

    Yee, H. C.

    1987-01-01

    The development of numerical methods for hyperbolic conservation laws has been a rapidly growing area for the last ten years. Many of the fundamental concepts and state-of-the-art developments can only be found in meeting proceedings or internal reports. This review paper attempts to give an overview and a unified formulation of a class of shock-capturing methods. Special emphasis is on the construction of the basic nonlinear scalar second-order schemes and the methods of extending these nonlinear scalar schemes to nonlinear systems via the extact Riemann solver, approximate Riemann solvers, and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows is discussed. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas dynamics problems.

  4. Improving the Long-Lead Predictability of El Niño Using a Novel Forecasting Scheme Based on a Dynamic Components Model

    NASA Astrophysics Data System (ADS)

    Petrova, Desislava; Koopman, Siem Jan; Ballester, Joan; Garcia, Markel; Rodo, Xavier

    2016-04-01

    El Niño Southern Oscillation (ENSO) is a dominant feature of climate variability on inter-annual time scales and predictions for it are issued on a regular basis by a wide array of prediction schemes and climate centres around the world. We have explored a novel method for ENSO forecasting. In the state-of-the-art the advantageous statistical technique of Structural (Unobserved Components) Time Series has not been applied. Therefore, we have developed such a model with regression parameters obtained by a State Space approach. Its distinguishing feature is that observations consist of several unobserved components - trend, seasonality, cycles, disturbance, and explanatory regression covariates. These components are modeled separately and ultimately combined in a single forecasting scheme. We introduce a new domain of predictor regression variables accounting for the state of the subsurface ocean temperature in the western and central equatorial Pacific as it has been shown by previous studies that subsurface processes and heat accumulation there are fundamental for the genesis of El Niño. An important feature of the scheme is that different regression predictors are used at different lead months, thus capturing the dynamical evolution of the system and rendering more efficient forecasts. The new model has been tested with the prediction of all warm events that occurred in the period 1980-2015. Retrospective forecasts of these events were successfully made for long lead times of at least two years. Hence, we demonstrate that the theoretical limit of ENSO prediction should be sought much longer than the commonly accepted "Spring Barrier". Our statistical approach is found to exhibit similar skill to the best dynamical forecasting models for ENSO. Thus, the novel way in which the proposed modeling scheme has been structured could also be used for improving other statistical and dynamical prediction systems.

  5. Stress Test for Quantum Dynamics Approximations: Deep Tunneling in the Muonium Exchange Reaction D + HMu → DMu + H.

    PubMed

    Pérez de Tudela, Ricardo; Suleimanov, Yury V; Richardson, Jeremy O; Sáez Rábanos, Vicente; Green, William H; Aoiz, F J

    2014-12-04

    Quantum effects play a crucial role in chemical reactions involving light atoms at low temperatures, especially when a light particle is exchanged between two heavier partners. Different theoretical methodologies have been developed in the last decades attempting to describe zero-point energy and tunneling effects without abandoning a classical or semiclassical framework. In this work, we have chosen the D + HMu → DMu + H reaction as a stress test system for three well-established methods: two representative versions of transition state theory (TST), canonical variational theory and semiclassical instanton, and ring polymer molecular dynamics (RPMD). These calculations will be compared with accurate quantum mechanical results. Despite its apparent simplicity, the exchange of the extremely light muonium atom (0.114 u) becomes a most challenging reaction for conventional methods. The main result of this work is that RPMD provides an overall better performance than TST-based methods for such a demanding reaction. RPMD might well turn out to be a useful tool beyond TST applicability.

  6. Wave spectra of a strongly coupled magnetized one-component plasma: quasilocalized charge approximation versus harmonic lattice theory and molecular dynamics.

    PubMed

    Ott, T; Baiko, D A; Kählert, H; Bonitz, M

    2013-04-01

    Two different approaches to the calculation of the wave spectra of magnetized strongly coupled liquid one-component plasmas are analzyed: the semianalytical quasilocalized charge approximation (QLCA) and the angle-averaged harmonic lattice (AAHL) theory. Both theories are benchmarked against the numerical evidence obtained from molecular dynamics simulations. It is found that not too far from the melting transition (Γ≳100), the AAHL theory is superior to the QLCA, while further away from the transition, the QLCA performs comparably to or better than the AAHL theory.

  7. Piecewise linear approximations to model the dynamics of adaptation to osmotic stress by food-borne pathogens.

    PubMed

    Métris, Aline; George, Susie M; Ropers, Delphine

    2017-01-02

    Addition of salt to food is one of the most ancient and most common methods of food preservation. However, little is known of how bacterial cells adapt to such conditions. We propose to use piecewise linear approximations to model the regulatory adaptation of Escherichiacoli to osmotic stress. We apply the method to eight selected genes representing the functions known to be at play during osmotic adaptation. The network is centred on the general stress response factor, sigma S, and also includes a module representing the catabolic repressor CRP-cAMP. Glutamate, potassium and supercoiling are combined to represent the intracellular regulatory signal during osmotic stress induced by salt. The output is a module where growth is represented by the concentration of stable RNAs and the transcription of the osmotic gene osmY. The time course of gene expression of transport of osmoprotectant represented by the symporter proP and of the osmY is successfully reproduced by the network. The behaviour of the rpoS mutant predicted by the model is in agreement with experimental data. We discuss the application of the model to food-borne pathogens such as Salmonella; although the genes considered have orthologs, it seems that supercoiling is not regulated in the same way. The model is limited to a few selected genes, but the regulatory interactions are numerous and span different time scales. In addition, they seem to be condition specific: the links that are important during the transition from exponential to stationary phase are not all needed during osmotic stress. This model is one of the first steps towards modelling adaptation to stress in food safety and has scope to be extended to other genes and pathways, other stresses relevant to the food industry, and food-borne pathogens. The method offers a good compromise between systems of ordinary differential equations, which would be unmanageable because of the size of the system and for which insufficient data are available

  8. Black hole triple dynamics: a breakdown of the orbit average approximation and implications for gravitational wave detections

    SciTech Connect

    Antonini, Fabio; Murray, Norman; Mikkola, Seppo

    2014-01-20

    Coalescing black hole (BH) binaries forming in the dense core of globular clusters (GCs) are expected to be one of the brightest sources of gravitational wave (GW) radiation for the next generation of ground-based laser interferometers. Favorable conditions for a merger are initiated by the Kozai resonance in which the gravitational interaction with a third distant object, typically another BH, induces quasi-periodic variations of the inner BH binary eccentricity. In this article we perform high precision three-body simulations of the long-term evolution of hierarchical BH triples and investigate the conditions that lead to the merging of the BH binary and the way it might become an observable source of GW radiation. We find that the secular orbit average treatment, which was adopted in previous works, does not reliably describe the dynamics of these systems if the binary is orbited by the outer BH on a highly inclined orbit at a moderate distance. We show that 50% of coalescing BH binaries driven by the Kozai mechanism in GCs will have eccentricities larger than 0.1, with 10% of them being extremely eccentric, (1 – e) ≲ 10{sup –4}, when they first chirp in the frequency band of ground-based laser interferometers. This implies that a large fraction of such GW sources could be missed if conventional quasi-circular templates are used for analysis of GW detector data. The efficient detection of all coalescing BH binaries in GCs will therefore require template banks of eccentric inspiral waveforms for matched-filtering and dedicated search strategies.

  9. Dynamics of neuroinflammation in the macrosphere model of arterio-arterial embolic focal ischemia: an approximation to human stroke patterns

    PubMed Central

    2010-01-01

    Background Neuroinflammation evolves as a multi-facetted response to focal cerebral ischemia. It involves activation of resident glia cell populations, recruitment of blood-derived leucocytes as well as humoral responses. Among these processes, phagocyte accumulation has been suggested to be a surrogate marker of neuroinflammation. We previously assessed phagocyte accumulation in human stroke by MRI. We hypothesize that phagocyte accumulation in the macrosphere model may resemble the temporal and spatial patterns observed in human stroke. Methods In a rat model of permanent focal ischemia by embolisation of TiO2-spheres we assessed key features of post-ischemic neuroinflammation by the means of histology, immunocytochemistry of glial activation and influx of hematogeneous cells, and quantitative PCR of TNF-α, IL-1, IL-18, and iNOS mRNA. Results In the boundary zone of the infarct, a transition of ramified microglia into ameboid phagocytic microglia was accompanied by an up-regulation of MHC class II on the cells after 3 days. By day 7, a hypercellular infiltrate consisting of activated microglia and phagocytic cells formed a thick rim around the ischemic infarct core. Interestingly, in the ischemic core microglia could only be observed at day 7. TNF-α was induced rapidly within hours, IL-1β and iNOS peaked within days, and IL-18 later at around 1 week after ischemia. Conclusions The macrosphere model closely resembles the characteristical dynamics of postischemic inflammation previously observed in human stroke. We therefore suggest that the macrosphere model is highly appropriate for studying the pathophysiology of stroke in a translational approach from rodent to human. PMID:21171972

  10. A comparative study of the centroid and ring-polymer molecular dynamics methods for approximating quantum time correlation functions from path integrals

    NASA Astrophysics Data System (ADS)

    Pérez, Alejandro; Tuckerman, Mark E.; Müser, Martin H.

    2009-05-01

    The problems of ergodicity and internal consistency in the centroid and ring-polymer molecular dynamics methods are addressed in the context of a comparative study of the two methods. Enhanced sampling in ring-polymer molecular dynamics (RPMD) is achieved by first performing an equilibrium path integral calculation and then launching RPMD trajectories from selected, stochastically independent equilibrium configurations. It is shown that this approach converges more rapidly than periodic resampling of velocities from a single long RPMD run. Dynamical quantities obtained from RPMD and centroid molecular dynamics (CMD) are compared to exact results for a variety of model systems. Fully converged results for correlations functions are presented for several one dimensional systems and para-hydrogen near its triple point using an improved sampling technique. Our results indicate that CMD shows very similar performance to RPMD. The quality of each method is further assessed via a new χ2 descriptor constructed by transforming approximate real-time correlation functions from CMD and RPMD trajectories to imaginary time and comparing these to numerically exact imaginary time correlation functions. For para-hydrogen near its triple point, it is found that adiabatic CMD and RPMD both have similar χ2 error.

  11. Lagrangian advection scheme with shape matrix (LASM) v0.2: interparcel mixing, physics-dynamics coupling and 3-D extension

    NASA Astrophysics Data System (ADS)

    Dong, L.; Wang, B.; Liu, L.; Huang, Y.

    2015-08-01

    The interparcel mixing algorithm in the Lagrangian advection scheme with shape matrix (LASM) is updated to make the scheme more robust. The linear degeneration criterion is replaced by the maximum deviation of the skeleton points so that the new algorithm is more effective in controlling the shape of parcels, which is vital for long time simulation. LASM is inherently shape-preserving without any complicated filter or limiter, and it is linear. This fact contributes to the ability to preserve the sum of multiple tracers exactly on the parcels in LASM. A newly proposed terminator "toy"-chemistry test is used to test LASM, which shows that LASM can preserve the weighted sum of two reactive species precisely. The physics-dynamics coupling (i.e., tendency evaluation type) is also discussed. A flow generated by a WRF large-eddy simulation is also used to test the 3-D extension of LASM.

  12. Tracing few-femtosecond photodissociation dynamics on molecular oxygen with a single-color pump-probe scheme in the VUV

    NASA Astrophysics Data System (ADS)

    Schepp, Oliver; Baumann, Arne; Rompotis, Dimitrios; Gebert, Thomas; Azima, Armin; Wieland, Marek; Drescher, Markus

    2016-09-01

    Molecular wave-packet dynamics in oxygen are studied in the time domain, using a single-color VUV-pump-VUV-probe scheme. 17-fs VUV pulses, centered at 161 nm are generated via high-order harmonic generation driven by an intense 800-nm pulse leading to VUV pulse energies that reach 1.1 μ J per pulse. An all-reflective interferometric pump-probe scheme is used for studying the delay dependence of the molecular oxygen ion signal with simultaneous nonresonant photoionization of krypton as a precise timing-reference. Access to the excited dissociative state lifetime is provided by the resulting delay-dependent O2 + signal, ultimately limited by the molecular ionization window. The ability to use a two-photon VUV probe provides the delay-dependent detection of O+ as an additional observable, extending the dissociation observation window.

  13. Sensitivity of a Cloud-Resolving Model to Bulk and Explicit Bin Microphysical Schemes. Part 2; Cloud Microphysics and Storm Dynamics Interactions

    NASA Technical Reports Server (NTRS)

    Li, Xiaowen; Tao, Wei-Kuo; Khain, Alexander P.; Simpson, Joanne; Johnson, Daniel E.

    2009-01-01

    Part I of this paper compares two simulations, one using a bulk and the other a detailed bin microphysical scheme, of a long-lasting, continental mesoscale convective system with leading convection and trailing stratiform region. Diagnostic studies and sensitivity tests are carried out in Part II to explain the simulated contrasts in the spatial and temporal variations by the two microphysical schemes and to understand the interactions between cloud microphysics and storm dynamics. It is found that the fixed raindrop size distribution in the bulk scheme artificially enhances rain evaporation rate and produces a stronger near surface cool pool compared with the bin simulation. In the bulk simulation, cool pool circulation dominates the near-surface environmental wind shear in contrast to the near-balance between cool pool and wind shear in the bin simulation. This is the main reason for the contrasting quasi-steady states simulated in Part I. Sensitivity tests also show that large amounts of fast-falling hail produced in the original bulk scheme not only result in a narrow trailing stratiform region but also act to further exacerbate the strong cool pool simulated in the bulk parameterization. An empirical formula for a correction factor, r(q(sub r)) = 0.11q(sub r)(exp -1.27) + 0.98, is developed to correct the overestimation of rain evaporation in the bulk model, where r is the ratio of the rain evaporation rate between the bulk and bin simulations and q(sub r)(g per kilogram) is the rain mixing ratio. This formula offers a practical fix for the simple bulk scheme in rain evaporation parameterization.

  14. On the incorporation of the geometric phase in general single potential energy surface dynamics: A removable approximation to ab initio data

    NASA Astrophysics Data System (ADS)

    Malbon, Christopher L.; Zhu, Xiaolei; Guo, Hua; Yarkony, David R.

    2016-12-01

    For two electronic states coupled by conical intersections, the line integral of the derivative coupling can be used to construct a complex-valued multiplicative phase factor that makes the real-valued adiabatic electronic wave function single-valued, provided that the curl of the derivative coupling is zero. Unfortunately for ab initio determined wave functions, the curl is never rigorously zero. However, when the wave functions are determined from a coupled two diabatic state Hamiltonian Hd (fit to ab initio data), the resulting derivative couplings are by construction curl free, except at points of conical intersection. In this work we focus on a recently introduced diabatization scheme that produces the Hd by fitting ab initio determined energies, energy gradients, and derivative couplings to the corresponding Hd determined quantities in a least squares sense, producing a removable approximation to the ab initio determined derivative coupling. This approach and related numerical issues associated with the nonremovable ab initio derivative couplings are illustrated using a full 33-dimensional representation of phenol photodissociation. The use of this approach to provide a general framework for treating the molecular Aharonov Bohm effect is demonstrated.

  15. On the incorporation of the geometric phase in general single potential energy surface dynamics: A removable approximation to ab initio data.

    PubMed

    Malbon, Christopher L; Zhu, Xiaolei; Guo, Hua; Yarkony, David R

    2016-12-21

    For two electronic states coupled by conical intersections, the line integral of the derivative coupling can be used to construct a complex-valued multiplicative phase factor that makes the real-valued adiabatic electronic wave function single-valued, provided that the curl of the derivative coupling is zero. Unfortunately for ab initio determined wave functions, the curl is never rigorously zero. However, when the wave functions are determined from a coupled two diabatic state Hamiltonian H(d) (fit to ab initio data), the resulting derivative couplings are by construction curl free, except at points of conical intersection. In this work we focus on a recently introduced diabatization scheme that produces the H(d) by fitting ab initio determined energies, energy gradients, and derivative couplings to the corresponding H(d) determined quantities in a least squares sense, producing a removable approximation to the ab initio determined derivative coupling. This approach and related numerical issues associated with the nonremovable ab initio derivative couplings are illustrated using a full 33-dimensional representation of phenol photodissociation. The use of this approach to provide a general framework for treating the molecular Aharonov Bohm effect is demonstrated.

  16. Investigating flow patterns and related dynamics in multi-instability turbulent plasmas using a three-point cross-phase time delay estimation velocimetry scheme

    SciTech Connect

    Brandt, C.; Thakur, S. C.; Tynan, G. R.

    2016-04-15

    Complexities of flow patterns in the azimuthal cross-section of a cylindrical magnetized helicon plasma and the corresponding plasma dynamics are investigated by means of a novel scheme for time delay estimation velocimetry. The advantage of this introduced method is the capability of calculating the time-averaged 2D velocity fields of propagating wave-like structures and patterns in complex spatiotemporal data. It is able to distinguish and visualize the details of simultaneously present superimposed entangled dynamics and it can be applied to fluid-like systems exhibiting frequently repeating patterns (e.g., waves in plasmas, waves in fluids, dynamics in planetary atmospheres, etc.). The velocity calculations are based on time delay estimation obtained from cross-phase analysis of time series. Each velocity vector is unambiguously calculated from three time series measured at three different non-collinear spatial points. This method, when applied to fast imaging, has been crucial to understand the rich plasma dynamics in the azimuthal cross-section of a cylindrical linear magnetized helicon plasma. The capabilities and the limitations of this velocimetry method are discussed and demonstrated for two completely different plasma regimes, i.e., for quasi-coherent wave dynamics and for complex broadband wave dynamics involving simultaneously present multiple instabilities.

  17. Dynamic mean field theory for lattice gas models of fluids confined in porous materials: higher order theory based on the Bethe-Peierls and path probability method approximations.

    PubMed

    Edison, John R; Monson, Peter A

    2014-07-14

    Recently we have developed a dynamic mean field theory (DMFT) for lattice gas models of fluids in porous materials [P. A. Monson, J. Chem. Phys. 128(8), 084701 (2008)]. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable states for fluids in pores and is especially useful for studying system exhibiting adsorption/desorption hysteresis. In this paper we discuss the extension of the theory to higher order by means of the path probability method (PPM) of Kikuchi and co-workers. We show that this leads to a treatment of the dynamics that is consistent with thermodynamics coming from the Bethe-Peierls or Quasi-Chemical approximation for the equilibrium or metastable equilibrium states of the lattice model. We compare the results from the PPM with those from DMFT and from dynamic Monte Carlo simulations. We find that the predictions from PPM are qualitatively similar to those from DMFT but give somewhat improved quantitative accuracy, in part due to the superior treatment of the underlying thermodynamics. This comes at the cost of greater computational expense associated with the larger number of equations that must be solved.

  18. Dynamic mean field theory for lattice gas models of fluids confined in porous materials: Higher order theory based on the Bethe-Peierls and path probability method approximations

    SciTech Connect

    Edison, John R.; Monson, Peter A.

    2014-07-14

    Recently we have developed a dynamic mean field theory (DMFT) for lattice gas models of fluids in porous materials [P. A. Monson, J. Chem. Phys. 128(8), 084701 (2008)]. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable states for fluids in pores and is especially useful for studying system exhibiting adsorption/desorption hysteresis. In this paper we discuss the extension of the theory to higher order by means of the path probability method (PPM) of Kikuchi and co-workers. We show that this leads to a treatment of the dynamics that is consistent with thermodynamics coming from the Bethe-Peierls or Quasi-Chemical approximation for the equilibrium or metastable equilibrium states of the lattice model. We compare the results from the PPM with those from DMFT and from dynamic Monte Carlo simulations. We find that the predictions from PPM are qualitatively similar to those from DMFT but give somewhat improved quantitative accuracy, in part due to the superior treatment of the underlying thermodynamics. This comes at the cost of greater computational expense associated with the larger number of equations that must be solved.

  19. Correlation of Nonexponentiality with Dynamic Heterogeneity from Four-Point Dynamic Susceptibility X4(t) and Its Approximation XT(t)

    DTIC Science & Technology

    2010-01-01

    D. Fragiadakis,1 D. Coslovich, 2 S. Capaccioli,3 and K. L. Ngai1 1Naval Research Laboratory, Washington, DC 20375-5342, USA 2Institut fur...Theoretische Physik, Technische Universitat Wien, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria 3Dipartimento di Fisica , Università di Pisa, Largo Pontecorvo 3...correlating molecules22–24 Nc = max 4t 4 max. 2 Efforts to study dynamic heterogeneities have been stymied by the difficulty of determining 4t

  20. Improving the long-lead predictability of El Niño using a novel forecasting scheme based on a dynamic components model

    NASA Astrophysics Data System (ADS)

    Petrova, Desislava; Koopman, Siem Jan; Ballester, Joan; Rodó, Xavier

    2017-02-01

    El Niño (EN) is a dominant feature of climate variability on inter-annual time scales driving changes in the climate throughout the globe, and having wide-spread natural and socio-economic consequences. In this sense, its forecast is an important task, and predictions are issued on a regular basis by a wide array of prediction schemes and climate centres around the world. This study explores a novel method for EN forecasting. In the state-of-the-art the advantageous statistical technique of unobserved components time series modeling, also known as structural time series modeling, has not been applied. Therefore, we have developed such a model where the statistical analysis, including parameter estimation and forecasting, is based on state space methods, and includes the celebrated Kalman filter. The distinguishing feature of this dynamic model is the decomposition of a time series into a range of stochastically time-varying components such as level (or trend), seasonal, cycles of different frequencies, irregular, and regression effects incorporated as explanatory covariates. These components are modeled separately and ultimately combined in a single forecasting scheme. Customary statistical models for EN prediction essentially use SST and wind stress in the equatorial Pacific. In addition to these, we introduce a new domain of regression variables accounting for the state of the subsurface ocean temperature in the western and central equatorial Pacific, motivated by our analysis, as well as by recent and classical research, showing that subsurface processes and heat accumulation there are fundamental for the genesis of EN. An important feature of the scheme is that different regression predictors are used at different lead months, thus capturing the dynamical evolution of the system and rendering more efficient forecasts. The new model has been tested with the prediction of all warm events that occurred in the period 1996-2015. Retrospective forecasts of these

  1. Improving the long-lead predictability of El Niño using a novel forecasting scheme based on a dynamic components model

    NASA Astrophysics Data System (ADS)

    Petrova, Desislava; Koopman, Siem Jan; Ballester, Joan; Rodó, Xavier

    2016-05-01

    El Niño (EN) is a dominant feature of climate variability on inter-annual time scales driving changes in the climate throughout the globe, and having wide-spread natural and socio-economic consequences. In this sense, its forecast is an important task, and predictions are issued on a regular basis by a wide array of prediction schemes and climate centres around the world. This study explores a novel method for EN forecasting. In the state-of-the-art the advantageous statistical technique of unobserved components time series modeling, also known as structural time series modeling, has not been applied. Therefore, we have developed such a model where the statistical analysis, including parameter estimation and forecasting, is based on state space methods, and includes the celebrated Kalman filter. The distinguishing feature of this dynamic model is the decomposition of a time series into a range of stochastically time-varying components such as level (or trend), seasonal, cycles of different frequencies, irregular, and regression effects incorporated as explanatory covariates. These components are modeled separately and ultimately combined in a single forecasting scheme. Customary statistical models for EN prediction essentially use SST and wind stress in the equatorial Pacific. In addition to these, we introduce a new domain of regression variables accounting for the state of the subsurface ocean temperature in the western and central equatorial Pacific, motivated by our analysis, as well as by recent and classical research, showing that subsurface processes and heat accumulation there are fundamental for the genesis of EN. An important feature of the scheme is that different regression predictors are used at different lead months, thus capturing the dynamical evolution of the system and rendering more efficient forecasts. The new model has been tested with the prediction of all warm events that occurred in the period 1996-2015. Retrospective forecasts of these

  2. Output-Feedback Control of Unknown Linear Discrete-Time Systems With Stochastic Measurement and Process Noise via Approximate Dynamic Programming.

    PubMed

    Wang, Jun-Sheng; Yang, Guang-Hong

    2017-07-25

    This paper studies the optimal output-feedback control problem for unknown linear discrete-time systems with stochastic measurement and process noise. A dithered Bellman equation with the innovation covariance matrix is constructed via the expectation operator given in the form of a finite summation. On this basis, an output-feedback-based approximate dynamic programming method is developed, where the terms depending on the innovation covariance matrix are available with the aid of the innovation covariance matrix identified beforehand. Therefore, by iterating the Bellman equation, the resulting value function can converge to the optimal one in the presence of the aforementioned noise, and the nearly optimal control laws are delivered. To show the effectiveness and the advantages of the proposed approach, a simulation example and a velocity control experiment on a dc machine are employed.

  3. Dynamic disorder in single-molecule Michaelis-Menten kinetics: the reaction-diffusion formalism in the Wilemski-Fixman approximation.

    PubMed

    Chaudhury, Srabanti; Cherayil, Binny J

    2007-09-14

    Single-molecule equations for the Michaelis-Menten [Biochem. Z. 49, 333 (1913)] mechanism of enzyme action are analyzed within the Wilemski-Fixman [J. Chem. Phys. 58, 4009 (1973); 60, 866 (1974)] approximation after the effects of dynamic disorder--modeled by the anomalous diffusion of a particle in a harmonic well--are incorporated into the catalytic step of the reaction. The solution of the Michaelis-Menten equations is used to calculate the distribution of waiting times between successive catalytic turnovers in the enzyme beta-galactosidase. The calculated distribution is found to agree qualitatively with experimental results on this enzyme obtained at four different substrate concentrations. The calculations are also consistent with measurements of correlations in the fluctuations of the fluorescent light emitted during the course of catalysis, and with measurements of the concentration dependence of the randomness parameter.

  4. Performance Evaluation of PBL Schemes of ARW Model in Simulating Thermo-Dynamical Structure of Pre-Monsoon Convective Episodes over Kharagpur Using STORM Data Sets

    NASA Astrophysics Data System (ADS)

    Madala, Srikanth; Satyanarayana, A. N. V.; Srinivas, C. V.; Tyagi, Bhishma

    2016-05-01

    In the present study, advanced research WRF (ARW) model is employed to simulate convective thunderstorm episodes over Kharagpur (22°30'N, 87°20'E) region of Gangetic West Bengal, India. High-resolution simulations are conducted using 1 × 1 degree NCEP final analysis meteorological fields for initial and boundary conditions for events. The performance of two non-local [Yonsei University (YSU), Asymmetric Convective Model version 2 (ACM2)] and two local turbulence kinetic energy closures [Mellor-Yamada-Janjic (MYJ), Bougeault-Lacarrere (BouLac)] are evaluated in simulating planetary boundary layer (PBL) parameters and thermodynamic structure of the atmosphere. The model-simulated parameters are validated with available in situ meteorological observations obtained from micro-meteorological tower as well has high-resolution DigiCORA radiosonde ascents during STORM-2007 field experiment at the study location and Doppler Weather Radar (DWR) imageries. It has been found that the PBL structure simulated with the TKE closures MYJ and BouLac are in better agreement with observations than the non-local closures. The model simulations with these schemes also captured the reflectivity, surface pressure patterns such as wake-low, meso-high, pre-squall low and the convective updrafts and downdrafts reasonably well. Qualitative and quantitative comparisons reveal that the MYJ followed by BouLac schemes better simulated various features of the thunderstorm events over Kharagpur region. The better performance of MYJ followed by BouLac is evident in the lesser mean bias, mean absolute error, root mean square error and good correlation coefficient for various surface meteorological variables as well as thermo-dynamical structure of the atmosphere relative to other PBL schemes. The better performance of the TKE closures may be attributed to their higher mixing efficiency, larger convective energy and better simulation of humidity promoting moist convection relative to non

  5. Post-manufacturing, 17-times acceptable raw bit error rate enhancement, dynamic codeword transition ECC scheme for highly reliable solid-state drives, SSDs

    NASA Astrophysics Data System (ADS)

    Tanakamaru, Shuhei; Fukuda, Mayumi; Higuchi, Kazuhide; Esumi, Atsushi; Ito, Mitsuyoshi; Li, Kai; Takeuchi, Ken

    2011-04-01

    A dynamic codeword transition ECC scheme is proposed for highly reliable solid-state drives, SSDs. By monitoring the error number or the write/erase cycles, the ECC codeword dynamically increases from 512 Byte (+parity) to 1 KByte, 2 KByte, 4 KByte…32 KByte. The proposed ECC with a larger codeword decreases the failure rate after ECC. As a result, the acceptable raw bit error rate, BER, before ECC is enhanced. Assuming a NAND Flash memory which requires 8-bit correction in 512 Byte codeword ECC, a 17-times higher acceptable raw BER than the conventional fixed 512 Byte codeword ECC is realized for the mobile phone application without an interleaving. For the MP3 player, digital-still camera and high-speed memory card applications with a dual channel interleaving, 15-times higher acceptable raw BER is achieved. Finally, for the SSD application with 8 channel interleaving, 13-times higher acceptable raw BER is realized. Because the ratio of the user data to the parity bits is the same in each ECC codeword, no additional memory area is required. Note that the reliability of SSD is improved after the manufacturing without cost penalty. Compared with the conventional ECC with the fixed large 32 KByte codeword, the proposed scheme achieves a lower power consumption by introducing the "best-effort" type operation. In the proposed scheme, during the most of the lifetime of SSD, a weak ECC with a shorter codeword such as 512 Byte (+parity), 1 KByte and 2 KByte is used and 98% lower power consumption is realized. At the life-end of SSD, a strong ECC with a 32 KByte codeword is used and the highly reliable operation is achieved. The random read performance is also discussed. The random read performance is estimated by the latency. The latency is below 1.5 ms for ECC codeword up to 32 KByte. This latency is below the average latency of 15,000 rpm HDD, 2 ms.

  6. Modelling carbon-coupled energy and water dynamics of a boreal aspen forest in a general circulation model land surface scheme

    NASA Astrophysics Data System (ADS)

    Wang, Shusen; Grant, Robert F.; Verseghy, Diana L.; Black, T. Andrew

    2002-08-01

    The ecosystem carbon (C) and nitrogen (N) processes and the C-coupled energy and water dynamics were developed in the Canadian Land Surface Scheme (CLASS). The ecosystem C and N simulations include plant photosynthesis and respiration, plant tissue growth, senescence, root N uptake, soil heterotrophic respiration, and N mineralization and immobilization. These simulations are driven by variables (i.e. leaf temperature and water potential, and soil temperature and moisture) obtained from the C-coupled energy and water balance simulations and feed back the model-determined vegetation parameters (i.e. leaf area index, stomatal resistance, root length and distribution), which in turn control the land surface energy and water processes. In this paper, we introduce the C-coupled energy and water balance scheme. The water flow process developed for the soil-plant-atmosphere system includes leaf and canopy stomatal resistance driven by leaf net CO2 fixation, plant water capacitance, and soil rhizosphere and plant root resistances. This water flow scheme is dynamically coupled with the canopy energy balance so that the full water balance and energy balance equations can be solved simultaneously. The model was run at a time step of 30 min and tested in a stand-alone mode driven by meteorological observations obtained at the old aspen (Populus tremuloides) site in the southern study area of the Boreal Ecosystem-Atmosphere Study (BOREAS). Results show that the model reproduced the observed diurnal and seasonal patterns of energy fluxes fairly well. Canopy conductance in the mid-growing season was simulated to reach above 0.5 mol m-2 s-1. Plant water capacitance was found to buffer the plant water flow process significantly and affect the canopy latent heat exchange under dry soil conditions. Comparisons of modelled and measured daily evapotranspiration in the two years of 1994 and 1996 gave the root-mean-square error of 0.71 mm day-1 and correlation coefficient of 0.75.

  7. Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1986-01-01

    An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

  8. Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1988-01-01

    An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

  9. Electronic Friction-Based Vibrational Lifetimes of Molecular Adsorbates: Beyond the Independent-Atom Approximation

    NASA Astrophysics Data System (ADS)

    Rittmeyer, Simon P.; Meyer, Jörg; Juaristi, J. Iñaki; Reuter, Karsten

    2015-07-01

    We assess the accuracy of vibrational damping rates of diatomic adsorbates on metal surfaces as calculated within the local-density friction approximation (LDFA). An atoms-in-molecules (AIM) type charge partitioning scheme accounts for intramolecular contributions and overcomes the systematic underestimation of the nonadiabatic losses obtained within the prevalent independent-atom approximation. The quantitative agreement obtained with theoretical and experimental benchmark data suggests the LDFA-AIM scheme as an efficient and reliable approach to account for electronic dissipation in ab initio molecular dynamics simulations of surface chemical reactions.

  10. Electronic Friction-Based Vibrational Lifetimes of Molecular Adsorbates: Beyond the Independent-Atom Approximation.

    PubMed

    Rittmeyer, Simon P; Meyer, Jörg; Juaristi, J Iñaki; Reuter, Karsten

    2015-07-24

    We assess the accuracy of vibrational damping rates of diatomic adsorbates on metal surfaces as calculated within the local-density friction approximation (LDFA). An atoms-in-molecules (AIM) type charge partitioning scheme accounts for intramolecular contributions and overcomes the systematic underestimation of the nonadiabatic losses obtained within the prevalent independent-atom approximation. The quantitative agreement obtained with theoretical and experimental benchmark data suggests the LDFA-AIM scheme as an efficient and reliable approach to account for electronic dissipation in ab initio molecular dynamics simulations of surface chemical reactions.

  11. A Study of Flow Separation in Transonic Flow Using Inviscid and Viscous Computational Fluid Dynamics (CFD) Schemes

    NASA Technical Reports Server (NTRS)

    Rhodes, J. A.; Tiwari, S. N.; Vonlavante, E.

    1988-01-01

    A comparison of flow separation in transonic flows is made using various computational schemes which solve the Euler and the Navier-Stokes equations of fluid mechanics. The flows examined are computed using several simple two-dimensional configurations including a backward facing step and a bump in a channel. Comparison of the results obtained using shock fitting and flux vector splitting methods are presented and the results obtained using the Euler codes are compared to results on the same configurations using a code which solves the Navier-Stokes equations.

  12. Approximate spatial reasoning

    NASA Technical Reports Server (NTRS)

    Dutta, Soumitra

    1988-01-01

    Much of human reasoning is approximate in nature. Formal models of reasoning traditionally try to be precise and reject the fuzziness of concepts in natural use and replace them with non-fuzzy scientific explicata by a process of precisiation. As an alternate to this approach, it has been suggested that rather than regard human reasoning processes as themselves approximating to some more refined and exact logical process that can be carried out with mathematical precision, the essence and power of human reasoning is in its capability to grasp and use inexact concepts directly. This view is supported by the widespread fuzziness of simple everyday terms (e.g., near tall) and the complexity of ordinary tasks (e.g., cleaning a room). Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. Consider the case of crossing a traffic intersection. We have only an approximate idea of the locations and speeds of various obstacles (e.g., persons and vehicles), but we nevertheless manage to cross such traffic intersections without any harm. The details of our mental processes which enable us to carry out such intricate tasks in such apparently simple manner are not well understood. However, it is that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains.

  13. The maximum overlap method: A general and efficient scheme for reducing basis sets. Application to the generation of approximate AO's for the 3 d transition metal atoms and ions

    NASA Astrophysics Data System (ADS)

    Francisco, E.; Seijo, L.; Pueyo, L.

    1986-07-01

    The method of maximum overlap, often applied to the problem of basis set reduction, is formulated in terms of weighted least squares with orthogonality restrictions. An analytical solution for the linear parameters of the reduced set is given. In this form, the method is a general and efficient scheme for reducing basis sets. As an application, orthogonal radial wavefunctions of the STO type have been obtained for the 3 d transition metal atoms and ions by simulation of the high-quality sets of Clementi and Roetti. The performance of the reduction has been evaluated by examining several one- and two-electron interactions. Results of these tests reveal that the new functions are highly accurate simulations of the reference AO's. They appear to be appropriate for molecular and solid state calculations.

  14. A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space.

    PubMed

    Chakrabarti, Rajarshi; Sebastian, K L

    2009-12-14

    We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.

  15. Tangent map intermittency as an approximate analysis of intermittency in a high dimensional fully stochastic dynamical system: The Tangled Nature model

    NASA Astrophysics Data System (ADS)

    Diaz-Ruelas, Alvaro; Jeldtoft Jensen, Henrik; Piovani, Duccio; Robledo, Alberto

    2016-12-01

    It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g., by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal candidate for such a study, a significant model as it is capable of reproducing a broad range of the phenomenology of macroevolution and ecosystems. The TaNa model exhibits strong intermittency reminiscent of punctuated equilibrium and, like the fossil record of mass extinction, the intermittency in the model is found to be non-stationary, a feature typical of many complex systems. We derive a mean-field version for the evolution of the likelihood function controlling the reproduction of species and find a local map close to tangency. This mean-field map, by our own local approximation, is able to describe qualitatively only one episode of the intermittent dynamics of the full TaNa model. To complement this result, we construct a complete nonlinear dynamical system model consisting of successive tangent bifurcations that generates time evolution patterns resembling those of the full TaNa model in macroscopic scales. The switch from one tangent bifurcation to the next in the sequences produced in this model is stochastic in nature, based on criteria obtained from the local mean-field approximation, and capable of imitating the changing set of types of species and total population in the TaNa model. The model combines full deterministic dynamics with instantaneous parameter random jumps at stochastically drawn times. In spite of the limitations of our approach, which entails a drastic collapse of degrees of freedom, the description of a high-dimensional model system in terms of a low

  16. Tangent map intermittency as an approximate analysis of intermittency in a high dimensional fully stochastic dynamical system: The Tangled Nature model.

    PubMed

    Diaz-Ruelas, Alvaro; Jeldtoft Jensen, Henrik; Piovani, Duccio; Robledo, Alberto

    2016-12-01

    It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g., by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal candidate for such a study, a significant model as it is capable of reproducing a broad range of the phenomenology of macroevolution and ecosystems. The TaNa model exhibits strong intermittency reminiscent of punctuated equilibrium and, like the fossil record of mass extinction, the intermittency in the model is found to be non-stationary, a feature typical of many complex systems. We derive a mean-field version for the evolution of the likelihood function controlling the reproduction of species and find a local map close to tangency. This mean-field map, by our own local approximation, is able to describe qualitatively only one episode of the intermittent dynamics of the full TaNa model. To complement this result, we construct a complete nonlinear dynamical system model consisting of successive tangent bifurcations that generates time evolution patterns resembling those of the full TaNa model in macroscopic scales. The switch from one tangent bifurcation to the next in the sequences produced in this model is stochastic in nature, based on criteria obtained from the local mean-field approximation, and capable of imitating the changing set of types of species and total population in the TaNa model. The model combines full deterministic dynamics with instantaneous parameter random jumps at stochastically drawn times. In spite of the limitations of our approach, which entails a drastic collapse of degrees of freedom, the description of a high-dimensional model system in terms of a low

  17. Approximating subtree distances between phylogenies.

    PubMed

    Bonet, Maria Luisa; St John, Katherine; Mahindru, Ruchi; Amenta, Nina

    2006-10-01

    We give a 5-approximation algorithm to the rooted Subtree-Prune-and-Regraft (rSPR) distance between two phylogenies, which was recently shown to be NP-complete. This paper presents the first approximation result for this important tree distance. The algorithm follows a standard format for tree distances. The novel ideas are in the analysis. In the analysis, the cost of the algorithm uses a "cascading" scheme that accounts for possible wrong moves. This accounting is missing from previous analysis of tree distance approximation algorithms. Further, we show how all algorithms of this type can be implemented in linear time and give experimental results.

  18. Numerical approximations for a phase-field moving contact line model with variable densities and viscosities

    NASA Astrophysics Data System (ADS)

    Yu, Haijun; Yang, Xiaofeng

    2017-04-01

    We consider the numerical approximations of a two-phase hydrodynamics coupled phase-field model that incorporates the variable densities, viscosities and moving contact line boundary conditions. The model is a nonlinear, coupled system that consists of incompressible Navier-Stokes equations with the generalized Navier boundary condition, and the Cahn-Hilliard equations with moving contact line boundary conditions. By some subtle explicit-implicit treatments to nonlinear terms, we develop two efficient, unconditionally energy stable numerical schemes, in particular, a linear decoupled energy stable scheme for the system with static contact line condition, and a nonlinear energy stable scheme for the system with dynamic contact line condition. An efficient spectral-Galerkin spatial discretization is implemented to verify the accuracy and efficiency of proposed schemes. Various numerical results show that the proposed schemes are efficient and accurate.

  19. Approximating spectral impact of structural perturbations in large networks.

    PubMed

    Milanese, Attilio; Sun, Jie; Nishikawa, Takashi

    2010-04-01

    Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as synchronization and cascading processes on networks. Here we develop a theory for estimating the change of the largest eigenvalue of the adjacency matrix or the extreme eigenvalues of the graph Laplacian when small but arbitrary set of links are added or removed from the network. We demonstrate the effectiveness of our approximation schemes using both real and artificial networks, showing in particular that we can accurately obtain the spectral ranking of small subgraphs. We also propose a local iterative scheme which computes the relative ranking of a subgraph using only the connectivity information of its neighbors within a few links. Our results may not only contribute to our theoretical understanding of dynamical processes on networks, but also lead to practical applications in ranking subgraphs of real complex networks.

  20. Approximation methods for inverse problems involving the vibration of beams with tip bodies

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.

    1984-01-01

    Two cubic spline based approximation schemes for the estimation of structural parameters associated with the transverse vibration of flexible beams with tip appendages are outlined. The identification problem is formulated as a least squares fit to data subject to the system dynamics which are given by a hybrid system of coupled ordinary and partial differential equations. The first approximation scheme is based upon an abstract semigroup formulation of the state equation while a weak/variational form is the basis for the second. Cubic spline based subspaces together with a Rayleigh-Ritz-Galerkin approach were used to construct sequences of easily solved finite dimensional approximating identification problems. Convergence results are briefly discussed and a numerical example demonstrating the feasibility of the schemes and exhibiting their relative performance for purposes of comparison is provided.