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.
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.
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.
An Approximation Scheme for Delay Equations.
1980-06-16
C(-r,0. R) IR defined by m 10 D( ) 0 (O) - I B (-rj- B(s) b(s)ds, I(* A ,(-r ) + A(s) (s)ds, where 0 =r 0 < rI < ... < rm r. ’AJ,B are n x n matrices ...Approximations of delays by ordinary differen- tial equations, INCREST - Institutul de Matematica , Preprint series in Mathematics No. 22/1978. [14] F
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.
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.
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.
A class of difference schemes with flexible local approximation
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.
Level-treewidth property, exact algorithms and approximation schemes
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.
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.
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.
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.
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.
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.
Dynamic Restarting Schemes for Eigenvalue Problems
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.
Evaluating the Accuracy of Hessian Approximations for Direct Dynamics Simulations.
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.
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.
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.
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.
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.
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.
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.
Revisiting approximate dynamic programming and its convergence.
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.
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.
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.
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.
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.
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.
An Approximate Dynamic Programming Mode for Optimal MEDEVAC Dispatching
2015-03-26
An Approximate Dynamic Programming Model For MEDEVAC Dispatching THESIS MARCH 2015 Aaron J. Rettke, Captain, USA AFIT-ENS-MS-15-M-115 DEPARTMENT OF...and is not subject to copyright protection in the United States. AFIT-ENS-MS-15-M-115 AN APPROXIMATE DYNAMIC PROGRAMMING MODEL FOR MEDEVAC... APPROXIMATE DYNAMIC PROGRAMMING MODEL FOR MEDEVAC DISPATCHING THESIS Aaron J. Rettke, BS, MS Captain, USA Committee Membership: Lt Col Matthew J
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.
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.
Relaxation approximations to second-order traffic flow models by high-resolution schemes
Nikolos, I.K.; Delis, A.I.; Papageorgiou, M.
2015-03-10
A relaxation-type approximation of second-order non-equilibrium traffic models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms with the attractive feature that neither Riemann solvers nor characteristic decompositions are in need. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. To discretize the resulting relaxation system, high-resolution reconstructions in space are considered. Emphasis is given on a fifth-order WENO scheme and its performance. The computations reported demonstrate the simplicity and versatility of relaxation schemes as numerical solvers.
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.
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.
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.
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.
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.
Development of highly accurate approximate scheme for computing the charge transfer integral.
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.
Development of highly accurate approximate scheme for computing the charge transfer integral
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.
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.
Collisions of Halo Nuclei within a Dynamical Eikonal Approximation
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.
Approximate Bisimulation-Based Reduction of Power System Dynamic Models
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.
Dynamical nonlocal coherent-potential approximation for itinerant electron magnetism.
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.
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.
Approximation of stochastic equilibria for dynamic systems with colored noise
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.
Systematic Approximations to Susceptible-Infectious-Susceptible Dynamics on Networks
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
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.
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.
Approximating the dynamic response of strain-hardening structures
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.
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.
Dynamical eikonal approximation in breakup reactions of {sup 11}Be
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.
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.
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.
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
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.
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.
F -Discrepancy for Efficient Sampling in Approximate Dynamic Programming.
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.
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.
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.
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.
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.
Stability and dynamical properties of Rosenau-Hyman compactons using Padé approximants.
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.
Decentralized Bayesian search using approximate dynamic programming methods.
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.
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.
Compressible simulations of bubble dynamics with central-upwind schemes
NASA Astrophysics Data System (ADS)
Koukouvinis, Phoevos; Gavaises, Manolis; Georgoulas, Anastasios; Marengo, Marco
2016-02-01
This paper discusses the implementation of an explicit density-based solver, that utilises the central-upwind schemes for the simulation of cavitating bubble dynamic flows. It is highlighted that, in conjunction with the Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) scheme they are of second order in spatial accuracy; essentially they are high-order extensions of the Lax-Friedrichs method and are linked to the Harten Lax and van Leer (HLL) solver family. Basic comparison with the predicted wave pattern of the central-upwind schemes is performed with the exact solution of the Riemann problem, for an equation of state used in cavitating flows, showing excellent agreement. Next, the solver is used to predict a fundamental bubble dynamics case, the Rayleigh collapse, in which results are in accordance to theory. Then several different bubble configurations were tested. The methodology is able to handle the large pressure and density ratios appearing in cavitating flows, giving similar predictions in the evolution of the bubble shape, as the reference.
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.
Approximating the maximum weight clique using replicator dynamics.
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
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.
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.
Dynamic Obstacle Avoidance Using Bayesian Occupancy Filter and Approximate Inference
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
Exact and approximate many-body dynamics with stochastic one-body density matrix evolution
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.
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.
Secure Dynamic access control scheme of PHR in cloud computing.
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
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.
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.
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.
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.
The derivation and approximation of coarse-grained dynamics from Langevin dynamics
NASA Astrophysics Data System (ADS)
Ma, Lina; Li, Xiantao; Liu, Chun
2016-11-01
We present a derivation of a coarse-grained description, in the form of a generalized Langevin equation, from the Langevin dynamics model that describes the dynamics of bio-molecules. The focus is placed on the form of the memory kernel function, the colored noise, and the second fluctuation-dissipation theorem that connects them. Also presented is a hierarchy of approximations for the memory and random noise terms, using rational approximations in the Laplace domain. These approximations offer increasing accuracy. More importantly, they eliminate the need to evaluate the integral associated with the memory term at each time step. Direct sampling of the colored noise can also be avoided within this framework. Therefore, the numerical implementation of the generalized Langevin equation is much more efficient.
Equivalence Between Approximate Dynamic Inversion and Proportional-Integral Control
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
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.
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.
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.
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.
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.
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.
Kernel-Based Approximate Dynamic Programming Using Bellman Residual Elimination
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
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.
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.
Approximate photochemical dynamics of azobenzene with reactive force fields
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)
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).
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.
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.
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
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.
Improved dynamic ID-based authentication scheme for telecare medical information systems.
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.
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.
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.
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
Design and Analysis of a Dynamic Mobility Management Scheme for Wireless Mesh Network
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
Design and analysis of a dynamic mobility management scheme for wireless mesh network.
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.
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.
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.
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
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.
NASA Astrophysics Data System (ADS)
Antoine, Xavier; Besse, Christophe; Rispoli, Vittorio
2016-12-01
The aim of this paper is to build and validate some explicit high-order schemes, both in space and time, for simulating the dynamics of systems of nonlinear Schrödinger/Gross-Pitaevskii equations. The method is based on the combination of high-order IMplicit-EXplicit (IMEX) schemes in time and Fourier pseudo-spectral approximations in space. The resulting IMEXSP schemes are highly accurate, efficient and easy to implement. They are also robust when used in conjunction with an adaptive time stepping strategy and appear as an interesting alternative to time-splitting pseudo-spectral (TSSP) schemes. Finally, a complete numerical study is developed to investigate the properties of the IMEXSP schemes, in comparison with TSSP schemes, for one- and two-components systems of Gross-Pitaevskii equations.
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.
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.
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
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.
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.
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.
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.
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.
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.
Application of approximate entropy on dynamic characteristics of epileptic absence seizure☆
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
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.
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.
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.
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.
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.
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.
Hamilton-Jacobi-Bellman equations and approximate dynamic programming on time scales.
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.
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.
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.
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.
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.
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.
A Dynamic Probabilistic Based Broadcasting Scheme for MANETs
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
A Dynamic Probabilistic Based Broadcasting Scheme for MANETs.
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.
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.
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.
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.
Approximate Inference for Time-Varying Interactions and Macroscopic Dynamics of Neural Populations
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
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.
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
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.
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.
Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics.
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.
Dynamic load balance scheme for the DSMC algorithm
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%.
Study of multiband disordered systems using the typical medium dynamical cluster approximation
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
Study of multiband disordered systems using the typical medium dynamical cluster approximation
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 K_{x}Fe_{2-y}Se_{2} 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.
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.
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.
Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.
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.
Action versus Result-Oriented Schemes in a Grassland Agroecosystem: A Dynamic Modelling Approach
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
Dynamic demonstration of diffractive optic analog-to-digital converter scheme.
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.
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.
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
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.
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.
Novel gas-dynamic levitation scheme for noncontact coating of spherical ICF targets
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.
Cosmological dynamics: from the Eulerian to the Lagrangian frame. Part I. Newtonian approximation
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.
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.
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.
Sparse approximation of long-term biomedical signals for classification via dynamic PCA.
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.
Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows
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.
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.
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.
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.
Dynamic nuclear polarization via thermal mixing: Beyond the high temperature approximation.
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.
An Analog Gamma Correction Scheme for High Dynamic Range CMOS Logarithmic Image Sensors
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
Taylor-Lagrange renormalization scheme: Application to light-front dynamics
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.
An analog gamma correction scheme for high dynamic range CMOS logarithmic image sensors.
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.
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.
DYNAMICAL SPIN SUSCEPTIBILITY IN THE TD-LDA AND QSGW APPROXIMATIONS
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.
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
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.
Polaron dynamics with off-diagonal coupling: beyond the Ehrenfest approximation.
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.
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.
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.
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.
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.
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
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
Approximating high-dimensional dynamics by barycentric coordinates with linear programming.
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.
Analysis of Coulomb breakup experiments of {sup 8}B with a dynamical eikonal approximation
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.
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.
Approximating high-dimensional dynamics by barycentric coordinates with linear programming
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.
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.
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.
Quantum speed limits in open systems: Non-Markovian dynamics without rotating-wave approximation
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
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.
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.
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.
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.
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.
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
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.
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.
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.
Conditional Moment Closure Schemes for Studying Stochastic Dynamics of Genetic Circuits.
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.
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.
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
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.
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.
Dynamics of a planar vortex filament under the quantum local induction approximation
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
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.
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
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.
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
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
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.
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
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.
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.
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.
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.
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
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.
A high performance communications and memory caching scheme for molecular dynamics on the CM-5
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.
Systematic renormalization scheme in light-front dynamics with Fock space truncation
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.
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.
A new flux splitting scheme for Euler equations of gas dynamics
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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
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.
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.
Dynamics of high-risk nonvaccine human papillomavirus types after actual vaccination scheme.
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.
Dynamics of High-Risk Nonvaccine Human Papillomavirus Types after Actual Vaccination Scheme
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
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.
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).
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.
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).
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.
A Dynamically Computed Convective Time Scale for the Kain–Fritsch Convective Parameterization Scheme
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...
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.
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
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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
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.
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.
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.
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.
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).
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
2011-08-01
and Computational Studies for Dynamically Orthogonal Equations by Mattheus P. Ueckermann Pierre F. J. Lermusiaux Themis P. Sapsis...COVERED 00-00-2011 to 00-00-2011 4. TITLE AND SUBTITLE Numerical Schemes and Computational Studies for Dynamically Orthogonal Equations 5a...ocean ows, and other non-linear dynamical systems. The Dynamically Orthogonal (DO) eld equations provide an e cient time- dependent adaptive methodology
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
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.
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
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.
Approximations and Implementations of Nonlinear Filtering Schemes.
1988-02-01
SYSTEMS 13/14 (Blank) JP{ I LDMX MAJ=V AMOnUXIO rOQO v F 3LES LXIMKR STOCASTIC STSTEN A. a. Uaded an L 1. Verriest School of flectrical Engineering...1975. (15] P. G. Hoel , S. C. Port, and C. J. Stone, "Introduction to Stochastic Processes", Houghton Mifflin Co., 1972. (161 A. Isidori, "Nonlinear
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.
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.
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.
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
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.
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.
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.
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).
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
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.
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.
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
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.
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].
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
Inference for Optimal Dynamic Treatment Regimes using an Adaptive m-out-of-n Bootstrap Scheme
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
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.
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
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
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
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
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
Optimal approximation of harmonic growth clusters by orthogonal polynomials
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.
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.
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
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.
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.
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
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.
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.
Extended time-dependent mean-field approximation
Portes, D.A. Jr. |; Kodama, T.; de Toledo Piza, A.F.
1996-09-01
The time-dependent mean-field approximation for two dynamically coupled subsystems is extended to include correlation effects between the subsystems, allowing for decorrelation processes to develop in the reduced density matrices. The extended scheme is formulated in terms of the truncation to {ital M} terms of the Schmidt decomposition of the full density matrix. This {ital M} natural orbitals truncation scheme is compared to the exact numerical solution for a system of two coupled anharmonic oscillators in a factorized initial state. It is found that the approximation {ital M}=3 gives a good approximation to the exact results over several characteristic times of the system. {copyright} {ital 1996 The American Physical Society.}
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.
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.
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.
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
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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
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
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.
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.
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.
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.
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
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
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
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.
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.
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.
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.
Approximating subtree distances between phylogenies.
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.
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.
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.
Approximating spectral impact of structural perturbations in large networks.
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.
The nonlinear modified equation approach to analyzing finite difference schemes
NASA Technical Reports Server (NTRS)
Klopfer, G. H.; Mcrae, D. S.
1981-01-01
The nonlinear modified equation approach is taken in this paper to analyze the generalized Lax-Wendroff explicit scheme approximation to the unsteady one- and two-dimensional equations of gas dynamics. Three important applications of the method are demonstrated. The nonlinear modified equation analysis is used to (1) generate higher order accurate schemes, (2) obtain more accurate estimates of the discretization error for nonlinear systems of partial differential equations, and (3) generate an adaptive mesh procedure for the unsteady gas dynamic equations. Results are obtained for all three areas. For the adaptive mesh procedure, mesh point requirements for equal resolution of discontinuities were reduced by a factor of five for a 1-D shock tube problem solved by the explicit MacCormack scheme.
A Parallel Multiblock Mesh Movement Scheme For Complex Aeroelastic Applications
NASA Technical Reports Server (NTRS)
Potsdam, Mark A.; Guruswamy, Guru P.
2000-01-01
A scheme has been developed for the movement of multiblock, structured grids due to surface deformation arising from aeroelastics, control surface movement, or design optimization. Elements of the method include a blending of a surface spline approximation and nearest surface point movement for block boundaries. Transfinite interpolation is employed for volume grid deformation. The scheme is demonstrated on a range of simple and complex aeroelastic aircraft applications using Navier-Stokes computational fluid dynamics and modal structural analyses on parallel processors. Results are robust and accurate, requiring only minimal user input specification.
2016-01-01
Background Visceral leishmaniasis (VL) is a disease caused by two known vector-borne parasite species (Leishmania donovani, L. infantum), transmitted to man by phlebotomine sand flies (species: Phlebotomus and Lutzomyia), resulting in ≈50,000 human fatalities annually, ≈67% occurring on the Indian subcontinent. Indoor residual spraying is the current method of sand fly control in India, but alternative means of vector control, such as the treatment of livestock with systemic insecticide-based drugs, are being evaluated. We describe an individual-based, stochastic, life-stage-structured model that represents a sand fly vector population within a village in India and simulates the effects of vector control via fipronil-based drugs orally administered to cattle, which target both blood-feeding adults and larvae that feed on host feces. Principle findings Simulation results indicated efficacy of fipronil-based control schemes in reducing sand fly abundance depended on timing of drug applications relative to seasonality of the sand fly life cycle. Taking into account cost-effectiveness and logistical feasibility, two of the most efficacious treatment schemes reduced population peaks occurring from April through August by ≈90% (applications 3 times per year at 2-month intervals initiated in March) and >95% (applications 6 times per year at 2-month intervals initiated in January) relative to no control, with the cumulative number of sand fly days occurring April-August reduced by ≈83% and ≈97%, respectively, and more specifically during the summer months of peak human exposure (June-August) by ≈85% and ≈97%, respectively. Conclusions Our model should prove useful in a priori evaluation of the efficacy of fipronil-based drugs in controlling leishmaniasis on the Indian subcontinent and beyond. PMID:27537774
NASA Astrophysics Data System (ADS)
Chen, Yu-Chih; Cheng, Yu-Heng; Ingram, Patrick; Yoon, Euisik
2016-06-01
Proteolytic degradation of the extracellular matrix (ECM) is critical in cancer invasion, and recent work suggests that heterogeneous cancer populations cooperate in this process. Despite the importance of cell heterogeneity, conventional proteolytic assays measure average activity, requiring thousands of cells and providing limited information about heterogeneity and dynamics. Here, we developed a microfluidic platform that provides high-efficiency cell loading and simple valveless isolation, so the proteolytic activity of a small sample (10–100 cells) can be easily characterized. Combined with a single cell derived (clonal) sphere formation platform, we have successfully demonstrated the importance of microenvironmental cues for proteolytic activity and also investigated the difference between clones. Furthermore, the platform allows monitoring single cells at multiple time points, unveiling different cancer cell line dynamics in proteolytic activity. The presented tool facilitates single cell proteolytic analysis using small samples, and our findings illuminate the heterogeneous and dynamic nature of proteolytic activity.
Chen, Yu-Chih; Cheng, Yu-Heng; Ingram, Patrick; Yoon, Euisik
2016-01-01
Proteolytic degradation of the extracellular matrix (ECM) is critical in cancer invasion, and recent work suggests that heterogeneous cancer populations cooperate in this process. Despite the importance of cell heterogeneity, conventional proteolytic assays measure average activity, requiring thousands of cells and providing limited information about heterogeneity and dynamics. Here, we developed a microfluidic platform that provides high-efficiency cell loading and simple valveless isolation, so the proteolytic activity of a small sample (10–100 cells) can be easily characterized. Combined with a single cell derived (clonal) sphere formation platform, we have successfully demonstrated the importance of microenvironmental cues for proteolytic activity and also investigated the difference between clones. Furthermore, the platform allows monitoring single cells at multiple time points, unveiling different cancer cell line dynamics in proteolytic activity. The presented tool facilitates single cell proteolytic analysis using small samples, and our findings illuminate the heterogeneous and dynamic nature of proteolytic activity. PMID:27283981
Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations
NASA Technical Reports Server (NTRS)
Yee, H. C.; Warming, R. F.; Harten, A.
1983-01-01
The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.
Ruas, Alexandre; Guilbaud, Philippe; Den Auwer, Christophe; Moulin, Christophe; Simonin, Jean-Pierre; Turq, Pierre; Moisy, Philippe
2006-10-19
This work is aimed at a predictive description of the thermodynamic properties of actinide(III) salt solutions at high concentration and 25 degrees C. A new solution of the binding mean spherical approximation (BIMSA) theory, based on the Wertheim formalism, for taking into account 1:1 and also 1:2 complex formation, is used to reproduce, from a simple procedure, experimental osmotic coefficient variation with concentration for three binary salt solutions of the same lanthanide(III) cation: dysprosium(III) perchlorate, nitrate, and chloride. The relevance of the fitted parameters is discussed, and their values are compared with available literature values. UV-vis/near-IR, time-resolved laser-induced fluorescence spectroscopy experiments, and molecular dynamics (MD) calculations were conducted for dilute to concentrated solutions (ca. 3 mol.kg-1) for a study of the microscopic behavior of DyCl3 binary solutions. Coupling MD calculations and extended X-ray absorption fine structure led to the determination of reliable distances. The MD results were used for a discussion of the parameters used in the BIMSA.
Gao, Yangyang; Müller-Plathe, Florian
2016-02-25
By employing reverse nonequilibrium molecular dynamics simulations in a full atomistic resolution, the effect of surface-grafted chains on the thermal conductivity of graphene-polyamide-6.6 (PA) nanocomposites has been investigated. The interfacial thermal conductivity perpendicular to the graphene plane is proportional to the grafting density, while it first increases and then saturates with the grafting length. Meanwhile, the intrinsic in-plane thermal conductivity of graphene drops sharply as the grafting density increases. The maximum overall thermal conductivity of nanocomposites appears at an intermediate grafting density because of these two competing effects. The thermal conductivity of the composite parallel to the graphene plane increases with the grafting density and grafting length which is attributed to better interfacial coupling between graphene and PA. There exists an optimal balance between grafting density and grafting length to obtain the highest interfacial and parallel thermal conductivity. Two empirical formulas are suggested, which quantitatively account for the effects of grafting length and density on the interfacial and parallel thermal conductivity. Combined with effective medium approximation, for ungrafted graphene in random orientation, the model overestimates the thermal conductivity at low graphene volume fraction (f < 10%) compared with experiments, while it underestimates it at high graphene volume fraction (f > 10%). For unoriented grafted graphene, the model matches the experimental results well. In short, this work provides some valuable guides to obtain the nanocomposites with high thermal conductivity by grafting chain on the surface of graphene.
Weinberg, Seth H.; Smith, Gregory D.
2012-01-01
Cardiac myocyte calcium signaling is often modeled using deterministic ordinary differential equations (ODEs) and mass-action kinetics. However, spatially restricted “domains” associated with calcium influx are small enough (e.g., 10−17 liters) that local signaling may involve 1–100 calcium ions. Is it appropriate to model the dynamics of subspace calcium using deterministic ODEs or, alternatively, do we require stochastic descriptions that account for the fundamentally discrete nature of these local calcium signals? To address this question, we constructed a minimal Markov model of a calcium-regulated calcium channel and associated subspace. We compared the expected value of fluctuating subspace calcium concentration (a result that accounts for the small subspace volume) with the corresponding deterministic model (an approximation that assumes large system size). When subspace calcium did not regulate calcium influx, the deterministic and stochastic descriptions agreed. However, when calcium binding altered channel activity in the model, the continuous deterministic description often deviated significantly from the discrete stochastic model, unless the subspace volume is unrealistically large and/or the kinetics of the calcium binding are sufficiently fast. This principle was also demonstrated using a physiologically realistic model of calmodulin regulation of L-type calcium channels introduced by Yue and coworkers. PMID:23509597
NASA Astrophysics Data System (ADS)
Pontes, J.; Walgraef, D.; Christov, C. I.
2010-11-01
Strain localization and dislocation pattern formation are typical features of plastic deformation in metals and alloys. Glide and climb dislocation motion along with accompanying production/annihilation processes of dislocations lead to the occurrence of instabilities of initially uniform dislocation distributions. These instabilities result into the development of various types of dislocation micro-structures, such as dislocation cells, slip and kink bands, persistent slip bands, labyrinth structures, etc., depending on the externally applied loading and the intrinsic lattice constraints. The Walgraef-Aifantis (WA) (Walgraef and Aifanits, J. Appl. Phys., 58, 668, 1985) model is an example of a reaction-diffusion model of coupled nonlinear equations which describe 0 formation of forest (immobile) and gliding (mobile) dislocation densities in the presence of cyclic loading. This paper discuss two versions of the WA model and focus on a finite difference, second order in time 1-Nicolson semi-implicit scheme, with internal iterations at each time step and a spatial splitting using the Stabilizing, Correction (Christov and Pontes, Mathematical and Computer Modelling, 35, 87, 2002) for solving the model evolution equations in two dimensions. The results of two simulations are presented. More complete results will appear in a forthcoming paper.
NASA Astrophysics Data System (ADS)
McGraw, R.; Leng, L.; Zhu, W.; Riemer, N.; West, M.
2008-07-01
The method of moments (MOM) is a statistically based alternative to sectional and modal methods for aerosol simulation. The MOM is highly efficient as the aerosol distribution is represented by its lower-order moments and only these, not the full distribution itself, are tracked during simulation. Quadrature is introduced to close the moment equations under very general growth laws and to compute aerosol physical and optical properties directly from moments. In this paper the quadrature method of moments (QMOM) is used in a bivariate test tracking of aerosol mixing state. Two aerosol populations, one enriched in soot and the other in sulfate, are allowed to interact through coagulation to form a generally-mixed third particle population. Quadratures of varying complexity (including two candidate schemes for use in climate models) are described and compared with benchmark results obtained by using particle-resolved simulation. Low-order quadratures are found to be highly accurate, and Gauss and Gauss-Radau quadratures appear to give nested lower and upper bounds, respectively, to aerosol mixing rate. These results suggest that the QMOM makes it feasible to represent the generallymixed states of aerosols and track their evolution in climate models.
Yesylevskyy, S; Cardey, Bruno; Kraszewski, S; Foley, Sarah; Enescu, Mironel; da Silva, Antônio M; Dos Santos, Hélio F; Ramseyer, Christophe
2015-10-01
Parameterization of molecular complexes containing a metallic compound, such as cisplatin, is challenging due to the unconventional coordination nature of the bonds which involve platinum atoms. In this work, we develop a new methodology of parameterization for such compounds based on quantum dynamics (QD) calculations. We show that the coordination bonds and angles are more flexible than in normal covalent compounds. The influence of explicit solvent is also shown to be crucial to determine the flexibility of cisplatin in quantum dynamics simulations. Two empirical topologies of cisplatin were produced by fitting its atomic fluctuations against QD in vacuum and QD with explicit first solvation shell of water molecules respectively. A third topology built in a standard way from the static optimized structure was used for comparison. The later one leads to an excessively rigid molecule and exhibits much smaller fluctuations of the bonds and angles than QD reveals. It is shown that accounting for the high flexibility of cisplatin molecule is needed for adequate description of its first hydration shell. MD simulations with flexible QD-based topology also reveal a significant decrease of the barrier of passive diffusion of cisplatin accross the model lipid bilayer. These results confirm that flexibility of organometallic compounds is an important feature to be considered in classical molecular dynamics topologies. Proposed methodology based on QD simulations provides a systematic way of building such topologies.
NASA Astrophysics Data System (ADS)
Kiang, N. Y.; Yang, W.; Ni-Meister, W.; Aleinov, I. D.; Jonas, J.
2014-12-01
Vegetation cover was introduced into general circulations models (GCMs) in the 1980's to account for the effect of land surface albedo and water vapor conductance on the Earth's climate. Schemes assigning canopy albedoes by broad biome type have been superceded in 1990's by canopy radiative transfer schemes for homogeneous canopies obeying Beer's Law extinction as a function of leaf area index (LAI). Leaf albedo and often canopy height are prescribed by plant functional type (PFT). It is recognized that this approach does not effectively describe geographic variation in the radiative transfer of vegetated cover, particularly for mixed and sparse canopies. GCM-coupled dynamic global vegetation models (DGVMs) have retained these simple canopy representations, with little further evaluation of their albedos. With the emergence lidar-derived canopy vertical structure data, DGVM modelers are now revisiting albedo simulation. We present preliminary prognostic global land surface albedo produced by the Ent Terrestrial Biosphere Model (TBM), a DGVM coupled to the NASA Goddard Institute for Space Studies (GISS) GCM. The Ent TBM is a next generation DGVM designed to incorporate variation in canopy heights, and mixed and sparse canopies. For such dynamically varying canopy structure, it uses the Analytical Clumped Two-Stream (ACTS) canopy radiative transfer model, which is derived from gap probability theory for canopies of tree cohorts with ellipsoidal crowns, and accounts for soil, snow, and bare stems. We have developed a first-order global vegetation structure data set (GVSD), which gives a year of satellite-derived geographic variation in canopy height, maximum canopy leaf area, and seasonal LAI. Combined with Ent allometric relations, this data set provides population density and foliage clumping within crowns. We compare the Ent prognostic albedoes to those of the previous GISS GCM scheme, and to satellite estimates. The impact of albedo differences on surface
On Some Numerical Dissipation Schemes
NASA Technical Reports Server (NTRS)
Swanson, R. C.; Radespiel, R.; Turkel, E.
1998-01-01
Several schemes for introducing an artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar dissipation and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical solutions are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme. The coarse-grid accuracy for the original CUSP scheme is improved by modifying the limiter function used with the scheme, giving comparable accuracy to that obtained with the MATD scheme. The modifications reduce the background dissipation and provide control over the regions where the scheme can become first order.
Second Approximation to Conical Flows
1950-12-01
Public Release WRIGHT AIR DEVELOPMENT CENTER AF-WP-(B)-O-29 JUL 53 100 NOTICES ’When Government drawings, specifications, or other data are used V...so that the X, the approximation always depends on the ( "/)th, etc. Here the second approximation, i.e., the terms in C and 62, are computed and...the scheme shown in Fig. 1, the isentropic equations of motion are (cV-X2) +~X~C 6 +- 4= -x- 1 It is assumed that + Ux !E . $O’/ + (8) Introducing Eqs
Liu, Jin-Ming; Yu, Hua; Shi, Yao-Jun; Li, Hao; He, Liang; Li, Jian-Xi; Dong, Chang-Hua; Xie, Qiao; Jin, Ya-Mei; Lu, Ke; Lin, Jiao-Jiao
2013-11-15
Schistosomiasis japonica remains a major public health problem and the Poyang Lake region in Jiangxi province is one of the worst affected endemic areas. Buffaloes play a major role in the transmission of Schistosoma japonicum to humans. The aim of the present study was to increase understanding of the epidemic characteristics of schistosomiasis japonica in water buffaloes in the Poyang Lake region, after achieving the national mid-term goal, and to provide a basis for further interventions. The baseline prevalence in two villages in the Poyang Lake region in May 2010 was compared with respect to usage, sex and age in the total study population. Seasonal dynamics from May 2010 to May 2011 were observed in a natural village in the studied area. The baseline prevalence of infection in both villages (Caohui and Gaozhou) was 4.94% in May 2010. The prevalence in buffalo younger than 12 months was 12.82% in Caohui and 15.11% in Gaozhou, which was significantly higher than that found in those aged 13-24 months and older than 24 months. Of the 28 infected buffaloes, 82.14% (23) were younger than 12 months. The flow of seasonal dynamics showed that S. japonicum infection buffaloes were found from May to July and from November to January of the following year. This survey suggested that it is necessary to conduct two mass treatments (especially for young animals) in late March or early April and November, with an additional treatment of positive animals in July or June.
NASA Astrophysics Data System (ADS)
Oh, Kwang Jin; Kang, Ji Hoon; Myung, Hun Joo
2012-02-01
We have revised a general purpose parallel molecular dynamics simulation program mm_par using the object-oriented programming. We parallelized the revised version using a hierarchical scheme in order to utilize more processors for a given system size. The benchmark result will be presented here. New version program summaryProgram title: mm_par2.0 Catalogue identifier: ADXP_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXP_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 2 390 858 No. of bytes in distributed program, including test data, etc.: 25 068 310 Distribution format: tar.gz Programming language: C++ Computer: Any system operated by Linux or Unix Operating system: Linux Classification: 7.7 External routines: We provide wrappers for FFTW [1], Intel MKL library [2] FFT routine, and Numerical recipes [3] FFT, random number generator, and eigenvalue solver routines, SPRNG [4] random number generator, Mersenne Twister [5] random number generator, space filling curve routine. Catalogue identifier of previous version: ADXP_v1_0 Journal reference of previous version: Comput. Phys. Comm. 174 (2006) 560 Does the new version supersede the previous version?: Yes Nature of problem: Structural, thermodynamic, and dynamical properties of fluids and solids from microscopic scales to mesoscopic scales. Solution method: Molecular dynamics simulation in NVE, NVT, and NPT ensemble, Langevin dynamics simulation, dissipative particle dynamics simulation. Reasons for new version: First, object-oriented programming has been used, which is known to be open for extension and closed for modification. It is also known to be better for maintenance. Second, version 1.0 was based on atom decomposition and domain decomposition scheme [6] for parallelization. However, atom
Kasahara, Kota; Ma, Benson; Goto, Kota; Dasgupta, Bhaskar; Higo, Junichi; Fukuda, Ikuo; Mashimo, Tadaaki; Akiyama, Yutaka; Nakamura, Haruki
2016-01-01
Molecular dynamics (MD) is a promising computational approach to investigate dynamical behavior of molecular systems at the atomic level. Here, we present a new MD simulation engine named “myPresto/omegagene” that is tailored for enhanced conformational sampling methods with a non-Ewald electrostatic potential scheme. Our enhanced conformational sampling methods, e.g., the virtual-system-coupled multi-canonical MD (V-McMD) method, replace a multi-process parallelized run with multiple independent runs to avoid inter-node communication overhead. In addition, adopting the non-Ewald-based zero-multipole summation method (ZMM) makes it possible to eliminate the Fourier space calculations altogether. The combination of these state-of-the-art techniques realizes efficient and accurate calculations of the conformational ensemble at an equilibrium state. By taking these advantages, myPresto/omegagene is specialized for the single process execution with Graphics Processing Unit (GPU). We performed benchmark simulations for the 20-mer peptide, Trp-cage, with explicit solvent. One of the most thermodynamically stable conformations generated by the V-McMD simulation is very similar to an experimentally solved native conformation. Furthermore, the computation speed is four-times faster than that of our previous simulation engine, myPresto/psygene-G. The new simulator, myPresto/omegagene, is freely available at the following URLs: http://www.protein.osaka-u.ac.jp/rcsfp/pi/omegagene/ and http://presto.protein.osaka-u.ac.jp/myPresto4/. PMID:27924276
Kasahara, Kota; Ma, Benson; Goto, Kota; Dasgupta, Bhaskar; Higo, Junichi; Fukuda, Ikuo; Mashimo, Tadaaki; Akiyama, Yutaka; Nakamura, Haruki
2016-01-01
Molecular dynamics (MD) is a promising computational approach to investigate dynamical behavior of molecular systems at the atomic level. Here, we present a new MD simulation engine named "myPresto/omegagene" that is tailored for enhanced conformational sampling methods with a non-Ewald electrostatic potential scheme. Our enhanced conformational sampling methods, e.g., the virtual-system-coupled multi-canonical MD (V-McMD) method, replace a multi-process parallelized run with multiple independent runs to avoid inter-node communication overhead. In addition, adopting the non-Ewald-based zero-multipole summation method (ZMM) makes it possible to eliminate the Fourier space calculations altogether. The combination of these state-of-the-art techniques realizes efficient and accurate calculations of the conformational ensemble at an equilibrium state. By taking these advantages, myPresto/omegagene is specialized for the single process execution with Graphics Processing Unit (GPU). We performed benchmark simulations for the 20-mer peptide, Trp-cage, with explicit solvent. One of the most thermodynamically stable conformations generated by the V-McMD simulation is very similar to an experimentally solved native conformation. Furthermore, the computation speed is four-times faster than that of our previous simulation engine, myPresto/psygene-G. The new simulator, myPresto/omegagene, is freely available at the following URLs: http://www.protein.osaka-u.ac.jp/rcsfp/pi/omegagene/ and http://presto.protein.osaka-u.ac.jp/myPresto4/.
Approximation algorithms for scheduling unrelated parallel machines with release dates
NASA Astrophysics Data System (ADS)
Avdeenko, T. V.; Mesentsev, Y. A.; Estraykh, I. V.
2017-01-01
In this paper we propose approaches to optimal scheduling of unrelated parallel machines with release dates. One approach is based on the scheme of dynamic programming modified with adaptive narrowing of search domain ensuring its computational effectiveness. We discussed complexity of the exact schedules synthesis and compared it with approximate, close to optimal, solutions. Also we explain how the algorithm works for the example of two unrelated parallel machines and five jobs with release dates. Performance results that show the efficiency of the proposed approach have been given.
Spline approximations for nonlinear hereditary control systems
NASA Technical Reports Server (NTRS)
Daniel, P. L.
1982-01-01
A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
A nearly-linear computational-cost scheme for the forward dynamics of an N-body pendulum
NASA Technical Reports Server (NTRS)
Chou, Jack C. K.
1989-01-01
The dynamic equations of motion of an n-body pendulum with spherical joints are derived to be a mixed system of differential and algebraic equations (DAE's). The DAE's are kept in implicit form to save arithmetic and preserve the sparsity of the system and are solved by the robust implicit integration method. At each solution point, the predicted solution is corrected to its exact solution within given tolerance using Newton's iterative method. For each iteration, a linear system of the form J delta X = E has to be solved. The computational cost for solving this linear system directly by LU factorization is O(n exp 3), and it can be reduced significantly by exploring the structure of J. It is shown that by recognizing the recursive patterns and exploiting the sparsity of the system the multiplicative and additive computational costs for solving J delta X = E are O(n) and O(n exp 2), respectively. The formulation and solution method for an n-body pendulum is presented. The computational cost is shown to be nearly linearly proportional to the number of bodies.
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing; Steffen, Christopher J., Jr.
1991-01-01
A new flux splitting scheme is proposed. The scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of Roe's solver in the Euler and Navier-Stokes solutions performed in this study. The scheme is robust and converges as fast as the Roe splitting. An approximately defined cell-face advection Mach number is proposed using values from the two straddling cells via associated characteristic speeds. This interface Mach number is then used to determine the upwind extrapolation for the convective quantities. Accordingly, the name of the scheme is coined as Advection Upstream Splitting Method (AUSM). A new pressure splitting is introduced which is shown to behave successfully, yielding much smoother results than other existing pressure splittings. Of particular interest is the supersonic blunt body problem in which the Roe scheme gives anomalous solutions. The AUSM produces correct solutions without difficulty for a wide range of flow conditions as well as grids.
JIMWLK evolution in the Gaussian approximation
NASA Astrophysics Data System (ADS)
Iancu, E.; Triantafyllopoulos, D. N.
2012-04-01
We demonstrate that the Balitsky-JIMWLK equations describing the high-energy evolution of the n-point functions of the Wilson lines (the QCD scattering amplitudes in the eikonal approximation) admit a controlled mean field approximation of the Gaussian type, for any value of the number of colors N c . This approximation is strictly correct in the weak scattering regime at relatively large transverse momenta, where it re-produces the BFKL dynamics, and in the strong scattering regime deeply at saturation, where it properly describes the evolution of the scattering amplitudes towards the respective black disk limits. The approximation scheme is fully specified by giving the 2-point function (the S-matrix for a color dipole), which in turn can be related to the solution to the Balitsky-Kovchegov equation, including at finite N c . Any higher n-point function with n ≥ 4 can be computed in terms of the dipole S-matrix by solving a closed system of evolution equations (a simplified version of the respective Balitsky-JIMWLK equations) which are local in the transverse coordinates. For simple configurations of the projectile in the transverse plane, our new results for the 4-point and the 6-point functions coincide with the high-energy extrapolations of the respective results in the McLerran-Venugopalan model. One cornerstone of our construction is a symmetry property of the JIMWLK evolution, that we notice here for the first time: the fact that, with increasing energy, a hadron is expanding its longitudinal support symmetrically around the light-cone. This corresponds to invariance under time reversal for the scattering amplitudes.
Low coherence fiber differentiating interferometer and its passive demodulation schemes
NASA Astrophysics Data System (ADS)
Fang, Wentan; Jia, Qiumin; Zhen, Shenglai; Chen, Jian; Cheng, Xiaoyan; Yu, Benli
2015-01-01
In this paper, a low coherence fiber differentiating interferometer and its passive demodulation schemes are presented and experimentally demonstrated. The interferometer which adopts a broadband light resource and balanced detection is a hybrid configuration of Mach-Zehnder and Sagnac interferometer. The two passive demodulation schemes employ an approximate method and a differential-and-cross-multiply (DCM) method to obtain the vibration signal. The phase measurement resolution (PMR) of both methods can reach 6 × 10-5 rad. Comparing with the approximate method which is usually adopted to restore weak signal, the experiment results demonstrated the dynamic range of the DCM demodulation method has increased 30 dB, which extends the measurement range and can be used widely in various physical fields.
Mohanty, Pratap Ranjan; Panda, Anup Kumar
2016-11-01
This paper is concerned to performance improvement of boost PFC converter under large random load fluctuation, ensuring unity power factor (UPF) at source end and regulated voltage at load side. To obtain such performance, a nonlinear controller based on dynamic evolution path theory is designed and its robustness is examined under both heavy and light loading condition. In this paper, %THD and zero-cross-over dead-zone of input current is significantly reduced. Also, very less response time of input current and output voltage to that of load and reference variation is remarked. A simulation model of proposed system is designed and it is realized using dSPACE 1104 signal processor for a 390VDC, 500W prototype. The relevant experimental and simulation waveforms are presented.
Interpolation and Approximation Theory.
ERIC Educational Resources Information Center
Kaijser, Sten
1991-01-01
Introduced are the basic ideas of interpolation and approximation theory through a combination of theory and exercises written for extramural education at the university level. Topics treated are spline methods, Lagrange interpolation, trigonometric approximation, Fourier series, and polynomial approximation. (MDH)
Finite element solution techniques for large-scale problems in computational fluid dynamics
NASA Technical Reports Server (NTRS)
Liou, J.; Tezduyar, T. E.
1987-01-01
Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global matrices. In the adaptive implicit-explicit scheme, the implicit elements are selected dynamically based on element level stability and accuracy considerations. This scheme provides implicit refinement where it is needed. The methods are applied to various problems governed by the convection-diffusion and incompressible Navier-Stokes equations. In all cases studied, the results obtained are indistinguishable from those obtained by the implicit formulations.
Scalable Nonlinear Compact Schemes
Ghosh, Debojyoti; Constantinescu, Emil M.; Brown, Jed
2014-04-01
In this work, we focus on compact schemes resulting in tridiagonal systems of equations, specifically the fifth-order CRWENO scheme. We propose a scalable implementation of the nonlinear compact schemes by implementing a parallel tridiagonal solver based on the partitioning/substructuring approach. We use an iterative solver for the reduced system of equations; however, we solve this system to machine zero accuracy to ensure that no parallelization errors are introduced. It is possible to achieve machine-zero convergence with few iterations because of the diagonal dominance of the system. The number of iterations is specified a priori instead of a norm-based exit criterion, and collective communications are avoided. The overall algorithm thus involves only point-to-point communication between neighboring processors. Our implementation of the tridiagonal solver differs from and avoids the drawbacks of past efforts in the following ways: it introduces no parallelization-related approximations (multiprocessor solutions are exactly identical to uniprocessor ones), it involves minimal communication, the mathematical complexity is similar to that of the Thomas algorithm on a single processor, and it does not require any communication and computation scheduling.
Approximation error in PDE-based modelling of vehicular platoons
NASA Astrophysics Data System (ADS)
Hao, He; Barooah, Prabir
2012-08-01
We study the problem of how much error is introduced in approximating the dynamics of a large vehicular platoon by using a partial differential equation, as was done in Barooah, Mehta, and Hespanha [Barooah, P., Mehta, P.G., and Hespanha, J.P. (2009), 'Mistuning-based Decentralised Control of Vehicular Platoons for Improved Closed Loop Stability', IEEE Transactions on Automatic Control, 54, 2100-2113], Hao, Barooah, and Mehta [Hao, H., Barooah, P., and Mehta, P.G. (2011), 'Stability Margin Scaling Laws of Distributed Formation Control as a Function of Network Structure', IEEE Transactions on Automatic Control, 56, 923-929]. In particular, we examine the difference between the stability margins of the coupled-ordinary differential equations (ODE) model and its partial differential equation (PDE) approximation, which we call the approximation error. The stability margin is defined as the absolute value of the real part of the least stable pole. The PDE model has proved useful in the design of distributed control schemes (Barooah et al. 2009; Hao et al. 2011); it provides insight into the effect of gains of local controllers on the closed-loop stability margin that is lacking in the coupled-ODE model. Here we show that the ratio of the approximation error to the stability margin is O(1/N), where N is the number of vehicles. Thus, the PDE model is an accurate approximation of the coupled-ODE model when N is large. Numerical computations are provided to corroborate the analysis.
NASA Astrophysics Data System (ADS)
Tikhonov, D. A.; Sobolev, E. V.
2011-04-01
A method of integral equations of the theory of liquids in the reference interaction site model (RISM) approximation is used to estimate the Gibbs energy averaged over equilibrium trajectories computed by molecular mechanics. Peptide oxytocin is selected as the object of interest. The Gibbs energy is calculated using all chemical potential formulas introduced in the RISM approach for the excess chemical potential of solvation and is compared with estimates by the generalized Born model. Some formulas are shown to give the wrong sign of Gibbs energy changes when peptide passes from the gas phase into water environment; the other formulas give overestimated Gibbs energy changes with the right sign. Note that allowance for the repulsive correction in the approximate analytical expressions for the Gibbs energy derived by thermodynamic perturbation theory is not a remedy.
Difference equation state approximations for nonlinear hereditary control problems
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1984-01-01
Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589
Difference equation state approximations for nonlinear hereditary control problems
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1982-01-01
Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.
Approximate String Matching with Reduced Alphabet
NASA Astrophysics Data System (ADS)
Salmela, Leena; Tarhio, Jorma
We present a method to speed up approximate string matching by mapping the factual alphabet to a smaller alphabet. We apply the alphabet reduction scheme to a tuned version of the approximate Boyer-Moore algorithm utilizing the Four-Russians technique. Our experiments show that the alphabet reduction makes the algorithm faster. Especially in the k-mismatch case, the new variation is faster than earlier algorithms for English data with small values of k.
Finite volume renormalization scheme for fermionic operators
Monahan, Christopher; Orginos, Kostas
2013-11-01
We propose a new finite volume renormalization scheme. Our scheme is based on the Gradient Flow applied to both fermion and gauge fields and, much like the Schr\\"odinger functional method, allows for a nonperturbative determination of the scale dependence of operators using a step-scaling approach. We give some preliminary results for the pseudo-scalar density in the quenched approximation.
Bdzil, J.B.; Jackson, T.L.; Stewart, D.S.
1999-02-02
In the design of explosive systems the generic problem that one must consider is the propagation of a well-developed detonation wave sweeping through an explosive charge with a complex shape. At a given instant of time the lead detonation shock is a surface that occupies a region of the explosive and has a dimension that is characteristic of the explosive device, typically on the scale of meters. The detonation shock is powered by a detonation reaction zone, sitting immediately behind the shock, which is on the scale of 1 millimeter or less. Thus, the ratio of the reaction zone thickness to the device dimension is of the order of 1/1,000 or less. This scale disparity can lead to great difficulties in computing three-dimensional detonation dynamics. An attack on the dilemma for the computation of detonation systems has lead to the invention of sub-scale models for a propagating detonation front that they refer to herein as program burn models. The program burn model seeks not to resolve the fine scale of the reaction zone in the sense of a DNS simulation. The goal of a program burn simulation is to resolve the hydrodynamics in the inert product gases on a grid much coarser than that required to resolve a physical reaction zone. The authors first show that traditional program burn algorithms for detonation hydrocodes used for explosive design are inconsistent and yield incorrect shock dynamic behavior. To overcome these inconsistencies, they are developing a new class of program burn models based on detonation shock dynamic (DSD) theory. It is hoped that this new class will yield a consistent and robust algorithm which reflects the correct shock dynamic behavior.
NASA Astrophysics Data System (ADS)
Craco, L.; Faria, J. L. B.
2016-02-01
Iron sulfides are promising candidates for the next generation of rechargeable lithium-ion battery materials. Motivated thereby, we present a detailed study of correlation- and doping-induced electronic reconstruction in troilite. Based on local-density-approximation plus dynamical-mean-field-theory, we stress the importance of multi-orbital Coulomb interactions in concert with first-principles band structure calculations for a consistent understanding of intrinsic Mott-Hubbard insulating state in FeS. We explore the anomalous nature of electron doping-induced insulator-bad metal transition, showing that it is driven by orbital-selective dynamical spectral weight transfer. Our results are relevant for understanding charge dynamics upon electrochemical lithiation of iron monosulfides electrode materials for lithium-ion batteries.
Rasin, A.
1994-04-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Approximation modeling for the online performance management of distributed computing systems.
Kusic, Dara; Kandasamy, Nagarajan; Jiang, Guofei
2008-10-01
A promising method of automating management tasks in computing systems is to formulate them as control or optimization problems in terms of performance metrics. For an online optimization scheme to be of practical value in a distributed setting, however, it must successfully tackle the curses of dimensionality and modeling. This paper develops a hierarchical control framework to solve performance management problems in distributed computing systems operating in a data center. Concepts from approximation theory are used to reduce the computational burden of controlling such large-scale systems. The relevant approximations are made in the construction of the dynamical models to predict system behavior and in the solution of the associated control equations. Using a dynamic resource-provisioning problem as a case study, we show that a computing system managed by the proposed control framework with approximation models realizes profit gains that are, in the best case, within 1% of a controller using an explicit model of the system.
An extension of the TV-HLL scheme for multi-dimensional compressible flows
NASA Astrophysics Data System (ADS)
Tiam Kapen, Pascalin; Tchuen, Ghislain
2015-03-01
This paper investigates a very simple method to numerically approximate the solution of the multi-dimensional Riemann problem for gas dynamics, using the literal extension of the Toro Vazquez-Harten Lax Leer (TV-HLL) scheme as its basis. Indeed, the present scheme is obtained by following the Toro-Vazquez splitting, and using the HLL algorithm with modified wave speeds for the pressure system. An essential feature of the TV-HLL scheme is its simplicity and its accuracy in computing multi-dimensional flows. The proposed scheme is carefully designed to simplify its eventual numerical implementation. It has been applied to numerical tests and its performances are demonstrated for some two-dimensional and three-dimensional test problems.
Approximating a nonlinear MTFDE from physiology
NASA Astrophysics Data System (ADS)
Teodoro, M. Filomena
2016-12-01
This paper describes a numerical scheme which approximates the solution of a nonlinear mixed type functional differential equation from nerve conduction theory. The solution of such equation is defined in all the entire real axis and tends to known values at ±∞. A numerical method extended from linear case is developed and applied to solve a nonlinear equation.
Yamada, Atsushi; Kojima, Hidekazu; Okazaki, Susumu
2014-08-28
In order to investigate proton transfer reaction in solution, mixed quantum-classical molecular dynamics calculations have been carried out based on our previously proposed quantum equation of motion for the reacting system [A. Yamada and S. Okazaki, J. Chem. Phys. 128, 044507 (2008)]. Surface hopping method was applied to describe forces acting on the solvent classical degrees of freedom. In a series of our studies, quantum and solvent effects on the reaction dynamics in solutions have been analysed in detail. Here, we report our mixed quantum-classical molecular dynamics calculations for intramolecular proton transfer of malonaldehyde in water. Thermally activated proton transfer process, i.e., vibrational excitation in the reactant state followed by transition to the product state and vibrational relaxation in the product state, as well as tunneling reaction can be described by solving the equation of motion. Zero point energy is, of course, included, too. The quantum simulation in water has been compared with the fully classical one and the wave packet calculation in vacuum. The calculated quantum reaction rate in water was 0.70 ps(-1), which is about 2.5 times faster than that in vacuum, 0.27 ps(-1). This indicates that the solvent water accelerates the reaction. Further, the quantum calculation resulted in the reaction rate about 2 times faster than the fully classical calculation, which indicates that quantum effect enhances the reaction rate, too. Contribution from three reaction mechanisms, i.e., tunneling, thermal activation, and barrier vanishing reactions, is 33:46:21 in the mixed quantum-classical calculations. This clearly shows that the tunneling effect is important in the reaction.
Yamada, Atsushi; Kojima, Hidekazu; Okazaki, Susumu
2014-08-28
In order to investigate proton transfer reaction in solution, mixed quantum-classical molecular dynamics calculations have been carried out based on our previously proposed quantum equation of motion for the reacting system [A. Yamada and S. Okazaki, J. Chem. Phys. 128, 044507 (2008)]. Surface hopping method was applied to describe forces acting on the solvent classical degrees of freedom. In a series of our studies, quantum and solvent effects on the reaction dynamics in solutions have been analysed in detail. Here, we report our mixed quantum-classical molecular dynamics calculations for intramolecular proton transfer of malonaldehyde in water. Thermally activated proton transfer process, i.e., vibrational excitation in the reactant state followed by transition to the product state and vibrational relaxation in the product state, as well as tunneling reaction can be described by solving the equation of motion. Zero point energy is, of course, included, too. The quantum simulation in water has been compared with the fully classical one and the wave packet calculation in vacuum. The calculated quantum reaction rate in water was 0.70 ps{sup −1}, which is about 2.5 times faster than that in vacuum, 0.27 ps{sup −1}. This indicates that the solvent water accelerates the reaction. Further, the quantum calculation resulted in the reaction rate about 2 times faster than the fully classical calculation, which indicates that quantum effect enhances the reaction rate, too. Contribution from three reaction mechanisms, i.e., tunneling, thermal activation, and barrier vanishing reactions, is 33:46:21 in the mixed quantum-classical calculations. This clearly shows that the tunneling effect is important in the reaction.
Sayyar-Rodsari, Bijan; Schweiger, Carl; Hartman, Eric
2007-10-07
The difficult problems being tackled in the accelerator community are those that are nonlinear, substantially unmodeled, and vary over time. Such problems are ideal candidates for model-based optimization and control if representative models of the problem can be developed that capture the necessary mathematical relations and remain valid throughout the operation region of the system, and through variations in system dynamics. The goal of this proposal is to develop the methodology and the algorithms for building high-fidelity mathematical representations of complex nonlinear systems via constrained training of combined first-principles and neural network models.
NASA Astrophysics Data System (ADS)
Niiniluoto, Ilkka
2014-03-01
Approximation of laws is an important theme in the philosophy of science. If we can make sense of the idea that two scientific laws are "close" to each other, then we can also analyze such methodological notions as approximate explanation of laws, approximate reduction of theories, approximate empirical success of theories, and approximate truth of laws. Proposals for measuring the distance between quantitative scientific laws were given in Niiniluoto (1982, 1987). In this paper, these definitions are reconsidered as a response to the interesting critical remarks by Liu (1999).
Approximating random quantum optimization problems
NASA Astrophysics Data System (ADS)
Hsu, B.; Laumann, C. R.; Läuchli, A. M.; Moessner, R.; Sondhi, S. L.
2013-06-01
We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem k-body quantum satisfiability (k-QSAT) on large random graphs. As an approximation strategy, we optimize the solution space over “classical” product states, which in turn introduces a novel autonomous classical optimization problem, PSAT, over a space of continuous degrees of freedom rather than discrete bits. Our central results are (i) the derivation of a set of bounds and approximations in various limits of the problem, several of which we believe may be amenable to a rigorous treatment; (ii) a demonstration that an approximation based on a greedy algorithm borrowed from the study of frustrated magnetism performs well over a wide range in parameter space, and its performance reflects the structure of the solution space of random k-QSAT. Simulated annealing exhibits metastability in similar “hard” regions of parameter space; and (iii) a generalization of belief propagation algorithms introduced for classical problems to the case of continuous spins. This yields both approximate solutions, as well as insights into the free energy “landscape” of the approximation problem, including a so-called dynamical transition near the satisfiability threshold. Taken together, these results allow us to elucidate the phase diagram of random k-QSAT in a two-dimensional energy-density-clause-density space.
Guarendi, Andrew N; Chandy, Abhilash J
2013-01-01
We extend a family of high-resolution, semidiscrete central schemes for hyperbolic systems of conservation laws to three-space dimensions. Details of the schemes, their implementation, and properties are presented together with results from several prototypical applications of hyperbolic conservation laws including a nonlinear scalar equation, the Euler equations of gas dynamics, and the ideal magnetohydrodynamic equations. Parallel scaling analysis and grid-independent results including contours and isosurfaces of density and velocity and magnetic field vectors are shown in this study, confirming the ability of these types of solvers to approximate the solutions of hyperbolic equations efficiently and accurately.
Approximate Counting of Graphical Realizations.
Erdős, Péter L; Kiss, Sándor Z; Miklós, István; Soukup, Lajos
2015-01-01
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erdős and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erdős and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations.
Approximate Counting of Graphical Realizations
2015-01-01
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erdős and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erdős and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations. PMID:26161994
Approximate reasoning using terminological models
NASA Technical Reports Server (NTRS)
Yen, John; Vaidya, Nitin
1992-01-01
Term Subsumption Systems (TSS) form a knowledge-representation scheme in AI that can express the defining characteristics of concepts through a formal language that has a well-defined semantics and incorporates a reasoning mechanism that can deduce whether one concept subsumes another. However, TSS's have very limited ability to deal with the issue of uncertainty in knowledge bases. The objective of this research is to address issues in combining approximate reasoning with term subsumption systems. To do this, we have extended an existing AI architecture (CLASP) that is built on the top of a term subsumption system (LOOM). First, the assertional component of LOOM has been extended for asserting and representing uncertain propositions. Second, we have extended the pattern matcher of CLASP for plausible rule-based inferences. Third, an approximate reasoning model has been added to facilitate various kinds of approximate reasoning. And finally, the issue of inconsistency in truth values due to inheritance is addressed using justification of those values. This architecture enhances the reasoning capabilities of expert systems by providing support for reasoning under uncertainty using knowledge captured in TSS. Also, as definitional knowledge is explicit and separate from heuristic knowledge for plausible inferences, the maintainability of expert systems could be improved.
NASA Technical Reports Server (NTRS)
Jameson, Antony
1994-01-01
The theory of non-oscillatory scalar schemes is developed in this paper in terms of the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. This principle can be used for multi-dimensional problems on both structured and unstructured meshes, while it is equivalent to the total variation diminishing (TVD) principle for one-dimensional problems. A new formulation of symmetric limited positive (SLIP) schemes is presented, which can be generalized to produce schemes with arbitrary high order of accuracy in regions where the solution contains no extrema, and which can also be implemented on multi-dimensional unstructured meshes. Systems of equations lead to waves traveling with distinct speeds and possibly in opposite directions. Alternative treatments using characteristic splitting and scalar diffusive fluxes are examined, together with modification of the scalar diffusion through the addition of pressure differences to the momentum equations to produce full upwinding in supersonic flow. This convective upwind and split pressure (CUSP) scheme exhibits very rapid convergence in multigrid calculations of transonic flow, and provides excellent shock resolution at very high Mach numbers.
NASA Technical Reports Server (NTRS)
Dutta, Soumitra
1988-01-01
A model for approximate spatial reasoning using fuzzy logic to represent the uncertainty in the environment is presented. Algorithms are developed which can be used to reason about spatial information expressed in the form of approximate linguistic descriptions similar to the kind of spatial information processed by humans. Particular attention is given to static spatial reasoning.
NASA Astrophysics Data System (ADS)
Barry, D. A.; Parlange, J.-Y.; Li, L.; Jeng, D.-S.; Crapper, M.
2005-10-01
The solution to the Green and Ampt infiltration equation is expressible in terms of the Lambert W-1 function. Approximations for Green and Ampt infiltration are thus derivable from approximations for the W-1 function and vice versa. An infinite family of asymptotic expansions to W-1 is presented. Although these expansions do not converge near the branch point of the W function (corresponds to Green-Ampt infiltration with immediate ponding), a method is presented for approximating W-1 that is exact at the branch point and asymptotically, with interpolation between these limits. Some existing and several new simple and compact yet robust approximations applicable to Green-Ampt infiltration and flux are presented, the most accurate of which has a maximum relative error of 5 × 10 -5%. This error is orders of magnitude lower than any existing analytical approximations.
Development of an establishment scheme for a DGVM
NASA Astrophysics Data System (ADS)
Song, Xiang; Zeng, Xiaodong; Zhu, Jiawen; Shao, Pu
2016-07-01
Environmental changes are expected to shift the distribution and abundance of vegetation by determining seedling establishment and success. However, most current ecosystem models only focus on the impacts of abiotic factors on biogeophysics (e.g., global distribution, etc.), ignoring their roles in the population dynamics (e.g., seedling establishment rate, mortality rate, etc.) of ecological communities. Such neglect may lead to biases in ecosystem population dynamics (such as changes in population density for woody species in forest ecosystems) and characteristics. In the present study, a new establishment scheme for introducing soil water as a function rather than a threshold was developed and validated, using version 1.0 of the IAP-DGVM as a test bed. The results showed that soil water in the establishment scheme had a remarkable influence on forest transition zones. Compared with the original scheme, the new scheme significantly improved simulations of tree population density, especially in the peripheral areas of forests and transition zones. Consequently, biases in forest fractional coverage were reduced in approximately 78.8% of the global grid cells. The global simulated areas of tree, shrub, grass and bare soil performed better, where the relative biases were reduced from 34.3% to 4.8%, from 27.6% to 13.1%, from 55.2% to 9.2%, and from 37.6% to 3.6%, respectively. Furthermore, the new scheme had more reasonable dependencies of plant functional types (PFTs) on mean annual precipitation, and described the correct dominant PFTs in the tropical rainforest peripheral areas of the Amazon and central Africa.
A family of high-order targeted ENO schemes for compressible-fluid simulations
NASA Astrophysics Data System (ADS)
Fu, Lin; Hu, Xiangyu Y.; Adams, Nikolaus A.
2016-01-01
Although classical WENO schemes have achieved great success and are widely accepted, they exhibit several shortcomings. They are too dissipative for direct simulations of turbulence and lack robustness when very-high-order versions are applied to complex flows. In this paper, we propose a family of high-order targeted ENO schemes which are applicable for compressible-fluid simulations involving a wide range of flow scales. In order to increase the numerical robustness as compared to very-high-order classical WENO schemes, the reconstruction dynamically assembles a set of low-order candidate stencils with incrementally increasing width. While discontinuities and small-scale fluctuations are efficiently separated, the numerical dissipation is significantly diminished by an ENO-like stencil selection, which either applies a candidate stencil with its original linear weight, or removes its contribution when it is crossed by a discontinuity. The background linear scheme is optimized under the constraint of preserving an approximate dispersion-dissipation relation. By means of quasi-linear analyses and practical numerical experiments, a set of case-independent parameters is determined. The general formulation of arbitrarily high-order schemes is presented in a straightforward way. A variety of benchmark-test problems, including broadband waves, strong shock and contact discontinuities are studied. Compared to well-established classical WENO schemes, the present schemes exhibit significantly improved robustness, low numerical dissipation and sharp discontinuity capturing. They are particularly suitable for DNS and LES of shock-turbulence interactions.
NASA Astrophysics Data System (ADS)
Guo, Yan; Xiong, Tao; Shi, Yufeng
2014-10-01
In this paper, a positivity-preserving fifth-order finite volume compact-WENO scheme is proposed for solving compressible Euler equations. As it is known, conservative compact finite volume schemes have high resolution properties while WENO (Weighted Essentially Non-Oscillatory) schemes are essentially non-oscillatory near flow discontinuities. We extend the idea of WENO schemes to some classical finite volume compact schemes [30], where lower order compact stencils are combined with WENO nonlinear weights to get a higher order finite volume compact-WENO scheme. The newly developed positivity-preserving limiter [43,42] is used to preserve positive density and internal energy for compressible Euler equations of fluid dynamics. The HLLC (Harten, Lax, and van Leer with Contact) approximate Riemann solver [37,4] is used to get the numerical flux at the cell interfaces. Numerical tests are presented to demonstrate the high-order accuracy, positivity-preserving, high-resolution and robustness of the proposed scheme.
Approximating maximum clique with a Hopfield network.
Jagota, A
1995-01-01
In a graph, a clique is a set of vertices such that every pair is connected by an edge. MAX-CLIQUE is the optimization problem of finding the largest clique in a given graph and is NP-hard, even to approximate well. Several real-world and theory problems can be modeled as MAX-CLIQUE. In this paper, we efficiently approximate MAX-CLIQUE in a special case of the Hopfield network whose stable states are maximal cliques. We present several energy-descent optimizing dynamics; both discrete (deterministic and stochastic) and continuous. One of these emulates, as special cases, two well-known greedy algorithms for approximating MAX-CLIQUE. We report on detailed empirical comparisons on random graphs and on harder ones. Mean-field annealing, an efficient approximation to simulated annealing, and a stochastic dynamics are the narrow but clear winners. All dynamics approximate much better than one which emulates a "naive" greedy heuristic.
Liu, Tianhui; Fu, Bina E-mail: zhangdh@dicp.ac.cn; Zhang, Dong H. E-mail: zhangdh@dicp.ac.cn
2014-11-21
A new finding of the site-averaging approximation was recently reported on the dissociative chemisorption of the HCl/DCl+Au(111) surface reaction [T. Liu, B. Fu, and D. H. Zhang, J. Chem. Phys. 139, 184705 (2013); T. Liu, B. Fu, and D. H. Zhang, J. Chem. Phys. 140, 144701 (2014)]. Here, in order to investigate the dependence of new site-averaging approximation on the initial vibrational state of H{sub 2} as well as the PES for the dissociative chemisorption of H{sub 2} on Cu(111) surface at normal incidence, we carried out six-dimensional quantum dynamics calculations using the initial state-selected time-dependent wave packet approach, with H{sub 2} initially in its ground vibrational state and the first vibrational excited state. The corresponding four-dimensional site-specific dissociation probabilities are also calculated with H{sub 2} fixed at bridge, center, and top sites. These calculations are all performed based on two different potential energy surfaces (PESs). It is found that the site-averaging dissociation probability over 15 fixed sites obtained from four-dimensional quantum dynamics calculations can accurately reproduce the six-dimensional dissociation probability for H{sub 2} (v = 0) and (v = 1) on the two PESs.
NASA Astrophysics Data System (ADS)
Massina, Christopher James
The feasibility of conducting long duration human spaceflight missions is largely dependent on the provision of consumables such as oxygen, water, and food. In addition to meeting crew metabolic needs, water sublimation has long served as the primary heat rejection mechanism in space suits during extravehicular activity (EVA). During a single eight hour EVA, approximately 3.6 kg (8 lbm) of water is lost from the current suit. Reducing the amount of expended water during EVA is a long standing goal of space suit life support systems designers; but to date, no alternate thermal control mechanism has demonstrated the ability to completely eliminate the loss. One proposed concept is to convert the majority of a space suit's surface area into a radiator such that the local environment can be used as a radiative thermal sink for rejecting heat without mass loss. Due to natural variations in both internal (metabolic) loads and external (environmental) sink temperatures, radiative transport must be actively modulated in order to maintain an acceptable thermal balance. Here, variable emissivity electrochromic devices are examined as the primary mechanism for enabling variable heat rejection. This dissertation focuses on theoretical and empirical evaluations performed to determine the feasibility of using a full suit, variable emissivity radiator architecture for space suit thermal control. Operational envelopes are described that show where a given environment and/or metabolic load combination may or may not be supported by the evaluated thermal architecture. Key integration considerations and guidelines include determining allowable thermal environments, defining skin-to-radiator heat transfer properties, and evaluating required electrochromic performance properties. Analysis also considered the impacts of dynamic environmental changes and the architecture's extensibility to EVA on the Martian surface. At the conclusion of this work, the full suit, variable emissivity
On Convergence of High Order Shock Capturing Difference Schemes
NASA Astrophysics Data System (ADS)
Ostapenko, V.
2010-11-01
A convergence of high order shock capturing difference schemes is analyzed. Notions of weak finite difference approximations which conserve a sense on discontinuous solutions are introduced. Necessary and sufficient conditions of these approximations are obtained. It is shown that among the explicit two-layer in time conservative difference schemes there are no schemes which can have high order of weak approximation. A compact scheme of the same third order of classical and weak approximations is constructed. There is demonstrated an advantage of this scheme in comparison to TVD scheme at shock-capturing computations. A difference approximation of ɛ Rankine-Hugoniot (RH) conditions is investigated. It is shown that TVD type schemes (in contrast to non-TVD schemes, whose numerical fluxes are smooth enough) can approximate ɛ RH-conditions at most with the first order. Given examples show that non-TVD schemes (in contrast to TVD schemes) can have the second order of integral convergence through the smearing shocks and as a result can conserve a higher accuracy in the post shock regions.
Dispersion-relation-preserving schemes for computational aeroacoustics
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.; Webb, Jay C.
1992-01-01
Finite difference schemes that have the same dispersion relations as the original partial differential equations are referred to as dispersion-relation-preserving (DRP) schemes. A method to construct time marching DRP schemes by optimizing the finite difference approximations of the space and time derivatives in the wave number and frequency space is presented. A sequence of numerical simulations is then performed.
Approximate methods for equations of incompressible fluid
NASA Astrophysics Data System (ADS)
Galkin, V. A.; Dubovik, A. O.; Epifanov, A. A.
2017-02-01
Approximate methods on the basis of sequential approximations in the theory of functional solutions to systems of conservation laws is considered, including the model of dynamics of incompressible fluid. Test calculations are performed, and a comparison with exact solutions is carried out.
The JWKB approximation in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Craig, David; Singh, Parampreet
2017-01-01
We explore the JWKB approximation in loop quantum cosmology in a flat universe with a scalar matter source. Exact solutions of the quantum constraint are studied at small volume in the JWKB approximation in order to assess the probability of tunneling to small or zero volume. Novel features of the approximation are discussed which appear due to the fact that the model is effectively a two-dimensional dynamical system. Based on collaborative work with Parampreet Singh.
Intrinsic Nilpotent Approximation.
1985-06-01
RD-A1II58 265 INTRINSIC NILPOTENT APPROXIMATION(U) MASSACHUSETTS INST 1/2 OF TECH CAMBRIDGE LAB FOR INFORMATION AND, DECISION UMCLRSSI SYSTEMS C...TYPE OF REPORT & PERIOD COVERED Intrinsic Nilpotent Approximation Technical Report 6. PERFORMING ORG. REPORT NUMBER LIDS-R-1482 7. AUTHOR(.) S...certain infinite-dimensional filtered Lie algebras L by (finite-dimensional) graded nilpotent Lie algebras or g . where x E M, (x,,Z) E T*M/O. It
Anomalous diffraction approximation limits
NASA Astrophysics Data System (ADS)
Videen, Gorden; Chýlek, Petr
It has been reported in a recent article [Liu, C., Jonas, P.R., Saunders, C.P.R., 1996. Accuracy of the anomalous diffraction approximation to light scattering by column-like ice crystals. Atmos. Res., 41, pp. 63-69] that the anomalous diffraction approximation (ADA) accuracy does not depend on particle refractive index, but instead is dependent on the particle size parameter. Since this is at odds with previous research, we thought these results warranted further discussion.
Stable Difference Schemes for the Neutron Transport Equation
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Taskin, Abdulgafur
2011-09-01
The initial boundary value problem for the neutron transport equation is considered. The first and second orders of accuracy difference schemes for the approximate solution of this problem are presented. In applications, the stability estimates for solutions of difference schemes for the approximate solution of the neutron transport equation are obtained. Numerical techniques are developed and algorithms are tested on an example in MATLAB.
Practical formulation of a positively conservative scheme
NASA Astrophysics Data System (ADS)
Obayashi, Shigeru; Wada, Yasuhiro
1994-05-01
Approximate Riemann solvers have been highly successful for computing the Euler/Navier-Stokes equations, but linearized Riemann solvers are known to fail occasionally by predicting non-physical states with negative density or internal energy. Positively conservative schemes, in contrast, guarantee physical solutions from realistic input. The Harten-Lax-van Leer-Einfeldt (HLLE) scheme is a typical example of a positively conservative scheme. However, the HLLE scheme is highly dissipative at contact discontinuities and shear layers and thus it is not applicable to practicle simulations. An existing modification to the HLLE scheme, known as HLLEM, enhances the resolution to that of the Roe scheme. However, this modification violates the positivity of density and internal energy. Precise derivation of the modification yields a quatratic inequality and thus requires a case-by-case treatment. This Note describes a new, modified HLLE scheme that satisfies the positively conservative condition approximately. Sample computationa are included to demonstrate the resolution and the robustness of the scheme.
Practical formulation of a positively conservative scheme
NASA Technical Reports Server (NTRS)
Obayashi, Shigeru; Wada, Yasuhiro
1994-01-01
Approximate Riemann solvers have been highly successful for computing the Euler/Navier-Stokes equations, but linearized Riemann solvers are known to fail occasionally by predicting non-physical states with negative density or internal energy. Positively conservative schemes, in contrast, guarantee physical solutions from realistic input. The Harten-Lax-van Leer-Einfeldt (HLLE) scheme is a typical example of a positively conservative scheme. However, the HLLE scheme is highly dissipative at contact discontinuities and shear layers and thus it is not applicable to practicle simulations. An existing modification to the HLLE scheme, known as HLLEM, enhances the resolution to that of the Roe scheme. However, this modification violates the positivity of density and internal energy. Precise derivation of the modification yields a quatratic inequality and thus requires a case-by-case treatment. This Note describes a new, modified HLLE scheme that satisfies the positively conservative condition approximately. Sample computationa are included to demonstrate the resolution and the robustness of the scheme.
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches.
A least squares closure approximation for liquid crystalline polymers
NASA Astrophysics Data System (ADS)
Sievenpiper, Traci Ann
2011-12-01
An introduction to existing closure schemes for the Doi-Hess kinetic theory of liquid crystalline polymers is provided. A new closure scheme is devised based on a least squares fit of a linear combination of the Doi, Tsuji-Rey, Hinch-Leal I, and Hinch-Leal II closure schemes. The orientation tensor and rate-of-strain tensor are fit separately using data generated from the kinetic solution of the Smoluchowski equation. The known behavior of the kinetic solution and existing closure schemes at equilibrium is compared with that of the new closure scheme. The performance of the proposed closure scheme in simple shear flow for a variety of shear rates and nematic polymer concentrations is examined, along with that of the four selected existing closure schemes. The flow phase diagram for the proposed closure scheme under the conditions of shear flow is constructed and compared with that of the kinetic solution. The study of the closure scheme is extended to the simulation of nematic polymers in plane Couette cells. The results are compared with existing kinetic simulations for a Landau-deGennes mesoscopic model with the application of a parameterized closure approximation. The proposed closure scheme is shown to produce a reasonable approximation to the kinetic results in the case of simple shear flow and plane Couette flow.
NASA Technical Reports Server (NTRS)
Banks, H. T.; Kunisch, K.
1982-01-01
Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.
Congruence Approximations for Entrophy Endowed Hyperbolic Systems
NASA Technical Reports Server (NTRS)
Barth, Timothy J.; Saini, Subhash (Technical Monitor)
1998-01-01
Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.
Approximate Dynamic Programming and Aerial Refueling
2007-06-01
were values derived from “AFPAM 10-1403, AIR MOBILITY PLANNING FACTORS” used by the US Air Force when making gross calculations of aerial refueling...Aerial Refueling. U.S. Centennial of Flight Commision. centennialofflight.gov/essay/EvolutionofT echnology /refueling?Tech22.htm. 20003. 5 [6] DOD Needs
Approximate Dynamic Programming for Military Resource Allocation
2014-12-26
UNLIMITED The views expressed in this thesis are those of the author and do not reflect the official policy or position of the United States Air... auction algo- rithm in a greedy fashion to an exact (but computationally expensive) branching and bounding technique. Sahin and Leblebicioglu [62] apply...network architectures. Brown et al. [18] apply a two-sided model to determine the optimal location to pre- position defensive platforms with the objective
NASA Astrophysics Data System (ADS)
Hamel, Sarah; Boulkroune, Abdesselem
2016-08-01
In this paper, a modified generalized function projective synchronization scheme for a class of master-slave chaotic systems subject to dynamic disturbances and input nonlinearities (dead-zone and sector nonlinearities) is investigated. This synchronization system can be seen as a generalization of many existing projective synchronization schemes (namely the function projective synchronization, the modified projective synchronization and so on), in the sense that the master system has a scaling function matrix and the slave system has a scaling factor matrix. To practically achieve this generalized function synchronization, an adaptive fuzzy variable-structure control system is designed. The fuzzy systems are used to appropriately approximate the uncertain nonlinear functions. A Lyapunov approach is employed to prove the boundedness of all signals of the closed-loop control system as well as the exponential convergence of the synchronization errors to an adjustable region. Simulations results are presented to illustrate the effectiveness of the proposed generalized function PS scheme.
Multicriteria approximation through decomposition
Burch, C.; Krumke, S.; Marathe, M.; Phillips, C.; Sundberg, E.
1998-06-01
The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of their technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. Their method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) the authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing; (2) they also show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.
Multicriteria approximation through decomposition
Burch, C. |; Krumke, S.; Marathe, M.; Phillips, C.; Sundberg, E. |
1997-12-01
The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of the technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. The method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) The authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing. (2) They show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.
ERIC Educational Resources Information Center
Wolff, Hans
This paper deals with a stochastic process for the approximation of the root of a regression equation. This process was first suggested by Robbins and Monro. The main result here is a necessary and sufficient condition on the iteration coefficients for convergence of the process (convergence with probability one and convergence in the quadratic…
Approximating Integrals Using Probability
ERIC Educational Resources Information Center
Maruszewski, Richard F., Jr.; Caudle, Kyle A.
2005-01-01
As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…
A diagonally inverted LU implicit multigrid scheme
NASA Technical Reports Server (NTRS)
Yokota, Jeffrey W.; Caughey, David A.; Chima, Rodrick V.
1988-01-01
A new Diagonally Inverted LU Implicit scheme is developed within the framework of the multigrid method for the 3-D unsteady Euler equations. The matrix systems that are to be inverted in the LU scheme are treated by local diagonalizing transformations that decouple them into systems of scalar equations. Unlike the Diagonalized ADI method, the time accuracy of the LU scheme is not reduced since the diagonalization procedure does not destroy time conservation. Even more importantly, this diagonalization significantly reduces the computational effort required to solve the LU approximation and therefore transforms it into a more efficient method of numerically solving the 3-D Euler equations.
Galilean invariant resummation schemes of cosmological perturbations
NASA Astrophysics Data System (ADS)
Peloso, Marco; Pietroni, Massimo
2017-01-01
Many of the methods proposed so far to go beyond Standard Perturbation Theory break invariance under time-dependent boosts (denoted here as extended Galilean Invariance, or GI). This gives rise to spurious large scale effects which spoil the small scale predictions of these approximation schemes. By using consistency relations we derive fully non-perturbative constraints that GI imposes on correlation functions. We then introduce a method to quantify the amount of GI breaking of a given scheme, and to correct it by properly tailored counterterms. Finally, we formulate resummation schemes which are manifestly GI, discuss their general features, and implement them in the so called Time-Flow, or TRG, equations.
NASA Astrophysics Data System (ADS)
Ohta, Ayumi; Kobayashi, Osamu; Danielache, Sebastian O.; Nanbu, Shinkoh
2017-03-01
The ultra-fast photoisomerization reactions between 1,3-cyclohexadiene (CHD) and 1,3,5-cis-hexatriene (HT) in both hexane and ethanol solvents were revealed by nonadiabatic ab initio molecular dynamics (AI-MD) with a particle-mesh Ewald summation method and our Own N-layered Integrated molecular Orbital and molecular Mechanics model (PME-ONIOM) scheme. Zhu-Nakamura version trajectory surface hopping method (ZN-TSH) was employed to treat the ultra-fast nonadiabatic decaying process. The results for hexane and ethanol simulations reasonably agree with experimental data. The high nonpolar-nonpolar affinity between CHD and the solvent was observed in hexane solvent, which definitely affected the excited state lifetimes, the product branching ratio of CHD:HT, and solute (CHD) dynamics. In ethanol solvent, however, the CHD solute was isomerized in the solvent cage caused by the first solvation shell. The photochemical dynamics in ethanol solvent results in the similar property to the process appeared in vacuo (isolated CHD dynamics).
Optimizing the Zeldovich approximation
NASA Technical Reports Server (NTRS)
Melott, Adrian L.; Pellman, Todd F.; Shandarin, Sergei F.
1994-01-01
We have recently learned that the Zeldovich approximation can be successfully used for a far wider range of gravitational instability scenarios than formerly proposed; we study here how to extend this range. In previous work (Coles, Melott and Shandarin 1993, hereafter CMS) we studied the accuracy of several analytic approximations to gravitational clustering in the mildly nonlinear regime. We found that what we called the 'truncated Zeldovich approximation' (TZA) was better than any other (except in one case the ordinary Zeldovich approximation) over a wide range from linear to mildly nonlinear (sigma approximately 3) regimes. TZA was specified by setting Fourier amplitudes equal to zero for all wavenumbers greater than k(sub nl), where k(sub nl) marks the transition to the nonlinear regime. Here, we study the cross correlation of generalized TZA with a group of n-body simulations for three shapes of window function: sharp k-truncation (as in CMS), a tophat in coordinate space, or a Gaussian. We also study the variation in the crosscorrelation as a function of initial truncation scale within each type. We find that k-truncation, which was so much better than other things tried in CMS, is the worst of these three window shapes. We find that a Gaussian window e(exp(-k(exp 2)/2k(exp 2, sub G))) applied to the initial Fourier amplitudes is the best choice. It produces a greatly improved crosscorrelation in those cases which most needed improvement, e.g. those with more small-scale power in the initial conditions. The optimum choice of kG for the Gaussian window is (a somewhat spectrum-dependent) 1 to 1.5 times k(sub nl). Although all three windows produce similar power spectra and density distribution functions after application of the Zeldovich approximation, the agreement of the phases of the Fourier components with the n-body simulation is better for the Gaussian window. We therefore ascribe the success of the best-choice Gaussian window to its superior treatment
A Trade-off Traitor Tracing Scheme
NASA Astrophysics Data System (ADS)
Ohtake, Go; Ogawa, Kazuto; Hanaoka, Goichiro; Imai, Hideki
There has been a wide-ranging discussion on the issue of content copyright protection in digital content distribution systems. Fiat and Tassa proposed the framework of dynamic traitor tracing. Their framework requires dynamic computation transactions according to the real-time responses of the pirate, and it presumes real-time observation of content redistribution. Therefore, it cannot be simply utilized in an application where such an assumption is not valid. In this paper, we propose a new scheme that provides the advantages of dynamic traitor tracing schemes and also overcomes their problems.
NASA Technical Reports Server (NTRS)
Merrill, W. C.
1978-01-01
The Routh approximation technique for reducing the complexity of system models was applied in the frequency domain to a 16th order, state variable model of the F100 engine and to a 43d order, transfer function model of a launch vehicle boost pump pressure regulator. The results motivate extending the frequency domain formulation of the Routh method to the time domain in order to handle the state variable formulation directly. The time domain formulation was derived and a characterization that specifies all possible Routh similarity transformations was given. The characterization was computed by solving two eigenvalue-eigenvector problems. The application of the time domain Routh technique to the state variable engine model is described, and some results are given. Additional computational problems are discussed, including an optimization procedure that can improve the approximation accuracy by taking advantage of the transformation characterization.
Topics in Metric Approximation
NASA Astrophysics Data System (ADS)
Leeb, William Edward
This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.
NASA Astrophysics Data System (ADS)
Li, Yongbo; Yang, Yuantao; Li, Guoyan; Xu, Minqiang; Huang, Wenhu
2017-07-01
Health condition identification of planetary gearboxes is crucial to reduce the downtime and maximize productivity. This paper aims to develop a novel fault diagnosis method based on modified multi-scale symbolic dynamic entropy (MMSDE) and minimum redundancy maximum relevance (mRMR) to identify the different health conditions of planetary gearbox. MMSDE is proposed to quantify the regularity of time series, which can assess the dynamical characteristics over a range of scales. MMSDE has obvious advantages in the detection of dynamical changes and computation efficiency. Then, the mRMR approach is introduced to refine the fault features. Lastly, the obtained new features are fed into the least square support vector machine (LSSVM) to complete the fault pattern identification. The proposed method is numerically and experimentally demonstrated to be able to recognize the different fault types of planetary gearboxes.
2011-10-01
hypotenuse of the black right triangle indicates the approximate location of the ocean surface. 654 W E A T H E R A N D F O R E C A S T I N G VOLUME 26...become a category 4 hurricane with maximum sustained winds of 115 kt at 0600 UTC 19 August. After passing approxi- mately 125 n mi west of Bermuda , Bill
Eno-Osher schemes for Euler equations
NASA Technical Reports Server (NTRS)
Vandervegt, Jacobus J.
1992-01-01
The combination of the Osher approximate Riemann solver for the Euler equations and various ENO schemes is discussed for one-dimensional flow. The three basic approaches, viz. the ENO scheme using primitive variable reconstruction, either with Cauchy-Kowalewski procedure for time integration or the TVD Runge-Kutta scheme, and the flux-ENO method are tested on different shock tube cases. The shock tube cases were chosen to present a serious challenge to the ENO schemes in order to test their ability to capture flow discontinuities, such as shocks. Also the effect of the ordering of the eigen values, viz. natural or reversed ordering, in the Osher scheme is investigated. The ENO schemes are tested up to fifth order accuracy in space and time. The ENO-Osher scheme using the Cauchy-Kowalewski procedure for time integration is found to be the most accurate and robust compared with the other methods and is also computationally efficient. The tests showed that the ENO schemes perform reasonably well, but have problems in cases where two discontinuities are close together. In that case there are not enough points in the smooth part of the flow to create a non-oscillatory interpolation.
An adaptive additive inflation scheme for Ensemble Kalman Filters
NASA Astrophysics Data System (ADS)
Sommer, Matthias; Janjic, Tijana
2016-04-01
Data assimilation for atmospheric dynamics requires an accurate estimate for the uncertainty of the forecast in order to obtain an optimal combination with available observations. This uncertainty has two components, firstly the uncertainty which originates in the the initial condition of that forecast itself and secondly the error of the numerical model used. While the former can be approximated quite successfully with an ensemble of forecasts (an additional sampling error will occur), little is known about the latter. For ensemble data assimilation, ad-hoc methods to address model error include multiplicative and additive inflation schemes, possibly also flow-dependent. The additive schemes rely on samples for the model error e.g. from short-term forecast tendencies or differences of forecasts with varying resolutions. However since these methods work in ensemble space (i.e. act directly on the ensemble perturbations) the sampling error is fixed and can be expected to affect the skill substiantially. In this contribution we show how inflation can be generalized to take into account more degrees of freedom and what improvements for future operational ensemble data assimilation can be expected from this, also in comparison with other inflation schemes.
Separable approximations of two-body interactions
NASA Astrophysics Data System (ADS)
Haidenbauer, J.; Plessas, W.
1983-01-01
We perform a critical discussion of the efficiency of the Ernst-Shakin-Thaler method for a separable approximation of arbitrary two-body interactions by a careful examination of separable 3S1-3D1 N-N potentials that were constructed via this method by Pieper. Not only the on-shell properties of these potentials are considered, but also a comparison is made of their off-shell characteristics relative to the Reid soft-core potential. We point out a peculiarity in Pieper's application of the Ernst-Shakin-Thaler method, which leads to a resonant-like behavior of his potential 3SD1D. It is indicated where care has to be taken in order to circumvent drawbacks inherent in the Ernst-Shakin-Thaler separable approximation scheme. NUCLEAR REACTIONS Critical discussion of the Ernst-Shakin-Thaler separable approximation method. Pieper's separable N-N potentials examined on shell and off shell.
An adaptive critic-based scheme for consensus control of nonlinear multi-agent systems
NASA Astrophysics Data System (ADS)
Heydari, Ali; Balakrishnan, S. N.
2014-12-01
The problem of decentralised consensus control of a network of heterogeneous nonlinear systems is formulated as an optimal tracking problem and a solution is proposed using an approximate dynamic programming based neurocontroller. The neurocontroller training comprises an initial offline training phase and an online re-optimisation phase to account for the fact that the reference signal subject to tracking is not fully known and available ahead of time, i.e., during the offline training phase. As long as the dynamics of the agents are controllable, and the communication graph has a directed spanning tree, this scheme guarantees the synchronisation/consensus even under switching communication topology and directed communication graph. Finally, an aerospace application is selected for the evaluation of the performance of the method. Simulation results demonstrate the potential of the scheme.
Trefftz difference schemes on irregular stencils
Tsukerman, Igor
2010-04-20
The recently developed Flexible Local Approximation MEthod (FLAME) produces accurate difference schemes by replacing the usual Taylor expansion with Trefftz functions - local solutions of the underlying differential equation. This paper advances and casts in a general form a significant modification of FLAME proposed recently by Pinheiro and Webb: a least-squares fit instead of the exact match of the approximate solution at the stencil nodes. As a consequence of that, FLAME schemes can now be generated on irregular stencils with the number of nodes substantially greater than the number of approximating functions. The accuracy of the method is preserved but its robustness is improved. For demonstration, the paper presents a number of numerical examples in 2D and 3D: electrostatic (magnetostatic) particle interactions, scattering of electromagnetic (acoustic) waves, and wave propagation in a photonic crystal. The examples explore the role of the grid and stencil size, of the number of approximating functions, and of the irregularity of the stencils.
Tagawa, Toshio; Ozoe, Hiroyuki
1996-08-23
Numerical calculations were carried out for natural convection of low-Prandtl-number fluid. These calculations include the inertial terms that were approximated by six kinds of schemes, i.e., upwind scheme, hybrid scheme, second-order central difference method, Kawamura-Kuwahara scheme, Utopia scheme, and fourth-order central difference method. The average Nusselt number depended significantly on the schemes. The occurrence of oscillatory flow also depended on the schemes for inertial terms. Higher order up-winding approximations for inertial terms appear to be required to calculate natural convection of low-Prandtl-number fluids like liquid metal, even if the Rayleigh number is not large enough.
Ackleh, Azmy S; Ma, Baoling; Thibodeaux, Jeremy J
2013-09-01
We develop a second-order high-resolution finite difference scheme to approximate the solution of a mathematical model describing the within-host dynamics of malaria infection. The model consists of two nonlinear partial differential equations coupled with three nonlinear ordinary differential equations. Convergence of the numerical method to the unique weak solution with bounded total variation is proved. Numerical simulations demonstrating the achievement of the designed accuracy are presented.
NASA Astrophysics Data System (ADS)
Chalons, Christophe; Coquel, Frédéric
2017-04-01
We are interested in the numerical approximation of the discontinuous solutions of non-conservative hyperbolic systems. We more precisely consider a non-conservative formulation of the usual gas dynamics equations and show how to slightly modify the so-called Roe-type path-conservative schemes to properly capture the underlying shock discontinuities. Numerical evidences are proposed. The present note follows a first comment on the computation of non-conservative products in [1].
Chalasani, P.; Saias, I.; Jha, S.
1996-04-08
As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.
Approximate Qualitative Temporal Reasoning
2001-01-01
i.e., their boundaries can be placed in such a way that they coincide with the cell boundaries of the appropriate partition of the time-line. (Think of...respect to some appropriate partition of the time-line. For example, I felt well on Saturday. When I measured my temperature I had a fever on Monday and on...Bittner / Approximate Qualitative Temporal Reasoning 49 [27] I. A. Goralwalla, Y. Leontiev , M. T. Özsu, D. Szafron, and C. Combi. Temporal granularity for
NASA Technical Reports Server (NTRS)
Swanson, R. C.; Rossow, C.-C.
2008-01-01
A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.
Comparison of Neutrino Transport Approximations in Supernova Simulations
NASA Astrophysics Data System (ADS)
Richers, Sherwood; Ott, C. D.; O'Connor, E.
2013-01-01
We explore the qualitative and quantitative differences between supernova simulations with various neutrino transport approximation schemes. Post-bounce simulations are done in one dimension (with both Newtonian and general relativistic spacetimes) with a non-rotating 15 solar-mass progenitor and the nuclear equation of state with incompressibility 220 MeV of Lattimer & Swesty (1991). We test the neutrino approximations of a simple lightbulb heating and analytic cooling scheme (Murphy & Burrows 2008), the O'Connor & Ott (2010) neutrino leakage scheme, and a two-moment transport scheme with analytic closure (O'Connor and Ott 2012). As it is the most simplistic, the MB method shows evidence of qualitative and quantitative shortcomings that are not present in the M1 scheme. At comparable neutrino luminosities, the simulations incorporating the MB method explode easily while the M1 runs do not. At the input neutrino luminosity suggested by Murphy & Burrows (2008), the MB scheme results in much larger proto-neutron star radii than the M1 scheme. The leakage scheme agrees more closely with M1, though it predicts a smaller proto-neutron star radius, shock radius, and neutrino luminosity than M1.
Asynchronous Communication Scheme For Hypercube Computer
NASA Technical Reports Server (NTRS)
Madan, Herb S.
1988-01-01
Scheme devised for asynchronous-message communication system for Mark III hypercube concurrent-processor network. Network consists of up to 1,024 processing elements connected electrically as though were at corners of 10-dimensional cube. Each node contains two Motorola 68020 processors along with Motorola 68881 floating-point processor utilizing up to 4 megabytes of shared dynamic random-access memory. Scheme intended to support applications requiring passage of both polled or solicited and unsolicited messages.
Van Weverberg, K.; Van Lipzig, N. P. M.; Delobbe, L.
2011-04-01
In this research the impact of modifying the size distribution assumptions of the precipitating hydrometeors in a bulk one-moment microphysics scheme on simulated surface precipitation and storm dynamics has been explored for long-lived low-topped supercells in Belgium. It was shown that weighting the largest precipitating ice species of the microphysics scheme to small graupel results in an increase of surface precipitation because of counteracting effects. On the one hand, the precipitation formation process slowed down, resulting in lower precipitation efficiency. On the other hand, latent heat release associated with freezing favored more intense storms. In contrast to previous studies finding decreased surface precipitation when graupel was present in the microphysics parameterization, storms were rather shallow in the authors simulations. This left little time for graupel sublimation. The impact of size distribution assumptions of snow was found to be small, but more realistic size distribution assumptions of rain led to the strongest effect on surface precipitation. Cold pools shrunk because of weaker rain evaporation at the cold pool boundaries, leading to a decreased surface rain area.
Subranging scheme for SQUID sensors
NASA Technical Reports Server (NTRS)
Penanen, Konstantin I. (Inventor)
2008-01-01
A readout scheme for measuring the output from a SQUID-based sensor-array using an improved subranging architecture that includes multiple resolution channels (such as a coarse resolution channel and a fine resolution channel). The scheme employs a flux sensing circuit with a sensing coil connected in series to multiple input coils, each input coil being coupled to a corresponding SQUID detection circuit having a high-resolution SQUID device with independent linearizing feedback. A two-resolution configuration (course and fine) is illustrated with a primary SQUID detection circuit for generating a fine readout, and a secondary SQUID detection circuit for generating a course readout, both having feedback current coupled to the respective SQUID devices via feedback/modulation coils. The primary and secondary SQUID detection circuits function and derive independent feedback. Thus, the SQUID devices may be monitored independently of each other (and read simultaneously) to dramatically increase slew rates and dynamic range.
NASA Technical Reports Server (NTRS)
Glocer, A.; Toth, G.; Ma, Y.; Gombosi, T.; Zhang, J.-C.; Kistler, L. M.
2009-01-01
The magnetosphere contains a significant amount of ionospheric O+, particularly during geomagnetically active times. The presence of ionospheric plasma in the magnetosphere has a notable impact on magnetospheric composition and processes. We present a new multifluid MHD version of the Block-Adaptive-Tree Solar wind Roe-type Upwind Scheme model of the magnetosphere to track the fate and consequences of ionospheric outflow. The multifluid MHD equations are presented as are the novel techniques for overcoming the formidable challenges associated with solving them. Our new model is then applied to the May 4, 1998 and March 31, 2001 geomagnetic storms. The results are juxtaposed with traditional single-fluid MHD and multispecies MHD simulations from a previous study, thereby allowing us to assess the benefits of using a more complex model with additional physics. We find that our multifluid MHD model (with outflow) gives comparable results to the multispecies MHD model (with outflow), including a more strongly negative Dst, reduced CPCP, and a drastically improved magnetic field at geosynchronous orbit, as compared to single-fluid MHD with no outflow. Significant differences in composition and magnetic field are found between the multispecies and multifluid approach further away from the Earth. We further demonstrate the ability to explore pressure and bulk velocity differences between H+ and O+, which is not possible when utilizing the other techniques considered
New formulas for approximation of π and other transcendental numbers
NASA Astrophysics Data System (ADS)
Kalantari, Bahman
2000-08-01
We derive many new formulas for the approximation of π. The formulas make use of a sequence of iteration functions called the basic family; a nontrivial determinantal generalization of Taylor's theorem; other ingredients; as well as several new results presented in the present paper. In one scheme, one evaluates members of the basic family, for an appropriately selected function, all at the same input. This scheme generates almost a fixed and preselected number of digits in each successive evaluation. The computation amounts to the evaluation of a homogeneous linear recursive formula and is equivalent to the computation of special Toeplitz matrix determinants. The approximations of π obtained via this scheme are within simple algebraic extensions of the rational field. In a second scheme, the fixed-point iteration is applied to any fixed member of the basic family, while selecting an appropriate function. In this scheme for each natural number m geqslant 2 we prove convergence of order m, starting from the initial point. We report on some preliminary computational results obtained via Maple. Analogous formulas can be used to approximate other transcendental numbers. For instance, we also give a formula for the approximation of e. In fact, our results give new formulas and arbitrary high-order methods for the approximation of roots of certain analytic functions.
NASA Astrophysics Data System (ADS)
Pin, G.; Filippo, M.; Pellegrino, F. A.; Fenu, G.; Parisini, T.
2013-05-01
The objective of this work consists in the offline approximation of possibly discontinuous model predictive control laws for nonlinear discrete-time systems, while enforcing hard constraints on state and input variables. Obtaining an offline approximation of the receding horizon control law may lead to a very significant reduction of the online computational burden with respect to algorithms based on iterated optimization, thus allowing the application to fast dynamics plants. The proposed approximation scheme allows to cope with discontinuous control laws, such as those arising from constrained nonlinear finite horizon optimal control problems. A detailed stability analysis of the closed-loop system driven by the approximated state-feedback controller shows that the devised technique guarantees the input-to-state practical stability with respect to the (non-fading) approximation-induced errors. Two examples are provided to show the effectiveness of the method when the approximator is chosen either as a discontinuous nearest point function or as a smooth neural network.
Jenkinson, Garrett; Goutsias, John
2013-05-28
The master equation is used extensively to model chemical reaction systems with stochastic dynamics. However, and despite its phenomenological simplicity, it is not in general possible to compute the solution of this equation. Drawing exact samples from the master equation is possible, but can be computationally demanding, especially when estimating high-order statistical summaries or joint probability distributions. As a consequence, one often relies on analytical approximations to the solution of the master equation or on computational techniques that draw approximative samples from this equation. Unfortunately, it is not in general possible to check whether a particular approximation scheme is valid. The main objective of this paper is to develop an effective methodology to address this problem based on statistical hypothesis testing. By drawing a moderate number of samples from the master equation, the proposed techniques use the well-known Kolmogorov-Smirnov statistic to reject the validity of a given approximation method or accept it with a certain level of confidence. Our approach is general enough to deal with any master equation and can be used to test the validity of any analytical approximation method or any approximative sampling technique of interest. A number of examples, based on the Schlögl model of chemistry and the SIR model of epidemiology, clearly illustrate the effectiveness and potential of the proposed statistical framework.
Approximating metal-insulator transitions
NASA Astrophysics Data System (ADS)
Danieli, Carlo; Rayanov, Kristian; Pavlov, Boris; Martin, Gaven; Flach, Sergej
2015-12-01
We consider quantum wave propagation in one-dimensional quasiperiodic lattices. We propose an iterative construction of quasiperiodic potentials from sequences of potentials with increasing spatial period. At each finite iteration step, the eigenstates reflect the properties of the limiting quasiperiodic potential properties up to a controlled maximum system size. We then observe approximate Metal-Insulator Transitions (MIT) at the finite iteration steps. We also report evidence on mobility edges, which are at variance to the celebrated Aubry-André model. The dynamics near the MIT shows a critical slowing down of the ballistic group velocity in the metallic phase, similar to the divergence of the localization length in the insulating phase.
Triangle based TVD schemes for hyperbolic conservation laws
NASA Technical Reports Server (NTRS)
Durlofsky, Louis J.; Osher, Stanley; Engquist, Bjorn
1990-01-01
A triangle based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux up to second order accuracy. Numerical results for linear advection and Burgers' equation are presented.
Hierarchical Approximate Bayesian Computation
Turner, Brandon M.; Van Zandt, Trisha
2013-01-01
Approximate Bayesian computation (ABC) is a powerful technique for estimating the posterior distribution of a model’s parameters. It is especially important when the model to be fit has no explicit likelihood function, which happens for computational (or simulation-based) models such as those that are popular in cognitive neuroscience and other areas in psychology. However, ABC is usually applied only to models with few parameters. Extending ABC to hierarchical models has been difficult because high-dimensional hierarchical models add computational complexity that conventional ABC cannot accommodate. In this paper we summarize some current approaches for performing hierarchical ABC and introduce a new algorithm called Gibbs ABC. This new algorithm incorporates well-known Bayesian techniques to improve the accuracy and efficiency of the ABC approach for estimation of hierarchical models. We then use the Gibbs ABC algorithm to estimate the parameters of two models of signal detection, one with and one without a tractable likelihood function. PMID:24297436
On the convergence of difference approximations to scalar conservation laws
NASA Technical Reports Server (NTRS)
Osher, Stanley; Tadmor, Eitan
1988-01-01
A unified treatment is given for time-explicit, two-level, second-order-resolution (SOR), total-variation-diminishing (TVD) approximations to scalar conservation laws. The schemes are assumed only to have conservation form and incremental form. A modified flux and a viscosity coefficient are introduced to obtain results in terms of the latter. The existence of a cell entropy inequality is discussed, and such an equality for all entropies is shown to imply that the scheme is an E scheme on monotone (actually more general) data, hence at most only first-order accurate in general. Convergence for TVD-SOR schemes approximating convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.
On the convergence of difference approximations to scalar conservation laws
NASA Technical Reports Server (NTRS)
Osher, S.; Tadmor, E.
1985-01-01
A unified treatment of explicit in time, two level, second order resolution, total variation diminishing, approximations to scalar conservation laws are presented. The schemes are assumed only to have conservation form and incremental form. A modified flux and a viscosity coefficient are introduced and results in terms of the latter are obtained. The existence of a cell entropy inequality is discussed and such an equality for all entropies is shown to imply that the scheme is an E scheme on monotone (actually more general) data, hence at most only first order accurate in general. Convergence for total variation diminishing-second order resolution schemes approximating convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.
NASA Astrophysics Data System (ADS)
Yu, Miao; Wang, Guiling; Chen, Haishan
2016-03-01
Assessing and quantifying the uncertainties in projected future changes of energy and water budgets over land surface are important steps toward improving our confidence in climate change projections. In this study, the contribution of land surface models to the inter-GCM variation of projected future changes in land surface energy and water fluxes are assessed based on output from 19 global climate models (GCMs) and offline Community Land Model version 4 (CLM4) simulations driven by meteorological forcing from the 19 GCMs. Similar offline simulations using CLM4 with its dynamic vegetation submodel are also conducted to investigate how dynamic vegetation feedback, a process that is being added to more earth system models, may amplify or moderate the intermodel variations of projected future changes. Projected changes are quantified as the difference between the 2081-2100 period from the Representative Concentration Pathway 8.5 (RCP8.5) future experiment and the 1981-2000 period from the historical simulation. Under RCP8.5, projected changes in surface water and heat fluxes show a high degree of model dependency across the globe. Although precipitation is very likely to increase in the high latitudes of the Northern Hemisphere, a high degree of model-related uncertainty exists for evapotranspiration, soil water content, and surface runoff, suggesting discrepancy among land surface models (LSMs) in simulating the surface hydrological processes and snow-related processes. Large model-related uncertainties for the surface water budget also exist in the Tropics including southeastern South America and Central Africa. These uncertainties would be reduced in the hypothetical scenario of a single near-perfect land surface model being used across all GCMs, suggesting the potential to reduce uncertainties through the use of more consistent approaches toward land surface model development. Under such a scenario, the most significant reduction is likely to be seen in the
Yu, Miao; Wang, Guiling; Chen, Haishan
2016-03-01
Assessing and quantifying the uncertainties in projected future changes of energy and water budgets over land surface are important steps toward improving our confidence in climate change projections. In our study, the contribution of land surface models to the inter-GCM variation of projected future changes in land surface energy and water fluxes are assessed based on output from 19 global climate models (GCMs) and offline Community Land Model version 4 (CLM4) simulations driven by meteorological forcing from the 19 GCMs. Similar offline simulations using CLM4 with its dynamic vegetation submodel are also conducted to investigate how dynamic vegetation feedback, a process that is being added to more earth system models, may amplify or moderate the intermodel variations of projected future changes. Projected changes are quantified as the difference between the 2081–2100 period from the Representative Concentration Pathway 8.5 (RCP8.5) future experiment and the 1981–2000 period from the historical simulation. Under RCP8.5, projected changes in surface water and heat fluxes show a high degree of model dependency across the globe. Although precipitation is very likely to increase in the high latitudes of the Northern Hemisphere, a high degree of model-related uncertainty exists for evapotranspiration, soil water content, and surface runoff, suggesting discrepancy among land surface models (LSMs) in simulating the surface hydrological processes and snow-related processes. Large model-related uncertainties for the surface water budget also exist in the Tropics including southeastern South America and Central Africa. Moreover, these uncertainties would be reduced in the hypothetical scenario of a single near-perfect land surface model being used across all GCMs, suggesting the potential to reduce uncertainties through the use of more consistent approaches toward land surface model development. Under such a scenario, the most significant reduction is likely to be seen
Yu, Miao; Wang, Guiling; Chen, Haishan
2016-03-01
Assessing and quantifying the uncertainties in projected future changes of energy and water budgets over land surface are important steps toward improving our confidence in climate change projections. In our study, the contribution of land surface models to the inter-GCM variation of projected future changes in land surface energy and water fluxes are assessed based on output from 19 global climate models (GCMs) and offline Community Land Model version 4 (CLM4) simulations driven by meteorological forcing from the 19 GCMs. Similar offline simulations using CLM4 with its dynamic vegetation submodel are also conducted to investigate how dynamic vegetation feedback, amore » process that is being added to more earth system models, may amplify or moderate the intermodel variations of projected future changes. Projected changes are quantified as the difference between the 2081–2100 period from the Representative Concentration Pathway 8.5 (RCP8.5) future experiment and the 1981–2000 period from the historical simulation. Under RCP8.5, projected changes in surface water and heat fluxes show a high degree of model dependency across the globe. Although precipitation is very likely to increase in the high latitudes of the Northern Hemisphere, a high degree of model-related uncertainty exists for evapotranspiration, soil water content, and surface runoff, suggesting discrepancy among land surface models (LSMs) in simulating the surface hydrological processes and snow-related processes. Large model-related uncertainties for the surface water budget also exist in the Tropics including southeastern South America and Central Africa. Moreover, these uncertainties would be reduced in the hypothetical scenario of a single near-perfect land surface model being used across all GCMs, suggesting the potential to reduce uncertainties through the use of more consistent approaches toward land surface model development. Under such a scenario, the most significant reduction is likely to
JOURNAL SCOPE GUIDELINES: Paper classification scheme
NASA Astrophysics Data System (ADS)
2005-06-01
This scheme is used to clarify the journal's scope and enable authors and readers to more easily locate the appropriate section for their work. For each of the sections listed in the scope statement we suggest some more detailed subject areas which help define that subject area. These lists are by no means exhaustive and are intended only as a guide to the type of papers we envisage appearing in each section. We acknowledge that no classification scheme can be perfect and that there are some papers which might be placed in more than one section. We are happy to provide further advice on paper classification to authors upon request (please email jphysa@iop.org). 1. Statistical physics numerical and computational methods statistical mechanics, phase transitions and critical phenomena quantum condensed matter theory Bose-Einstein condensation strongly correlated electron systems exactly solvable models in statistical mechanics lattice models, random walks and combinatorics field-theoretical models in statistical mechanics disordered systems, spin glasses and neural networks nonequilibrium systems network theory 2. Chaotic and complex systems nonlinear dynamics and classical chaos fractals and multifractals quantum chaos classical and quantum transport cellular automata granular systems and self-organization pattern formation biophysical models 3. Mathematical physics combinatorics algebraic structures and number theory matrix theory classical and quantum groups, symmetry and representation theory Lie algebras, special functions and orthogonal polynomials ordinary and partial differential equations difference and functional equations integrable systems soliton theory functional analysis and operator theory inverse problems geometry, differential geometry and topology numerical approximation and analysis geometric integration computational methods 4. Quantum mechanics and quantum information theory coherent states eigenvalue problems supersymmetric quantum mechanics
Countably QC-Approximating Posets
Mao, Xuxin; Xu, Luoshan
2014-01-01
As a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The main results are as follows: (1) a complete lattice is generalized completely distributive if and only if it is countably QC-approximating and weakly generalized countably approximating; (2) a poset L having countably directed joins is generalized countably approximating if and only if the lattice σc(L)op of all σ-Scott-closed subsets of L is weakly generalized countably approximating. PMID:25165730
NASA Astrophysics Data System (ADS)
Cassou, Christophe; Minvielle, Marie; Terray, Laurent; Périgaud, Claire
2011-01-01
The links between the observed variability of the surface ocean variables estimated from reanalysis and the overlying atmosphere decomposed in classes of large-scale atmospheric circulation via clustering are investigated over the Atlantic from 1958 to 2002. Daily 500 hPa geopotential height and 1,000 hPa wind anomaly maps are classified following a weather-typing approach to describe the North Atlantic and tropical Atlantic atmospheric dynamics, respectively. The algorithm yields patterns that correspond in the extratropics to the well-known North Atlantic-Europe weather regimes (NAE-WR) accounting for the barotropic dynamics, and in the tropics to wind classes (T-WC) representing the alteration of the trades. 10-m wind and 2-m temperature (T2) anomaly composites derived from regime/wind class occurrence are indicative of strong relationships between daily large-scale atmospheric circulation and ocean surface over the entire Atlantic basin. High temporal correlation values are obtained basin-wide at low frequency between the observed fields and their reconstruction by multiple linear regressions with the frequencies of occurrence of both NAE-WR and T-WC used as sole predictors. Additional multiple linear regressions also emphasize the importance of accounting for the strength of the daily anomalous atmospheric circulation estimated by the combined distances to all regimes centroids in order to reproduce the daily to interannual variability of the Atlantic ocean. We show that for most of the North Atlantic basin the occurrence of NAE-WR generally sets the sign of the ocean surface anomaly for a given day, and that the inter-regime distances are valuable predictors for the magnitude of that anomaly. Finally, we provide evidence that a large fraction of the low-frequency trends in the Atlantic observed at the surface over the last 50 years can be traced back, except for T2, to changes in occurrence of tropical and extratropical weather classes. All together, our
Hung, Shih-Lin
2014-01-01
This work presents a digital image processing approach with a unique hive triangle pattern by integrating subpixel analysis for noncontact measurement of structural dynamic response data. Feasibility of proposed approach is demonstrated based on numerical simulation of a photography experiment. According to those results, the measured time-history displacement of simulated image correlates well with the numerical solution. A small three-story frame is then mounted on a small shaker table, and a linear variation differential transformation (LVDT) is set on the second floor. Experimental results indicate that the relative error between data from LVDT and analyzed data from digital image correlation is below 0.007%, 0.0205 in terms of frequency and displacement, respectively. Additionally, the appropriate image block affects the estimation accuracy of the measurement system. Importantly, the proposed approach for evaluating pattern center and size is highly promising for use in assigning the adaptive block for a digital image correlation method. PMID:24955396
Hybrid functionals and GW approximation in the FLAPW method
NASA Astrophysics Data System (ADS)
Friedrich, Christoph; Betzinger, Markus; Schlipf, Martin; Blügel, Stefan; Schindlmayr, Arno
2012-07-01
We present recent advances in numerical implementations of hybrid functionals and the GW approximation within the full-potential linearized augmented-plane-wave (FLAPW) method. The former is an approximation for the exchange-correlation contribution to the total energy functional in density-functional theory, and the latter is an approximation for the electronic self-energy in the framework of many-body perturbation theory. All implementations employ the mixed product basis, which has evolved into a versatile basis for the products of wave functions, describing the incoming and outgoing states of an electron that is scattered by interacting with another electron. It can thus be used for representing the nonlocal potential in hybrid functionals as well as the screened interaction and related quantities in GW calculations. In particular, the six-dimensional space integrals of the Hamiltonian exchange matrix elements (and exchange self-energy) decompose into sums over vector-matrix-vector products, which can be evaluated easily. The correlation part of the GW self-energy, which contains a time or frequency dependence, is calculated on the imaginary frequency axis with a subsequent analytic continuation to the real axis or, alternatively, by a direct frequency convolution of the Green function G and the dynamically screened Coulomb interaction W along a contour integration path that avoids the poles of the Green function. Hybrid-functional and GW calculations are notoriously computationally expensive. We present a number of tricks that reduce the computational cost considerably, including the use of spatial and time-reversal symmetries, modifications of the mixed product basis with the aim to optimize it for the correlation self-energy and another modification that makes the Coulomb matrix sparse, analytic expansions of the interaction potentials around the point of divergence at k = 0, and a nested density and density-matrix convergence scheme for hybrid
Minimal dissipation hybrid bicompact schemes for hyperbolic equations
NASA Astrophysics Data System (ADS)
Bragin, M. D.; Rogov, B. V.
2016-06-01
New monotonicity-preserving hybrid schemes are proposed for multidimensional hyperbolic equations. They are convex combinations of high-order accurate central bicompact schemes and upwind schemes of first-order accuracy in time and space. The weighting coefficients in these combinations depend on the local difference between the solutions produced by the high- and low-order accurate schemes at the current space-time point. The bicompact schemes are third-order accurate in time, while having the fourth order of accuracy and the first difference order in space. At every time level, they can be solved by marching in each spatial variable without using spatial splitting. The upwind schemes have minimal dissipation among all monotone schemes constructed on a minimum space-time stencil. The hybrid schemes constructed has been successfully tested as applied to a number of two-dimensional gas dynamics benchmark problems.
Twin Signature Schemes, Revisited
NASA Astrophysics Data System (ADS)
Schäge, Sven
In this paper, we revisit the twin signature scheme by Naccache, Pointcheval and Stern from CCS 2001 that is secure under the Strong RSA (SRSA) assumption and improve its efficiency in several ways. First, we present a new twin signature scheme that is based on the Strong Diffie-Hellman (SDH) assumption in bilinear groups and allows for very short signatures and key material. A big advantage of this scheme is that, in contrast to the original scheme, it does not require a computationally expensive function for mapping messages to primes. We prove this new scheme secure under adaptive chosen message attacks. Second, we present a modification that allows to significantly increase efficiency when signing long messages. This construction uses collision-resistant hash functions as its basis. As a result, our improvements make the signature length independent of the message size. Our construction deviates from the standard hash-and-sign approach in which the hash value of the message is signed in place of the message itself. We show that in the case of twin signatures, one can exploit the properties of the hash function as an integral part of the signature scheme. This improvement can be applied to both the SRSA based and SDH based twin signature scheme.
The Cell Cycle Switch Computes Approximate Majority
NASA Astrophysics Data System (ADS)
Cardelli, Luca; Csikász-Nagy, Attila
2012-09-01
Both computational and biological systems have to make decisions about switching from one state to another. The `Approximate Majority' computational algorithm provides the asymptotically fastest way to reach a common decision by all members of a population between two possible outcomes, where the decision approximately matches the initial relative majority. The network that regulates the mitotic entry of the cell-cycle in eukaryotes also makes a decision before it induces early mitotic processes. Here we show that the switch from inactive to active forms of the mitosis promoting Cyclin Dependent Kinases is driven by a system that is related to both the structure and the dynamics of the Approximate Majority computation. We investigate the behavior of these two switches by deterministic, stochastic and probabilistic methods and show that the steady states and temporal dynamics of the two systems are similar and they are exchangeable as components of oscillatory networks.
Papaioannou, A; Louis, M; Dhital, B; Ho, H P; Chang, E J; Boutis, G S
2015-05-01
Methods for isolating elastin from fat, collagen, and muscle, commonly used in the design of artificial elastin based biomaterials, rely on exposing tissue to harsh pH levels and temperatures that usually denature many proteins. At present, a quantitative measurement of the modifications to elastin following isolation from other extracellular matrix constituents has not been reported. Using magic angle spinning (13)C NMR spectroscopy and relaxation methodologies, we have measured the modification in structure and dynamics following three known purification protocols. Our experimental data reveal that the (13)C spectra of the hydrated samples appear remarkably similar across the various purification methods. Subtle differences in the half maximum widths were observed in the backbone carbonyl suggesting possible structural heterogeneity across the different methods of purification. Additionally, small differences in the relative signal intensities were observed between purified samples. Lyophilizing the samples results in a reduction of backbone motion and reveals additional differences across the purification methods studied. These differences were most notable in the alanine motifs indicating possible changes in cross-linking or structural rigidity. The measured correlation times of glycine and proline moieties are observed to also vary considerably across the different purification methods, which may be related to peptide bond cleavage. Lastly, the relative concentration of desmosine cross-links in the samples quantified by MALDI mass spectrometry is reported.
NASA Technical Reports Server (NTRS)
Fukumori, Ichiro; Malanotte-Rizzoli, Paola
1995-01-01
A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kalman filter based on approximation of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the error's asymptotic steady state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudomeasurements are examined, including velocity, density, and volume transport at localized arrays and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform an empirical nudging scheme used in a previous study. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.
Towards an "All Speed" Unstructured Upwind Scheme
NASA Technical Reports Server (NTRS)
Loh, Ching Y.; Jorgenson, Philip C.E.
2009-01-01
In the authors previous studies [1], a time-accurate, upwind finite volume method (ETAU scheme) for computing compressible flows on unstructured grids was proposed. The scheme is second order accurate in space and time and yields high resolution in the presence of discontinuities. The scheme features a multidimensional limiter and multidimensional numerical dissipation. These help to stabilize the numerical process and to overcome the annoying pathological behaviors of upwind schemes. In the present paper, it will be further shown that such multidimensional treatments also lead to a nearly all-speed or Mach number insensitive upwind scheme. For flows at very high Mach number, e.g., 10, local numerical instabilities or the pathological behaviors are suppressed, while for flows at very low Mach number, e.g., 0.02, computation can be directly carried out without invoking preconditioning. For flows in different Mach number regimes, i.e., low, medium, and high Mach numbers, one only needs to adjust one or two parameters in the scheme. Several examples with low and high Mach numbers are demonstrated in this paper. Thus, the ETAU scheme is applicable to a broad spectrum of flow regimes ranging from high supersonic to low subsonic, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics).
Willcock, J J; Lumsdaine, A; Quinlan, D J
2008-08-19
Tabled execution is a generalization of memorization developed by the logic programming community. It not only saves results from tabled predicates, but also stores the set of currently active calls to them; tabled execution can thus provide meaningful semantics for programs that seemingly contain infinite recursions with the same arguments. In logic programming, tabled execution is used for many purposes, both for improving the efficiency of programs, and making tasks simpler and more direct to express than with normal logic programs. However, tabled execution is only infrequently applied in mainstream functional languages such as Scheme. We demonstrate an elegant implementation of tabled execution in Scheme, using a mix of continuation-passing style and mutable data. We also show the use of tabled execution in Scheme for a problem in formal language and automata theory, demonstrating that tabled execution can be a valuable tool for Scheme users.
Re-formulation and Validation of Cloud Microphysics Schemes
NASA Astrophysics Data System (ADS)
Wang, J.; Georgakakos, K. P.
2007-12-01
The research focuses on improving quantitative precipitation forecasts by removing significant uncertainties in current cloud microphysics schemes embedded in models such as WRF and MM5 and cloud-resolving models such as GCE. Reformulation of several production terms in these microphysics schemes was found necessary. When estimating four graupel production terms involved in the accretion between rain, snow and graupel, current microphysics schemes assumes that all raindrops and snow particles are falling at their appropriate mass-weighted mean terminal velocities and thus analytic solutions are able to be found for these production terms. Initial analysis and tests showed that these approximate analytic solutions give significant and systematic overestimates of these terms, and, thus, become one of major error sources of the graupel overproduction and associated extreme radar reflectivity in simulations. These results are corroborated by several reports. For example, the analytic solution overestimates the graupel production by collisions between raindrops and snow by up to 230%. The structure of "pure" snow (not rimed) and "pure graupel" (completely rimed) in current microphysics schemes excludes intermediate forms between "pure" snow and "pure" graupel and thus becomes a significant reason of graupel overproduction in hydrometeor simulations. In addition, the generation of the same density graupel by both the freezing of supercooled water and the riming of snow may cause underestimation of graupel production by freezing. A parameterization scheme of the riming degree of snow is proposed and then a dynamic fallspeed-diameter relationship and density- diameter relationship of rimed snow is assigned to graupel based on the diagnosed riming degree. To test if these new treatments can improve quantitative precipitation forecast, the Hurricane Katrina and a severe winter snowfall event in the Sierra Nevada Range are selected as case studies. A series of control
NASA Astrophysics Data System (ADS)
Nassar, Ahmed K.; Blackburn, G. Alan; Whyatt, J. Duncan
2016-09-01
This study aims to determine the dynamics and controls of Surface Urban Heat Sinks (SUHS) and Surface Urban Heat Islands (SUHI) in desert cities, using Dubai as a case study. A Local Climate Zone (LCZ) schema was developed to subdivide the city into different zones based on similarities in land cover and urban geometry. Proximity to the Gulf Coast was also determined for each LCZ. The LCZs were then used to sample seasonal and daily imagery from the MODIS thermal sensor to determine Land Surface Temperature (LST) variations relative to desert sand. Canonical correlation techniques were then applied to determine which factors explained the variability between urban and desert LST. Our results indicate that the daytime SUHS effect is greatest during the summer months (typically ∼3.0 °C) with the strongest cooling effects in open high-rise zones of the city. In contrast, the night-time SUHI effect is greatest during the winter months (typically ∼3.5 °C) with the strongest warming effects in compact mid-rise zones of the city. Proximity to the Arabian Gulf had the largest influence on both SUHS and SUHI phenomena, promoting daytime cooling in the summer months and night-time warming in the winter months. However, other parameters associated with the urban environment such as building height had an influence on daytime cooling, with larger buildings promoting shade and variations in airflow. Likewise, other parameters such as sky view factor contributed to night-time warming, with higher temperatures associated with limited views of the sky.
High resolution schemes and the entropy condition
NASA Technical Reports Server (NTRS)
Osher, S.; Chakravarthy, S.
1983-01-01
A systematic procedure for constructing semidiscrete, second order accurate, variation diminishing, five point band width, approximations to scalar conservation laws, is presented. These schemes are constructed to also satisfy a single discrete entropy inequality. Thus, in the convex flux case, convergence is proven to be the unique physically correct solution. For hyperbolic systems of conservation laws, this construction is used formally to extend the first author's first order accurate scheme, and show (under some minor technical hypotheses) that limit solutions satisfy an entropy inequality. Results concerning discrete shocks, a maximum principle, and maximal order of accuracy are obtained. Numerical applications are also presented.
Quantum analysis applied to thermo field dynamics on dissipative systems
Hashizume, Yoichiro; Okamura, Soichiro; Suzuki, Masuo
2015-03-10
Thermo field dynamics is one of formulations useful to treat statistical mechanics in the scheme of field theory. In the present study, we discuss dissipative thermo field dynamics of quantum damped harmonic oscillators. To treat the effective renormalization of quantum dissipation, we use the Suzuki-Takano approximation. Finally, we derive a dissipative von Neumann equation in the Lindbrad form. In the present treatment, we can easily obtain the initial damping shown previously by Kubo.
Local discontinuous Galerkin approximations to Richards’ equation
NASA Astrophysics Data System (ADS)
Li, H.; Farthing, M. W.; Dawson, C. N.; Miller, C. T.
2007-03-01
We consider the numerical approximation to Richards' equation because of its hydrological significance and intrinsic merit as a nonlinear parabolic model that admits sharp fronts in space and time that pose a special challenge to conventional numerical methods. We combine a robust and established variable order, variable step-size backward difference method for time integration with an evolving spatial discretization approach based upon the local discontinuous Galerkin (LDG) method. We formulate the approximation using a method of lines approach to uncouple the time integration from the spatial discretization. The spatial discretization is formulated as a set of four differential algebraic equations, which includes a mass conservation constraint. We demonstrate how this system of equations can be reduced to the solution of a single coupled unknown in space and time and a series of local constraint equations. We examine a variety of approximations at discontinuous element boundaries, permeability approximations, and numerical quadrature schemes. We demonstrate an optimal rate of convergence for smooth problems, and compare accuracy and efficiency for a wide variety of approaches applied to a set of common test problems. We obtain robust and efficient results that improve upon existing methods, and we recommend a future path that should yield significant additional improvements.
Robustness of controllers designed using Galerkin type approximations
NASA Technical Reports Server (NTRS)
Morris, K. A.
1990-01-01
One of the difficulties in designing controllers for infinite-dimensional systems arises from attempting to calculate a state for the system. It is shown that Galerkin type approximations can be used to design controllers which will perform as designed when implemented on the original infinite-dimensional system. No assumptions, other than those typically employed in numerical analysis, are made on the approximating scheme.
Regnier, D.; Verriere, M.; Dubray, N.; Schunck, N.
2015-11-30
In this study, we describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in NN-dimensions (N ≥ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank–Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle a realistic calculation of fission dynamics.
DALI: Derivative Approximation for LIkelihoods
NASA Astrophysics Data System (ADS)
Sellentin, Elena
2015-07-01
DALI (Derivative Approximation for LIkelihoods) is a fast approximation of non-Gaussian likelihoods. It extends the Fisher Matrix in a straightforward way and allows for a wider range of posterior shapes. The code is written in C/C++.
Measurement-induced chaos and quantum state discrimination in an iterated Tavis-Cummings scheme
NASA Astrophysics Data System (ADS)
Torres, Juan Mauricio; Bernád, József Zsolt; Alber, Gernot; Kálmán, Orsolya; Kiss, Tamás
2017-02-01
A cavity quantum electrodynamical scenario is proposed for implementing a Schrödinger microscope capable of amplifying differences between nonorthogonal atomic quantum states. The scheme involves an ensemble of identically prepared two-level atoms interacting pairwise with a single mode of the radiation field as described by the Tavis-Cummings model. By repeated measurements of the cavity field and of one atom within each pair a measurement-induced nonlinear quantum transformation of the relevant atomic states can be realized. The intricate dynamical properties of this nonlinear quantum transformation, which exhibits measurement-induced chaos, allow approximate orthogonalization of atomic states by purification after a few iterations of the protocol and thus the application of the scheme for quantum state discrimination.
Taylor Approximations and Definite Integrals
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2007-01-01
We investigate the possibility of approximating the value of a definite integral by approximating the integrand rather than using numerical methods to approximate the value of the definite integral. Particular cases considered include examples where the integral is improper, such as an elliptic integral. (Contains 4 tables and 2 figures.)
Placidi, M.; Jung, J. -Y.; Ratti, A.; Sun, C.
2014-07-25
This paper describes beam distribution schemes adopting a novel implementation based on low amplitude vertical deflections combined with horizontal ones generated by Lambertson-type septum magnets. This scheme offers substantial compactness in the longitudinal layouts of the beam lines and increased flexibility for beam delivery of multiple beam lines on a shot-to-shot basis. Fast kickers (FK) or transverse electric field RF Deflectors (RFD) provide the low amplitude deflections. Initially proposed at the Stanford Linear Accelerator Center (SLAC) as tools for beam diagnostics and more recently adopted for multiline beam pattern schemes, RFDs offer repetition capabilities and a likely better amplitude reproducibility when compared to FKs, which, in turn, offer more modest financial involvements both in construction and operation. Both solutions represent an ideal approach for the design of compact beam distribution systems resulting in space and cost savings while preserving flexibility and beam quality.
NASA Astrophysics Data System (ADS)
Placidi, M.; Jung, J.-Y.; Ratti, A.; Sun, C.
2014-12-01
This paper describes beam distribution schemes adopting a novel implementation based on low amplitude vertical deflections combined with horizontal ones generated by Lambertson-type septum magnets. This scheme offers substantial compactness in the longitudinal layouts of the beam lines and increased flexibility for beam delivery of multiple beam lines on a shot-to-shot basis. Fast kickers (FK) or transverse electric field RF Deflectors (RFD) provide the low amplitude deflections. Initially proposed at the Stanford Linear Accelerator Center (SLAC) as tools for beam diagnostics and more recently adopted for multiline beam pattern schemes, RFDs offer repetition capabilities and a likely better amplitude reproducibility when compared to FKs, which, in turn, offer more modest financial involvements both in construction and operation. Both solutions represent an ideal approach for the design of compact beam distribution systems resulting in space and cost savings while preserving flexibility and beam quality.
The effectiveness of Hong Kong's Construction Waste Disposal Charging Scheme.
Hao, Jane L; Hills, Martin J; Tam, Vivian W Y
2008-12-01
The Hong Kong Government introduced the Construction Waste Disposal Charging Scheme in December 2005 to ensure that disposal of construction and demolition (C&D) waste is properly priced to reduce such waste. The charging scheme is not only intended to provide an economic incentive for contractors and developers to reduce waste but also to encourage reuse and recycling of waste material thereby slowing down the depletion of limited landfill and public filling capacities. This paper examines the effectiveness of the charging scheme 1 year after implementation. A survey was conducted at Tseung Kwan O Area 137 and Tuen Mun Area 38, and daily C&D waste records were collected from landfills and public filling facilities between January 2006 and December 2006. The results of the survey show that waste has been reduced by approximately 60% in landfills, by approximately 23% in public fills, and by approximately 65% in total waste between 2005 and 2006. Suggestions for improving the scheme are provided.
New sensitivity-enhancing scheme for a fibre-optic interferometer utilising two optical loops
NASA Astrophysics Data System (ADS)
Arai, K.; Hayashi, K.; Iiyama, K.; Ida, Y.; Mori, T.
1988-08-01
To improve the sensitivity or dynamic range of fiber-optic interferometer systems a new scheme utilizing two optical loops is presented. The validity of the scheme is also experimentally confirmed by a tentative bulk-optic configuration.
NASA Astrophysics Data System (ADS)
Rampf, Cornelius; Villa, Eleonora; Bertacca, Daniele; Bruni, Marco
2016-10-01
We study the nonlinear gravitational dynamics of a universe filled with a pressureless fluid and a cosmological constant Λ in the context of Newtonian gravity, and in the relativistic post-Friedmann approach proposed in paper I [I. Milillo et al., Phys. Rev. D 92, 023519 (2015)]. The post-Friedmann approximation scheme is based on the 1 /c expansion of the space-time metric and the energy-momentum tensor, and includes nonlinear Newtonian cosmology. Here we establish the nonlinear post-Friedmann framework in the Lagrangian-coordinates approach for structure formation. For this we first identify a Lagrangian gauge which is suitable for incorporating nonzero vorticity. We analyze our results in two limits: at the leading order we recover the fully nonlinear Newtonian cosmological equations in the Lagrangian formulation, and we provide a space-time metric consistent from the perspective of general relativity. We then linearize our expressions and recover the relativistic results at first order in cosmological perturbation theory. Therefore, the introduced approximation scheme provides a unified treatment for the two leading-order regimes, from the small scales described by Newtonian gravity to the large linear scale, where first-order relativistic cosmological perturbation theory gives a very good description of structure formation.
Fixed Wordsize Implementation of Lifting Schemes
NASA Astrophysics Data System (ADS)
Karp, Tanja
2006-12-01
We present a reversible nonlinear discrete wavelet transform with predefined fixed wordsize based on lifting schemes. Restricting the dynamic range of the wavelet domain coefficients due to a fixed wordsize may result in overflow. We show how this overflow has to be handled in order to maintain reversibility of the transform. We also perform an analysis on how large a wordsize of the wavelet coefficients is needed to perform optimal lossless and lossy compressions of images. The scheme is advantageous to well-known integer-to-integer transforms since the wordsize of adders and multipliers can be predefined and does not increase steadily. This also results in significant gains in hardware implementations.
An improved SPH scheme for cosmological simulations
NASA Astrophysics Data System (ADS)
Beck, A. M.; Murante, G.; Arth, A.; Remus, R.-S.; Teklu, A. F.; Donnert, J. M. F.; Planelles, S.; Beck, M. C.; Förster, P.; Imgrund, M.; Dolag, K.; Borgani, S.
2016-01-01
We present an implementation of smoothed particle hydrodynamics (SPH) with improved accuracy for simulations of galaxies and the large-scale structure. In particular, we implement and test a vast majority of SPH improvement in the developer version of GADGET-3. We use the Wendland kernel functions, a particle wake-up time-step limiting mechanism and a time-dependent scheme for artificial viscosity including high-order gradient computation and shear flow limiter. Additionally, we include a novel prescription for time-dependent artificial conduction, which corrects for gravitationally induced pressure gradients and improves the SPH performance in capturing the development of gas-dynamical instabilities. We extensively test our new implementation in a wide range of hydrodynamical standard tests including weak and strong shocks as well as shear flows, turbulent spectra, gas mixing, hydrostatic equilibria and self-gravitating gas clouds. We jointly employ all modifications; however, when necessary we study the performance of individual code modules. We approximate hydrodynamical states more accurately and with significantly less noise than standard GADGET-SPH. Furthermore, the new implementation promotes the mixing of entropy between different fluid phases, also within cosmological simulations. Finally, we study the performance of the hydrodynamical solver in the context of radiative galaxy formation and non-radiative galaxy cluster formation. We find galactic discs to be colder and more extended and galaxy clusters showing entropy cores instead of steadily declining entropy profiles. In summary, we demonstrate that our improved SPH implementation overcomes most of the undesirable limitations of standard GADGET-SPH, thus becoming the core of an efficient code for large cosmological simulations.
Approximate Solvability of Forward-Backward Stochastic Differential Equations
Ma, J. Yong, J.
2002-07-01
The solvability of forward-backward stochastic differential equations (FBSDEs for short) has been studied extensively in recent years. To guarantee the existence and uniqueness of adapted solutions, many different conditions, some quite restrictive, have been imposed. In this paper we propose a new notion: the approximate solvability of FBSDEs, based on the method of optimal control introduced in our primary work [15]. The approximate solvability of a class of FBSDEs is shown under mild conditions; and a general scheme for constructing approximate adapted solutions is proposed.
Approximate active fault detection and control
NASA Astrophysics Data System (ADS)
Škach, Jan; Punčochář, Ivo; Šimandl, Miroslav
2014-12-01
This paper deals with approximate active fault detection and control for nonlinear discrete-time stochastic systems over an infinite time horizon. Multiple model framework is used to represent fault-free and finitely many faulty models. An imperfect state information problem is reformulated using a hyper-state and dynamic programming is applied to solve the problem numerically. The proposed active fault detector and controller is illustrated in a numerical example of an air handling unit.
Microscopic justification of the equal filling approximation
Perez-Martin, Sara; Robledo, L. M.
2008-07-15
The equal filling approximation, a procedure widely used in mean-field calculations to treat the dynamics of odd nuclei in a time-reversal invariant way, is justified as the consequence of a variational principle over an average energy functional. The ideas of statistical quantum mechanics are employed in the justification. As an illustration of the method, the ground and lowest-lying states of some octupole deformed radium isotopes are computed.
ERIC Educational Resources Information Center
Wheeler, Mary L.
1994-01-01
Discusses the study of identification codes and check-digit schemes as a way to show students a practical application of mathematics and introduce them to coding theory. Examples include postal service money orders, parcel tracking numbers, ISBN codes, bank identification numbers, and UPC codes. (MKR)
Ren, Yihui; Eubank, Stephen; Nath, Madhurima
2016-10-01
Network reliability is the probability that a dynamical system composed of discrete elements interacting on a network will be found in a configuration that satisfies a particular property. We introduce a reliability property, Ising feasibility, for which the network reliability is the Ising model's partition function. As shown by Moore and Shannon, the network reliability can be separated into two factors: structural, solely determined by the network topology, and dynamical, determined by the underlying dynamics. In this case, the structural factor is known as the joint density of states. Using methods developed to approximate the structural factor for other reliability properties, we simulate the joint density of states, yielding an approximation for the partition function. Based on a detailed examination of why naïve Monte Carlo sampling gives a poor approximation, we introduce a parallel scheme for estimating the joint density of states using a Markov-chain Monte Carlo method with a spin-exchange random walk. This parallel scheme makes simulating the Ising model in the presence of an external field practical on small computer clusters for networks with arbitrary topology with ∼10^{6} energy levels and more than 10^{308} microstates.
NASA Astrophysics Data System (ADS)
Ren, Yihui; Eubank, Stephen; Nath, Madhurima
2016-10-01
Network reliability is the probability that a dynamical system composed of discrete elements interacting on a network will be found in a configuration that satisfies a particular property. We introduce a reliability property, Ising feasibility, for which the network reliability is the Ising model's partition function. As shown by Moore and Shannon, the network reliability can be separated into two factors: structural, solely determined by the network topology, and dynamical, determined by the underlying dynamics. In this case, the structural factor is known as the joint density of states. Using methods developed to approximate the structural factor for other reliability properties, we simulate the joint density of states, yielding an approximation for the partition function. Based on a detailed examination of why naïve Monte Carlo sampling gives a poor approximation, we introduce a parallel scheme for estimating the joint density of states using a Markov-chain Monte Carlo method with a spin-exchange random walk. This parallel scheme makes simulating the Ising model in the presence of an external field practical on small computer clusters for networks with arbitrary topology with ˜106 energy levels and more than 10308 microstates.
NASA Astrophysics Data System (ADS)
Mignone, A.
2014-08-01
High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the zone-average values to reconstruct left and right interface states from within a computational zone to arbitrary order of accuracy by inverting a Vandermonde-like linear system of equations with spatially varying coefficients. The approach is general and can be used on uniform and non-uniform meshes although explicit expressions are derived for polynomials from second to fifth degree in cylindrical and spherical geometries with uniform grid spacing. It is shown that, in regions of large curvature, the resulting expressions differ considerably from their Cartesian counterparts and that the lack of such corrections can severely degrade the accuracy of the solution close to the coordinate origin. Limiting techniques and monotonicity constraints are revised for conventional reconstruction schemes, namely, the piecewise linear method (PLM), third-order weighted essentially non-oscillatory (WENO) scheme and the piecewise parabolic method (PPM). The performance of the improved reconstruction schemes is investigated in a number of selected numerical benchmarks involving the solution of both scalar and systems of nonlinear equations (such as the equations of gas dynamics and magnetohydrodynamics) in cylindrical and spherical geometries in one and two dimensions. Results confirm that the proposed approach yields considerably smaller errors, higher convergence rates and it avoid spurious numerical effects at a symmetry axis.
Andonian, G.; Hemsing, E.; Xiang, D.; Musumeci, P.; Murokh, A.; Tochitsky, S.; Rosenzweig, J.B.; /UCLA
2012-05-03
High-resolution measurement of the longitudinal profile of a relativistic electron beam is of utmost importance for linac based free-electron lasers and other advanced accelerator facilities that employ ultrashort bunches. In this paper, we investigate a novel scheme to measure ultrashort bunches (subpicosecond) with exceptional temporal resolution (hundreds of attoseconds) and dynamic range. The scheme employs two orthogonally oriented deflecting sections. The first imparts a short-wavelength (fast temporal resolution) horizontal angular modulation on the beam, while the second imparts a long-wavelength (slow) angular kick in the vertical dimension. Both modulations are observable on a standard downstream screen in the form of a streaked sinusoidal beam structure. We demonstrate, using scaled variables in a quasi-1D approximation, an expression for the temporal resolution of the scheme and apply it to a proof-of-concept experiment at the UCLA Neptune high-brightness injector facility. The scheme is also investigated for application at the SLAC NLCTA facility, where we show that the subfemtosecond resolution is sufficient to resolve the temporal structure of the beam used in the echo-enabled free-electron laser. We employ beam simulations to verify the effect for typical Neptune and NLCTA parameter sets and demonstrate the feasibility of the concept.
A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation
NASA Astrophysics Data System (ADS)
Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohamed A.; Hafez, Ramy M.
2014-02-01
This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers' equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers' equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.