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.
Toni, Tina; Welch, David; Strelkowa, Natalja; Ipsen, Andreas; Stumpf, Michael P.H.
2008-01-01
Approximate Bayesian computation (ABC) methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper, we discuss and apply an ABC method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC provides information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well-known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus. PMID:19205079
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.
Approximation Schemes for Scheduling with Availability Constraints
NASA Astrophysics Data System (ADS)
Fu, Bin; Huo, Yumei; Zhao, Hairong
We investigate the problems of scheduling n weighted jobs to m identical machines with availability constraints. We consider two different models of availability constraints: the preventive model where the unavailability is due to preventive machine maintenance, and the fixed job model where the unavailability is due to a priori assignment of some of the n jobs to certain machines at certain times. Both models have applications such as turnaround scheduling or overlay computing. In both models, the objective is to minimize the total weighted completion time. We assume that m is a constant, and the jobs are non-resumable. For the preventive model, it has been shown that there is no approximation algorithm if all machines have unavailable intervals even when w i = p i for all jobs. In this paper, we assume there is one machine permanently available and the processing time of each job is equal to its weight for all jobs. We develop the first PTAS when there are constant number of unavailable intervals. One main feature of our algorithm is that the classification of large and small jobs is with respect to each individual interval, thus not fixed. This classification allows us (1) to enumerate the assignments of large jobs efficiently; (2) and to move small jobs around without increasing the objective value too much, and thus derive our PTAS. Then we show that there is no FPTAS in this case unless P = NP.
An Approximate KAM-Renormalization-Group Scheme for Hamiltonian Systems
NASA Astrophysics Data System (ADS)
Chandre, C.; Jauslin, H. R.; Benfatto, G.
1999-01-01
We construct an approximate renormalization scheme for Hamiltonian systems with two degrees of freedom. This scheme is a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. It makes the connection between the approximate renormalization procedure derived by Escande and Doveil and a systematic expansion of the transformation. In particular, we show that the two main approximations, consisting in keeping only the quadratic terms in the actions and the two main resonances, keep the essential information on the threshold of the breakup of invariant tori.
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.
Implicit lower-upper/approximate-factorization schemes for incompressible flows
Briley, W.R.; Neerarambam, S.S.; Whitfield, D.L.
1996-10-01
A lower-upper/approximate-factorization (LU/AF) scheme is developed for the incompressible Euler or Navier-Stokes equations. The LU/AF scheme contains an iteration parameter that can be adjusted to improve iterative convergence rate. The LU/AF scheme is to be used in conjunction with linearized implicit approximations and artificial compressibility to compute steady solutions, and within sub-iterations to compute unsteady solutions. Formulations based on time linearization with and without sub-iteration and on Newton linearization are developed using spatial difference operators. The spatial approximation used includes upwind differencing based on Roe`s approximate Riemann solver and van Leer`s MUSCL scheme, with numerically computed implicit flux linearizations. Simple one-dimensional diffusion and advection/diffusion problems are first studied analytically to provide insight for development of the Navier-Stokes algorithm. The optimal values of both time step and LU/AF parameter are determined for a test problem consisting of two-dimensional flow past a NACA 0012 airfoil, with a highly stretched grid. The optimal parameter provides a consistent improvement in convergence rate for four test cases having different grids and Reynolds numbers and, also, for an inviscid case. The scheme can be easily extended to three dimensions and adapted for compressible flows. 24 refs., 11 figs., 2 tabs.
A nonconservative scheme for isentropic gas dynamics
Chen, Gui-Qiang |; Liu, Jian-Guo
1994-05-01
In this paper, we construct a second-order nonconservative for the system of isentropic gas dynamics to capture the physical invariant regions for preventing negative density, to treat the vacuum singularity, and to control the local entropy from dramatically increasing near shock waves. The main difference in the construction of the scheme discussed here is that we use piecewise linear functions to approximate the Riemann invariants w and z instead of the physical variables {rho} and m. Our scheme is a natural extension of the schemes for scalar conservation laws and it can be numerical implemented easily because the system is diagonalized in this coordinate system. Another advantage of using Riemann invariants is that the Hessian matrix of any weak entropy has no singularity in the Riemann invariant plane w-z, whereas the Hessian matrices of the weak entropies have singularity at the vacuum points in the physical plane p-m. We prove that this scheme converges to an entropy solution for the Cauchy problem with L{sup {infinity}} initial data. By convergence here we mean that there is a subsequent convergence to a generalized solution satisfying the entrophy condition. As long as the entropy solution is unique, the whole sequence converges to a physical solution. This shows that this kind of scheme is quite reliable from theoretical view of point. In addition to being interested in the scheme itself, we wish to provide an approach to rigorously analyze nonconservative finite difference schemes.
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.
NASA Astrophysics Data System (ADS)
Luo, Hongjun; Kolb, Dietmar; Flad, Heinz-Jurgen; Hackbusch, Wolfgang; Koprucki, Thomas
2002-08-01
We have studied various aspects concerning the use of hyperbolic wavelets and adaptive approximation schemes for wavelet expansions of correlated wave functions. In order to analyze the consequences of reduced regularity of the wave function at the electron-electron cusp, we first considered a realistic exactly solvable many-particle model in one dimension. Convergence rates of wavelet expansions, with respect to L2 and H1 norms and the energy, were established for this model. We compare the performance of hyperbolic wavelets and their extensions through adaptive refinement in the cusp region, to a fully adaptive treatment based on the energy contribution of individual wavelets. Although hyperbolic wavelets show an inferior convergence behavior, they can be easily refined in the cusp region yielding an optimal convergence rate for the energy. Preliminary results for the helium atom are presented, which demonstrate the transferability of our observations to more realistic systems. We propose a contraction scheme for wavelets in the cusp region, which reduces the number of degrees of freedom and yields a favorable cost to benefit ratio for the evaluation of matrix elements.
A dynamic bandwidth allocation scheme for EPON
NASA Astrophysics Data System (ADS)
Li, Xiuyuan; Wu, Xiaojuan; Ma, Maode; Li, Wenming; Zhang, Yuanyuan
2008-11-01
This paper analyses current bandwidth schemes and proposes a novel dynamic bandwidth allocation scheme for EPON. According the scheme, we define four kinds of multimedia services such as Unsolicited Request Service (URS), Realtime Service (rt-S), Non-Real-time Service (nrt-S) and Best Effort (BE). Different kinds of services have different Quality of Service (QoS) requirements. Our scheme considers the diverse QoS request, e.g., delay for rt-S, throughput for nrt-S and fairness for BE. The simulation results show this novel scheme can ensure the quality of service (QoS) and improve bandwidth utilization.
Convergence of the Approximation Scheme to American Option Pricing via the Discrete Morse Semiflow
Ishii, Katsuyuki; Omata, Seiro
2011-12-15
We consider the approximation scheme to the American call option via the discrete Morse semiflow, which is a minimizing scheme of a time semi-discretized variational functional. In this paper we obtain a rate of convergence of approximate solutions and the convergence of approximate free boundaries. We mainly apply the theory of variational inequalities and that of viscosity solutions to prove our results.
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.
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.
Evaluating the Accuracy of Hessian Approximations for Direct Dynamics Simulations.
Zhuang, Yu; Siebert, Matthew R; Hase, William L; Kay, Kenneth G; Ceotto, Michele
2013-01-01
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. PMID:26589009
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.
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.
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.
Dynamical Vertex Approximation for the Hubbard Model
NASA Astrophysics Data System (ADS)
Toschi, Alessandro
A full understanding of correlated electron systems in the physically relevant situations of three and two dimensions represents a challenge for the contemporary condensed matter theory. However, in the last years considerable progress has been achieved by means of increasingly more powerful quantum many-body algorithms, applied to the basic model for correlated electrons, the Hubbard Hamiltonian. Here, I will review the physics emerging from studies performed with the dynamical vertex approximation, which includes diagrammatic corrections to the local description of the dynamical mean field theory (DMFT). In particular, I will first discuss the phase diagram in three dimensions with a special focus on the commensurate and incommensurate magnetic phases, their (quantum) critical properties, and the impact of fluctuations on electronic lifetimes and spectral functions. In two dimensions, the effects of non-local fluctuations beyond DMFT grow enormously, determining the appearance of a low-temperature insulating behavior for all values of the interaction in the unfrustrated model: Here the prototypical features of the Mott-Hubbard metal-insulator transition, as well as the existence of magnetically ordered phases, are completely overwhelmed by antiferromagnetic fluctuations of exponentially large extension, in accordance with the Mermin-Wagner theorem. Eventually, by a fluctuation diagnostics analysis of cluster DMFT self-energies, the same magnetic fluctuations are identified as responsible for the pseudogap regime in the holed-doped frustrated case, with important implications for the theoretical modeling of the cuprate physics.
On a family of monotone finite-difference schemes of the second order of approximation
NASA Astrophysics Data System (ADS)
Gushchin, Valentin A.
2015-11-01
Using a simple model of a linear transport equation a family of hybrid monotone finite difference schemes has been constructed. By the analysis of the differential approximation it was shown that the resulting family has a secondorder approximation in the spatial variable, has minimal scheme viscosity and dispersion and monotonous. It is shown that the region of operability of the base schemes (Modified Central Difference Schemes (MCDS) and Modified Upwind Difference Schemes (MUDS)) is a non-empty set. The local criterion for switching between the base schemes is based on the sign of the product of the velocity, the first and second differences of the transferred functions at the considered point. On the solution of the Cauchy problem provides a graphical comparison of the calculation results obtained using the known schemes of the first, second and third order approximation. This work has been partly supported by Russian Foundation for Basic Research (grants No. 14-01-00428, 15-51-50023), by the program of the Presidium of RAS No. 8 and by the program No. 3 of the Department of Mathematical Sciences of RAS.
Iterated upwind schemes for gas dynamics
Smolarkiewicz, Piotr K. Szmelter, Joanna
2009-01-10
A class of high-resolution schemes established in integration of anelastic equations is extended to fully compressible flows, and documented for unsteady (and steady) problems through a span of Mach numbers from zero to supersonic. The schemes stem from iterated upwind technology of the multidimensional positive definite advection transport algorithm (MPDATA). The derived algorithms employ standard and modified forms of the equations of gas dynamics for conservation of mass, momentum and either total or internal energy as well as potential temperature. Numerical examples from elementary wave propagation, through computational aerodynamics benchmarks, to atmospheric small- and large-amplitude acoustics with intricate wave-flow interactions verify the approach for both structured and unstructured meshes, and demonstrate its flexibility and robustness.
Towards syntactic characterizations of approximation schemes via predicate and graph decompositions
Hunt, H.B. III; Stearns, R.E.; Jacob, R.; Marathe, M.V.
1998-12-01
The authors present a simple extensible theoretical framework for devising polynomial time approximation schemes for problems represented using natural syntactic (algebraic) specifications endowed with natural graph theoretic restrictions on input instances. Direct application of the technique yields polynomial time approximation schemes for all the problems studied in [LT80, NC88, KM96, Ba83, DTS93, HM+94a, HM+94] as well as the first known approximation schemes for a number of additional combinatorial problems. One notable aspect of the work is that it provides insights into the structure of the syntactic specifications and the corresponding algorithms considered in [KM96, HM+94]. The understanding allows them to extend the class of syntactic specifications for which generic approximation schemes can be developed. The results can be shown to be tight in many cases, i.e. natural extensions of the specifications can be shown to yield non-approximable problems. The results provide a non-trivial characterization of a class of problems having a PTAS and extend the earlier work on this topic by [KM96, HM+94].
NASA Astrophysics Data System (ADS)
Bishop, R. F.; Li, P. H. Y.
2011-04-01
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.
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.
S{sub N} Schemes, Linear Infinite-Medium Solutions, and the Diffusion Approximation
Larsen, E.W.
2001-06-17
It is standard practice to require an S{sub N} spatial discretization scheme to preserve the ''flat infinite-medium'' solution of the transport equation. This solution consists of a spatially independent source that gives rise to a spatially independent flux. However, there exist many other exact solutions of the transport equation that are typically not preserved by approximation schemes. Here, we discuss one of these: a source that is linear in space giving rise to an angular flux that is linear in space and angle. For one-group, planar-geometry S{sub N} problems, we show that (a) among the class of weighted-diamond schemes, only one - the diamond-difference scheme - preserves this exact ''linear'' solution; (b) consequently, only the diamond scheme preserves the correct Fick's Law; and (c) as a further consequence, nondiamond schemes can produce significant errors (not observed in the diamond solution) for diffusive problems with spatial cells that are not optically thin. These results demonstrate that it is advantageous for S{sub N} discretization schemes to preserve the ''flat'' and ''linear'' infinite-medium solutions.
Ceotto, Michele; Zhuang, Yu; Hase, William L
2013-02-01
This paper shows how a compact finite difference Hessian approximation scheme can be proficiently implemented into semiclassical initial value representation molecular dynamics. Effects of the approximation on the monodromy matrix calculation are tested by propagating initial sampling distributions to determine power spectra for analytic potential energy surfaces and for "on the fly" carbon dioxide direct dynamics. With the approximation scheme the computational cost is significantly reduced, making ab initio direct semiclassical dynamics computationally more feasible and, at the same time, properly reproducing important quantum effects inherent in the monodromy matrix and the pre-exponential factor of the semiclassical propagator. PMID:23406107
NASA Astrophysics Data System (ADS)
Mackay, R. S.
1998-10-01
An approximate renormalisation scheme is derived for the breakup of invariant tori of arbitrary winding ratio in Hamiltonian systems of one and a half degrees of freedom, similar to that of Escande and Doveil. It is a free semi-group with two generators. This scheme is solved exactly for its orbits, stable manifolds, unstable manifolds and critical set. Various results are found, including a Cantor set of universal fractal diagrams, the robustness of noble tori, and a scaling law for areas near critical circles.
NASA Astrophysics Data System (ADS)
Mackay, R. S.
1988-10-01
An approximate renormalisation scheme is derived for the breakup of invariant tori of arbitrary winding ratio in Hamiltonian systems of one and a half degrees of freedom, similar to that of Escande and Doveil. It is a free semi-group with two generators. This scheme is solved exactly for its orbits, stable manifolds, unstable manifolds and critical set. Various results are found, including a Cantor set of universal fractal diagrams, the robustness of noble tori, and a scaling law for areas near critical circles.
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.
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.
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.
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.
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.
On the existence of polynomial time approximation schemes for OBDD minimization
NASA Astrophysics Data System (ADS)
Sieling, Detlef
The size of Ordered Binary Decision Diagrams (OBDDs) is determined by the chosen variable ordering. A poor choice may cause an OBDD to be too large to fit into the available memory. The decision variant of the variable ordering problem is known to be NP-complete. We strengthen this result by showing that there is no polynomial time approximation scheme for the variable ordering problem unless P = NP. We also prove a small lower bound on the performance ratio of a polynomial time approximation algorithm under the assumption P ≠ NP.
Tight-binding density functional theory: an approximate Kohn-Sham DFT scheme.
Seifert, G
2007-07-01
The DFTB method is an approximate KS-DFT scheme with an LCAO representation of the KS orbitals, which can be derived within a variational treatment of an approximate KS energy functional. But it may also be related to cellular Wigner-Seitz methods and to the Harris functional. It is an approximate method, but it avoids any empirical parametrization by calculating the Hamiltonian and overlap matrices out of DFT-derived local orbitals (atomic orbitals, AO's). The method includes ab initio concepts in relating the Kohn-Sham orbitals of the atomic configuration to a minimal basis of the localized atomic valence orbitals of the atoms. Consistent with this approximation, the Hamiltonian matrix elements can strictly be restricted to a two-center representation. Taking advantage of the compensation of the so-called "double counting terms" and the nuclear repulsion energy in the DFT total energy expression, the energy may be approximated as a sum of the occupied KS single-particle energies and a repulsive energy, which can be obtained from DFT calculations in properly chosen reference systems. This relates the method to common standard "tight-binding" (TB) schemes, as they are well-known in solid-state physics. This approach defines the density-functional tight-binding (DFTB) method in its original (non-self-consistent) version. PMID:17439198
The Newtonian approximation in Causal Dynamical Triangulations
NASA Astrophysics Data System (ADS)
Getchell, Adam
2015-04-01
I review how to derive Newton's law of universal gravitation from the Weyl strut between two Chazy-Curzon particles. I also briefly review Causal Dynamical Triangulations (CDT), a method for evaluating the path integral from canonical quantum gravity using Regge calculus and restrictions of the class of simplicial manifolds evaluated to those with a defined time foliation, thus enforcing a causal structure. I then discuss how to apply this approach to Causal Dynamical Triangulations, in particular modifying the algorithm to keep two simplicial submanifolds with curvature (i.e. mass) a fixed distance from each other, modulo regularized deviations and across all time slices. I then discuss how to determine if CDT produces an equivalent Weyl strut, which can then be used to obtain the Newtonian limit. I wrap up with a brief discussion of computational methods and code development.
STOVL propulsion system volume dynamics approximations
NASA Technical Reports Server (NTRS)
Drummond, Colin K.
1989-01-01
Two approaches to modeling turbofan engine component volume dynamics are explored and compared with a view toward application to real-time simulation of short take-off vertical landing (STOVL) aircraft propulsion systems. The first (and most popular) approach considers only heat and mass balances; the second approach includes a momentum balance and substitutes the heat equation with a complete energy balance. Results for a practical test case are presented and discussed.
The relativistic scheme for eliminating small components Hamiltonian: Analysis of approximations
NASA Astrophysics Data System (ADS)
Barysz, Maria
2000-09-01
The derivation of the recently proposed one-component relativistic Hamiltonian, and the resulting relativistic scheme by eliminating small components (RESC) method of Nakajima and Hirao, are analyzed in terms of the Foldy-Wouthuysen transformation of the Dirac Hamiltonian. This approach reveals the meaning of different approximations used in the derivation of the RESC Hamiltonian and its close relation to approximate relativistic Hamiltonians resulting from the free-particle Foldy-Wouthuysen transformation. Moreover, the present derivation combined with what is called the classical approximation in Nakajima and Hirao's approach shows that there is a whole family of the RESC-type Hamiltonians. Some of them, including the original RESC Hamiltonian, are analyzed numerically. It is documented that neither of the RESC-type Hamiltonians offers variational stability. As a consequence the RESC methods may suffer from the variational collapse for heavier systems. On the other hand the energy differences (e.g., ionization potentials) computed within the RESC approach turn out to be close to the values obtained in the Douglas-Kroll scheme.
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.
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. PMID:26298117
NASA Astrophysics Data System (ADS)
Zhong, Zhi-Rong
2008-05-01
An alternative scheme to approximately conditionally teleport entangled two-mode cavity state without Bell state measurement in cavity QED is proposed. The scheme is based on the resonant interaction of a ladder-type three-level atom with two bimodal cavities. The entangled cavity state is reconstructed with only one atom interacting with the two cavities successively.
A multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations
NASA Technical Reports Server (NTRS)
Yoon, Seokkwan; Jameson, Antony
1986-01-01
A new efficient relaxation scheme in conjunction with a multigrid method is developed for the Euler equations. The LU SSOR scheme is based on a central difference scheme and does not need flux splitting for Newton iteration. Application to transonic flow shows that the new method surpasses the performance of the LU implicit scheme.
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.
Some approximations in the linear dynamic equations of thin cylinders
NASA Technical Reports Server (NTRS)
El-Raheb, M.; Babcock, C. D., Jr.
1981-01-01
Theoretical analysis is performed on the linear dynamic equations of thin cylindrical shells to find the error committed by making the Donnell assumption and the neglect of in-plane inertia. At first, the effect of these approximations is studied on a shell with classical simply supported boundary condition. The same approximations are then investigated for other boundary conditions from a consistent approximate solution of the eigenvalue problem. The Donnell assumption is valid at frequencies high compared with the ring frequencies, for finite length thin shells. The error in the eigenfrequencies from omitting tangential inertia is appreciable for modes with large circumferential and axial wavelengths, independent of shell thickness and boundary conditions.
Analysis of the dynamical cluster approximation for the Hubbard model
NASA Astrophysics Data System (ADS)
Aryanpour, K.; Hettler, M. H.; Jarrell, M.
2002-04-01
We examine a central approximation of the recently introduced dynamical cluster approximation (DCA) by example of the Hubbard model. By both analytical and numerical means we study noncompact and compact contributions to the thermodynamic potential. We show that approximating noncompact diagrams by their cluster analogs results in a larger systematic error as compared to the compact diagrams. Consequently, only the compact contributions should be taken from the cluster, whereas noncompact graphs should be inferred from the appropriate Dyson equation. The distinction between noncompact and compact diagrams persists even in the limit of infinite dimensions. Nonlocal corrections beyond the DCA exist for the noncompact diagrams, whereas they vanish for compact diagrams.
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.
XML Reconstruction View Selection in XML Databases: Complexity Analysis and Approximation Scheme
NASA Astrophysics Data System (ADS)
Chebotko, Artem; Fu, Bin
Query evaluation in an XML database requires reconstructing XML subtrees rooted at nodes found by an XML query. Since XML subtree reconstruction can be expensive, one approach to improve query response time is to use reconstruction views - materialized XML subtrees of an XML document, whose nodes are frequently accessed by XML queries. For this approach to be efficient, the principal requirement is a framework for view selection. In this work, we are the first to formalize and study the problem of XML reconstruction view selection. The input is a tree T, in which every node i has a size c i and profit p i , and the size limitation C. The target is to find a subset of subtrees rooted at nodes i 1, ⋯ , i k respectively such that c_{i_1}+\\cdots +c_{i_k}le C, and p_{i_1}+\\cdots +p_{i_k} is maximal. Furthermore, there is no overlap between any two subtrees selected in the solution. We prove that this problem is NP-hard and present a fully polynomial-time approximation scheme (FPTAS) as a solution.
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.
On a renormalization group scheme for causal dynamical triangulations
NASA Astrophysics Data System (ADS)
Cooperman, Joshua H.
2016-03-01
The causal dynamical triangulations approach aims to construct a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. A renormalization group scheme—in concert with finite size scaling analysis—is essential to this aim. Formulating and implementing such a scheme in the present context raises novel and notable conceptual and technical problems. I explored these problems, and, building on standard techniques, suggested potential solutions in a previous paper (Cooperman, arXiv:gr-qc/1410.0026). As an application of these solutions, I now propose a renormalization group scheme for causal dynamical triangulations. This scheme differs significantly from that studied recently by Ambjørn, Görlich, Jurkiewicz, Kreienbuehl, and Loll.
Implicit Time Integration for Multiscale Molecular Dynamics Using Transcendental Padé Approximants.
Abi Mansour, Andrew; Ortoleva, Peter J
2016-04-12
Molecular dynamics systems evolve through the interplay of collective and localized disturbances. As a practical consequence, there is a restriction on the time step imposed by the broad spectrum of time scales involved. To resolve this restriction, multiscale factorization was introduced for molecular dynamics as a method that exploits the separation of time scales by coevolving the coarse-grained and atom-resolved states via Trotter factorization. Developing a stable time-marching scheme for this coevolution, however, is challenging because the coarse-grained dynamical equations depend on the microstate; therefore, these equations cannot be expressed in closed form. The objective of this paper is to develop an implicit time integration scheme for multiscale simulation of large systems over long periods of time and with high accuracy. The scheme uses Padé approximants to account for both the stochastic and deterministic features of the coarse-grained dynamics. The method is demonstrated for a protein either undergoing a conformational change or migrating under the influence of an external force. The method shows promise in accelerating multiscale molecular dynamics without a loss of atomic precision or the need to conjecture the form of coarse-grained governing equations. PMID:26845510
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.
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.
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.
Dynamics of false vacuum bubbles: beyond the thin shell approximation
NASA Astrophysics Data System (ADS)
Hansen, Jakob; Hwang, Dong-il; Yeom, Dong-han
2009-11-01
We numerically study the dynamics of false vacuum bubbles which are inside an almost flat background; we assumed spherical symmetry and the size of the bubble is smaller than the size of the background horizon. According to the thin shell approximation and the null energy condition, if the bubble is outside of a Schwarzschild black hole, unless we assume Farhi-Guth-Guven tunneling, expanding and inflating solutions are impossible. In this paper, we extend our method to beyond the thin shell approximation: we include the dynamics of fields and assume that the transition layer between a true vacuum and a false vacuum has non-zero thickness. If a shell has sufficiently low energy, as expected from the thin shell approximation, it collapses (Type 1). However, if the shell has sufficiently large energy, it tends to expand. Here, via the field dynamics, field values of inside of the shell slowly roll down to the true vacuum and hence the shell does not inflate (Type 2). If we add sufficient exotic matters to regularize the curvature near the shell, inflation may be possible without assuming Farhi-Guth-Guven tunneling. In this case, a wormhole is dynamically generated around the shell (Type 3). By tuning our simulation parameters, we could find transitions between Type 1 and Type 2, as well as between Type 2 and Type 3. Between Type 2 and Type 3, we could find another class of solutions (Type 4). Finally, we discuss the generation of a bubble universe and the violation of unitarity. We conclude that the existence of a certain combination of exotic matter fields violates unitarity.
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.
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
Parameterizing large-scale dynamics with the weak pressure gradient approximation
NASA Astrophysics Data System (ADS)
Edman, J. P.; Romps, D. M.
2013-12-01
Cloud-resolving and single-column models are useful tools for understanding the dynamics of convection and developing convective parameterizations. However, these tools are severely limited by their inherent inability to simulate the dynamics of the environment in which they are imagined to be immersed. Previous attempts to solve this problem have resulted in various ';supra-domain scale' parameterizations, which allow the model to prescribe its own vertical velocity profile based on some limited information about the external environment (e.g. pressure and potential temperature profiles). Here we present a new implementation of one of these schemes, the weak pressure gradient approximation (WPG), which is shown to reproduce both the transient and steady state dynamics of a 3D atmosphere in a single column. Further, we demonstrate the skill of this new WPG method at replicating observed time series of precipitation and vertical velocity in a series of cloud-resolving simulations.
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. PMID:26241987
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.
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. PMID:25616741
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. PMID:20866355
Interlaced coarse-graining for the dynamical cluster approximation
NASA Astrophysics Data System (ADS)
Haehner, Urs; Staar, Peter; Jiang, Mi; Maier, Thomas; Schulthess, Thomas
The negative sign problem remains a challenging limiting factor in quantum Monte Carlo simulations of strongly correlated fermionic many-body systems. The dynamical cluster approximation (DCA) makes this problem less severe by coarse-graining the momentum space to map the bulk lattice to a cluster embedded in a dynamical mean-field host. Here, we introduce a new form of an interlaced coarse-graining and compare it with the traditional coarse-graining. We show that it leads to more controlled results with weaker cluster shape and smoother cluster size dependence, which with increasing cluster size converge to the results obtained using the standard coarse-graining. In addition, the new coarse-graining reduces the severity of the fermionic sign problem. Therefore, it enables calculations on much larger clusters and can allow the evaluation of the exact infinite cluster size result via finite size scaling. To demonstrate this, we study the hole-doped two-dimensional Hubbard model and show that the interlaced coarse-graining in combination with the DCA+ algorithm permits the determination of the superconducting Tc on cluster sizes, for which the results can be fitted with the Kosterlitz-Thouless scaling law. This research used resources of the Oak Ridge Leadership Computing Facility (OLCF) awarded by the INCITE program, and of the Swiss National Supercomputing Center. OLCF is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725.
Interlaced coarse-graining for the dynamic cluster approximation
NASA Astrophysics Data System (ADS)
Staar, P.; Jiang, M.; Hähner, U. R.; Schulthess, T. C.; Maier, T. A.
2016-04-01
The dynamical cluster approximation (DCA) and its DCA+ extension use coarse-graining of the momentum space to reduce the complexity of quantum many-body problems, thereby mapping the bulk lattice to a cluster embedded in a dynamical mean-field host. Here, we introduce a new form of an interlaced coarse-graining and compare it with the traditional coarse-graining. While it gives a more localized self-energy for a given cluster size, we show that it leads to more controlled results with weaker cluster shape and smoother cluster size dependence, which converge to the results obtained from the standard coarse-graining with increasing cluster size. Most importantly, the new coarse-graining reduces the severity of the fermionic sign problem of the underlying quantum Monte Carlo cluster solver and thus allows for calculations on larger clusters. This enables the treatment of correlations longer ranged than those accessible with the standard coarse-graining and thus can allow for the evaluation of the exact infinite cluster size result via finite size scaling. As a demonstration, we study the hole-doped two-dimensional Hubbard model and show that the interlaced coarse-graining in combination with the extended DCA+ algorithm permits the determination of the superconducting Tc on cluster sizes for which the results can be fit with a Kosterlitz-Thouless scaling law.
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
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
Approximations for inclusion of rotor lag dynamics in helicopter flight dynamics models
NASA Technical Reports Server (NTRS)
Mckillip, Robert, Jr.; Curtiss, Howard C., Jr.
1991-01-01
Approximate forms are suggested for augmenting linear rotor/body response models to include rotor lag dynamics. Use of an analytically linearized rotor/body model has shown that the primary effect comes from the additional angular rate contributions of the lag inertial response. Addition of lag dynamics may be made assuming these dynamics are represented by an isolated rotor with no shaft motion. Implications of such an approximation are indicated through comparison with flight test data and sensitivity of stability levels with body rate feedback.
Self-consistency based control scheme for magnetization dynamics
Albuquerque, G.; Miltat, J.; Thiaville, A.
2001-06-01
A numerical framework is presented for the solution of the Landau{endash}Lifshitz{endash}Gilbert equation of magnetization motion using a semi-implicit Crank{endash}Nicholson integration scheme. Along with the details of both space and time domain discretizations, we report on the development of a physically based self-consistency criterion that allows for a quantitative measurement of error in dynamic micromagnetic simulations. In essence, this criterion relies in recalculating from actual magnetization motion the imposed phenomenological damping constant. Test calculations were performed with special attention paid to the determination of suitable integration time steps. {copyright} 2001 American Institute of Physics.
NASA Astrophysics Data System (ADS)
Kel'manov, A. V.; Khandeev, V. I.
2016-02-01
The strongly NP-hard problem of partitioning a finite set of points of Euclidean space into two clusters of given sizes (cardinalities) minimizing the sum (over both clusters) of the intracluster sums of squared distances from the elements of the clusters to their centers is considered. It is assumed that the center of one of the sought clusters is specified at the desired (arbitrary) point of space (without loss of generality, at the origin), while the center of the other one is unknown and determined as the mean value over all elements of this cluster. It is shown that unless P = NP, there is no fully polynomial-time approximation scheme for this problem, and such a scheme is substantiated in the case of a fixed space dimension.
NASA Technical Reports Server (NTRS)
Ballhaus, W. F.; Jameson, A.; Albert, J.
1977-01-01
Implicit approximate-factorization algorithms (AF) are developed for the solution of steady-state transonic flow problems. The performance of the AF solution method is evaluated relative to that of the standard solution method for transonic flow problems, successive line over-relaxation (SLOR). Both methods are applied to the solution of the nonlinear, two-dimensional transonic small-disturbance equation. Results indicate that the AF method requires substantially less computer time than SLOR to solve the nonlinear finite-difference matrix equation for a transonic flow field. This increase in computational efficiency is achieved with no appreciable increase in computer storage or coding complexity.
Dynamic obstacle avoidance using Bayesian Occupancy Filter and approximate inference.
Llamazares, Angel; 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 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
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
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.
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.
Approximate supernova remnant dynamics with cosmic ray production
NASA Technical Reports Server (NTRS)
Voelk, H. J.; Dorfi, E. A.; Drury, L. O.
1985-01-01
Supernova explosions are the most violent and energetic events in the galaxy and have long been considered probably sources of Cosmic Rays. Recent shock acceleration models treating the Cosmic Rays (CR's) as test particles nb a prescribed Supernova Remnant (SNR) evolution, indeed indicate an approximate power law momentum distribution f sub source (p) approximation p(-a) for the particles ultimately injected into the Interstellar Medium (ISM). This spectrum extends almost to the momentum p = 1 million GeV/c, where the break in the observed spectrum occurs. The calculated power law index approximately less than 4.2 agrees with that inferred for the galactic CR sources. The absolute CR intensity can however not be well determined in such a test particle approximation.
An Efficient Molecular Dynamics Scheme for Predicting Dopant Implant Profiles in Semiconductors
Beardmore, K.M.; Gronbech-Jensen, N.
1998-09-15
The authors present a highly efficient molecular dynamics scheme for calculating the concentration profile of dopants implanted in group-IV alloy, and III-V zinc blende structure materials. The program incorporates methods for reducing computational overhead, plus a rare event algorithm to give statistical accuracy over several orders of magnitude change in the dopant concentration. The code uses a molecular dynamics (MD) model, instead of the binary collision approximation (BCA) used in implant simulators such as TRIM and Marlowe, to describe ion-target interactions. Atomic interactions are described by a combination of 'many-body' and screened Coulomb potentials. Inelastic energy loss is accounted for using a Firsov model, and electronic stopping is described by a Brandt-Kitagawa model which contains the single adjustable parameter for the entire scheme. Thus, the program is easily extensible to new ion-target combinations with the minimum of tuning, and is predictive over a wide range of implant energies and angles. The scheme is especially suited for calculating profiles due to low energy, large angle implants, and for situations where a predictive capability is required with the minimum of experimental validation. They give examples of using their code to calculate concentration profiles and 2D 'point response' profiles of dopants in crystalline silicon, silicon-germanium blends, and gallium-arsenide. They can predict the experimental profiles over five orders of magnitude for <100> and <110> channeling and for non-channeling implants at energies up to hundreds of keV.
Exact and approximate gas dynamics using the tangent gas
NASA Technical Reports Server (NTRS)
Daripa, P. K.; Sirovich, L.
1986-01-01
For the determination of aerodynamic characteristics such as lift, drag, and moment coefficients, it is crucial to compute the properties of steady flow past an airfoil. This investigation provides a set of flow dependent grid systems and initial flowfield guesses which substantially improve convergence rates when applied to the Euler equations for flows past an airfoil. The basic equations are examined, taking into account nonlinear equations which are difficult to solve. A good approximation to these equations under certain conditions can be obtained by introducing the so-called 'tangent gas approximation' considered by Woods (1961), in which the isentropic relation between rho and p is replaced by a tangent to a curve. Attention is given to the solution procedure, the analysis (direct) problem, and a comparison of the tangent gas solution with the converged Euler solution.
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.
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
Development of new flux splitting schemes. [computational fluid dynamics algorithms
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing; Steffen, Christopher J., Jr.
1992-01-01
Maximizing both accuracy and efficiency has been the primary objective in designing a numerical algorithm for computational fluid dynamics (CFD). This is especially important for solutions of complex three dimensional systems of Navier-Stokes equations which often include turbulence modeling and chemistry effects. Recently, upwind schemes have been well received for their capability in resolving discontinuities. With this in mind, presented are two new flux splitting techniques for upwind differencing. The first method is based on High-Order Polynomial Expansions (HOPE) of the mass flux vector. The second new flux splitting is based on the Advection Upwind Splitting Method (AUSM). The calculation of the hypersonic conical flow demonstrates the accuracy of the splitting in resolving the flow in the presence of strong gradients. A second series of tests involving the two dimensional inviscid flow over a NACA 0012 airfoil demonstrates the ability of the AUSM to resolve the shock discontinuity at transonic speed. A third case calculates a series of supersonic flows over a circular cylinder. Finally, the fourth case deals with tests of a two dimensional shock wave/boundary layer interaction.
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. PMID:23345091
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)
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.
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.
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
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.
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.
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. PMID:25486894
High resolution difference schemes for compressible gas dynamics
Woodward, P.; Colella, P.
1980-07-30
The advantages and disadvantages of four new high-resolution difference schemes, namely the von Neumann-Richtmyer, Godunovs, MUSCL and Glimms, for mathematically representing physical conditions in compressible gas flows are compared. (LCL)
On the convergence of difference schemes for the equations of ocean dynamics
Drutsa, Alexey V; Kobel'kov, Georgii M
2012-08-31
The difference scheme which approximates the equations of large-scale ocean dynamics in a unit cube to the second degree in the space variables is investigated. It is shown that the solutions converge to the solution of the differential problem. Namely, under the assumption that the solution is sufficiently smooth it is proved that (max)/0{<=}m{<=}M||u(m{tau})-v{sup m}||=O({tau}+h{sup 3/2}), M{tau}=T, where ||{center_dot}|| is the grid L{sub 2}-norm with respect to the space variables, v is the solution of the grid problem, and u is the solution of the differential problem. Bibliography: 7 titles.
On the convergence of difference schemes for the equations of ocean dynamics
NASA Astrophysics Data System (ADS)
Drutsa, Alexey V.; Kobel'kov, Georgii M.
2012-08-01
The difference scheme which approximates the equations of large-scale ocean dynamics in a unit cube to the second degree in the space variables is investigated. It is shown that the solutions converge to the solution of the differential problem. Namely, under the assumption that the solution is sufficiently smooth it is proved that \\displaystyle \\max_{0\\le m\\le M}\\Vert{\\mathbf u}(m\\tau)-{\\mathbf v}^m\\Vert=O(\\tau+h^{3/2}),\\qquadM\\tau=T, where \\Vert\\cdot\\Vert is the grid L_2-norm with respect to the space variables, \\mathbf v is the solution of the grid problem, and \\mathbf u is the solution of the differential problem. Bibliography: 7 titles.
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
An efficient scheme for sampling fast dynamics at a low average data acquisition rate
NASA Astrophysics Data System (ADS)
Philippe, A.; Aime, S.; Roger, V.; Jelinek, R.; Prévot, G.; Berthier, L.; Cipelletti, L.
2016-02-01
We introduce a temporal scheme for data sampling, based on a variable delay between two successive data acquisitions. The scheme is designed so as to reduce the average data flow rate, while still retaining the information on the data evolution on fast time scales. The practical implementation of the scheme is discussed and demonstrated in light scattering and microscopy experiments that probe the dynamics of colloidal suspensions using CMOS or CCD cameras as detectors.
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.
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
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
Restoration scheme for multi-failures based on protection ring with dynamic weight in WDM networks
NASA Astrophysics Data System (ADS)
Huang, Hai; Zhao, Yongli; Zhang, Jie; Wang, Dajiang; Gu, Wanyi
2011-12-01
A novel restoration scheme for multi-failures based on protection ring with dynamic weight (PRDW) is proposed in this paper. This scheme effectively resolves the multi-failures which is in one service and the conflicts by restoration between services. PRDW use Dijkstra's algorithm to compute path and protection ring. These rings rely on protection weight which is dynamic, so that they can as much as possible to divide multi-failures to single ones. Meanwhile PRDW introduce independent protection weight to balance load, which effectively gets combat for resources less vicious. Simulation results show that PRDW works better than traditional schemes.
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.
NASA Astrophysics Data System (ADS)
Thoma, M.; Grosfeld, K.; Barbi, D.; Determann, J.; Goeller, S.; Mayer, C.; Pattyn, F.
2014-01-01
Glaciers and ice caps exhibit currently the largest cryospheric contributions to sea level rise. Modelling the dynamics and mass balance of the major ice sheets is therefore an important issue to investigate the current state and the future response of the cryosphere in response to changing environmental conditions, namely global warming. This requires a powerful, easy-to-use, versatile multi-approximation ice dynamics model. Based on the well-known and established ice sheet model of Pattyn (2003) we develop the modular multi-approximation thermomechanic ice model RIMBAY, in which we improve the original version in several aspects like a shallow ice-shallow shelf coupler and a full 3D-grounding-line migration scheme based on Schoof's (2007) heuristic analytical approach. We summarise the full Stokes equations and several approximations implemented within this model and we describe the different numerical discretisations. The results are cross-validated against previous publications dealing with ice modelling, and some additional artificial set-ups demonstrate the robustness of the different solvers and their internal coupling. RIMBAY is designed for an easy adaption to new scientific issues. Hence, we demonstrate in very different set-ups the applicability and functionality of RIMBAY in Earth system science in general and ice modelling in particular.
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.
Cen, Zhaohui; Wei, Jiaolong; Jiang, Rui
2013-12-01
A novel gray-box neural network model (GBNNM), including multi-layer perception (MLP) neural network (NN) and integrators, is proposed for a model identification and fault estimation (MIFE) scheme. With the GBNNM, both the nonlinearity and dynamics of a class of nonlinear dynamic systems can be approximated. Unlike previous NN-based model identification methods, the GBNNM directly inherits system dynamics and separately models system nonlinearities. This model corresponds well with the object system and is easy to build. The GBNNM is embedded online as a normal model reference to obtain the quantitative residual between the object system output and the GBNNM output. This residual can accurately indicate the fault offset value, so it is suitable for differing fault severities. To further estimate the fault parameters (FPs), an improved extended state observer (ESO) using the same NNs (IESONN) from the GBNNM is proposed to avoid requiring the knowledge of ESO nonlinearity. Then, the proposed MIFE scheme is applied for reaction wheels (RW) in a satellite attitude control system (SACS). The scheme using the GBNNM is compared with other NNs in the same fault scenario, and several partial loss of effect (LOE) faults with different severities are considered to validate the effectiveness of the FP estimation and its superiority. PMID:24156668
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
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. PMID:27019868
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
On the accuracy of the state space restriction approximation for spin dynamics simulations
NASA Astrophysics Data System (ADS)
Karabanov, Alexander; Kuprov, Ilya; Charnock, G. T. P.; van der Drift, Anniek; Edwards, Luke J.; Köckenberger, Walter
2011-08-01
We present an algebraic foundation for the state space restriction approximation in spin dynamics simulations and derive applicability criteria as well as minimal basis set requirements for practically encountered simulation tasks. The results are illustrated with nuclear magnetic resonance (NMR), electron spin resonance (ESR), dynamic nuclear polarization (DNP), and spin chemistry simulations. It is demonstrated that state space restriction yields accurate results in systems where the time scale of spin relaxation processes approximately matches the time scale of the experiment. Rigorous error bounds and basis set requirements are derived.
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. PMID:26772559
NASA Astrophysics Data System (ADS)
Homman, Ahmed-Amine; Maillet, Jean-Bernard; Roussel, Julien; Stoltz, Gabriel
2016-01-01
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.
Study on utility of an approximated transfer function of dynamically tuned dry gyro
NASA Astrophysics Data System (ADS)
Shingu, H.; Otsuki, M.; Hayano, T.
The use of a dry gyro in analog rebalance loops is described and a method to improve the static and dynamic characteristics is presented. The transfer function is derived by transforming a generalized equation into the approximated form based on the design specifications of the mechanical parts. This approximation is proved to be reasonable by the result that the differences between the numerical solutions of a generalized equation and those of an approximated equation are less than 1.0%, and their mean values are less than 0.003%. Noninteracting control is analyzed and the stability conditions are investigated. A fundamental design conception for rebalance loops was established.
Dynamic Analyses of Result Quality in Energy-Aware Approximate Programs
NASA Astrophysics Data System (ADS)
RIngenburg, Michael F.
Energy efficiency is a key concern in the design of modern computer systems. One promising approach to energy-efficient computation, approximate computing, trades off output precision for energy efficiency. However, this tradeoff can have unexpected effects on computation quality. This thesis presents dynamic analysis tools to study, debug, and monitor the quality and energy efficiency of approximate computations. We propose three styles of tools: prototyping tools that allow developers to experiment with approximation in their applications, online tools that instrument code to determine the key sources of error, and online tools that monitor the quality of deployed applications in real time. Our prototyping tool is based on an extension to the functional language OCaml. We add approximation constructs to the language, an approximation simulator to the runtime, and profiling and auto-tuning tools for studying and experimenting with energy-quality tradeoffs. We also present two online debugging tools and three online monitoring tools. The first online tool identifies correlations between output quality and the total number of executions of, and errors in, individual approximate operations. The second tracks the number of approximate operations that flow into a particular value. Our online tools comprise three low-cost approaches to dynamic quality monitoring. They are designed to monitor quality in deployed applications without spending more energy than is saved by approximation. Online monitors can be used to perform real time adjustments to energy usage in order to meet specific quality goals. We present prototype implementations of all of these tools and describe their usage with several applications. Our prototyping, profiling, and autotuning tools allow us to experiment with approximation strategies and identify new strategies, our online tools succeed in providing new insights into the effects of approximation on output quality, and our monitors succeed in
Chen, Hung-Ming; Lo, Jung-Wen; Yeh, Chang-Kuo
2012-12-01
The rapidly increased availability of always-on broadband telecommunication environments and lower-cost vital signs monitoring devices bring the advantages of telemedicine directly into the patient's home. Hence, the control of access to remote medical servers' resources has become a crucial challenge. A secure authentication scheme between the medical server and remote users is therefore needed to safeguard data integrity, confidentiality and to ensure availability. Recently, many authentication schemes that use low-cost mobile devices have been proposed to meet these requirements. In contrast to previous schemes, Khan et al. proposed a dynamic ID-based remote user authentication scheme that reduces computational complexity and includes features such as a provision for the revocation of lost or stolen smart cards and a time expiry check for the authentication process. However, Khan et al.'s scheme has some security drawbacks. To remedy theses, this study proposes an enhanced authentication scheme that overcomes the weaknesses inherent in Khan et al.'s scheme and demonstrated this scheme is more secure and robust for use in a telecare medical information system. PMID:22673892
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-model based estimation method for dynamic response of forging processes
NASA Astrophysics Data System (ADS)
Lei, Jie; Lu, Xinjiang; Li, Yibo; Huang, Minghui; Zou, Wei
2015-03-01
Many high-quality forging productions require the large-sized hydraulic press machine (HPM) to have a desirable dynamic response. Since the forging process is complex under the low velocity, its response is difficult to estimate. And this often causes the desirable low-velocity forging condition difficult to obtain. So far little work has been found to estimate the dynamic response of the forging process under low velocity. In this paper, an approximate-model based estimation method is proposed to estimate the dynamic response of the forging process under low velocity. First, an approximate model is developed to represent the forging process of this complex HPM around the low-velocity working point. Under guaranteeing the modeling performance, the model may greatly ease the complexity of the subsequent estimation of the dynamic response because it has a good linear structure. On this basis, the dynamic response is estimated and the conditions for stability, vibration, and creep are derived according to the solution of the velocity. All these analytical results are further verified by both simulations and experiment. In the simulation verification for modeling, the original movement model and the derived approximate model always have the same dynamic responses with very small approximate error. The simulations and experiment finally demonstrate and test the effectiveness of the derived conditions for stability, vibration, and creep, and these conditions will benefit both the prediction of the dynamic response of the forging process and the design of the controller for the high-quality forging. The proposed method is an effective solution to achieve the desirable low-velocity forging condition.
NASA Astrophysics Data System (ADS)
Bologna, Mauro; Svenkeson, Adam; West, Bruce J.; Grigolini, Paolo
2015-07-01
Diffusion processes in heterogeneous media, and biological systems in particular, are riddled with the difficult theoretical issue of whether the true origin of anomalous behavior is renewal or memory, or a special combination of the two. Accounting for the possible mixture of renewal and memory sources of subdiffusion is challenging from a computational point of view as well. This problem is exacerbated by the limited number of techniques available for solving fractional diffusion equations with time-dependent coefficients. We propose an iterative scheme for solving fractional differential equations with time-dependent coefficients that is based on a parametric expansion in the fractional index. We demonstrate how this method can be used to predict the long-time behavior of nonautonomous fractional differential equations by studying the anomalous diffusion process arising from a mixture of renewal and memory sources.
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.
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. PMID:18632378
Faster Approximation Schemes and Parameterized Algorithms on H-Minor-Free and Odd-Minor-Free Graphs
NASA Astrophysics Data System (ADS)
Tazari, Siamak
We improve the running time of the general algorithmic technique known as Baker's approach (1994) on H-minor-free graphs from O(n^{f(|H|)}) to O(f(|H|) n^{O(1)}). The numerous applications include, e.g. a 2-approximation for coloring and PTASes for various problems such as dominating set and max-cut, where we obtain similar improvements.
NASA Astrophysics Data System (ADS)
Yang, Zeng-hui; Peng, Haowei; Sun, Jianwei; Perdew, John P.
2016-05-01
Unlike the local density approximation (LDA) and the generalized gradient approximation (GGA), calculations with meta-generalized gradient approximations (meta-GGA) are usually done according to the generalized Kohn-Sham (gKS) formalism. The exchange-correlation potential of the gKS equation is nonmultiplicative, which prevents systematic comparison of meta-GGA band structures to those of the LDA and the GGA. We implement the optimized effective potential (OEP) of the meta-GGA for periodic systems, which allows us to carry out meta-GGA calculations in the same KS manner as for the LDA and the GGA. We apply the OEP to several meta-GGAs, including the new SCAN functional [Phys. Rev. Lett. 115, 036402 (2015), 10.1103/PhysRevLett.115.036402]. We find that the KS gaps and KS band structures of meta-GGAs are close to those of GGAs. They are smaller than the more realistic gKS gaps of meta-GGAs, but probably close to the less-realistic gaps in the band structure of the exact KS potential, as can be seen by comparing with the gaps of the EXX+RPA OEP potential. The well-known grid sensitivity of meta-GGAs is much more severe in OEP calculations.
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%.
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.
Uncertainty of establishment scheme in the Community Land Model-Dynamic Global Vegetation Model
NASA Astrophysics Data System (ADS)
Song, X.; Zeng, X.
2010-12-01
Dynamic global vegetation models are very important tools to simulate and predict the relationship between terrestrial ecosystem processes and climate change. They usually consist of several main sub-models, such as establishment, growth, mortality due to stress, competition, reproductive and so forth. In this study, we focus on the establishment sub-model. Establishment sub-model describes the processes of germination of tree seeds and establishment of seedlings. However, due to the complexity of the ecological process and the lack of observation data, current DGVMs use different parameterization schemes of establishment, and the uncertainties of these establishment scheme as well as their impacts on vegetation distribution remain largely unknown. Our work is to introduce several new different establishment schemes, each based on different physical and ecological considerations, into a modified Community Land Model - Dynamic Global Vegetation Model (CLM-DGVM). The sensitivities of the vegetation distribution to different establishment schemes and some essential parameters in the schemes are investigated in different vegetation zones. Our research indicates that establishment scheme has remarkable effects not only on the percent of coverage and population density of different plant functional types (PFTs) but also the community structure such as coexistence of PFTs and even the dominant vegetation. Such changes will alter the ecosystem functioning, and hence have further impacts on climate through the vegetation-atmosphere feedback.
Shirdel-Havar, A. H. Masoudian Saadabad, R.
2015-03-21
Based on ballistic-diffusive approximation, a method is presented to model heat transfer in nanocomposites containing metal nanoparticles. This method provides analytical expression for the temperature dynamics of metallic nanoparticles embedded in a dielectric medium. In this study, nanoparticles are considered as spherical shells, so that Boltzmann equation is solved using ballistic-diffusive approximation to calculate the electron and lattice thermal dynamics in gold nanoparticles, while thermal exchange between the particles is taken into account. The model was used to investigate the influence of particle size and metal concentration of the medium on the electron and lattice thermal dynamics. It is shown that these two parameters are crucial in determining the nanocomposite thermal behavior. Our results showed that the heat transfer rate from nanoparticles to the matrix decreases as the nanoparticle size increases. On the other hand, increasing the metal concentration of the medium can also decrease the heat transfer rate.
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. PMID:23345092
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
The Relation between Approximation in Distribution and Shadowing in Molecular Dynamics
NASA Astrophysics Data System (ADS)
Tupper, Paul
2009-01-01
Molecular dynamics refers to the computer simulation of a material at the atomic level. An open problem in numerical analysis is to explain the apparent reliability of molecular dynamics simulations. The difficulty is that individual trajectories computed in molecular dynamics are accurate for only short time intervals, whereas apparently reliable information can be extracted from very long-time simulations. It has been conjectured that long molecular dynamics trajectories have low-dimensional statistical features that accurately approximate those of the original system. Another conjecture is that numerical trajectories satisfy the shadowing property: they are close over long time intervals to exact trajectories but with different initial conditions. We prove that these two views are actually equivalent to each other, after we suitably modify the concept of shadowing. A key ingredient of our result is a general theorem that allows us to take random elements of a metric space that are close in distribution and embed them in the same probability space so that they are close in a strong sense. This result is similar to the Strassen-Dudley theorem except that a mapping is provided between the two random elements. Our results on shadowing are motivated by molecular dynamics but apply to the approximation of any dynamical system when initial conditions are selected according to a probability measure.
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. PMID:25820090
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
Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics
NASA Astrophysics Data System (ADS)
Montoya-Castillo, Andrés; Reichman, David R.
2016-05-01
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.
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. PMID:27179468
NASA Astrophysics Data System (ADS)
Rana, N. K.; Gautam, S. S.; Samanta, S.
2014-10-01
An approximate analysis has been carried out for short journal bearing to determine the dynamic behavior under micropolar turbulent flow condition. In this analysis, the Constantinescu's turbulent shear coefficient has been considered, which was later proposed by Taylor and Dowson. For the calculation of dynamic pressures, the classical Reynolds equation has been modified to incorporate turbulence and micropolar fluid parameters. The analysis has been further extended to determine the mass and whirl parameters to analyze the stability of the bearing. The bearing is found to be more stable with increase in eccentricity with high speed and large Reynolds number.
Xing, Xiaobo; Zheng, Jiapeng; Li, Fengjia; Sun, Chao; Cai, Xiang; Zhu, Debin; Lei, Liang; Wu, Ting; Zhou, Bin; Evans, Julian; Chen, Ziyi
2014-01-01
Thermal microbubbles generally grow directly from the heater and are spherical to minimize surface tension. We demonstrate a novel type of microbubble indirectly generated from a graphene oxide-microheater. Graphene oxide's photothermal properties allowed for efficient generation of a thermal gradient field on the microscale. A series of approximately ellipsoidal microbubbles were generated on the smooth microwire based on heterogeneous nucleation. Other dynamic behaviors induced by the microheater such as constant growth, directional transport and coalescence were also investigated experimentally and theoretically. The results are not only helpful for understanding the bubble dynamics but also useful for developing novel photothermal bubble-based devices. PMID:25124694
NASA Astrophysics Data System (ADS)
Moteki, Nobuhiro
2016-07-01
An accurate and efficient simulation of light scattering by an atmospheric black carbon (BC)-containing aerosol-a fractal-like cluster of hundreds of carbon monomers that is internally mixed with other aerosol compounds such as sulfates, organics, and water-remains challenging owing to the enormous diversities of such aerosols' size, shape, and mixing state. Although the discrete dipole approximation (DDA) is theoretically an exact numerical method that is applicable to arbitrary non-spherical inhomogeneous targets, in practice, it suffers from severe granularity-induced error and degradation of computational efficiency for such extremely complex targets. To solve this drawback, we propose herein a hybrid DDA method designed for arbitrary BC-containing aerosols: the monomer-dipole assumption is applied to a cluster of carbon monomers, whereas the efficient cubic-lattice discretization is applied to the remaining particle volume consisting of other materials. The hybrid DDA is free from the error induced by the surface granularity of carbon monomers that occurs in conventional cubic-lattice DDA. In the hybrid DDA, we successfully mitigate the artifact of neglecting the higher-order multipoles in the monomer-dipole assumption by incorporating the magnetic dipole in addition to the electric dipole into our DDA formulations. Our numerical experiments show that the hybrid DDA method is an efficient light-scattering solver for BC-containing aerosols in arbitrary mixing states. The hybrid DDA could be also useful for a cluster of metallic nanospheres associated with other dielectric materials.
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 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.
Image communication scheme based on dynamic visual cryptography and computer generated holography
NASA Astrophysics Data System (ADS)
Palevicius, Paulius; Ragulskis, Minvydas
2015-01-01
Computer generated holograms are often exploited to implement optical encryption schemes. This paper proposes the integration of dynamic visual cryptography (an optical technique based on the interplay of visual cryptography and time-averaging geometric moiré) with Gerchberg-Saxton algorithm. A stochastic moiré grating is used to embed the secret into a single cover image. The secret can be visually decoded by a naked eye if only the amplitude of harmonic oscillations corresponds to an accurately preselected value. The proposed visual image encryption scheme is based on computer generated holography, optical time-averaging moiré and principles of dynamic visual cryptography. Dynamic visual cryptography is used both for the initial encryption of the secret image and for the final decryption. Phase data of the encrypted image are computed by using Gerchberg-Saxton algorithm. The optical image is decrypted using the computationally reconstructed field of amplitudes.
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.
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.
Discrete-time nonlinear HJB solution using approximate dynamic programming: convergence proof.
Al-Tamimi, Asma; Lewis, Frank L; Abu-Khalaf, Murad
2008-08-01
Convergence of the value-iteration-based heuristic dynamic programming (HDP) algorithm is proven in the case of general nonlinear systems. That is, it is shown that HDP converges to the optimal control and the optimal value function that solves the Hamilton-Jacobi-Bellman equation appearing in infinite-horizon discrete-time (DT) nonlinear optimal control. It is assumed that, at each iteration, the value and action update equations can be exactly solved. The following two standard neural networks (NN) are used: a critic NN is used to approximate the value function, whereas an action network is used to approximate the optimal control policy. It is stressed that this approach allows the implementation of HDP without knowing the internal dynamics of the system. The exact solution assumption holds for some classes of nonlinear systems and, specifically, in the specific case of the DT linear quadratic regulator (LQR), where the action is linear and the value quadratic in the states and NNs have zero approximation error. It is stressed that, for the LQR, HDP may be implemented without knowing the system A matrix by using two NNs. This fact is not generally appreciated in the folklore of HDP for the DT LQR, where only one critic NN is generally used. PMID:18632382
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
2014-01-01
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
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
An effective fitting scheme for the dynamic structure of pure liquids.
Wax, J-F; Bryk, Taras
2013-08-14
A scheme of analysis for the dynamic structure functions in pure liquids is presented which can be implemented with both experimental and simulation data. Expressions for contributions of relaxing and propagating modes proposed earlier in the framework of the generalized collective modes approach are optimized in order to strictly fulfil three among the required sum-rules. The method is applied to simulation data for liquid cesium, the description of which appears to only require one relaxing and one propagating mode in the investigated wavevector range. These expressions are able to account for the dynamics in both the hydrodynamic and the kinetic regimes, being quantitatively accurate up to the onset of the first peak of the static structure factor and qualitatively beyond. Features of the modes can thus be obtained easily, without resorting to heavy formalism. The scheme of analysis can be straightforwardly extended to account for a higher number of relaxing and propagating modes. PMID:23860372
A fast chaotic cryptographic scheme with dynamic look-up table
NASA Astrophysics Data System (ADS)
Wong, K. W.
2002-06-01
We propose a fast chaotic cryptographic scheme based on iterating a logistic map. In particular, no random numbers need to be generated and the look-up table used in the cryptographic process is updated dynamically. Simulation results show that the proposed method leads to a substantial reduction in the encryption and decryption time. As a result, chaotic cryptography becomes more practical in the secure transmission of large multi-media files over public data communication network.
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.
A New Image Encryption Scheme Based on Dynamic S-Boxes and Chaotic Maps
NASA Astrophysics Data System (ADS)
Rehman, Atique Ur; Khan, Jan Sher; Ahmad, Jawad; Hwang, Soeng Oun
2016-03-01
Substitution box is a unique and nonlinear core component of block ciphers. A better designing technique of substitution box can boost up the quality of ciphertexts. In this paper, a new encryption method based on dynamic substitution boxes is proposed via using two chaotic maps. To break the correlation in an original image, pixels values of the original plaintext image are permuted row- and column-wise through random sequences. The aforementioned random sequences are generated by 2-D Burgers chaotic map. For the generation of dynamic substitution boxes, Logistic chaotic map is employed. In the process of diffusion, the permuted image is divided into blocks and each block is substituted via different dynamic substitution boxes. In contrast to conventional encryption schemes, the proposed scheme does not undergo the fixed block cipher and hence the security level can be enhanced. Extensive security analysis including histogram test is applied on the proposed image encryption technique. All experimental results reveal that the proposed scheme has a high level of security and robustness for transmission of digital images on insecure communication channels.
Recent advances in the development of implicit schemes for the equations of fluid dynamics
NASA Technical Reports Server (NTRS)
Warming, R. F.; Beam, R. M.
1981-01-01
Innovations and extensions of implicit schemes for equations of fluid dynamics are presented. The notation and theory for linear multistep methods are reviewed, and extensions of work by Beam and Warming (1979) include the implementation of one-leg methods, ADI methods for equations with mixed derivatives, flux vector splitting, the P-dimensional wave equation, and boundary conditions. Numerical experiments indicate that implicit treatment of the boundary conditions is necessary for unconditional stability, and the improvement and implementation of the boundary condition theory should improve the implicit algorithms for gas dynamic equations.
NASA Astrophysics Data System (ADS)
Mazzuca, James; Garashchuk, Sophya; Jakowski, Jacek
2012-07-01
An approximate dynamics method, based on donor and acceptor quantum trajectory ensembles, is employed to model hydrogen tunneling and the kinetic isotope effect (KIE) in soybean lipoxygenase-1. The proton is treated as a three-dimensional quantum-mechanical particle moving between the donor and acceptor wells for multiple configurations of the active site. Substitution of the proton with a deuteron reduces the transmission probability, integrated over enzyme configurations, by a factor of 51, which is in reasonable agreement with the experimental value of KIE equal to 81, validating the applicability of the current approach in biological systems.
Coherent Dynamics in Dressed Optical Lattices Beyond the Born-Oppenheimer Approximation
NASA Astrophysics Data System (ADS)
Reeves, Jeremy; Krinner, Ludwig; Stewart, Mike; Pazmino, Arturo; Schneble, Dominik
2015-05-01
Usual treatments of matter-wave diffraction assume that the zero-point energy in the diffracting potential is much smaller than the gap between the dressed levels. However, in near-resonant weak-driving scenarios, zero-point motion can mix the adiabatic dressed states, making the diffracting potentials highly non-adiabatic, such that the usual Born-Oppenheimer approximation for the external and internal degrees of freedom no longer applies. We model the dynamics of a matter wave in a microwave-coupled state-dependent lattice in this regime, and quantify the importance of these effects on recent experiments. Supported by NSF grant PHY-1205894.
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.
Dynamics of Jaynes-Cummings Model in the Absence of Rotating-Wave Approximation
NASA Astrophysics Data System (ADS)
Fan, Yun-Xia; Liu, Tao; Feng, Mang; Wang, Ke-Lin
2007-05-01
The Jaynes-Cummings model (JCM) is studied in the absence of the rotating-wave approximation (RWA) by a coherent-state expansion technique. In comparison with the previous paper in which the coherent-state expansion was performed only to the third order, we carry out in this paper a complete expansion to demonstrate exactly the dynamics of the JCM without the RWA. Our study gives a systematic method to solve the non-RWA problem, which would be useful in various physical systems, e.g., in a system with an ultracold trapped ion experiencing the running waves of lasers.
Approximating a Giving Up Smoking Dynamic on Adolescent Nicotine Dependence in Fractional Order
2016-01-01
In this work, we consider giving up smoking dynamic on adolescent nicotine dependence. First, we use the Caputo derivative to develop the model in fractional order. Then we apply two different numerical methods to compute accurate approximate solutions of this new model in fractional order and compare their results. In order to do this, we consider the generalized Euler method (GEM) and multi-step generalized differential transform method (MSGDTM). We also show the unique positive solution for this model and present numerical results graphically. PMID:27105426
Approximating a Giving Up Smoking Dynamic on Adolescent Nicotine Dependence in Fractional Order.
Zeb, Anwar; Zaman, Gul; Erturk, Vedat Suat; Alzalg, Baha; Yousafzai, Faisal; Khan, Madad
2016-01-01
In this work, we consider giving up smoking dynamic on adolescent nicotine dependence. First, we use the Caputo derivative to develop the model in fractional order. Then we apply two different numerical methods to compute accurate approximate solutions of this new model in fractional order and compare their results. In order to do this, we consider the generalized Euler method (GEM) and multi-step generalized differential transform method (MSGDTM). We also show the unique positive solution for this model and present numerical results graphically. PMID:27105426
NASA Astrophysics Data System (ADS)
Jiang, Bin; Song, Hongwei; Yang, Minghui; Guo, Hua
2016-04-01
The quantum dynamics of water dissociative chemisorption on the rigid Ni(111) surface is investigated using a recently developed nine-dimensional potential energy surface. The quantum dynamical model includes explicitly seven degrees of freedom of D2O at fixed surface sites, and the final results were obtained with a site-averaging model. The mode specificity in the site-specific results is reported and analyzed. Finally, the approximate sticking probabilities for various vibrationally excited states of D2O are obtained considering surface lattice effects and formally all nine degrees of freedom. The comparison with experiment reveals the inaccuracy of the density functional theory and suggests the need to improve the potential energy surface.
Linear-response dynamics from the time-dependent Gutzwiller approximation
NASA Astrophysics Data System (ADS)
Bünemann, J.; Capone, M.; Lorenzana, J.; Seibold, G.
2013-05-01
Within a Lagrangian formalism, we derive the time-dependent Gutzwiller approximation for general multi-band Hubbard models. Our approach explicitly incorporates the coupling between time-dependent variational parameters and a time-dependent density matrix from which we obtain dynamical correlation functions in the linear-response regime. Our results are illustrated for the one-band model where we show that the interacting system can be mapped to an effective problem of fermionic quasiparticles coupled to ‘doublon’ (double occupancy) bosonic fluctuations. The latter have an energy on the scale of the on-site Hubbard repulsion U in the dilute limit but become soft at the Brinkman-Rice transition, which is shown to be related to an emerging conservation law of doublon charge and the associated gauge invariance. Coupling with the boson mode produces a structure in the charge response and we find that a similar structure appears in dynamical mean-field theory.
Jiang, Bin; Song, Hongwei; Yang, Minghui; Guo, Hua
2016-04-28
The quantum dynamics of water dissociative chemisorption on the rigid Ni(111) surface is investigated using a recently developed nine-dimensional potential energy surface. The quantum dynamical model includes explicitly seven degrees of freedom of D2O at fixed surface sites, and the final results were obtained with a site-averaging model. The mode specificity in the site-specific results is reported and analyzed. Finally, the approximate sticking probabilities for various vibrationally excited states of D2O are obtained considering surface lattice effects and formally all nine degrees of freedom. The comparison with experiment reveals the inaccuracy of the density functional theory and suggests the need to improve the potential energy surface. PMID:27131562
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.
NASA Astrophysics Data System (ADS)
Van Raemdonck, Mario; Alcoba, Diego R.; Poelmans, Ward; De Baerdemacker, Stijn; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E.; Van Neck, Dimitri; Bultinck, Patrick
2015-09-01
A class of polynomial scaling methods that approximate Doubly Occupied Configuration Interaction (DOCI) wave functions and improve the description of dynamic correlation is introduced. The accuracy of the resulting wave functions is analysed by comparing energies and studying the overlap between the newly developed methods and full configuration interaction wave functions, showing that a low energy does not necessarily entail a good approximation of the exact wave function. Due to the dependence of DOCI wave functions on the single-particle basis chosen, several orbital optimisation algorithms are introduced. An energy-based algorithm using the simulated annealing method is used as a benchmark. As a computationally more affordable alternative, a seniority number minimising algorithm is developed and compared to the energy based one revealing that the seniority minimising orbital set performs well. Given a well-chosen orbital basis, it is shown that the newly developed DOCI based wave functions are especially suitable for the computationally efficient description of static correlation and to lesser extent dynamic correlation.
Van Raemdonck, Mario; Alcoba, Diego R; Poelmans, Ward; De Baerdemacker, Stijn; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E; Van Neck, Dimitri; Bultinck, Patrick
2015-09-14
A class of polynomial scaling methods that approximate Doubly Occupied Configuration Interaction (DOCI) wave functions and improve the description of dynamic correlation is introduced. The accuracy of the resulting wave functions is analysed by comparing energies and studying the overlap between the newly developed methods and full configuration interaction wave functions, showing that a low energy does not necessarily entail a good approximation of the exact wave function. Due to the dependence of DOCI wave functions on the single-particle basis chosen, several orbital optimisation algorithms are introduced. An energy-based algorithm using the simulated annealing method is used as a benchmark. As a computationally more affordable alternative, a seniority number minimising algorithm is developed and compared to the energy based one revealing that the seniority minimising orbital set performs well. Given a well-chosen orbital basis, it is shown that the newly developed DOCI based wave functions are especially suitable for the computationally efficient description of static correlation and to lesser extent dynamic correlation. PMID:26374017
Dynamic and balanced capacity allocation scheme with uniform bandwidth for OFDM-PON systems
NASA Astrophysics Data System (ADS)
Lei, Cheng; Chen, Hongwei; Chen, Minghua; Yu, Ying; Guo, Qiang; Yang, Sigang; Xie, Shizhong
2015-03-01
As the bitrate of orthogonal frequency division multiplexing passive optical network (OFDM-PON) system is continuously increasing, how to effectively allocate the system bandwidth among the huge number of optical network units (ONUs) is one of the key problems before OFDM-PON can be practical deployed. Unlike traditional bandwidth allocation scheme, in this paper, the transmission performance of single ONU is for the first time taken into consideration and optimized. To reduce the manufacturing complexity and fully utilize the processing ability of the receivers, the system bandwidth is equally distributed to the ONUs. Bit loading is used to allocate the total transmission capacity, and power loading is used to guarantee the ONUs have balanced transmission performance even if they operate at different bitrate. In this way, a dynamic and balanced capacity allocation scheme with uniform bandwidth for OFDM-PON systems can be realized. At last, an experimental system is established to verify the feasibility of the proposed scheme, and the influence that the scheme brings to the whole system is also analyzed.
Finite-approximation-error-based discrete-time iterative adaptive dynamic programming.
Wei, Qinglai; Wang, Fei-Yue; Liu, Derong; Yang, Xiong
2014-12-01
In this paper, a new iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for infinite horizon discrete-time nonlinear systems with finite approximation errors. First, a new generalized value iteration algorithm of ADP is developed to make the iterative performance index function converge to the solution of the Hamilton-Jacobi-Bellman equation. The generalized value iteration algorithm permits an arbitrary positive semi-definite function to initialize it, which overcomes the disadvantage of traditional value iteration algorithms. When the iterative control law and iterative performance index function in each iteration cannot accurately be obtained, for the first time a new "design method of the convergence criteria" for the finite-approximation-error-based generalized value iteration algorithm is established. A suitable approximation error can be designed adaptively to make the iterative performance index function converge to a finite neighborhood of the optimal performance index function. Neural networks are used to implement the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the developed method. PMID:25265640
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
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.
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.
Prolonging qubit coherence: dynamical decoupling schemes studied in a Penning ion trap
NASA Astrophysics Data System (ADS)
Uys, Hermann; Biercuk, Michael J.; VanDevender, Aaron P.; Shiga, Nobuyasu; Itano, Wayne M.; Bollinger, John J.
2009-02-01
We present a study of dynamical decoupling schemes for the suppression of phase errors from various noise environments using ions in a Penning trap as a model ensemble of qubits. By injecting frequency noise we demonstrate that in an ohmic noise spectrum with a sharp, high-frequency cutoff the recently proposed UDD decoupling sequence gives noise suppression superior to the traditional CPMG technique. Under only the influence of ambient magnetic field fluctuations with a 1/ω4 power spectrum, we find little benefit from using the UDD sequence, consistent with theoretical predictions for dynamical decoupling performance in the presence of noise spectra with soft cutoffs. Finally, we implement an optimization algorithm using measurement feedback, demonstrating that local optimization of dynamical decoupling can further lead to significant gains in error suppression over known sequences.
Exact and approximate dynamics of the quantum mechanical O(N) model
Mihaila, Bogdan; Athan, Tara; Cooper, Fred; Dawson, John; Habib, Salman
2000-12-15
We study the dynamics of the quantum mechanical O(N) model as a specific example to investigate the systematics of a 1/N expansion. The closed time path formalism melded with an expansion in 1/N is used to derive time evolution equations valid to order 1/N (next-to-leading order). The effective potential is also obtained to this order and its properties are elucidated. In order to compare theoretical predictions against numerical solutions of the time-dependent Schro''dinger equation, we consider two initial conditions consistent with O(N) symmetry, one of them a quantum roll, the other a wave packet initially to one side of the potential minimum, whose center has all coordinates equal. For the case of the quantum roll we map out the domain of validity of the large-N expansion. We also discuss the existence of unitarity violation in this expansion, a well-known problem faced by moment truncation techniques. The 1/N results, both static and dynamic, are contrasted with those given by a Hartree variational ansatz at given values of N. A comparison against numerical results leads us to conclude that late-time dynamical behavior, where nonlinear effects are significant, is not well described by either approximation.
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
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.
Dynamics of a spinning particle in a linear in spin Hamiltonian approximation
NASA Astrophysics Data System (ADS)
Lukes-Gerakopoulos, Georgios; Katsanikas, Matthaios; Patsis, Panos A.; Seyrich, Jonathan
2016-07-01
We investigate for order and chaos the dynamical system of a spinning test particle of mass m moving in the spacetime background of a Kerr black hole of mass M . This system is approximated in our investigation by the linear in spin Hamiltonian function [E. Barausse and A. Buonanno, Phys. Rev. D 81, 084024 (2010)]. We study the corresponding phase space by using 2D projections on a surface of section and the method of color and rotation on a 4D Poincaré section. Various topological structures coming from the nonintegrability of the linear in spin Hamiltonian are found and discussed. Moreover, an interesting result is that from the value of the dimensionless spin S /(m M )=10-4 of the particle and below, the impact of the nonintegrability of the system on the motion of the particle seems to be negligible.
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
Moment approximation of infection dynamics in a population of moving hosts.
Bonté, Bruno; Mathias, Jean-Denis; Duboz, Raphaël
2012-01-01
The modelling of contact processes between hosts is of key importance in epidemiology. Current studies have mainly focused on networks with stationary structures, although we know these structures to be dynamic with continuous appearance and disappearance of links over time. In the case of moving individuals, the contact network cannot be established. Individual-based models (IBMs) can simulate the individual behaviours involved in the contact process. However, with very large populations, they can be hard to simulate and study due to the computational costs. We use the moment approximation (MA) method to approximate a stochastic IBM with an aggregated deterministic model. We illustrate the method with an application in animal epidemiology: the spread of the highly pathogenic virus H5N1 of avian influenza in a poultry flock. The MA method is explained in a didactic way so that it can be reused and extended. We compare the simulation results of three models: 1. an IBM, 2. a MA, and 3. a mean-field (MF). The results show a close agreement between the MA model and the IBM. They highlight the importance for the models to capture the displacement behaviours and the contact processes in the study of disease spread. We also illustrate an original way of using different models of the same system to learn more about the system itself, and about the representation we build of it. PMID:23272160
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. PMID:27039526
Moment Approximation of Infection Dynamics in a Population of Moving Hosts
Bonté, Bruno; Mathias, Jean-Denis; Duboz, Raphaël
2012-01-01
The modelling of contact processes between hosts is of key importance in epidemiology. Current studies have mainly focused on networks with stationary structures, although we know these structures to be dynamic with continuous appearance and disappearance of links over time. In the case of moving individuals, the contact network cannot be established. Individual-based models (IBMs) can simulate the individual behaviours involved in the contact process. However, with very large populations, they can be hard to simulate and study due to the computational costs. We use the moment approximation (MA) method to approximate a stochastic IBM with an aggregated deterministic model. We illustrate the method with an application in animal epidemiology: the spread of the highly pathogenic virus H5N1 of avian influenza in a poultry flock. The MA method is explained in a didactic way so that it can be reused and extended. We compare the simulation results of three models: 1. an IBM, 2. a MA, and 3. a mean-field (MF). The results show a close agreement between the MA model and the IBM. They highlight the importance for the models to capture the displacement behaviours and the contact processes in the study of disease spread. We also illustrate an original way of using different models of the same system to learn more about the system itself, and about the representation we build of it. PMID:23272160
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
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.
Analytical descriptions of cross-polarisation dynamics: relaxing the secular approximations
NASA Astrophysics Data System (ADS)
Hirschinger, J.; Raya, J.
2015-11-01
In this work, analytical expressions of the cross-polarisation (CP) dynamics under both static and magic-angle spinning (MAS) conditions are obtained by solving the generalised Liouville-von Neumann quantum mechanical equation beyond the standard approximations, i.e., reintroducing neglected non-secular terms in the system superoperator. Although the simple model of a two-spin system interacting with a spin bath gives a rather crude description of CP dynamics, it accounts well for the orientation dependence of CP in a static sample of ferrocene powder and permits to detect slight departures from the Hartmann-Hahn matching condition. This approach also has the advantage of yielding manageable analytical expressions that can be used even by less inclined or experienced workers to obtain results that are good enough in an operational sense. Moreover, the resulting spin diffusion rate constants containing different sources of anisotropy of the system-environment interaction as well as their dependence on the MAS frequency are related semi-quantitatively to the local network of dipolar interactions. Finally, it is shown that non-secular solutions improve significantly the analysis of CPMAS-based separated-local-field spectroscopy experimental data in the absence of homonuclear decoupling.
NASA Astrophysics Data System (ADS)
Galler, Anna; Gunacker, Patrik; Tomczak, Jan; Thunström, Patrik; Held, Karsten
Recently, approaches such as the dynamical vertex approximation (D ΓA) or the dual-fermion method have been developed. These diagrammatic approaches are going beyond dynamical mean field theory (DMFT) by including nonlocal electronic correlations on all length scales as well as the local DMFT correlations. Here we present our efforts to extend the D ΓA methodology to ab-initio materials calculations (ab-initio D ΓA). Our approach is a unifying framework which includes both GW and DMFT-type of diagrams, but also important nonlocal correlations beyond, e.g. nonlocal spin fluctuations. In our multi-band implementation we are using a worm sampling technique within continuous-time quantum Monte Carlo in the hybridization expansion to obtain the DMFT vertex, from which we construct the reducible vertex function using the two particle-hole ladders. As a first application we show results for transition metal oxides. Support by the ERC project AbinitioDGA (306447) is acknowledged.
Chao, Fa-An; Byrd, R Andrew
2016-06-15
A new computational strategy is reported that provides a fast approximation of numerical solutions of differential equations in general. The method is demonstrated with the analysis of NMR adiabatic relaxation dispersion experiments to reveal biomolecular dynamics. When an analytical solution to the theoretical equations describing a physical process is not available, the new approach can significantly accelerate the computational speed of the conventional numerical integration up to 10(5) times. NMR adiabatic relaxation dispersion experiments enhanced with optimized proton-decoupled pulse sequences, although extremely powerful, have previously been refractory to quantitative analysis. Both simulations and experimental validation demonstrate detectable "slow" (microsecond to millisecond) conformational exchange rates from 10(2) to 10(5) s(-1). This greatly expanded time-scale range enables the characterization of a wide array of conformational fluctuations for individual residues, which correlate with biomolecular function and were previously inaccessible. Moreover, the new computational method can be potentially generalized for analysis of new types of relaxation dispersion experiments to characterize the various dynamics of biomolecular systems. PMID:27225523
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.
NASA Astrophysics Data System (ADS)
Rodriguez, C. O.; Methfessel, M.
1992-01-01
A scheme for the calculation of total energies from first principles is described which is intermediate between the popular linear muffin-tin-orbital method in the atomic-sphere approximation (LMTO-ASA) and an exact full-potential treatment. The local-density total energy is evaluated accurately for the output charge density from the ASA potential. This method is applied to the study of static structural properties and the pressure-induced phase transformation from B1 (NaCl-structure) to B2 (CsCl-structure) phases for the partially ionic alkaki-metal hydrides NaH and KH and the alkali halide NaCl. Good agreement with experimental transition pressures and volumes is obtained. The series NaH, KH, and NaCl shows the observed strong cation and weak anion dependence. Charge densities and band structures are given at zero and high pressure. Calculated energy-volume curves for LiH show no transition up to 1 Mbar, in agreement with experimental data.
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.
An extended-Lagrangian scheme for charge equilibration in reactive molecular dynamics simulations
NASA Astrophysics Data System (ADS)
Nomura, Ken-ichi; Small, Patrick E.; Kalia, Rajiv K.; Nakano, Aiichiro; Vashishta, Priya
2015-07-01
Reactive molecular dynamics (RMD) simulations describe chemical reactions at orders-of-magnitude faster computing speed compared with quantum molecular dynamics (QMD) simulations. A major computational bottleneck of RMD is charge-equilibration (QEq) calculation to describe charge transfer between atoms. Here, we eliminate the speed-limiting iterative minimization of the Coulombic energy in QEq calculation by adapting an extended-Lagrangian scheme that was recently proposed in the context of QMD simulations, Souvatzis and Niklasson (2014). The resulting XRMD simulation code drastically improves energy conservation compared with our previous RMD code, Nomura et al. (2008), while substantially reducing the time-to-solution. The XRMD code has been implemented on parallel computers based on spatial decomposition, achieving a weak-scaling parallel efficiency of 0.977 on 786,432 IBM Blue Gene/Q cores for a 67.6 billion-atom system.
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
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
Mao, Runfang; Lee, Ming-Tsung; Vishnyakov, Aleksey; Neimark, Alexander V
2015-09-01
Using dissipative particle dynamics (DPD) simulations, we explore the specifics of micellization in the solutions of anionic and cationic surfactants and their mixtures. Anionic surfactant sodium dodecyl sulfate (SDS) and cationic surfactant cetyltrimethylammonium bromide (CTAB) are chosen as characteristic examples. Coarse-grained models of the surfactants are constructed and parameterized using a combination of atomistic molecular simulation and infinite dilution activity coefficient calibration. Electrostatic interactions of charged beads are treated using a smeared charge approximation: the surfactant heads and dissociated counterions are modeled as beads with charges distributed around the bead center in an implicit dielectric medium. The proposed models semiquantitatively describe self-assembly in solutions of SDS and CTAB at various surfactant concentrations and molarities of added electrolyte. In particular, the model predicts a decline in the free surfactant concentration with the increase of the total surfactant loading, as well as characteristic aggregation transitions in single-component surfactant solutions caused by the addition of salt. The calculated values of the critical micelle concentration reasonably agree with experimental observations. Modeling of catanionic SDS-CTAB mixtures show consecutive transitions to worm-like micelles and then to vesicles caused by the addition of CTAB to micellar solution of SDS. PMID:26241704
Classical dynamics of a charged particle in a laser field beyond the dipole approximation
NASA Astrophysics Data System (ADS)
Jameson, Paul; Khvedelidze, Arsen
2008-05-01
The classical dynamics of a charged particle traveling in a laser field modeled by an elliptically polarized monochromatic electromagnetic plane wave is discussed within the time reparametrization invariant form of the nonrelativistic Hamilton-Jacobi theory. The exact parametric representation for a particle’s orbit in an arbitrary plane wave background beyond the dipole approximation and including effect of the magnetic field is derived. For an elliptically polarized monochromatic plane wave the particle’s trajectory, as an explicit function of the laboratory frame’s time, is given in terms of the Jacobian elliptic functions, whose modulus is proportional to the laser’s intensity and depends on the polarization of radiation. It is shown that the system exposes the intensity duality, correspondence between the motion in the backgrounds with various intensities. In virtue of the modular properties of the Jacobian functions, by starting with the representative “fundamental solution” and applying a certain modular transformation one can obtain the particle’s orbit in the monochromatic plane wave background with arbitrarily prescribed characteristics.
A 3D GCL compatible cell-centered Lagrangian scheme for solving gas dynamics equations
NASA Astrophysics Data System (ADS)
Georges, Gabriel; Breil, Jérôme; Maire, Pierre-Henri
2016-01-01
Solving the gas dynamics equations under the Lagrangian formalism enables to simulate complex flows with strong shock waves. This formulation is well suited to the simulation of multi-material compressible fluid flows such as those encountered in the domain of High Energy Density Physics (HEDP). These types of flows are characterized by complex 3D structures such as hydrodynamic instabilities (Richtmyer-Meshkov, Rayleigh-Taylor, etc.). Recently, the 3D extension of different Lagrangian schemes has been proposed and appears to be challenging. More precisely, the definition of the cell geometry in the 3D space through the treatment of its non-planar faces and the limiting of a reconstructed field in 3D in the case of a second-order extension are of great interest. This paper proposes two new methods to solve these problems. A systematic and symmetric geometrical decomposition of polyhedral cells is presented. This method enables to define a discrete divergence operator leading to the respect of the Geometric Conservation Law (GCL). Moreover, a multi-dimensional minmod limiter is proposed. This new limiter constructs, from nodal gradients, a cell gradient which enables to ensure the monotonicity of the numerical solution even in presence of strong discontinuity. These new ingredients are employed into a cell-centered Lagrangian scheme. Robustness and accuracy are assessed against various representative test cases.
Three-dimensional flux-split Euler schemes involving unstructured dynamic meshes
NASA Technical Reports Server (NTRS)
Batina, John T.
1990-01-01
Improved algorithms for the solution of the three-dimensional time-dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time-integration scheme using a multi-stage Runge-Kutta procedure or an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, 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 flow results are presented for both the NACA 0012 airfoil and the ONERA M6 wing to demonstrate applications of the new Euler solvers. The paper presents a description of the Euler solvers along with results and comparisons which assess the capability.
Three-dimensional flux-split Euler schemes involving unstructured dynamic meshes
NASA Technical Reports Server (NTRS)
Batina, John T.
1990-01-01
Improved algorithms for the solution of the 3-D time dependent Euler equations are presented for 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 either an explicit time integration scheme using a multistage Runge-Kutta procedure or an implicit time integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, 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 flow results are presented for both the NACA 0012 airfoil and the ONERA M6 wing to demonstrate applications of the new Euler solvers. A description of the Euler solvers is presented along with results and comparisons which assess the capability.
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
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.
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.
Incorporation of an evaporative cooling scheme into a dynamic model of orographic precipitation
NASA Technical Reports Server (NTRS)
Barros, Ana Paula; Lettenmaier, Dennis P.
1994-01-01
A simple evaporative cooling scheme was incorporated into a dynamic model to estimate orographic precipitation in mountainous regions. The orographic precipitation model is based on the transport of atmospheric moisture and the quantification of preciptable water across a 3D representation of the terrain from the surface up to 250 hPa. Advective wind fields are computed independently and boundary conditions are extracted from radiosonde data. Precipitation rates are obtained through calibration of a spatially distributed precipitation efficiency parameter. The model was applied to the central Sierra Nevada. Results show a gain of the order of 20% in threat-score coefficients designed to measure the forecast ability of the model. Accuracy gains are largest at high elevations and during intense storms associated with warm air masses.
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.
NASA Astrophysics Data System (ADS)
Bottacin-Busolin, Andrea; Wörman, Anders; Zmijewski, Nicholas
2013-04-01
A main challenge for the planning and management of water resources is the development of strategies for regulation of multireservoir systems under a complex stochastic environment. The sequential decision problem involving the release of water from multiple reservoirs depends on the stochastic variability of the hydrologic inflows over a spectrum of time scales. An important distinction is made between short-term and mid-term planning: the first is associated with regulation on the hourly scale within the one-week time horizon, whilst the second is associated with the weekly scale within the one-year horizon. Although a variety of optimization methods have been suggested, the achievement of a global optimum in the operation of large-scale systems is hindered by their high dimensional state space and by the stochastic nature of the hydrologic inflows. In this work, operational plans for multireservoir systems are derived via an approximate dynamic programming approach using a policy iteration algorithm. The algorithm is based on an off-line learning process in which policies are evaluated for a number of stochastic inflow scenarios by constructing approximations of their value functions, and the resulting value functions are used iteratively to design new, improved policies. In the mid-term planning phase, inflow scenarios are generated with a periodic autoregressive model that is calibrated against historical inflow data, and the policy iteration algorithm leads to a cyclostationary operating policy. In the short-term planning phase, the mid-term value function is used to calculate the value of a policy at the end of the short-term operating horizon, and synthetic inflow scenarios are generated by perturbing streamflow forecasts with Gaussian noise, following Zhao et al. (Water Resour. Res., 48, W01540, 2012). The variance of the noise is assumed to increase linearly over time and converges to the local variance of the historical time series. A case study is
Zhang, Zhijun; Li, Zhijun; Zhang, Yunong; Luo, Yamei; Li, Yuanqing
2015-12-01
We propose a dual-arm cyclic-motion-generation (DACMG) scheme by a neural-dynamic method, which can remedy the joint-angle-drift phenomenon of a humanoid robot. In particular, according to a neural-dynamic design method, first, a cyclic-motion performance index is exploited and applied. This cyclic-motion performance index is then integrated into a quadratic programming (QP)-type scheme with time-varying constraints, called the time-varying-constrained DACMG (TVC-DACMG) scheme. The scheme includes the kinematic motion equations of two arms and the time-varying joint limits. The scheme can not only generate the cyclic motion of two arms for a humanoid robot but also control the arms to move to the desired position. In addition, the scheme considers the physical limit avoidance. To solve the QP problem, a recurrent neural network is presented and used to obtain the optimal solutions. Computer simulations and physical experiments demonstrate the effectiveness and the accuracy of such a TVC-DACMG scheme and the neural network solver. PMID:26340789
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
Dynamics of precessing binary black holes using the post-Newtonian approximation
Hartl, Michael D.; Buonanno, Alessandra
2005-01-15
We investigate the (conservative) dynamics of binary black holes using the Hamiltonian formulation of the post-Newtonian (PN) equations of motion. The Hamiltonian we use includes spin-orbit coupling, spin-spin coupling, and mass monopole/spin-induced quadrupole interaction terms. We investigate the qualitative effects of these terms on the orbits; in the case of both quasicircular and eccentric orbits, we search for the presence of chaos (using the method of Lyapunov exponents) for a large variety of initial conditions. For quasicircular orbits, we find no chaotic behavior for black holes with total mass 10-40M{sub {center_dot}} when initially at a separation corresponding to a Newtonian gravitational-wave (GW) frequency less than {approx}150 Hz. Only for rather small initial radial distances (corresponding to a GW frequency larger than {approx}150 Hz), for which spin-spin induced oscillations in the radial separation are rather important, do we find chaotic solutions, and even then they are rare. Moreover, these chaotic quasicircular orbits are of questionable astrophysical significance, since they originate from direct parametrization of the equations of motion rather than from widely separated binaries evolving to small separations under gravitational radiation reaction. In the case of highly eccentric orbits, which for ground-based interferometers are not astrophysically favored, we again find chaotic solutions, but only at pericenters so small that higher order PN corrections, especially higher spin PN corrections, should also be taken into account. Taken together, our surveys of quasicircular and eccentric orbits find chaos only for orbits that are either of dubious astrophysical interest for ground-based interferometers or which violate the approximations required for the equations of motion to be physically valid at the post-Newtonian order considered.
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
System-level performance of LTE-Advanced with joint transmission and dynamic point selection schemes
NASA Astrophysics Data System (ADS)
Määttänen, Helka-Liina; Hämäläinen, Kari; Venäläinen, Juha; Schober, Karol; Enescu, Mihai; Valkama, Mikko
2012-12-01
In this article, we present a practical coordinated multipoint (CoMP) system for LTE-Advanced. In this CoMP system, cooperation is enabled for cell-edge users via dynamic switching between the normal single-cell operation and CoMP. We first formulate a general CoMP system model of several CoMP schemes. We then investigate a practical finite-rate feedback design that simultaneously supports interference coordination, joint transmission (JT), and dynamic point selection (DPS) with a varying number of cooperating transmission points while operating a single-cell transmission as a fallback mode. We provide both link-level and system-level results for the evaluation of different feedback options for general CoMP operation. The results show that there are substantial performance gains in cell-edge throughputs for both JT and DPS CoMP over the baseline Release 10 LTE-Advanced with practical feedback options. We also show that CoMP can enable improved mobility management in real networks.
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.
Stadler, Tanja; Vaughan, Timothy G.; Gavryushkin, Alex; Guindon, Stephane; Kühnert, Denise; Leventhal, Gabriel E.; Drummond, Alexei J.
2015-01-01
One of the central objectives in the field of phylodynamics is the quantification of population dynamic processes using genetic sequence data or in some cases phenotypic data. Phylodynamics has been successfully applied to many different processes, such as the spread of infectious diseases, within-host evolution of a pathogen, macroevolution and even language evolution. Phylodynamic analysis requires a probability distribution on phylogenetic trees spanned by the genetic data. Because such a probability distribution is not available for many common stochastic population dynamic processes, coalescent-based approximations assuming deterministic population size changes are widely employed. Key to many population dynamic models, in particular epidemiological models, is a period of exponential population growth during the initial phase. Here, we show that the coalescent does not well approximate stochastic exponential population growth, which is typically modelled by a birth–death process. We demonstrate that introducing demographic stochasticity into the population size function of the coalescent improves the approximation for values of R0 close to 1, but substantial differences remain for large R0. In addition, the computational advantage of using an approximation over exact models vanishes when introducing such demographic stochasticity. These results highlight that we need to increase efforts to develop phylodynamic tools that correctly account for the stochasticity of population dynamic models for inference. PMID:25876846
Dynamic screening of an ion in a degenerate electron gas within the second-order Born approximation
NASA Astrophysics Data System (ADS)
Nersisyan, Hrachya B.; Fernández-Varea, José M.; Arista, Néstor R.
2015-07-01
The dynamic Friedel sum rule (FSR) is derived within the second-order Born (B2) approximation for an ion that moves in a fully degenerate electron gas and for an arbitrary spherically-symmetric electron-ion interaction potential. This results in an implicit equation for the dynamic B2 screening parameter which depends on the ion atomic number Z1 unlike the first-order Born (B1) dynamic screening parameter reported earlier by some authors. Furthermore, for typical metallic densities our analytical results for the Yukawa and hydrogenic potentials are compared, for both positive and negative ions, to the exact screening parameters calculated self-consistently by imposing the exact dynamic FSR requirement to the scattering phase shifts. The B1 and B2 screening parameters agree excellently with the exact values at large velocities, while at moderate and low velocities the B1 approximation deviates from the exact solution whereas the B2 approximation still remains close to it. In addition, a Padé approximant to the Born series yields a further improvement of the perturbative approach, showing an excellent agreement on the whole velocity range in the case of antiprotons.
Ionization dynamics beyond the dipole approximation induced by the pulse envelope
NASA Astrophysics Data System (ADS)
Simonsen, Aleksander Skjerlie; Kjellsson, Tor; Førre, Morten; Lindroth, Eva; Selstø, Sølve
2016-05-01
When atoms and molecules are ionized by laser pulses of finite duration and increasingly high intensities, the validity of the much-used dipole approximation, in which the spatial dependence and magnetic component of the external field are neglected, eventually breaks down. We report that, when going beyond the dipole approximation for the description of atoms exposed to ultraviolet light, the spatial dependence of the pulse shape, the envelope, provides the dominant correction, while the spatial dependence of the carrier is negligible. We present a first-order beyond-dipole correction to the Hamiltonian which accounts exclusively for nondipole effects stemming from the carrier envelope of the pulse. We demonstrate by ab initio calculations for hydrogen that this approximation, which we refer to as the envelope approximation, reproduces the full interaction beyond the dipole approximation for absolute and differential observables and proves to be valid for a broad range of high-frequency fields. This is done both for the Schrödinger and the Dirac equation. Moreover, it is demonstrated that the envelope approximation provides an interaction-term which gives rise to faster numerical convergence in terms of partial waves compared to its exact counterpart.
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.
Wildman, Jack; Repiščák, Peter; Paterson, Martin J; Galbraith, Ian
2016-08-01
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
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
Investigation of uncertainties of establishment schemes in dynamic global vegetation models
NASA Astrophysics Data System (ADS)
Song, Xiang; Zeng, Xiaodong
2014-01-01
In Dynamic Global Vegetation Models (DGVMs), the establishment of woody vegetation refers to flowering, fertilization, seed production, germination, and the growth of tree seedlings. It determines not only the population densities but also other important ecosystem structural variables. In current DGVMs, establishments of woody plant functional types (PFTs) are assumed to be either the same in the same grid cell, or largely stochastic. We investigated the uncertainties in the competition of establishment among coexisting woody PFTs from three aspects: the dependence of PFT establishments on vegetation states; background establishment; and relative establishment potentials of different PFTs. Sensitivity experiments showed that the dependence of establishment rate on the fractional coverage of a PFT favored the dominant PFT by increasing its share in establishment. While a small background establishment rate had little impact on equilibrium states of the ecosystem, it did change the timescale required for the establishment of alien species in pre-existing forest due to their disadvantage in seed competition during the early stage of invasion. Meanwhile, establishment purely from background (the scheme commonly used in current DGVMs) led to inconsistent behavior in response to the change in PFT specification (e.g., number of PFTs and their specification). Furthermore, the results also indicated that trade-off between individual growth and reproduction/colonization has significant influences on the competition of establishment. Hence, further development of establishment parameterization in DGVMs is essential in reducing the uncertainties in simulations of both ecosystem structures and successions.
NASA Astrophysics Data System (ADS)
Lubuma, J. M.-S.; Mureithi, E.; Terefe, Y. A.
2011-11-01
The classical SIS epidemiological model is extended in two directions: (a) The number of adequate contacts per infective in unit time is assumed to be a function of the total population in such a way that this number grows less rapidly as the total population increases; (b) A diffusion term is added to the SIS model and this leads to a reaction diffusion equation, which governs the spatial spread of the disease. With the parameter R0 representing the basic reproduction number, it is shown that R0 = 1 is a forward bifurcation for the model (a), with the disease-free equilibrium being globally asymptotic stable when R0 is less than 1. In the case when R0 is greater than 1, traveling wave solutions are found for the model (b). Nonstandard finite difference (NSFD) schemes that replicate the dynamics of the continuous models are presented. In particular, for the model (a), a nonstandard version of the Runge-Kutta method having high order of convergence is investigated. Numerical experiments that support the theory are provided.
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 Astrophysics Data System (ADS)
Sahu, B. K.; Ahuja, R.; Kumar, Rajesh; Suman, S. K.; Mathuria, D. S.; Rai, A.; Patra, P.; Pandey, A.; Karmakar, J.; Chowdhury, G. K.; Dutt, R. N.; Joshi, G.; Ghosh, S.; Kanjilal, D.; Roy, A.
2015-03-01
The superconducting heavy ion linear accelerator at Inter-University Accelerator Centre Delhi has been in operation since 2007. Initially, the superconducting niobium Quarter Wave Resonators (QWRs) in the linac were phase locked using a combination of electronic and mechanical controls which operated in fast (~10 μsec) and slow (~sec) time scales respectively. In this scheme, fast control was achieved through dynamic phase control whereas slow control of the frequency was done through the niobium tuner bellows installed at the drift tube end of the resonator and flexed using helium gas to change the resonance frequency. In order to improve the dynamics of this control system, an alternate scheme using piezoelectric actuator, instead of helium gas, to flex the same niobium bellows, has been implemented in the QWRs of the second and third accelerating modules of the linac. The piezoelectric actuator is used in closed loop along with the fast dynamic phase control scheme. The feedback loop of the piezoelectric control includes a dual control scheme - an integral control loop to arrest the slow drift, and the positive position feedback (PPF) based control loop to damp the microphonics. This control scheme has been found to arrest slow drifts in the resonator frequency more tightly along with damping of low frequency microphonics (~few tens of Hz) picked up by the resonator from its surrounding environment. This has substantially eased the load from the fast electronic control, resulting in the reduction of the radio frequency (RF) power requirement during operation. In addition, it has improved the stability of phase and amplitude of the QWRs. The details of the new scheme along with results obtained during the online run of the linac for beam acceleration are presented.
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.
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...
Lagrangian approach to the semirelativistic electron dynamics in the mean-field approximation
NASA Astrophysics Data System (ADS)
Dixit, Anant; Hinschberger, Yannick; Zamanian, Jens; Manfredi, Giovanni; Hervieux, Paul-Antoine
2013-09-01
We derive a mean-field model that is based on a two-component Pauli-like equation and incorporates quantum, spin, and relativistic effects up to second order in 1/c. Using a Lagrangian approach, we obtain the self-consistent charge and current densities that act as sources in the Maxwell equations. A physical interpretation is provided for the second-order corrections to the sources. The Maxwell equations are also expanded to the same order. The resulting self-consistent model constitutes a suitable semirelativistic approximation to the full Dirac-Maxwell equations.
NASA Astrophysics Data System (ADS)
Camporeale, E.; Delzanno, G.; Zaharia, S. G.; Koller, J.
2012-12-01
The particle dynamics in the Earth's radiation belt is generally modeled by means of a two-dimensional diffusion equation for the particle distribution function in energy and pitch angle. In this work we survey and compare different numerical schemes for the solution of the diffusion equation, with the goal of outlining which is the optimal strategy from a numerical point of view. We focus on the general (and more computationally challenging) case where the mixed terms in the diffusion tensor are retained. We compare fully-implicit and semi-implicit schemes. For the former we have analyzed a direct solver based on a LU decomposition routine for sparse matrices, and an iterative ILU-preconditioned GMRES. For the semi-implicit scheme we have studied an Alternating Direction Implicit scheme. We present a convergence study for a realistic case that shows that the timestep and grid size are strongly constrained by the desired accuracy of the solution. We show that the fully-implicit scheme is to be preferred in most cases as the more computationally efficient.
NASA Astrophysics Data System (ADS)
Camporeale, E.; Delzanno, G. L.; Zaharia, S.; Koller, J.
2013-06-01
The particle dynamics in the Earth's radiation belt is generally modeled by means of a two-dimensional diffusion equation for the particle distribution function in energy and pitch angle. The goal of this paper is to survey and compare different numerical schemes for the solution of the diffusion equation, and to outline the optimal strategy from a numerical point of view. We focus on the general (and more computationally challenging) case where the mixed terms in the diffusion tensor are retained. In Part 1, we compare fully implicit and semi-implicit schemes. For the former, we have analyzed a direct solver based on a LU decomposition routine for sparse matrices, and an iterative incomplete LU preconditioned Generalized Minimal REsidual solver. For the semi-implicit scheme, we have studied an alternating direction implicit scheme. We present a convergence study for a realistic case that shows that the time step and grid size are strongly constrained by the desired accuracy of the solution. We show that the fully implicit scheme is to be preferred in most cases as the more computationally efficient.
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.
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; Bowman, Joel; Paesani, Francesco; Ceriotti, Michele
2014-11-14
Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here, we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer model and a mixed quantum-classical model as representatives of the first family of methods, and centroid molecular dynamics and thermostatted ring polymer molecular dynamics as examples of the latter. We use as benchmarks D{sub 2}O doped with HOD and pure H{sub 2}O at three distinct thermodynamic state points (ice Ih at 150 K, and the liquid at 300 K and 600 K), modeled with the simple q-TIP4P/F potential energy and dipole moment surfaces. With few exceptions the different techniques yield IR absorption frequencies that are consistent with one another within a few tens of cm{sup −1}. Comparison with classical molecular dynamics demonstrates the importance of nuclear quantum effects up to the highest temperature, and a detailed discussion of the discrepancies between the various methods let us draw some (circumstantial) conclusions about the impact of the very different approximations that underlie them. Such cross validation between radically different approaches could indicate a way forward to further improve the state of the art in simulations of condensed-phase quantum dynamics.
NASA Astrophysics Data System (ADS)
Rossi, Mariana; Liu, Hanchao; Paesani, Francesco; Bowman, Joel; Ceriotti, Michele
2014-11-01
Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here, we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer model and a mixed quantum-classical model as representatives of the first family of methods, and centroid molecular dynamics and thermostatted ring polymer molecular dynamics as examples of the latter. We use as benchmarks D2O doped with HOD and pure H2O at three distinct thermodynamic state points (ice Ih at 150 K, and the liquid at 300 K and 600 K), modeled with the simple q-TIP4P/F potential energy and dipole moment surfaces. With few exceptions the different techniques yield IR absorption frequencies that are consistent with one another within a few tens of cm-1. Comparison with classical molecular dynamics demonstrates the importance of nuclear quantum effects up to the highest temperature, and a detailed discussion of the discrepancies between the various methods let us draw some (circumstantial) conclusions about the impact of the very different approximations that underlie them. Such cross validation between radically different approaches could indicate a way forward to further improve the state of the art in simulations of condensed-phase quantum dynamics.
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. PMID:25399122
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)
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)
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 Technical Reports Server (NTRS)
Pulliam, T. H.; Steger, J. L.
1985-01-01
In 1977 and 1978, general purpose centrally space differenced implicit finite difference codes in two and three dimensions have been introduced. These codes, now called ARC2D and ARC3D, can run either in inviscid or viscous mode for steady or unsteady flow. Since the introduction of the ARC2D and ARC3D codes, overall computational efficiency could be improved by making use of a number of algorithmic changes. These changes are related to the use of a spatially varying time step, the use of a sequence of mesh refinements to establish approximate solutions, implementation of various ways to reduce inversion work, improved numerical dissipation terms, and more implicit treatment of terms. The present investigation has the objective to describe the considered improvements and to quantify advantages and disadvantages. It is found that using established and simple procedures, a computer code can be maintained which is competitive with specialized codes.
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)
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
Numeric modeling approximation of the fluid dynamics in an optical fiber trap
NASA Astrophysics Data System (ADS)
Hernández Zavala, J. E.; Cerecedo Nuñez, H. H.; Vigueras Zuñiga, M. O.; Padilla Sosa, P.
2014-09-01
This document presents a first approach to study the behavior of a static fluid radiated by infrared light (980nm,100mW) transmitted by a single-mode optical fiber, for this simulation temperature and radiation pressure are calculated based on the intensity delivered by a laser diode. The Computing Fluid Dynamics (CFD) results were based on a mesh Tet/Hybrid, TGrid for a Silica micro-particle and a mesh Hex/Wedge, Cooper for the beam. The results show that as the particle moves along the axis, temperature and pressure decreases, having the points of mayor temperature and pressure around the axis. The conclusion of this work is that it is possible to simulate the interactions between the beam, the micro-particle and the surrounding medium in terms of temperature, velocity and pressure using the energy and viscous model.
Chen Qinghu; Yang Yuan; Liu Tao; Wang Kelin
2010-11-15
Entanglement evolution of two independent Jaynes-Cummings atoms without the rotating-wave approximation (RWA) is studied by a numerically exact approach. Previous results based on the RWA are essentially modified in the strong-coupling regime (g{>=}0.1), which has been reached in the recent experiments on the flux qubit coupled to the LC resonator. For the initial Bell state with anticorrelated spins, entanglement sudden death (ESD) is absent in the RWA but does appear in the present numerical calculation without the RWA. Aperiodic entanglement evolution in the strong-coupling regime is observed. The strong atom-cavity coupling facilitates the ESD. The sign of the detuning plays an essential role in the entanglement evolution for strong coupling, which is irrelevant in the RWA. Analytical results based on an unitary transformation are also given, which could not modify the RWA picture essentially. It is suggested that the activation of the photons may be the origin of ESD in this system.
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. PMID:26349222
NASA Astrophysics Data System (ADS)
Milton, Graeme Walter
In the two separate parts of this thesis, some special exactly solvable models are defined and analysed. In Part I it is proved rigorously that the coherent potential approximation is exact for the effective conductivity of a wide class of hierarchical models made of spherical grains of various conductivities. In Part II the existence of continuum fluid models that exhibit a discontinuity in the pressure versus density isotherms is established by explicit construction of a class of examples. Part II also incorporates a broad study of discontinuities in thermodynamic variables. The basic models of Part I are constructed as follows: the starting material 0 in the hierarchy is chosen arbitrarily, otherwise material j = 1, 2, ..., consists of equisized spheres, say j-spheres, of arbitrary conductivities embedded in material (j - 1). The distribution of the j-spheres must satisfy a mild homogeneity condition and their radius r(,j) must, asymptotically, increase faster than expotentially with j. The minimum spacing, 2s(,j), between the j-spheres is such that s(,j)/r(,j) diverges. On the basis of these and other ancillary conditions it is established that the coherent potential approximation becomes exact for the effective conductivity (or the dielectric constant or the magnetic permeability) of material j ( --->) (INFIN). The model composites and the proof of realizability may be generalised to allow non-spherical grains. By introducing ensembles of composites the homogeneity condition and the spacing condition can be relaxed somewhat. Another related approximation, the iterated dilute limit approximation is also proved to be realizable. In Part II, one-dimensional continuum models are defined in which classical particles interact through many -body potentials meeting conditions sufficient to ensure a proper thermodynamic limit. An exact analysis proves that for certain ranges of parameter values the pressure versus density isotherms are discontinuous. Extended models
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.; 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 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
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)
Lotfipour, H.; Allameh, Z.; Roknizadeh, R.; Heydari, H.
2016-03-01
Using two different schemes, a non-classical-squeezed state of light is detected and characterized. In the first scheme, in a one-dimensional cavity with a moving mirror (non-stationary Casimir effect) in the principal mode, we study the photon generation rate for two modes (squeezed and coherent state) of a driving field. Since the cavity with the moving mirror (similar to an optomechanical system) can be considered an analogue to a Kerr-like medium, in the second scheme, the probability amplitude for multi-photon absorption in a nonlinear (Kerr) medium will be quantum mechanically calculated. It is shown that because of the presence of nonlinear effects, the responses of these two systems to the squeezed versus coherent state are considerably distinguishable. The drastic difference between the results of these two states of light can be viewed as a proposal for detecting non-classical states.
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. PMID:26927234
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. PMID:23355184
NASA Technical Reports Server (NTRS)
Bickers, N. E.; Scalapino, D. J.; White, S. R.
1989-01-01
A semianalytical approach is described for strongly correlated electronic systems which satisfies microscopic conservation laws, treats strong frequency and momentum dependences, and provides information on both static and dynamic properties. This approach may be used to treat large systems and temperatures lower than those currently accessible to finite-temperature quantum Monte Carlo techniques. Examples of such systems include heavy-electron compounds, organic Bechegaard salts, bis-(ethylenedithiolo)-TTF superconductors, and the oxide superconductors. The technique is based on the derivation and self-consistent solution of infinite-order conserving approximations. The technique is used to derive a low-temperature phase diagram and dynamic correlation functions for the two-dimensional Hubbard lattice model.
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.
Calculator Function Approximation.
ERIC Educational Resources Information Center
Schelin, Charles W.
1983-01-01
The general algorithm used in most hand calculators to approximate elementary functions is discussed. Comments on tabular function values and on computer function evaluation are given first; then the CORDIC (Coordinate Rotation Digital Computer) scheme is described. (MNS)
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. PMID:27369498
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.