Sample records for hamilton-jacobi equations

  1. Numerical Solution of Hamilton-Jacobi Equations in High Dimension

    DTIC Science & Technology

    2012-11-23

    high dimension FA9550-10-1-0029 Maurizio Falcone Dipartimento di Matematica SAPIENZA-Universita di Roma P. Aldo Moro, 2 00185 ROMA AH930...solution of Hamilton-Jacobi equations in high dimension AFOSR contract n. FA9550-10-1-0029 Maurizio Falcone Dipartimento di Matematica SAPIENZA

  2. Discontinuous solutions of Hamilton-Jacobi equations on networks

    NASA Astrophysics Data System (ADS)

    Graber, P. J.; Hermosilla, C.; Zidani, H.

    2017-12-01

    This paper studies optimal control problems on networks without controllability assumptions at the junctions. The Value Function associated with the control problem is characterized as the solution to a system of Hamilton-Jacobi equations with appropriate junction conditions. The novel feature of the result lies in that the controllability conditions are not needed and the characterization remains valid even when the Value Function is not continuous.

  3. Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations

    NASA Astrophysics Data System (ADS)

    Kao, Chiu Yen; Osher, Stanley; Qian, Jianliang

    2004-05-01

    We propose a simple, fast sweeping method based on the Lax-Friedrichs monotone numerical Hamiltonian to approximate viscosity solutions of arbitrary static Hamilton-Jacobi equations in any number of spatial dimensions. By using the Lax-Friedrichs numerical Hamiltonian, we can easily obtain the solution at a specific grid point in terms of its neighbors, so that a Gauss-Seidel type nonlinear iterative method can be utilized. Furthermore, by incorporating a group-wise causality principle into the Gauss-Seidel iteration by following a finite group of characteristics, we have an easy-to-implement, sweeping-type, and fast convergent numerical method. However, unlike other methods based on the Godunov numerical Hamiltonian, some computational boundary conditions are needed in the implementation. We give a simple recipe which enforces a version of discrete min-max principle. Some convergence analysis is done for the one-dimensional eikonal equation. Extensive 2-D and 3-D numerical examples illustrate the efficiency and accuracy of the new approach. To our knowledge, this is the first fast numerical method based on discretizing the Hamilton-Jacobi equation directly without assuming convexity and/or homogeneity of the Hamiltonian.

  4. Central Schemes for Multi-Dimensional Hamilton-Jacobi Equations

    NASA Technical Reports Server (NTRS)

    Bryson, Steve; Levy, Doron; Biegel, Bryan (Technical Monitor)

    2002-01-01

    We present new, efficient central schemes for multi-dimensional Hamilton-Jacobi equations. These non-oscillatory, non-staggered schemes are first- and second-order accurate and are designed to scale well with an increasing dimension. Efficiency is obtained by carefully choosing the location of the evolution points and by using a one-dimensional projection step. First-and second-order accuracy is verified for a variety of multi-dimensional, convex and non-convex problems.

  5. Hamilton-Jacobi theory in multisymplectic classical field theories

    NASA Astrophysics Data System (ADS)

    de León, Manuel; Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso; Vilariño, Silvia

    2017-09-01

    The geometric framework for the Hamilton-Jacobi theory developed in the studies of Cariñena et al. [Int. J. Geom. Methods Mod. Phys. 3(7), 1417-1458 (2006)], Cariñena et al. [Int. J. Geom. Methods Mod. Phys. 13(2), 1650017 (2015)], and de León et al. [Variations, Geometry and Physics (Nova Science Publishers, New York, 2009)] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.

  6. Structural aspects of Hamilton-Jacobi theory

    NASA Astrophysics Data System (ADS)

    Cariñena, J. F.; Gràcia, X.; Marmo, G.; Martínez, E.; Muñoz-Lecanda, M. C.; Román-Roy, N.

    2016-12-01

    In our previous papers [J. F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M. C. Muñoz-Lecanda and N. Román-Roy, Geometric Hamilton-Jacobi theory, Int. J. Geom. Meth. Mod. Phys. 3 (2006) 1417-1458; Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems, Int. J. Geom. Meth. Mod. Phys. 7 (2010) 431-454] we showed that the Hamilton-Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how constants of the motion help to solve the Hamilton-Jacobi equation. Here we want to delve into this interpretation by considering the most general case: a dynamical system on a manifold that is described in terms of a family of dynamics (slicing vector fields) on lower-dimensional manifolds. We identify the relevant geometric structures that lead from this decomposition of the dynamics to the classical Hamilton-Jacobi theory, by considering special cases like fibered manifolds and Hamiltonian dynamics, in the symplectic framework and the Poisson one. We also show how a set of functions on a tangent bundle can determine a second-order dynamics for which they are constants of the motion.

  7. Derivation of the Schrodinger Equation from the Hamilton-Jacobi Equation in Feynman's Path Integral Formulation of Quantum Mechanics

    ERIC Educational Resources Information Center

    Field, J. H.

    2011-01-01

    It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

  8. Complex quantum Hamilton-Jacobi equation with Bohmian trajectories: Application to the photodissociation dynamics of NOCl

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

    2014-03-14

    The complex quantum Hamilton-Jacobi equation-Bohmian trajectories (CQHJE-BT) method is introduced as a synthetic trajectory method for integrating the complex quantum Hamilton-Jacobi equation for the complex action function by propagating an ensemble of real-valued correlated Bohmian trajectories. Substituting the wave function expressed in exponential form in terms of the complex action into the time-dependent Schrödinger equation yields the complex quantum Hamilton-Jacobi equation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation describing the rate of change in the complex action transported along Bohmian trajectories is simultaneouslymore » integrated with the guidance equation for Bohmian trajectories, and the time-dependent wave function is readily synthesized. The spatial derivatives of the complex action required for the integration scheme are obtained by solving one moving least squares matrix equation. In addition, the method is applied to the photodissociation of NOCl. The photodissociation dynamics of NOCl can be accurately described by propagating a small ensemble of trajectories. This study demonstrates that the CQHJE-BT method combines the considerable advantages of both the real and the complex quantum trajectory methods previously developed for wave packet dynamics.« less

  9. High-Order Central WENO Schemes for 1D Hamilton-Jacobi Equations

    NASA Technical Reports Server (NTRS)

    Bryson, Steve; Levy, Doron; Biegel, Bryan A. (Technical Monitor)

    2002-01-01

    In this paper we derive fully-discrete Central WENO (CWENO) schemes for approximating solutions of one dimensional Hamilton-Jacobi (HJ) equations, which combine our previous works. We introduce third and fifth-order accurate schemes, which are the first central schemes for the HJ equations of order higher than two. The core ingredient is the derivation of our schemes is a high-order CWENO reconstructions in space.

  10. High-Order Semi-Discrete Central-Upwind Schemes for Multi-Dimensional Hamilton-Jacobi Equations

    NASA Technical Reports Server (NTRS)

    Bryson, Steve; Levy, Doron; Biegel, Bryan (Technical Monitor)

    2002-01-01

    We present the first fifth order, semi-discrete central upwind method for approximating solutions of multi-dimensional Hamilton-Jacobi equations. Unlike most of the commonly used high order upwind schemes, our scheme is formulated as a Godunov-type scheme. The scheme is based on the fluxes of Kurganov-Tadmor and Kurganov-Tadmor-Petrova, and is derived for an arbitrary number of space dimensions. A theorem establishing the monotonicity of these fluxes is provided. The spacial discretization is based on a weighted essentially non-oscillatory reconstruction of the derivative. The accuracy and stability properties of our scheme are demonstrated in a variety of examples. A comparison between our method and other fifth-order schemes for Hamilton-Jacobi equations shows that our method exhibits smaller errors without any increase in the complexity of the computations.

  11. Compressed Semi-Discrete Central-Upwind Schemes for Hamilton-Jacobi Equations

    NASA Technical Reports Server (NTRS)

    Bryson, Steve; Kurganov, Alexander; Levy, Doron; Petrova, Guergana

    2003-01-01

    We introduce a new family of Godunov-type semi-discrete central schemes for multidimensional Hamilton-Jacobi equations. These schemes are a less dissipative generalization of the central-upwind schemes that have been recently proposed in series of works. We provide the details of the new family of methods in one, two, and three space dimensions, and then verify their expected low-dissipative property in a variety of examples.

  12. Unified formalism for the generalized kth-order Hamilton-Jacobi problem

    NASA Astrophysics Data System (ADS)

    Colombo, Leonardo; de Léon, Manuel; Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

    2014-08-01

    The geometric formulation of the Hamilton-Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unified Lagrangian-Hamiltonian formalism for the geometric Hamilton-Jacobi theory on higher-order autonomous dynamical systems described by regular Lagrangian functions.

  13. A Hamilton-Jacobi theory for implicit differential systems

    NASA Astrophysics Data System (ADS)

    Esen, Oǧul; de León, Manuel; Sardón, Cristina

    2018-02-01

    In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, described in terms of Lagrangian submanifolds of TT*Q generated by Morse families. The implicit character implies the nonexistence of a Hamiltonian function describing the dynamics. This fact is here amended by a generating family of Morse functions which plays the role of a Hamiltonian. A Hamilton-Jacobi equation is obtained with the aid of this generating family of functions. To conclude, we apply our results to singular Lagrangians by employing the construction of special symplectic structures.

  14. The nonconvex multi-dimensional Riemann problem for Hamilton-Jacobi equations

    NASA Technical Reports Server (NTRS)

    Osher, Stanley

    1989-01-01

    Simple inequalities for the Riemann problem for a Hamilton-Jacobi equation in N space dimension when neither the initial data nor the Hamiltonian need be convex (or concave) are presented. The initial data is globally continuous, affine in each orthant, with a possible jump in normal derivative across each coordinate plane, x sub i = 0. The inequalities become equalities wherever a maxmin equals a minmax and thus an exact closed form solution to this problem is then obtained.

  15. Quantitative Compactness Estimates for Hamilton-Jacobi Equations

    NASA Astrophysics Data System (ADS)

    Ancona, Fabio; Cannarsa, Piermarco; Nguyen, Khai T.

    2016-02-01

    We study quantitative compactness estimates in {W^{1,1}_{loc}} for the map {S_t}, {t > 0} that is associated with the given initial data {u_0in Lip (R^N)} for the corresponding solution {S_t u_0} of a Hamilton-Jacobi equation u_t+Hbig(nabla_{x} ubig)=0, qquad t≥ 0,quad xinR^N, with a uniformly convex Hamiltonian {H=H(p)}. We provide upper and lower estimates of order {1/\\varepsilon^N} on the Kolmogorov {\\varepsilon}-entropy in {W^{1,1}} of the image through the map S t of sets of bounded, compactly supported initial data. Estimates of this type are inspired by a question posed by Lax (Course on Hyperbolic Systems of Conservation Laws. XXVII Scuola Estiva di Fisica Matematica, Ravello, 2002) within the context of conservation laws, and could provide a measure of the order of "resolution" of a numerical method implemented for this equation.

  16. A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations

    NASA Technical Reports Server (NTRS)

    Hu, Changqing; Shu, Chi-Wang

    1998-01-01

    In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method.

  17. Escape rates over potential barriers: variational principles and the Hamilton-Jacobi equation

    NASA Astrophysics Data System (ADS)

    Cortés, Emilio; Espinosa, Francisco

    We describe a rigorous formalism to study some extrema statistics problems, like maximum probability events or escape rate processes, by taking into account that the Hamilton-Jacobi equation completes, in a natural way, the required set of boundary conditions of the Euler-Lagrange equation, for this kind of variational problem. We apply this approach to a one-dimensional stochastic process, driven by colored noise, for a double-parabola potential, where we have one stable and one unstable steady states.

  18. On global solutions of the random Hamilton-Jacobi equations and the KPZ problem

    NASA Astrophysics Data System (ADS)

    Bakhtin, Yuri; Khanin, Konstantin

    2018-04-01

    In this paper, we discuss possible qualitative approaches to the problem of KPZ universality. Throughout the paper, our point of view is based on the geometrical and dynamical properties of minimisers and shocks forming interlacing tree-like structures. We believe that the KPZ universality can be explained in terms of statistics of these structures evolving in time. The paper is focussed on the setting of the random Hamilton-Jacobi equations. We formulate several conjectures concerning global solutions and discuss how their properties are connected to the KPZ scalings in dimension 1  +  1. In the case of general viscous Hamilton-Jacobi equations with non-quadratic Hamiltonians, we define generalised directed polymers. We expect that their behaviour is similar to the behaviour of classical directed polymers, and present arguments in favour of this conjecture. We also define a new renormalisation transformation defined in purely geometrical terms and discuss conjectural properties of the corresponding fixed points. Most of our conjectures are widely open, and supported by only partial rigorous results for particular models.

  19. The nonconvex multi-dimensional Riemann problem for Hamilton-Jacobi equations

    NASA Technical Reports Server (NTRS)

    Bardi, Martino; Osher, Stanley

    1991-01-01

    Simple inequalities are presented for the viscosity solution of a Hamilton-Jacobi equation in N space dimensions when neither the initial data nor the Hamiltonian need be convex (or concave). The initial data are uniformly Lipschitz and can be written as the sum of a convex function in a group of variables and a concave function in the remaining variables, therefore including the nonconvex Riemann problem. The inequalities become equalities wherever a 'maxmin' equals a 'minmax', and thus a representation formula for this problem is obtained, generalizing the classical Hopi formulas.

  20. Solving the Hamilton-Jacobi equation for general relativity

    NASA Astrophysics Data System (ADS)

    Parry, J.; Salopek, D. S.; Stewart, J. M.

    1994-03-01

    We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly invariant under reparametrizations of the spatial coordinates (``gauge invariant''). At each order we solve the Hamiltonian constraint using a conformal transformation of the three-metric as well as a line integral in superspace. This gives a recursion relation for the generating functional which then may be solved to arbitrary order simply by functionally differentiating previous orders. At fourth order in spatial gradients we demonstrate solutions for irrotational dust as well as for a scalar field. We explicitly evolve the three-metric to the same order. This method can be used to derive the Zel'dovich approximation for general relativity.

  1. Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains

    NASA Technical Reports Server (NTRS)

    Barth, Timothy J.; Sethian, James A.

    2006-01-01

    Borrowing from techniques developed for conservation law equations, we have developed both monotone and higher order accurate numerical schemes which discretize the Hamilton-Jacobi and level set equations on triangulated domains. The use of unstructured meshes containing triangles (2D) and tetrahedra (3D) easily accommodates mesh adaptation to resolve disparate level set feature scales with a minimal number of solution unknowns. The minisymposium talk will discuss these algorithmic developments and present sample calculations using our adaptive triangulation algorithm applied to various moving interface problems such as etching, deposition, and curvature flow.

  2. On the Geometry of the Hamilton-Jacobi Equation and Generating Functions

    NASA Astrophysics Data System (ADS)

    Ferraro, Sebastián; de León, Manuel; Marrero, Juan Carlos; Martín de Diego, David; Vaquero, Miguel

    2017-10-01

    In this paper we develop a geometric version of the Hamilton-Jacobi equation in the Poisson setting. Specifically, we "geometrize" what is usually called a complete solution of the Hamilton-Jacobi equation. We use some well-known results about symplectic groupoids, in particular cotangent groupoids, as a keystone for the construction of our framework. Our methodology follows the ambitious program proposed by Weinstein (In Mechanics day (Waterloo, ON, 1992), volume 7 of fields institute communications, American Mathematical Society, Providence, 1996) in order to develop geometric formulations of the dynamical behavior of Lagrangian and Hamiltonian systems on Lie algebroids and Lie groupoids. This procedure allows us to take symmetries into account, and, as a by-product, we recover results from Channell and Scovel (Phys D 50(1):80-88, 1991), Ge (Indiana Univ. Math. J. 39(3):859-876, 1990), Ge and Marsden (Phys Lett A 133(3):134-139, 1988), but even in these situations our approach is new. A theory of generating functions for the Poisson structures considered here is also developed following the same pattern, solving a longstanding problem of the area: how to obtain a generating function for the identity transformation and the nearby Poisson automorphisms of Poisson manifolds. A direct application of our results gives the construction of a family of Poisson integrators, that is, integrators that conserve the underlying Poisson geometry. These integrators are implemented in the paper in benchmark problems. Some conclusions, current and future directions of research are shown at the end of the paper.

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

    PubMed

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

    2008-08-01

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

  4. High-Order Central WENO Schemes for Multi-Dimensional Hamilton-Jacobi Equations

    NASA Technical Reports Server (NTRS)

    Bryson, Steve; Levy, Doron; Biegel, Bryan (Technical Monitor)

    2002-01-01

    We present new third- and fifth-order Godunov-type central schemes for approximating solutions of the Hamilton-Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greater than two. In two space dimensions we present two versions for the third-order scheme: one scheme that is based on a genuinely two-dimensional Central WENO reconstruction, and another scheme that is based on a simpler dimension-by-dimension reconstruction. The simpler dimension-by-dimension variant is then extended to a multi-dimensional fifth-order scheme. Our numerical examples in one, two and three space dimensions verify the expected order of accuracy of the schemes.

  5. Hybrid massively parallel fast sweeping method for static Hamilton-Jacobi equations

    NASA Astrophysics Data System (ADS)

    Detrixhe, Miles; Gibou, Frédéric

    2016-10-01

    The fast sweeping method is a popular algorithm for solving a variety of static Hamilton-Jacobi equations. Fast sweeping algorithms for parallel computing have been developed, but are severely limited. In this work, we present a multilevel, hybrid parallel algorithm that combines the desirable traits of two distinct parallel methods. The fine and coarse grained components of the algorithm take advantage of heterogeneous computer architecture common in high performance computing facilities. We present the algorithm and demonstrate its effectiveness on a set of example problems including optimal control, dynamic games, and seismic wave propagation. We give results for convergence, parallel scaling, and show state-of-the-art speedup values for the fast sweeping method.

  6. Periodic solutions of the Hamilton-Jacobi equation with a periodic non-homogeneous term and Aubry-Mather theory

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sobolevskii, A N

    It is proved that the one-dimensional Hamilton-Jacobi equation with a periodic non-homogeneous term admits a family of generalized solutions, each of which can be represented as the sum of a linear and a periodic function; a condition for the uniqueness of such a solution is given in terms of Aubry-Mather theory.

  7. Separation of variables in the special diagonal Hamilton-Jacobi equation: Application to the dynamical problem of a particle constrained on a moving surface

    NASA Technical Reports Server (NTRS)

    Blanchard, D. L.; Chan, F. K.

    1973-01-01

    For a time-dependent, n-dimensional, special diagonal Hamilton-Jacobi equation a necessary and sufficient condition for the separation of variables to yield a complete integral of the form was established by specifying the admissible forms in terms of arbitrary functions. A complete integral was then expressed in terms of these arbitrary functions and also the n irreducible constants. As an application of the results obtained for the two-dimensional Hamilton-Jacobi equation, analysis was made for a comparatively wide class of dynamical problems involving a particle moving in Euclidean three-dimensional space under the action of external forces but constrained on a moving surface. All the possible cases in which this equation had a complete integral of the form were obtained and these are tubulated for reference.

  8. Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations

    NASA Technical Reports Server (NTRS)

    Osher, Stanley; Sethian, James A.

    1987-01-01

    New numerical algorithms are devised (PSC algorithms) for following fronts propagating with curvature-dependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, which resemble Hamilton-Jacobi equations with parabolic right-hand-sides, by using techniques from the hyperbolic conservation laws. Non-oscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps in the moving fronts. The algorithms handle topological merging and breaking naturally, work in any number of space dimensions, and do not require that the moving surface be written as a function. The methods can be used also for more general Hamilton-Jacobi-type problems. The algorithms are demonstrated by computing the solution to a variety of surface motion problems.

  9. Algorithm for Overcoming the Curse of Dimensionality for Certain Non-convex Hamilton-Jacobi Equations, Projections and Differential Games

    DTIC Science & Technology

    2016-05-01

    Algorithm for Overcoming the Curse of Dimensionality for Certain Non-convex Hamilton-Jacobi Equations, Projections and Differential Games Yat Tin...subproblems. Our approach is expected to have wide applications in continuous dynamic games , control theory problems, and elsewhere. Mathematics...differential dynamic games , control theory problems, and dynamical systems coming from the physical world, e.g. [11]. An important application is to

  10. Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains

    NASA Technical Reports Server (NTRS)

    Barth, Timothy J.; Sethian, James A.

    1997-01-01

    Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the Hamilton-Jacobi (H-J), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the H-J equations. Unfortunately, the basic scheme lacks proper Lipschitz continuity of the numerical Hamiltonian. By employing a virtual edge flipping technique, Lipschitz continuity of the numerical flux is restored on acute triangulations. Next, schemes are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous Hamiltonians. These schemes possess a discrete maximum principle on arbitrary triangulations and naturally exhibit proper Lipschitz continuity of the numerical Hamiltonian. Finally, a class of Petrov-Galerkin approximations are considered. These schemes are stabilized via a least-squares bilinear form. The Petrov-Galerkin schemes do not possess a discrete maximum principle but generalize to high order accuracy.

  11. General relativity in two dimensions: A Hamilton-Jacobi analysis

    NASA Astrophysics Data System (ADS)

    Bertin, M. C.; Pimentel, B. M.; Pompeia, P. J.

    2010-11-01

    We analyzed the constraint structure of the Einstein-Hilbert first-order action in two dimensions using the Hamilton-Jacobi approach. We were able to find a set of involutive, as well as a set of non-involutive constraints. Using generalized brackets we showed how to assure integrability of the theory, to eliminate the set of non-involutive constraints and how to build the field equations.

  12. High-Order Semi-Discrete Central-Upwind Schemes for Multi-Dimensional Hamilton-Jacobi Equations

    NASA Technical Reports Server (NTRS)

    Bryson, Steve; Levy, Doron; Biegel, Bran R. (Technical Monitor)

    2002-01-01

    We present high-order semi-discrete central-upwind numerical schemes for approximating solutions of multi-dimensional Hamilton-Jacobi (HJ) equations. This scheme is based on the use of fifth-order central interpolants like those developed in [1], in fluxes presented in [3]. These interpolants use the weighted essentially nonoscillatory (WENO) approach to avoid spurious oscillations near singularities, and become "central-upwind" in the semi-discrete limit. This scheme provides numerical approximations whose error is as much as an order of magnitude smaller than those in previous WENO-based fifth-order methods [2, 1]. Thee results are discussed via examples in one, two and three dimensions. We also pregnant explicit N-dimensional formulas for the fluxes, discuss their monotonicity and tl!e connection between this method and that in [2].

  13. Matched asymptotic expansion of the Hamilton-Jacobi-Bellman equation for aeroassisted plane-change maneuvers

    NASA Technical Reports Server (NTRS)

    Calise, Anthony J.; Melamed, Nahum

    1993-01-01

    In this paper we develop a general procedure for constructing a matched asymptotic expansion of the Hamilton-Jacobi-Bellman equation based on the method of characteristics. The development is for a class of perturbation problems whose solution exhibits two-time-scale behavior. A regular expansion for problems of this type is inappropriate since it is not uniformly valid over a narrow range of the independent variable. Of particular interest here is the manner in which matching and boundary conditions are enforced when the expansion is carried out to first order. Two cases are distinguished - one where the left boundary condition coincides with or lies to the right of the singular region and one where the left boundary condition lies to the left of the singular region. A simple example is used to illustrate the procedure, and its potential application to aeroassisted plane change is described.

  14. A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

    NASA Astrophysics Data System (ADS)

    Witte, J. H.; Reisinger, C.

    2010-09-01

    We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desireable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to an order of O(1/ρ), where ρ>0 is the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.

  15. Hamilton-Jacobi modelling of relative motion for formation flying.

    PubMed

    Kolemen, Egemen; Kasdin, N Jeremy; Gurfil, Pini

    2005-12-01

    A precise analytic model for the relative motion of a group of satellites in slightly elliptic orbits is introduced. With this aim, we describe the relative motion of an object relative to a circular or slightly elliptic reference orbit in the rotating Hill frame via a low-order Hamiltonian, and solve the Hamilton-Jacobi equation. This results in a first-order solution to the relative motion identical to the Clohessy-Wiltshire approach; here, however, rather than using initial conditions as our constants of the motion, we utilize the canonical momenta and coordinates. This allows us to treat perturbations in an identical manner, as in the classical Delaunay formulation of the two-body problem. A precise analytical model for the base orbit is chosen with the included effect of zonal harmonics (J(2), J(3), J(4)). A Hamiltonian describing the real relative motion is formed and by differing this from the nominal Hamiltonian, the perturbing Hamiltonian is obtained. Using the Hamilton equations, the variational equations for the new constants are found. In a manner analogous to the center manifold reduction procedure, the non-periodic part of the motion is canceled through a magnitude analysis leading to simple boundedness conditions that cancel the drift terms due to the higher order perturbations. Using this condition, the variational equations are integrated to give periodic solutions that closely approximate the results from numerical integration (1 mm/per orbit for higher order and eccentricity perturbations and 30 cm/per orbit for zonal perturbations). This procedure provides a compact and insightful analytic description of the resulting relative motion.

  16. Classification of Hamilton-Jacobi separation in orthogonal coordinates with diagonal curvature

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Rajaratnam, Krishan, E-mail: k2rajara@uwaterloo.ca; McLenaghan, Raymond G., E-mail: rgmclenaghan@uwaterloo.ca

    2014-08-15

    We find all orthogonal metrics where the geodesic Hamilton-Jacobi equation separates and the Riemann curvature tensor satisfies a certain equation (called the diagonal curvature condition). All orthogonal metrics of constant curvature satisfy the diagonal curvature condition. The metrics we find either correspond to a Benenti system or are warped product metrics where the induced metric on the base manifold corresponds to a Benenti system. Furthermore, we show that most metrics we find are characterized by concircular tensors; these metrics, called Kalnins-Eisenhart-Miller metrics, have an intrinsic characterization which can be used to obtain them on a given space. In conjunction withmore » other results, we show that the metrics we found constitute all separable metrics for Riemannian spaces of constant curvature and de Sitter space.« less

  17. Restoration of four-dimensional diffeomorphism covariance in canonical general relativity: An intrinsic Hamilton-Jacobi approach

    NASA Astrophysics Data System (ADS)

    Salisbury, Donald; Renn, Jürgen; Sundermeyer, Kurt

    2016-02-01

    Classical background independence is reflected in Lagrangian general relativity through covariance under the full diffeomorphism group. We show how this independence can be maintained in a Hamilton-Jacobi approach that does not accord special privilege to any geometric structure. Intrinsic space-time curvature-based coordinates grant equal status to all geometric backgrounds. They play an essential role as a starting point for inequivalent semiclassical quantizations. The scheme calls into question Wheeler’s geometrodynamical approach and the associated Wheeler-DeWitt equation in which 3-metrics are featured geometrical objects. The formalism deals with variables that are manifestly invariant under the full diffeomorphism group. Yet, perhaps paradoxically, the liberty in selecting intrinsic coordinates is precisely as broad as is the original diffeomorphism freedom. We show how various ideas from the past five decades concerning the true degrees of freedom of general relativity can be interpreted in light of this new constrained Hamiltonian description. In particular, we show how the Kuchař multi-fingered time approach can be understood as a means of introducing full four-dimensional diffeomorphism invariants. Every choice of new phase space variables yields new Einstein-Hamilton-Jacobi constraining relations, and corresponding intrinsic Schrödinger equations. We show how to implement this freedom by canonical transformation of the intrinsic Hamiltonian. We also reinterpret and rectify significant work by Dittrich on the construction of “Dirac observables.”

  18. Hamilton-Jacobi formalism for Podolsky's electromagnetic theory on the null-plane

    NASA Astrophysics Data System (ADS)

    Bertin, M. C.; Pimentel, B. M.; Valcárcel, C. E.; Zambrano, G. E. R.

    2017-08-01

    We develop the Hamilton-Jacobi formalism for Podolsky's electromagnetic theory on the null-plane. The main goal is to build the complete set of Hamiltonian generators of the system as well as to study the canonical and gauge transformations of the theory.

  19. Hamilton-Jacobi formalism for inflation with non-minimal derivative coupling

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sheikhahmadi, Haidar; Saridakis, Emmanuel N.; Aghamohammadi, Ali

    2016-10-01

    In inflation with nonminimal derivative coupling there is not a conformal transformation to the Einstein frame where calculations are straightforward, and thus in order to extract inflationary observables one needs to perform a detailed and lengthy perturbation investigation. In this work we bypass this problem by performing a Hamilton-Jacobi analysis, namely rewriting the cosmological equations considering the scalar field to be the time variable. We apply the method to two specific models, namely the power-law and the exponential cases, and for each model we calculate various observables such as the tensor-to-scalar ratio, and the spectral index and its running. Wemore » compare them with 2013 and 2015 Planck data, and we show that they are in a very good agreement with observations.« less

  20. Axisymmetric black holes allowing for separation of variables in the Klein-Gordon and Hamilton-Jacobi equations

    NASA Astrophysics Data System (ADS)

    Konoplya, R. A.; Stuchlík, Z.; Zhidenko, A.

    2018-04-01

    We determine the class of axisymmetric and asymptotically flat black-hole spacetimes for which the test Klein-Gordon and Hamilton-Jacobi equations allow for the separation of variables. The known Kerr, Kerr-Newman, Kerr-Sen and some other black-hole metrics in various theories of gravity are within the class of spacetimes described here. It is shown that although the black-hole metric in the Einstein-dilaton-Gauss-Bonnet theory does not allow for the separation of variables (at least in the considered coordinates), for a number of applications it can be effectively approximated by a metric within the above class. This gives us some hope that the class of spacetimes described here may be not only generic for the known solutions allowing for the separation of variables, but also a good approximation for a broader class of metrics, which does not admit such separation. Finally, the generic form of the axisymmetric metric is expanded in the radial direction in terms of the continued fractions and the connection with other black-hole parametrizations is discussed.

  1. Hamilton-Jacobi formalism to warm inflationary scenario

    NASA Astrophysics Data System (ADS)

    Sayar, K.; Mohammadi, A.; Akhtari, L.; Saaidi, Kh.

    2017-01-01

    The Hamilton-Jacobi formalism as a powerful method is being utilized to reconsider the warm inflationary scenario, where the scalar field as the main component driving inflation interacts with other fields. Separating the context into strong and weak dissipative regimes, the goal is followed for two popular functions of Γ . Applying slow-rolling approximation, the required perturbation parameters are extracted and, by comparing to the latest Planck data, the free parameters are restricted. The possibility of producing an acceptable inflation is studied where the result shows that for all cases the model could successfully suggest the amplitude of scalar perturbation, scalar spectral index, its running, and the tensor-to-scalar ratio.

  2. Viscous warm inflation: Hamilton-Jacobi formalism

    NASA Astrophysics Data System (ADS)

    Akhtari, L.; Mohammadi, A.; Sayar, K.; Saaidi, Kh.

    2017-04-01

    Using Hamilton-Jacobi formalism, the scenario of warm inflation with viscous pressure is considered. The formalism gives a way of computing the slow-rolling parameter without extra approximation, and it is well-known as a powerful method in cold inflation. The model is studied in detail for three different cases of the dissipation and bulk viscous pressure coefficients. In the first case where both coefficients are taken as constant, it is shown that the case could not portray warm inflationary scenario compatible with observational data even it is possible to restrict the model parameters. For other cases, the results shows that the model could properly predicts the perturbation parameters in which they stay in perfect agreement with Planck data. As a further argument, r -ns and αs -ns are drown that show the acquired result could stand in acceptable area expressing a compatibility with observational data.

  3. Constants of the motion, universal time and the Hamilton-Jacobi function in general relativity

    NASA Astrophysics Data System (ADS)

    O'Hara, Paul

    2013-04-01

    In most text books of mechanics, Newton's laws or Hamilton's equations of motion are first written down and then solved based on initial conditions to determine the constants of the motions and to describe the trajectories of the particles. In this essay, we take a different starting point. We begin with the metrics of general relativity and show how they can be used to construct by inspection constants of motion, which can then be used to write down the equations of the trajectories. This will be achieved by deriving a Hamiltonian-Jacobi function from the metric and showing that its existence requires all of the above mentioned properties. The article concludes by showing that a consistent theory of such functions also requires the need for a universal measure of time which can be identified with the "worldtime" parameter, first introduced by Steuckelberg and later developed by Horwitz and Piron.

  4. Symmetric tops in combined electric fields: Conditional quasisolvability via the quantum Hamilton-Jacobi theory

    NASA Astrophysics Data System (ADS)

    Schatz, Konrad; Friedrich, Bretislav; Becker, Simon; Schmidt, Burkhard

    2018-05-01

    We make use of the quantum Hamilton-Jacobi (QHJ) theory to investigate conditional quasisolvability of the quantum symmetric top subject to combined electric fields (symmetric top pendulum). We derive the conditions of quasisolvability of the time-independent Schrödinger equation as well as the corresponding finite sets of exact analytic solutions. We do so for this prototypical trigonometric system as well as for its anti-isospectral hyperbolic counterpart. An examination of the algebraic and numerical spectra of these two systems reveals mutually closely related patterns. The QHJ approach allows us to retrieve the closed-form solutions for the spherical and planar pendula and the Razavy system that had been obtained in our earlier work via supersymmetric quantum mechanics as well as to find a cornucopia of additional exact analytic solutions.

  5. The classical limit of minimal length uncertainty relation: revisit with the Hamilton-Jacobi method

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Guo, Xiaobo; Wang, Peng; Yang, Haitang, E-mail: guoxiaobo@swust.edu.cn, E-mail: pengw@scu.edu.cn, E-mail: hyanga@scu.edu.cn

    2016-05-01

    The existence of a minimum measurable length could deform not only the standard quantum mechanics but also classical physics. The effects of the minimal length on classical orbits of particles in a gravitation field have been investigated before, using the deformed Poisson bracket or Schwarzschild metric. In this paper, we first use the Hamilton-Jacobi method to derive the deformed equations of motion in the context of Newtonian mechanics and general relativity. We then employ them to study the precession of planetary orbits, deflection of light, and time delay in radar propagation. We also set limits on the deformation parameter bymore » comparing our results with the observational measurements. Finally, comparison with results from previous papers is given at the end of this paper.« less

  6. A second order discontinuous Galerkin fast sweeping method for Eikonal equations

    NASA Astrophysics Data System (ADS)

    Li, Fengyan; Shu, Chi-Wang; Zhang, Yong-Tao; Zhao, Hongkai

    2008-09-01

    In this paper, we construct a second order fast sweeping method with a discontinuous Galerkin (DG) local solver for computing viscosity solutions of a class of static Hamilton-Jacobi equations, namely the Eikonal equations. Our piecewise linear DG local solver is built on a DG method developed recently [Y. Cheng, C.-W. Shu, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, Journal of Computational Physics 223 (2007) 398-415] for the time-dependent Hamilton-Jacobi equations. The causality property of Eikonal equations is incorporated into the design of this solver. The resulting local nonlinear system in the Gauss-Seidel iterations is a simple quadratic system and can be solved explicitly. The compactness of the DG method and the fast sweeping strategy lead to fast convergence of the new scheme for Eikonal equations. Extensive numerical examples verify efficiency, convergence and second order accuracy of the proposed method.

  7. Optimization of the launcher ascent trajectory leading to the global optimum without any initialization: the breakthrough of the Hamilton-Jacobi-Bellman approach

    NASA Astrophysics Data System (ADS)

    Bourgeois, E.; Bokanowski, O.; Zidani, H.; Désilles, A.

    2018-06-01

    The resolution of the launcher ascent trajectory problem by the so-called Hamilton-Jacobi-Bellman (HJB) approach, relying on the Dynamic Programming Principle, has been investigated. The method gives a global optimum and does not need any initialization procedure. Despite these advantages, this approach is seldom used because of the dicculties of computing the solution of the HJB equation for high dimension problems. The present study shows that an eccient resolution is found. An illustration of the method is proposed on a heavy class launcher, for a typical GEO (Geostationary Earth Orbit) mission. This study has been performed in the frame of the Centre National d'Etudes Spatiales (CNES) Launchers Research & Technology Program.

  8. Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

    NASA Technical Reports Server (NTRS)

    Tucker, Paul G.; Rumsey, Christopher L.; Bartels, Robert E.; Biedron, Robert T.

    2003-01-01

    Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson s Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

  9. Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

    NASA Technical Reports Server (NTRS)

    Tucker, Paul G.; Rumsey, Christopher L.; Bartels, Robert E.; Biedron, Robert T.

    2003-01-01

    Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson's Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

  10. Computations of Wall Distances Based on Differential Equations

    NASA Technical Reports Server (NTRS)

    Tucker, Paul G.; Rumsey, Chris L.; Spalart, Philippe R.; Bartels, Robert E.; Biedron, Robert T.

    2004-01-01

    The use of differential equations such as Eikonal, Hamilton-Jacobi and Poisson for the economical calculation of the nearest wall distance d, which is needed by some turbulence models, is explored. Modifications that could palliate some turbulence-modeling anomalies are also discussed. Economy is of especial value for deforming/adaptive grid problems. For these, ideally, d is repeatedly computed. It is shown that the Eikonal and Hamilton-Jacobi equations can be easy to implement when written in implicit (or iterated) advection and advection-diffusion equation analogous forms, respectively. These, like the Poisson Laplacian term, are commonly occurring in CFD solvers, allowing the re-use of efficient algorithms and code components. The use of the NASA CFL3D CFD program to solve the implicit Eikonal and Hamilton-Jacobi equations is explored. The re-formulated d equations are easy to implement, and are found to have robust convergence. For accurate Eikonal solutions, upwind metric differences are required. The Poisson approach is also found effective, and easiest to implement. Modified distances are not found to affect global outputs such as lift and drag significantly, at least in common situations such as airfoil flows.

  11. A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation

    NASA Astrophysics Data System (ADS)

    Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohamed A.; Hafez, Ramy M.

    2014-02-01

    This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers' equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers' equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.

  12. From nonlinear Schrödinger hierarchy to some (2+1)-dimensional nonlinear pseudodifferential equations

    NASA Astrophysics Data System (ADS)

    Yang, Xiao; Du, Dianlou

    2010-08-01

    The Poisson structure on CN×RN is introduced to give the Hamiltonian system associated with a spectral problem which yields the nonlinear Schrödinger (NLS) hierarchy. The Hamiltonian system is proven to be Liouville integrable. Some (2+1)-dimensional equations including NLS equation, Kadomtesev-Petviashvili I (KPI) equation, coupled KPI equation, and modified Kadomtesev-Petviashvili (mKP) equation, are decomposed into Hamilton flows via the NLS hierarchy. The algebraic curve, Abel-Jacobi coordinates, and Riemann-Jacobi inversion are used to obtain the algebrogeometric solutions of these equations.

  13. Effect of the refractive index on the hawking temperature: an application of the Hamilton-Jacobi method

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sakalli, I., E-mail: izzet.sakalli@emu.edu.tr; Mirekhtiary, S. F., E-mail: fatemeh.mirekhtiary@emu.edu.tr

    2013-10-15

    Hawking radiation of a non-asymptotically flat 4-dimensional spherically symmetric and static dilatonic black hole (BH) via the Hamilton-Jacobi (HJ) method is studied. In addition to the naive coordinates, we use four more different coordinate systems that are well-behaved at the horizon. Except for the isotropic coordinates, direct computation by the HJ method leads to the standard Hawking temperature for all coordinate systems. The isotropic coordinates allow extracting the index of refraction from the Fermat metric. It is explicitly shown that the index of refraction determines the value of the tunneling rate and its natural consequence, the Hawking temperature. The isotropicmore » coordinates in the conventional HJ method produce a wrong result for the temperature of the linear dilaton. Here, we explain how this discrepancy can be resolved by regularizing the integral possessing a pole at the horizon.« less

  14. A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

    NASA Astrophysics Data System (ADS)

    Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohammed A.

    2014-09-01

    In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach

  15. Nonlinear Feedback Controllers and Compensators: A State-Dependent Riccati Equation Approach

    DTIC Science & Technology

    2003-01-01

    Nonlinear Feedback Controllers and Compensators: A State-Dependent Riccati Equation Approach H. T. Banks∗ B. M. Lewis † H. T. Tran‡ Department of...Mathematics Center for Research in Scientific Computation North Carolina State University Raleigh, NC 27695 Abstract State-dependent Riccati equation ...estimating the solution of the Hamilton- Jacobi-Bellman (HJB) equation can be found in a comprehensive review article [5]. Each of these ∗htbanks

  16. Jacobi-Gauss-Lobatto collocation method for the numerical solution of 1+1 nonlinear Schrödinger equations

    NASA Astrophysics Data System (ADS)

    Doha, E. H.; Bhrawy, A. H.; Abdelkawy, M. A.; Van Gorder, Robert A.

    2014-03-01

    A Jacobi-Gauss-Lobatto collocation (J-GL-C) method, used in combination with the implicit Runge-Kutta method of fourth order, is proposed as a numerical algorithm for the approximation of solutions to nonlinear Schrödinger equations (NLSE) with initial-boundary data in 1+1 dimensions. Our procedure is implemented in two successive steps. In the first one, the J-GL-C is employed for approximating the functional dependence on the spatial variable, using (N-1) nodes of the Jacobi-Gauss-Lobatto interpolation which depends upon two general Jacobi parameters. The resulting equations together with the two-point boundary conditions induce a system of 2(N-1) first-order ordinary differential equations (ODEs) in time. In the second step, the implicit Runge-Kutta method of fourth order is applied to solve this temporal system. The proposed J-GL-C method, used in combination with the implicit Runge-Kutta method of fourth order, is employed to obtain highly accurate numerical approximations to four types of NLSE, including the attractive and repulsive NLSE and a Gross-Pitaevskii equation with space-periodic potential. The numerical results obtained by this algorithm have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively few nodes used, the absolute error in our numerical solutions is sufficiently small.

  17. A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations

    NASA Astrophysics Data System (ADS)

    Bhrawy, A. H.; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.

    2015-07-01

    In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann-Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The validity and effectiveness of the method are demonstrated by solving five numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier.

  18. New formulae between Jacobi polynomials and some fractional Jacobi functions generalizing some connection formulae

    NASA Astrophysics Data System (ADS)

    Abd-Elhameed, W. M.

    2017-07-01

    In this paper, a new formula relating Jacobi polynomials of arbitrary parameters with the squares of certain fractional Jacobi functions is derived. The derived formula is expressed in terms of a certain terminating hypergeometric function of the type _4F3(1) . With the aid of some standard reduction formulae such as Pfaff-Saalschütz's and Watson's identities, the derived formula can be reduced in simple forms which are free of any hypergeometric functions for certain choices of the involved parameters of the Jacobi polynomials and the Jacobi functions. Some other simplified formulae are obtained via employing some computer algebra algorithms such as the algorithms of Zeilberger, Petkovsek and van Hoeij. Some connection formulae between some Jacobi polynomials are deduced. From these connection formulae, some other linearization formulae of Chebyshev polynomials are obtained. As an application to some of the introduced formulae, a numerical algorithm for solving nonlinear Riccati differential equation is presented and implemented by applying a suitable spectral method.

  19. Canonical equations of Hamilton for the nonlinear Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Liang, Guo; Guo, Qi; Ren, Zhanmei

    2015-09-01

    We define two different systems of mathematical physics: the second order differential system (SODS) and the first order differential system (FODS). The Newton's second law of motion and the nonlinear Schrödinger equation (NLSE) are the exemplary SODS and FODS, respectively. We obtain a new kind of canonical equations of Hamilton (CEH), which exhibit some kind of symmetry in form and are formally different from the conventional CEH without symmetry [H. Goldstein, C. Poole, J. Safko, Classical Mechanics, third ed., Addison- Wesley, 2001]. We also prove that the number of the CEHs is equal to the number of the generalized coordinates for the FODS, but twice the number of the generalized coordinates for the SODS. We show that the FODS can only be expressed by the new CEH, but not introduced by the conventional CEH, while the SODS can be done by both the new and the conventional CEHs. As an example, we prove that the nonlinear Schrödinger equation can be expressed with the new CEH in a consistent way.

  20. Quantum Hamilton equations of motion for bound states of one-dimensional quantum systems

    NASA Astrophysics Data System (ADS)

    Köppe, J.; Patzold, M.; Grecksch, W.; Paul, W.

    2018-06-01

    On the basis of Nelson's stochastic mechanics derivation of the Schrödinger equation, a formal mathematical structure of non-relativistic quantum mechanics equivalent to the one in classical analytical mechanics has been established in the literature. We recently were able to augment this structure by deriving quantum Hamilton equations of motion by finding the Nash equilibrium of a stochastic optimal control problem, which is the generalization of Hamilton's principle of classical mechanics to quantum systems. We showed that these equations allow a description and numerical determination of the ground state of quantum problems without using the Schrödinger equation. We extend this approach here to deliver the complete discrete energy spectrum and related eigenfunctions for bound states of one-dimensional stationary quantum systems. We exemplify this analytically for the one-dimensional harmonic oscillator and numerically by analyzing a quartic double-well potential, a model of broad importance in many areas of physics. We furthermore point out a relation between the tunnel splitting of such models and mean first passage time concepts applied to Nelson's diffusion paths in the ground state.

  1. A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations

    NASA Astrophysics Data System (ADS)

    Bhrawy, A. H.; Zaky, M. A.

    2015-01-01

    In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and ϑ. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.

  2. The method of Ritz applied to the equation of Hamilton. [for pendulum systems

    NASA Technical Reports Server (NTRS)

    Bailey, C. D.

    1976-01-01

    Without any reference to the theory of differential equations, the initial value problem of the nonlinear, nonconservative double pendulum system is solved by the application of the method of Ritz to the equation of Hamilton. Also shown is an example of the reduction of the traditional eigenvalue problem of linear, homogeneous, differential equations of motion to the solution of a set of nonhomogeneous algebraic equations. No theory of differential equations is used. Solution of the time-space path of the linear oscillator is demonstrated and compared to the exact solution.

  3. Numerical study on the incompressible Euler equations as a Hamiltonian system: Sectional curvature and Jacobi field

    NASA Astrophysics Data System (ADS)

    Ohkitani, K.

    2010-05-01

    We study some of the key quantities arising in the theory of [Arnold "Sur la geometrie differentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluides parfaits," Annales de l'institut Fourier 16, 319 (1966)] of the incompressible Euler equations both in two and three dimensions. The sectional curvatures for the Taylor-Green vortex and the ABC flow initial conditions are calculated exactly in three dimensions. We trace the time evolution of the Jacobi fields by direct numerical simulations and, in particular, see how the sectional curvatures get more and more negative in time. The spatial structure of the Jacobi fields is compared to the vorticity fields by visualizations. The Jacobi fields are found to grow exponentially in time for the flows with negative sectional curvatures. In two dimensions, a family of initial data proposed by Arnold (1966) is considered. The sectional curvature is observed to change its sign quickly even if it starts from a positive value. The Jacobi field is shown to be correlated with the passive scalar gradient in spatial structure. On the basis of Rouchon's physical-space based expression for the sectional curvature (1984), the origin of negative curvature is investigated. It is found that a "potential" αξ appearing in the definition of covariant time derivative plays an important role, in that a rapid growth in its gradient makes a major contribution to the negative curvature.

  4. Derivation of Hamilton's equations of motion for mechanical systems with constraints on the basis of Pontriagin's maximum principle

    NASA Astrophysics Data System (ADS)

    Kovalev, A. M.

    The problem of the motion of a mechanical system with constraints conforming to Hamilton's principle is stated as an optimum control problem, with equations of motion obtained on the basis of Pontriagin's principle. A Hamiltonian function in Rodrigues-Hamilton parameters for a gyrostat in a potential force field is obtained as an example. Equations describing the motion of a skate on a sloping surface and the motion of a disk on a horizontal plane are examined.

  5. Efficient High Order Central Schemes for Multi-Dimensional Hamilton-Jacobi Equations: Talk Slides

    NASA Technical Reports Server (NTRS)

    Bryson, Steve; Levy, Doron; Biegel, Brian R. (Technical Monitor)

    2002-01-01

    This viewgraph presentation presents information on the attempt to produce high-order, efficient, central methods that scale well to high dimension. The central philosophy is that the equations should evolve to the point where the data is smooth. This is accomplished by a cyclic pattern of reconstruction, evolution, and re-projection. One dimensional and two dimensional representational methods are detailed, as well.

  6. Hybrid massively parallel fast sweeping method for static Hamilton–Jacobi equations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Detrixhe, Miles, E-mail: mdetrixhe@engineering.ucsb.edu; University of California Santa Barbara, Santa Barbara, CA, 93106; Gibou, Frédéric, E-mail: fgibou@engineering.ucsb.edu

    The fast sweeping method is a popular algorithm for solving a variety of static Hamilton–Jacobi equations. Fast sweeping algorithms for parallel computing have been developed, but are severely limited. In this work, we present a multilevel, hybrid parallel algorithm that combines the desirable traits of two distinct parallel methods. The fine and coarse grained components of the algorithm take advantage of heterogeneous computer architecture common in high performance computing facilities. We present the algorithm and demonstrate its effectiveness on a set of example problems including optimal control, dynamic games, and seismic wave propagation. We give results for convergence, parallel scaling,more » and show state-of-the-art speedup values for the fast sweeping method.« less

  7. Inhomogeneous Jacobi equation for minimal surfaces and perturbative change in holographic entanglement entropy

    NASA Astrophysics Data System (ADS)

    Ghosh, Avirup; Mishra, Rohit

    2018-04-01

    The change in holographic entanglement entropy (HEE) for small fluctuations about pure anti-de Sitter (AdS) is obtained by a perturbative expansion of the area functional in terms of the change in the bulk metric and the embedded extremal surface. However it is known that change in the embedding appears at second order or higher. It was shown that these changes in the embedding can be calculated in the 2 +1 dimensional case by solving a "generalized geodesic deviation equation." We generalize this result to arbitrary dimensions by deriving an inhomogeneous form of the Jacobi equation for minimal surfaces. The solutions of this equation map a minimal surface in a given space time to a minimal surface in a space time which is a perturbation over the initial space time. Using this we perturbatively calculate the changes in HEE up to second order for boosted black brane like perturbations over AdS4.

  8. Exact results in the large system size limit for the dynamics of the chemical master equation, a one dimensional chain of equations.

    PubMed

    Martirosyan, A; Saakian, David B

    2011-08-01

    We apply the Hamilton-Jacobi equation (HJE) formalism to solve the dynamics of the chemical master equation (CME). We found exact analytical expressions (in large system-size limit) for the probability distribution, including explicit expression for the dynamics of variance of distribution. We also give the solution for some simple cases of the model with time-dependent rates. We derived the results of the Van Kampen method from the HJE approach using a special ansatz. Using the Van Kampen method, we give a system of ordinary differential equations (ODEs) to define the variance in a two-dimensional case. We performed numerics for the CME with stationary noise. We give analytical criteria for the disappearance of bistability in the case of stationary noise in one-dimensional CMEs.

  9. Semiclassical Wheeler-DeWitt equation: Solutions for long-wavelength fields

    NASA Astrophysics Data System (ADS)

    Salopek, D. S.; Stewart, J. M.; Parry, J.

    1993-07-01

    In the long-wavelength approximation, a general set of semiclassical wave functionals is given for gravity and matter interacting in 3+1 dimensions. In the long-wavelength theory, one neglects second-order spatial gradients in the energy constraint. These solutions satisfy the Hamilton-Jacobi equation, the momentum constraint, and the equation of continuity. It is essential to introduce inhomogeneities to discuss the role of time. The time hypersurface is chosen to be a homogeneous field in the wave functional. It is shown how to introduce tracer particles through a dust field χ into the dynamical system. The formalism can be used to describe stochastic inflation.

  10. Hamiltonian approach to GR - Part 1: covariant theory of classical gravity

    NASA Astrophysics Data System (ADS)

    Cremaschini, Claudio; Tessarotto, Massimo

    2017-05-01

    A challenging issue in General Relativity concerns the determination of the manifestly covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant Hamilton-Jacobi theory. The task is achieved by adopting a synchronous variational principle requiring distinction between the prescribed deterministic metric tensor \\widehat{g}(r)≡ { \\widehat{g}_{μ ν }(r)} solution of the Einstein field equations which determines the geometry of the background space-time and suitable variational fields x≡ { g,π } obeying an appropriate set of continuum Hamilton equations, referred to here as GR-Hamilton equations. It is shown that a prerequisite for reaching such a goal is that of casting the same equations in evolutionary form by means of a Lagrangian parametrization for a suitably reduced canonical state. As a result, the corresponding Hamilton-Jacobi theory is established in manifestly covariant form. Physical implications of the theory are discussed. These include the investigation of the structural stability of the GR-Hamilton equations with respect to vacuum solutions of the Einstein equations, assuming that wave-like perturbations are governed by the canonical evolution equations.

  11. Fundamental Study on Quantum Nanojets

    DTIC Science & Technology

    2004-08-01

    Pergamon Press. Bell , J. S . 1966 On the problem of hidden variables in quantum mechanics. Rev. of Modern Phys., 38, 447. Berndl, K., Daumer, M...fluid dynamics based on two quantum mechanical perspectives; Schrödinger’s wave mechanics and quantum fluid dynamics based on Hamilton-Jacoby...References 8 2). Direct Problems a). Quantum fluid dynamics formalism based on Hamilton-Jacoby equation are adapted for the numerical

  12. Applications of a Property of the Schrödinger Equation to the Modeling of Conservative Discrete Systems

    NASA Astrophysics Data System (ADS)

    Popa, Alexandru

    1998-08-01

    Recently we have demonstrated in a mathematical paper the following property: The energy which results from the Schrödinger equation can be rigorously calculated by line integrals of analytical functions, if the Hamilton-Jacobi equation, written for the same system, is satisfied in the space of coordinates by a periodical trajectory. We present now an accurate analysis model of the conservative discrete systems, that is based on this property. The theory is checked for a lot of atomic systems. The experimental data, which are ionization energies, are taken from well known books.

  13. Modifications of the PCPT method for HJB equations

    NASA Astrophysics Data System (ADS)

    Kossaczký, I.; Ehrhardt, M.; Günther, M.

    2016-10-01

    In this paper we will revisit the modification of the piecewise constant policy timestepping (PCPT) method for solving Hamilton-Jacobi-Bellman (HJB) equations. This modification is called piecewise predicted policy timestepping (PPPT) method and if properly used, it may be significantly faster. We will quickly recapitulate the algorithms of PCPT, PPPT methods and of the classical implicit method and apply them on a passport option pricing problem with non-standard payoff. We will present modifications needed to solve this problem effectively with the PPPT method and compare the performance with the PCPT method and the classical implicit method.

  14. On the relationship between the classical Dicke-Jaynes-Cummings-Gaudin model and the nonlinear Schroedinger equation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Du, Dianlou; Geng, Xue

    2013-05-15

    In this paper, the relationship between the classical Dicke-Jaynes-Cummings-Gaudin (DJCG) model and the nonlinear Schroedinger (NLS) equation is studied. It is shown that the classical DJCG model is equivalent to a stationary NLS equation. Moreover, the standard NLS equation can be solved by the classical DJCG model and a suitably chosen higher order flow. Further, it is also shown that classical DJCG model can be transformed into the classical Gaudin spin model in an external magnetic field through a deformation of Lax matrix. Finally, the separated variables are constructed on the common level sets of Casimir functions and the generalizedmore » action-angle coordinates are introduced via the Hamilton-Jacobi equation.« less

  15. Efficient relaxed-Jacobi smoothers for multigrid on parallel computers

    NASA Astrophysics Data System (ADS)

    Yang, Xiang; Mittal, Rajat

    2017-03-01

    In this Technical Note, we present a family of Jacobi-based multigrid smoothers suitable for the solution of discretized elliptic equations. These smoothers are based on the idea of scheduled-relaxation Jacobi proposed recently by Yang & Mittal (2014) [18] and employ two or three successive relaxed Jacobi iterations with relaxation factors derived so as to maximize the smoothing property of these iterations. The performance of these new smoothers measured in terms of convergence acceleration and computational workload, is assessed for multi-domain implementations typical of parallelized solvers, and compared to the lexicographic point Gauss-Seidel smoother. The tests include the geometric multigrid method on structured grids as well as the algebraic grid method on unstructured grids. The tests demonstrate that unlike Gauss-Seidel, the convergence of these Jacobi-based smoothers is unaffected by domain decomposition, and furthermore, they outperform the lexicographic Gauss-Seidel by factors that increase with domain partition count.

  16. On shifted Jacobi spectral method for high-order multi-point boundary value problems

    NASA Astrophysics Data System (ADS)

    Doha, E. H.; Bhrawy, A. H.; Hafez, R. M.

    2012-10-01

    This paper reports a spectral tau method for numerically solving multi-point boundary value problems (BVPs) of linear high-order ordinary differential equations. The construction of the shifted Jacobi tau approximation is based on conventional differentiation. This use of differentiation allows the imposition of the governing equation at the whole set of grid points and the straight forward implementation of multiple boundary conditions. Extension of the tau method for high-order multi-point BVPs with variable coefficients is treated using the shifted Jacobi Gauss-Lobatto quadrature. Shifted Jacobi collocation method is developed for solving nonlinear high-order multi-point BVPs. The performance of the proposed methods is investigated by considering several examples. Accurate results and high convergence rates are achieved.

  17. Efficient spectral-Galerkin algorithms for direct solution for second-order differential equations using Jacobi polynomials

    NASA Astrophysics Data System (ADS)

    Doha, E.; Bhrawy, A.

    2006-06-01

    It is well known that spectral methods (tau, Galerkin, collocation) have a condition number of ( is the number of retained modes of polynomial approximations). This paper presents some efficient spectral algorithms, which have a condition number of , based on the Jacobi?Galerkin methods of second-order elliptic equations in one and two space variables. The key to the efficiency of these algorithms is to construct appropriate base functions, which lead to systems with specially structured matrices that can be efficiently inverted. The complexities of the algorithms are a small multiple of operations for a -dimensional domain with unknowns, while the convergence rates of the algorithms are exponentials with smooth solutions.

  18. Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) Collocation Method for Solving Linear and Nonlinear Fokker-Planck Equations

    NASA Astrophysics Data System (ADS)

    Parand, K.; Latifi, S.; Moayeri, M. M.; Delkhosh, M.

    2018-05-01

    In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and for the space variable, a numerical method based on Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) collocation method is applied. It leads to in solving the equation in a series of time steps and at each time step, the problem is reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. One can observe that the proposed method is simple and accurate. Indeed, one of its merits is that it is derivative-free and by proposing a formula for derivative matrices, the difficulty aroused in calculation is overcome, along with that it does not need to calculate the General Lagrange basis and matrices; they have Kronecker property. Linear and nonlinear Fokker-Planck equations are given as examples and the results amply demonstrate that the presented method is very valid, effective, reliable and does not require any restrictive assumptions for nonlinear terms.

  19. Application of Hamilton's law of varying action

    NASA Technical Reports Server (NTRS)

    Bailey, C. D.

    1975-01-01

    The law of varying action enunciated by Hamilton in 1834-1835 permits the direct analytical solution of the problems of mechanics, both stationary and nonstationary, without consideration of force equilibrium and the theory of differential equations associated therewith. It has not been possible to obtain direct analytical solutions to nonstationary systems through the use of energy theory, which has been limited for 140 years to the principle of least action and to Hamilton's principle. It is shown here that Hamilton's law permits the direct analytical solution to nonstationary, initial value systems in the mechanics of solids without any knowledge or use of the theory of differential equations. Solutions are demonstrated for nonconservative, nonstationary particle motion, both linear and nonlinear.

  20. Some Theoretical Aspects of Nonzero Sum Differential Games and Applications to Combat Problems

    DTIC Science & Technology

    1971-06-01

    the Equilibrium Solution . 7 Hamilton-Jacobi-Bellman Partial Differential Equations ............. .............. 9 Influence Function Differential...Linearly .......... ............ 18 Problem Statement .......... ............ 18 Formulation of LJB Equations, Influence Function Equations and the TPBVP...19 Control Lawe . . .. ...... ........... 21 Conditions for Influence Function Continuity along Singular Surfaces

  1. Computational complexities and storage requirements of some Riccati equation solvers

    NASA Technical Reports Server (NTRS)

    Utku, Senol; Garba, John A.; Ramesh, A. V.

    1989-01-01

    The linear optimal control problem of an nth-order time-invariant dynamic system with a quadratic performance functional is usually solved by the Hamilton-Jacobi approach. This leads to the solution of the differential matrix Riccati equation with a terminal condition. The bulk of the computation for the optimal control problem is related to the solution of this equation. There are various algorithms in the literature for solving the matrix Riccati equation. However, computational complexities and storage requirements as a function of numbers of state variables, control variables, and sensors are not available for all these algorithms. In this work, the computational complexities and storage requirements for some of these algorithms are given. These expressions show the immensity of the computational requirements of the algorithms in solving the Riccati equation for large-order systems such as the control of highly flexible space structures. The expressions are also needed to compute the speedup and efficiency of any implementation of these algorithms on concurrent machines.

  2. State transformations and Hamiltonian structures for optimal control in discrete systems

    NASA Astrophysics Data System (ADS)

    Sieniutycz, S.

    2006-04-01

    Preserving usual definition of Hamiltonian H as the scalar product of rates and generalized momenta we investigate two basic classes of discrete optimal control processes governed by the difference rather than differential equations for the state transformation. The first class, linear in the time interval θ, secures the constancy of optimal H and satisfies a discrete Hamilton-Jacobi equation. The second class, nonlinear in θ, does not assure the constancy of optimal H and satisfies only a relationship that may be regarded as an equation of Hamilton-Jacobi type. The basic question asked is if and when Hamilton's canonical structures emerge in optimal discrete systems. For a constrained discrete control, general optimization algorithms are derived that constitute powerful theoretical and computational tools when evaluating extremum properties of constrained physical systems. The mathematical basis is Bellman's method of dynamic programming (DP) and its extension in the form of the so-called Carathéodory-Boltyanski (CB) stage optimality criterion which allows a variation of the terminal state that is otherwise fixed in Bellman's method. For systems with unconstrained intervals of the holdup time θ two powerful optimization algorithms are obtained: an unconventional discrete algorithm with a constant H and its counterpart for models nonlinear in θ. We also present the time-interval-constrained extension of the second algorithm. The results are general; namely, one arrives at: discrete canonical equations of Hamilton, maximum principles, and (at the continuous limit of processes with free intervals of time) the classical Hamilton-Jacobi theory, along with basic results of variational calculus. A vast spectrum of applications and an example are briefly discussed with particular attention paid to models nonlinear in the time interval θ.

  3. Accurate analytic solution of chemical master equations for gene regulation networks in a single cell

    NASA Astrophysics Data System (ADS)

    Huang, Guan-Rong; Saakian, David B.; Hu, Chin-Kun

    2018-01-01

    Studying gene regulation networks in a single cell is an important, interesting, and hot research topic of molecular biology. Such process can be described by chemical master equations (CMEs). We propose a Hamilton-Jacobi equation method with finite-size corrections to solve such CMEs accurately at the intermediate region of switching, where switching rate is comparable to fast protein production rate. We applied this approach to a model of self-regulating proteins [H. Ge et al., Phys. Rev. Lett. 114, 078101 (2015), 10.1103/PhysRevLett.114.078101] and found that as a parameter related to inducer concentration increases the probability of protein production changes from unimodal to bimodal, then to unimodal, consistent with phenotype switching observed in a single cell.

  4. Lie-Hamilton systems on the plane: Properties, classification and applications

    NASA Astrophysics Data System (ADS)

    Ballesteros, A.; Blasco, A.; Herranz, F. J.; de Lucas, J.; Sardón, C.

    2015-04-01

    We study Lie-Hamilton systems on the plane, i.e. systems of first-order differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional real Lie algebra of planar Hamiltonian vector fields with respect to a Poisson structure. We start with the local classification of finite-dimensional real Lie algebras of vector fields on the plane obtained in González-López, Kamran, and Olver (1992) [23] and we interpret their results as a local classification of Lie systems. By determining which of these real Lie algebras consist of Hamiltonian vector fields relative to a Poisson structure, we provide the complete local classification of Lie-Hamilton systems on the plane. We present and study through our results new Lie-Hamilton systems of interest which are used to investigate relevant non-autonomous differential equations, e.g. we get explicit local diffeomorphisms between such systems. We also analyse biomathematical models, the Milne-Pinney equations, second-order Kummer-Schwarz equations, complex Riccati equations and Buchdahl equations.

  5. Multi-indexed Meixner and little q-Jacobi (Laguerre) polynomials

    NASA Astrophysics Data System (ADS)

    Odake, Satoru; Sasaki, Ryu

    2017-04-01

    As the fourth stage of the project multi-indexed orthogonal polynomials, we present the multi-indexed Meixner and little q-Jacobi (Laguerre) polynomials in the framework of ‘discrete quantum mechanics’ with real shifts defined on the semi-infinite lattice in one dimension. They are obtained, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier, from the quantum mechanical systems corresponding to the original orthogonal polynomials by multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of virtual state vectors. The virtual state vectors are the solutions of the matrix Schrödinger equation on all the lattice points having negative energies and infinite norm. This is in good contrast to the (q-)Racah systems defined on a finite lattice, in which the ‘virtual state’ vectors satisfy the matrix Schrödinger equation except for one of the two boundary points.

  6. Local, smooth, and consistent Jacobi set simplification

    DOE PAGES

    Bhatia, Harsh; Wang, Bei; Norgard, Gregory; ...

    2014-10-31

    The relation between two Morse functions defined on a smooth, compact, and orientable 2-manifold can be studied in terms of their Jacobi set. The Jacobi set contains points in the domain where the gradients of the two functions are aligned. Both the Jacobi set itself as well as the segmentation of the domain it induces, have shown to be useful in various applications. In practice, unfortunately, functions often contain noise and discretization artifacts, causing their Jacobi set to become unmanageably large and complex. Although there exist techniques to simplify Jacobi sets, they are unsuitable for most applications as they lackmore » fine-grained control over the process, and heavily restrict the type of simplifications possible. In this paper, we introduce a new framework that generalizes critical point cancellations in scalar functions to Jacobi set in two dimensions. We present a new interpretation of Jacobi set simplification based on the perspective of domain segmentation. Generalizing the cancellation of critical points from scalar functions to Jacobi sets, we focus on simplifications that can be realized by smooth approximations of the corresponding functions, and show how these cancellations imply simultaneous simplification of contiguous subsets of the Jacobi set. Using these extended cancellations as atomic operations, we introduce an algorithm to successively cancel subsets of the Jacobi set with minimal modifications to some user-defined metric. We show that for simply connected domains, our algorithm reduces a given Jacobi set to its minimal configuration, that is, one with no birth–death points (a birth–death point is a specific type of singularity within the Jacobi set where the level sets of the two functions and the Jacobi set have a common normal direction).« less

  7. Dynamic optimization and its relation to classical and quantum constrained systems

    NASA Astrophysics Data System (ADS)

    Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo

    2017-08-01

    We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac's bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closed-loop λ-strategy, the optimality condition for the action gives a consistency relation, which is associated to the Hamilton-Jacobi-Bellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Ψ(x , t) =e iS(x , t) in the quantum Schrödinger equation, a non-linear partial equation is obtained for the S function. For the right-hand side quantization, this is the Hamilton-Jacobi-Bellman equation, when S(x , t) is identified with the optimal value function. Thus, the Hamilton-Jacobi-Bellman equation in Bellman's maximum principle, can be interpreted as the quantum approach of the optimization problem.

  8. Quantum demolition filtering and optimal control of unstable systems.

    PubMed

    Belavkin, V P

    2012-11-28

    A brief account of the quantum information dynamics and dynamical programming methods for optimal control of quantum unstable systems is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme, we exploit the separation theorem of filtering and control aspects as in the usual case of quantum stable systems with non-demolition observation. This allows us to start with the Belavkin quantum filtering equation generalized to demolition observations and derive the generalized Hamilton-Jacobi-Bellman equation using standard arguments of classical control theory. This is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term if the control is restricted to Hamiltonian terms in the filtering equation. An unstable controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure quantum qubit state from a mixed one.

  9. A new Jacobi spectral collocation method for solving 1+1 fractional Schrödinger equations and fractional coupled Schrödinger systems

    NASA Astrophysics Data System (ADS)

    Bhrawy, A. H.; Doha, E. H.; Ezz-Eldien, S. S.; Van Gorder, Robert A.

    2014-12-01

    The Jacobi spectral collocation method (JSCM) is constructed and used in combination with the operational matrix of fractional derivatives (described in the Caputo sense) for the numerical solution of the time-fractional Schrödinger equation (T-FSE) and the space-fractional Schrödinger equation (S-FSE). The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, the presented approach is also applied to solve the time-fractional coupled Schrödinger system (T-FCSS). In order to demonstrate the validity and accuracy of the numerical scheme proposed, several numerical examples with their approximate solutions are presented with comparisons between our numerical results and those obtained by other methods.

  10. Jacobi spectral Galerkin method for elliptic Neumann problems

    NASA Astrophysics Data System (ADS)

    Doha, E.; Bhrawy, A.; Abd-Elhameed, W.

    2009-01-01

    This paper is concerned with fast spectral-Galerkin Jacobi algorithms for solving one- and two-dimensional elliptic equations with homogeneous and nonhomogeneous Neumann boundary conditions. The paper extends the algorithms proposed by Shen (SIAM J Sci Comput 15:1489-1505, 1994) and Auteri et al. (J Comput Phys 185:427-444, 2003), based on Legendre polynomials, to Jacobi polynomials with arbitrary α and β. The key to the efficiency of our algorithms is to construct appropriate basis functions with zero slope at the endpoints, which lead to systems with sparse matrices for the discrete variational formulations. The direct solution algorithm developed for the homogeneous Neumann problem in two-dimensions relies upon a tensor product process. Nonhomogeneous Neumann data are accounted for by means of a lifting. Numerical results indicating the high accuracy and effectiveness of these algorithms are presented.

  11. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sergyeyev, Artur; Krtous, Pavel; Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague, V Holesovickach 2, Prague

    We consider the Klein-Gordon equation in generalized higher-dimensional Kerr-NUT-(A)dS spacetime without imposing any restrictions on the functional parameters characterizing the metric. We establish commutativity of the second-order operators constructed from the Killing tensors found in [J. High Energy Phys. 02 (2007) 004] and show that these operators, along with the first-order operators originating from the Killing vectors, form a complete set of commuting symmetry operators (i.e., integrals of motion) for the Klein-Gordon equation. Moreover, we demonstrate that the separated solutions of the Klein-Gordon equation obtained in [J. High Energy Phys. 02 (2007) 005] are joint eigenfunctions for all of thesemore » operators. We also present an explicit form of the zero mode for the Klein-Gordon equation with zero mass. In the semiclassical approximation we find that the separated solutions of the Hamilton-Jacobi equation for geodesic motion are also solutions for a set of Hamilton-Jacobi-type equations which correspond to the quadratic conserved quantities arising from the above Killing tensors.« less

  12. Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

    We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-upsmore » that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.« less

  13. Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems

    DOE PAGES

    Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

    2015-12-01

    We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-upsmore » that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.« less

  14. Boundary conditions estimation on a road network using compressed sensing.

    DOT National Transportation Integrated Search

    2016-02-01

    This report presents a new boundary condition estimation framework for transportation networks in which : the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a : Hamilton-Jacobi equation, we pose th...

  15. Scheduled Relaxation Jacobi method: Improvements and applications

    NASA Astrophysics Data System (ADS)

    Adsuara, J. E.; Cordero-Carrión, I.; Cerdá-Durán, P.; Aloy, M. A.

    2016-09-01

    Elliptic partial differential equations (ePDEs) appear in a wide variety of areas of mathematics, physics and engineering. Typically, ePDEs must be solved numerically, which sets an ever growing demand for efficient and highly parallel algorithms to tackle their computational solution. The Scheduled Relaxation Jacobi (SRJ) is a promising class of methods, atypical for combining simplicity and efficiency, that has been recently introduced for solving linear Poisson-like ePDEs. The SRJ methodology relies on computing the appropriate parameters of a multilevel approach with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances. The efficiency in the reduction of the residual increases with the number of levels employed in the algorithm. Applying the original methodology to compute the algorithm parameters with more than 5 levels notably hinders obtaining optimal SRJ schemes, as the mixed (non-linear) algebraic-differential system of equations from which they result becomes notably stiff. Here we present a new methodology for obtaining the parameters of SRJ schemes that overcomes the limitations of the original algorithm and provide parameters for SRJ schemes with up to 15 levels and resolutions of up to 215 points per dimension, allowing for acceleration factors larger than several hundreds with respect to the Jacobi method for typical resolutions and, in some high resolution cases, close to 1000. Most of the success in finding SRJ optimal schemes with more than 10 levels is based on an analytic reduction of the complexity of the previously mentioned system of equations. Furthermore, we extend the original algorithm to apply it to certain systems of non-linear ePDEs.

  16. Towards Quantum Cybernetics:. Optimal Feedback Control in Quantum Bio Informatics

    NASA Astrophysics Data System (ADS)

    Belavkin, V. P.

    2009-02-01

    A brief account of the quantum information dynamics and dynamical programming methods for the purpose of optimal control in quantum cybernetics with convex constraints and cońcave cost and bequest functions of the quantum state is given. Consideration is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme with continuous observations we exploit the separation theorem of filtering and control aspects for quantum stochastic micro-dynamics of the total system. This allows to start with the Belavkin quantum filtering equation and derive the generalized Hamilton-Jacobi-Bellman equation using standard arguments of classical control theory. This is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term if the control is restricted to only Hamiltonian terms in the filtering equation. A controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure quantum qubit state from a mixed one.

  17. Application of shifted Jacobi pseudospectral method for solving (in)finite-horizon min-max optimal control problems with uncertainty

    NASA Astrophysics Data System (ADS)

    Nikooeinejad, Z.; Delavarkhalafi, A.; Heydari, M.

    2018-03-01

    The difficulty of solving the min-max optimal control problems (M-MOCPs) with uncertainty using generalised Euler-Lagrange equations is caused by the combination of split boundary conditions, nonlinear differential equations and the manner in which the final time is treated. In this investigation, the shifted Jacobi pseudospectral method (SJPM) as a numerical technique for solving two-point boundary value problems (TPBVPs) in M-MOCPs for several boundary states is proposed. At first, a novel framework of approximate solutions which satisfied the split boundary conditions automatically for various boundary states is presented. Then, by applying the generalised Euler-Lagrange equations and expanding the required approximate solutions as elements of shifted Jacobi polynomials, finding a solution of TPBVPs in nonlinear M-MOCPs with uncertainty is reduced to the solution of a system of algebraic equations. Moreover, the Jacobi polynomials are particularly useful for boundary value problems in unbounded domain, which allow us to solve infinite- as well as finite and free final time problems by domain truncation method. Some numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. A comparative study between the proposed method and other existing methods shows that the SJPM is simple and accurate.

  18. The Magnus problem in Rodrigues-Hamilton parameters

    NASA Astrophysics Data System (ADS)

    Koshliakov, V. N.

    1984-04-01

    The formalism of Rodrigues-Hamilton parameters is applied to the Magnus problem related to the systematic drift of a gimbal-mounted astatic gyroscope due to the nutational vibration of the main axis of the rotor. It is shown that the use of the above formalism makes it possible to limit the analysis to a consideration of a linear system of differential equations written in perturbed values of Rodrigues-Hamilton parameters. A refined formula for the drift of the main axis of the gyroscope rotor is obtained, and an estimation is made of the effect of the truncation of higher-order terms.

  19. Multivariant function model generation

    NASA Technical Reports Server (NTRS)

    1974-01-01

    The development of computer programs applicable to space vehicle guidance was conducted. The subjects discussed are as follows: (1) determination of optimum reentry trajectories, (2) development of equations for performance of trajectory computation, (3) vehicle control for fuel optimization, (4) development of equations for performance trajectory computations, (5) applications and solution of Hamilton-Jacobi equation, and (6) stresses in dome shaped shells with discontinuities at the apex.

  20. The cosmological model with a wormhole and Hawking temperature near apparent horizon

    NASA Astrophysics Data System (ADS)

    Kim, Sung-Won

    2018-05-01

    In this paper, a cosmological model with an isotropic form of the Morris-Thorne type wormhole was derived in a similar way to the McVittie solution to the black hole in the expanding universe. By solving Einstein's field equation with plausible matter distribution, we found the exact solution of the wormhole embedded in Friedmann-Lemaître-Robertson-Walker universe. We also found the apparent cosmological horizons from the redefined metric and analyzed the geometric natures, including causal and dynamic structures. The Hawking temperature for thermal radiation was obtained by the WKB approximation using the Hamilton-Jacobi equation and Hamilton's equation, near the apparent cosmological horizon.

  1. Stochastic Differential Games with Asymmetric Information

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Cardaliaguet, Pierre, E-mail: Pierre.Cardaliaguet@univ-brest.fr; Rainer, Catherine

    2009-02-15

    We investigate a two-player zero-sum stochastic differential game in which the players have an asymmetric information on the random payoff. We prove that the game has a value and characterize this value in terms of dual viscosity solutions of some second order Hamilton-Jacobi equation.

  2. Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States

    NASA Astrophysics Data System (ADS)

    Bertini, L.; de Sole, A.; Gabrielli, D.; Jona-Lasinio, G.; Landim, C.

    2002-05-01

    We formulate a dynamical fluctuation theory for stationary non-equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within this theory we derive the following results: the modification of the Onsager-Machlup theory in the SNS; a general Hamilton-Jacobi equation for the macroscopic entropy; a non-equilibrium, nonlinear fluctuation dissipation relation valid for a wide class of systems; an H theorem for the entropy. We discuss in detail two models of stochastic boundary driven lattice gases: the zero range and the simple exclusion processes. In the first model the invariant measure is explicitly known and we verify the predictions of the general theory. For the one dimensional simple exclusion process, as recently shown by Derrida, Lebowitz, and Speer, it is possible to express the macroscopic entropy in terms of the solution of a nonlinear ordinary differential equation; by using the Hamilton-Jacobi equation, we obtain a logically independent derivation of this result.

  3. About an Optimal Visiting Problem

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bagagiolo, Fabio, E-mail: bagagiol@science.unitn.it; Benetton, Michela

    In this paper we are concerned with the optimal control problem consisting in minimizing the time for reaching (visiting) a fixed number of target sets, in particular more than one target. Such a problem is of course reminiscent of the famous 'Traveling Salesman Problem' and brings all its computational difficulties. Our aim is to apply the dynamic programming technique in order to characterize the value function of the problem as the unique viscosity solution of a suitable Hamilton-Jacobi equation. We introduce some 'external' variables, one per target, which keep in memory whether the corresponding target is already visited or not,more » and we transform the visiting problem in a suitable Mayer problem. This fact allows us to overcome the lacking of the Dynamic Programming Principle for the originary problem. The external variables evolve with a hysteresis law and the Hamilton-Jacobi equation turns out to be discontinuous.« less

  4. Jacobi bundles and the BFV-complex

    NASA Astrophysics Data System (ADS)

    Lê, Hông Vân; Tortorella, Alfonso G.; Vitagliano, Luca

    2017-11-01

    We extend the construction of the BFV-complex of a coisotropic submanifold from the Poisson setting to the Jacobi setting. In particular, our construction applies in the contact and l.c.s. settings. The BFV-complex of a coisotropic submanifold S controls the coisotropic deformation problem of S under both Hamiltonian and Jacobi equivalence.

  5. EPR & Klein Paradoxes in Complex Hamiltonian Dynamics and Krein Space Quantization

    NASA Astrophysics Data System (ADS)

    Payandeh, Farrin

    2015-07-01

    Negative energy states are applied in Krein space quantization approach to achieve a naturally renormalized theory. For example, this theory by taking the full set of Dirac solutions, could be able to remove the propagator Green function's divergences and automatically without any normal ordering, to vanish the expected value for vacuum state energy. However, since it is a purely mathematical theory, the results are under debate and some efforts are devoted to include more physics in the concept. Whereas Krein quantization is a pure mathematical approach, complex quantum Hamiltonian dynamics is based on strong foundations of Hamilton-Jacobi (H-J) equations and therefore on classical dynamics. Based on complex quantum Hamilton-Jacobi theory, complex spacetime is a natural consequence of including quantum effects in the relativistic mechanics, and is a bridge connecting the causality in special relativity and the non-locality in quantum mechanics, i.e. extending special relativity to the complex domain leads to relativistic quantum mechanics. So that, considering both relativistic and quantum effects, the Klein-Gordon equation could be derived as a special form of the Hamilton-Jacobi equation. Characterizing the complex time involved in an entangled energy state and writing the general form of energy considering quantum potential, two sets of positive and negative energies will be realized. The new states enable us to study the spacetime in a relativistic entangled “space-time” state leading to 12 extra wave functions than the four solutions of Dirac equation for a free particle. Arguing the entanglement of particle and antiparticle leads to a contradiction with experiments. So, in order to correct the results, along with a previous investigation [1], we realize particles and antiparticles as physical entities with positive energy instead of considering antiparticles with negative energy. As an application of modified descriptions for entangled (space

  6. On the Hamilton approach of the dissipative systems

    NASA Astrophysics Data System (ADS)

    Zimin, B. A.; Zorin, I. S.; Sventitskaya, V. E.

    2018-05-01

    In this paper we consider the problem of constructing equations describing the states of dissipative dynamical systems (media with absorption or damping). The approaches of Lagrange and Hamilton are discussed. A non-symplectic extension of the Poisson brackets is formulated. The application of the Hamiltonian formalism here makes it possible to obtain explicit equations for the dynamics of a nonlinear elastic system with damping and a one-dimensional continuous medium with internal friction.

  7. Reinforcement learning solution for HJB equation arising in constrained optimal control problem.

    PubMed

    Luo, Biao; Wu, Huai-Ning; Huang, Tingwen; Liu, Derong

    2015-11-01

    The constrained optimal control problem depends on the solution of the complicated Hamilton-Jacobi-Bellman equation (HJBE). In this paper, a data-based off-policy reinforcement learning (RL) method is proposed, which learns the solution of the HJBE and the optimal control policy from real system data. One important feature of the off-policy RL is that its policy evaluation can be realized with data generated by other behavior policies, not necessarily the target policy, which solves the insufficient exploration problem. The convergence of the off-policy RL is proved by demonstrating its equivalence to the successive approximation approach. Its implementation procedure is based on the actor-critic neural networks structure, where the function approximation is conducted with linearly independent basis functions. Subsequently, the convergence of the implementation procedure with function approximation is also proved. Finally, its effectiveness is verified through computer simulations. Copyright © 2015 Elsevier Ltd. All rights reserved.

  8. Teardrop and heart orbits of a swinging Atwood's machine

    NASA Astrophysics Data System (ADS)

    Tufillaro, Nicholas B.

    1994-03-01

    An exact solution is presented for a swinging Atwood's machine. This teardrop-heart orbit is constructed using Hamilton-Jacobi theory. The example nicely illustrates the utility of the Hamilton-Jacobi method for finding solutions to nonlinear mechanical systems when more elementary techniques fail.

  9. Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management

    NASA Astrophysics Data System (ADS)

    Koleva, M. N.

    2011-11-01

    In this work we consider a nonlinear parabolic equation, obtained from Riccati like transformation of the Hamilton-Jacobi-Bellman equation, arising in pension saving management. We discuss two numerical iterative methods for solving the model problem—fully implicit Picard method and mixed Picard-Newton method, which preserves the parabolic characteristics of the differential problem. Numerical experiments for comparison the accuracy and effectiveness of the algorithms are discussed. Finally, observations are given.

  10. Trajectory-based modeling of fluid transport in a medium with smoothly varying heterogeneity

    DOE PAGES

    Vasco, D. W.; Pride, Steven R.; Commer, Michael

    2016-03-04

    Using an asymptotic methodology, valid in the presence of smoothly varying heterogeneity and prescribed boundaries, we derive a trajectory-based solution for tracer transport. The analysis produces a Hamilton-Jacobi partial differential equation for the phase of the propagating tracer front. The trajectories follow from the characteristic equations that are equivalent to the Hamilton-Jacobi equation. The paths are determined by the fluid velocity field, the total porosity, and the dispersion tensor. Due to their dependence upon the local hydrodynamic dispersion, they differ from conventional streamlines. This difference is borne out in numerical calculations for both uniform and dipole flow fields. In anmore » application to the computational X-ray imaging of a saline tracer test, we illustrate that the trajectories may serve as the basis for a form of tracer tomography. In particular, we use the onset time of a change in attenuation for each volume element of the X-ray image as a measure of the arrival time of the saline tracer. In conclusion, the arrival times are used to image the spatial variation of the effective hydraulic conductivity within the laboratory sample.« less

  11. Tensor calculus in polar coordinates using Jacobi polynomials

    NASA Astrophysics Data System (ADS)

    Vasil, Geoffrey M.; Burns, Keaton J.; Lecoanet, Daniel; Olver, Sheehan; Brown, Benjamin P.; Oishi, Jeffrey S.

    2016-11-01

    Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built out of Jacobi polynomials, and associated operators for solving scalar, vector, and tensor partial differential equations in polar coordinates on a unit disk. By construction, the bases satisfy regularity conditions at r = 0 for any tensorial field. The coordinate singularity in a disk is a prototypical case for many coordinate singularities. The work presented here extends to other geometries. The operators represent covariant derivatives, multiplication by azimuthally symmetric functions, and the tensorial relationship between fields. These arise naturally from relations between classical orthogonal polynomials, and form a Heisenberg algebra. Other past work uses more specific polynomial bases for solving equations in polar coordinates. The main innovation in this paper is to use a larger set of possible bases to achieve maximum bandedness of linear operations. We provide a series of applications of the methods, illustrating their ease-of-use and accuracy.

  12. Quantum approach of mesoscopic magnet dynamics with spin transfer torque

    NASA Astrophysics Data System (ADS)

    Wang, Yong; Sham, L. J.

    2013-05-01

    We present a theory of magnetization dynamics driven by spin-polarized current in terms of the quantum master equation. In the spin coherent state representation, the master equation becomes a Fokker-Planck equation, which naturally includes the spin transfer and quantum fluctuation. The current electron scattering state is correlated to the magnet quantum states, giving rise to quantum correction to the electron transport properties in the usual semiclassical theory. In the large-spin limit, the magnetization dynamics is shown to obey the Hamilton-Jacobi equation or the Hamiltonian canonical equations.

  13. Higher order derivatives of R-Jacobi polynomials

    NASA Astrophysics Data System (ADS)

    Das, Sourav; Swaminathan, A.

    2016-06-01

    In this work, the R-Jacobi polynomials defined on the nonnegative real axis related to F-distribution are considered. Using their Sturm-Liouville system higher order derivatives are constructed. Orthogonality property of these higher ordered R-Jacobi polynomials are obtained besides their normal form, self-adjoint form and hypergeometric representation. Interesting results on the Interpolation formula and Gaussian quadrature formulae are obtained with numerical examples.

  14. Neural network based online simultaneous policy update algorithm for solving the HJI equation in nonlinear H∞ control.

    PubMed

    Wu, Huai-Ning; Luo, Biao

    2012-12-01

    It is well known that the nonlinear H∞ state feedback control problem relies on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that has proven to be impossible to solve analytically. In this paper, a neural network (NN)-based online simultaneous policy update algorithm (SPUA) is developed to solve the HJI equation, in which knowledge of internal system dynamics is not required. First, we propose an online SPUA which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment. The proposed online SPUA updates control and disturbance policies simultaneously; thus, only one iterative loop is needed. Second, the convergence of the online SPUA is established by proving that it is mathematically equivalent to Newton's method for finding a fixed point in a Banach space. Third, we develop an actor-critic structure for the implementation of the online SPUA, in which only one critic NN is needed for approximating the cost function, and a least-square method is given for estimating the NN weight parameters. Finally, simulation studies are provided to demonstrate the effectiveness of the proposed algorithm.

  15. Inverse resonance scattering for Jacobi operators

    NASA Astrophysics Data System (ADS)

    Korotyaev, E. L.

    2011-12-01

    The Jacobi operator ( Jf) n = a n-1 f n-1 + a n f n+1 + b n f n on ℤ with real finitely supported sequences ( a n - 1) n∈ℤ and ( b n ) n∈ℤ is considered. The inverse problem for two mappings (including their characterization): ( a n , b n , n ∈ ℤ) → {the zeros of the reflection coefficient} and ( a n , b n , n ∈ ℤ) → {the eigenvalues and the resonances} is solved. All Jacobi operators with the same eigenvalues and resonances are also described.

  16. Continuous-time safety-first portfolio selection with jump-diffusion processes

    NASA Astrophysics Data System (ADS)

    Yan, Wei

    2012-04-01

    This article is concerned with continuous-time portfolio selection based on a safety-first criterion under discontinuous price processes (jump-diffusion processes). The solution of the corresponding Hamilton-Jacobi-Bellman equation of the problem is demonstrated. The analytical solutions are presented when there does not exist any riskless asset. Moreover, the problem is also discussed while there exists one riskless asset.

  17. Quantum mechanics from an equivalence principle

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Faraggi, A.E.; Matone, M.

    1997-05-15

    The authors show that requiring diffeomorphic equivalence for one-dimensional stationary states implies that the reduced action S{sub 0} satisfies the quantum Hamilton-Jacobi equation with the Planck constant playing the role of a covariantizing parameter. The construction shows the existence of a fundamental initial condition which is strictly related to the Moebius symmetry of the Legendre transform and to its involutive character. The universal nature of the initial condition implies the Schroedinger equation in any dimension.

  18. Convergence to Diagonal Form of Block Jacobi-type Processes

    NASA Astrophysics Data System (ADS)

    Hari, Vjeran

    2008-09-01

    The main result of recent research on convergence to diagonal form of block Jacobi-type processes is presented. For this purpose, all notions needed to describe the result are introduced. In particular, elementary block transformation matrices, simple and non-simple algorithms, block pivot strategies together with the appropriate equivalence relations are defined. The general block Jacobi-type process considered here can be specialized to take the form of almost any known Jacobi-type method for solving the ordinary or the generalized matrix eigenvalue and singular value problems. The assumptions used in the result are satisfied by many concrete methods.

  19. Complex-valued derivative propagation method with approximate Bohmian trajectories: Application to electronic nonadiabatic dynamics

    NASA Astrophysics Data System (ADS)

    Wang, Yu; Chou, Chia-Chun

    2018-05-01

    The coupled complex quantum Hamilton-Jacobi equations for electronic nonadiabatic transitions are approximately solved by propagating individual quantum trajectories in real space. Equations of motion are derived through use of the derivative propagation method for the complex actions and their spatial derivatives for wave packets moving on each of the coupled electronic potential surfaces. These equations for two surfaces are converted into the moving frame with the same grid point velocities. Excellent wave functions can be obtained by making use of the superposition principle even when nodes develop in wave packet scattering.

  20. Eruptive Massive Vector Particles of 5-Dimensional Kerr-Gödel Spacetime

    NASA Astrophysics Data System (ADS)

    Övgün, A.; Sakalli, I.

    2018-02-01

    In this paper, we investigate Hawking radiation of massive spin-1 particles from 5-dimensional Kerr-Gödel spacetime. By applying the WKB approximation and the Hamilton-Jacobi ansatz to the relativistic Proca equation, we obtain the quantum tunneling rate of the massive vector particles. Using the obtained tunneling rate, we show how one impeccably computes the Hawking temperature of the 5-dimensional Kerr-Gödel spacetime.

  1. Nonlinear Filtering and Approximation Techniques

    DTIC Science & Technology

    1991-09-01

    filtering. UNIT8 Q RECERCE**No 1223 Programme 5 A utomatique, Productique, Traitement dui Signal et des Donnc~es CONSISTENT PARAMETER ESTIMATION FOR...ue’e[71 E C 2.’(Rm x [0,7]; R) is the unique solution of the Hamilton-Jacobi-Bellman equation 9u,’[7](x, t) - EAu "’[ 7](x,t) + He,’[ 7](x,t,Du,[ 7](x,t

  2. On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials

    NASA Astrophysics Data System (ADS)

    Doha, E. H.

    2004-01-01

    Formulae expressing explicitly the Jacobi coefficients of a general-order derivative (integral) of an infinitely differentiable function in terms of its original expansion coefficients, and formulae for the derivatives (integrals) of Jacobi polynomials in terms of Jacobi polynomials themselves are stated. A formula for the Jacobi coefficients of the moments of one single Jacobi polynomial of certain degree is proved. Another formula for the Jacobi coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its original expanded coefficients is also given. A simple approach in order to construct and solve recursively for the connection coefficients between Jacobi-Jacobi polynomials is described. Explicit formulae for these coefficients between ultraspherical and Jacobi polynomials are deduced, of which the Chebyshev polynomials of the first and second kinds and Legendre polynomials are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Jacobi and Hermite-Jacobi are developed.

  3. Fifty years with the Hamilton scales for anxiety and depression. A tribute to Max Hamilton.

    PubMed

    Bech, P

    2009-01-01

    From the moment Max Hamilton started his psychiatric education, he considered psychometrics to be a scientific discipline on a par with biochemistry or pharmacology in clinical research. His clinimetric skills were in operation in the 1950s when randomised clinical trials were established as the method for the evaluation of the clinical effects of psychotropic drugs. Inspired by Eysenck, Hamilton took the long route around factor analysis in order to qualify his scales for anxiety (HAM-A) and depression (HAM-D) as scientific tools. From the moment when, 50 years ago, Hamilton published his first placebo-controlled trial with an experimental anti-anxiety drug, he realized the dialectic problem in using the total score on HAM-A as a sufficient statistic for the measurement of outcome. This dialectic problem has been investigated for more than 50 years with different types of factor analyses without success. Using modern psychometric methods, the solution to this problem is a simple matter of reallocating the Hamilton scale items according to the scientific hypothesis under examination. Hamilton's original intention, to measure the global burden of the symptoms experienced by the patients with affective disorders, is in agreement with the DSM-IV and ICD-10 classification systems. Scale reliability and obtainment of valid information from patients and their relatives were the most important clinimetric innovations to be developed by Hamilton. Max Hamilton therefore belongs to the very exclusive family of eminent physicians celebrated by this journal with a tribute. 2009 S. Karger AG, Basel.

  4. Inverse Problems and Imaging (Pitman Research Notes in Mathematics Series Number 245)

    DTIC Science & Technology

    1991-01-01

    Multiparamcter spectral theory in Hilbert space functional differential cquations B D Sleeman F Kappel and W Schappacher 24 Mathematical modelling...techniques 49 Sequence spaces R Aris W 11 Ruckle 25 Singular points of smooth mappings 50 Recent contributions to nonlinear C G Gibson partial...of convergence in the central limit T Husain theorem 86 Hamilton-Jacobi equations in Hilbert spaces Peter Hall V Barbu and G Da Prato 63 Solution of

  5. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Krtous, Pavel; Frolov, Valeri P.; Kubiznak, David

    We prove that the most general solution of the Einstein equations with the cosmological constant which admits a principal conformal Killing-Yano tensor is the Kerr-NUT-(A)dS metric. Even when the Einstein equations are not imposed, any spacetime admitting such hidden symmetry can be written in a canonical form which guarantees the following properties: it is of the Petrov type D, it allows the separation of variables for the Hamilton-Jacobi, Klein-Gordon, and Dirac equations, the geodesic motion in such a spacetime is completely integrable. These results naturally generalize the results obtained earlier in four dimensions.

  6. Computational time analysis of the numerical solution of 3D electrostatic Poisson's equation

    NASA Astrophysics Data System (ADS)

    Kamboh, Shakeel Ahmed; Labadin, Jane; Rigit, Andrew Ragai Henri; Ling, Tech Chaw; Amur, Khuda Bux; Chaudhary, Muhammad Tayyab

    2015-05-01

    3D Poisson's equation is solved numerically to simulate the electric potential in a prototype design of electrohydrodynamic (EHD) ion-drag micropump. Finite difference method (FDM) is employed to discretize the governing equation. The system of linear equations resulting from FDM is solved iteratively by using the sequential Jacobi (SJ) and sequential Gauss-Seidel (SGS) methods, simulation results are also compared to examine the difference between the results. The main objective was to analyze the computational time required by both the methods with respect to different grid sizes and parallelize the Jacobi method to reduce the computational time. In common, the SGS method is faster than the SJ method but the data parallelism of Jacobi method may produce good speedup over SGS method. In this study, the feasibility of using parallel Jacobi (PJ) method is attempted in relation to SGS method. MATLAB Parallel/Distributed computing environment is used and a parallel code for SJ method is implemented. It was found that for small grid size the SGS method remains dominant over SJ method and PJ method while for large grid size both the sequential methods may take nearly too much processing time to converge. Yet, the PJ method reduces computational time to some extent for large grid sizes.

  7. Covariance Method of the Tunneling Radiation from High Dimensional Rotating Black Holes

    NASA Astrophysics Data System (ADS)

    Li, Hui-Ling; Han, Yi-Wen; Chen, Shuai-Ru; Ding, Cong

    2018-04-01

    In this paper, Angheben-Nadalini-Vanzo-Zerbini (ANVZ) covariance method is used to study the tunneling radiation from the Kerr-Gödel black hole and Myers-Perry black hole with two independent angular momentum. By solving the Hamilton-Jacobi equation and separating the variables, the radial motion equation of a tunneling particle is obtained. Using near horizon approximation and the distance of the proper pure space, we calculate the tunneling rate and the temperature of Hawking radiation. Thus, the method of ANVZ covariance is extended to the research of high dimensional black hole tunneling radiation.

  8. Hawking Radiation of Massive Bosons via Tunneling from Black Strings

    NASA Astrophysics Data System (ADS)

    Feng, Zhong-Wen

    2017-12-01

    In the present paper, the Hawking radiation of massive bosons from 4-dimensional and 5-dimensional black strings are studied in quantum tunneling formalism. First, we derive the Hamilton-Jacobi equation set via the Proca equation and WKB approximation. Then, the tunneling rates and Hawking temperatures of the black strings are obtained. Our calculations show that the tunneling rates and Hawking temperatures are related to the properties of black strings' spacetime. When compare our results with those of scalars and fermions cases, it finds that they are the same.

  9. Hawking Radiation of Massive Bosons via Tunneling from Black Strings

    NASA Astrophysics Data System (ADS)

    Feng, Zhong-Wen

    2018-03-01

    In the present paper, the Hawking radiation of massive bosons from 4-dimensional and 5-dimensional black strings are studied in quantum tunneling formalism. First, we derive the Hamilton-Jacobi equation set via the Proca equation and WKB approximation. Then, the tunneling rates and Hawking temperatures of the black strings are obtained. Our calculations show that the tunneling rates and Hawking temperatures are related to the properties of black strings' spacetime. When compare our results with those of scalars and fermions cases, it finds that they are the same.

  10. Modelling on optimal portfolio with exchange rate based on discontinuous stochastic process

    NASA Astrophysics Data System (ADS)

    Yan, Wei; Chang, Yuwen

    2016-12-01

    Considering the stochastic exchange rate, this paper is concerned with the dynamic portfolio selection in financial market. The optimal investment problem is formulated as a continuous-time mathematical model under mean-variance criterion. These processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and its efferent frontier is obtained. Moreover, the optimal strategy is also derived under safety-first criterion.

  11. The Correlated Jacobi and the Correlated Cauchy-Lorentz Ensembles

    NASA Astrophysics Data System (ADS)

    Wirtz, Tim; Waltner, Daniel; Kieburg, Mario; Kumar, Santosh

    2016-01-01

    We calculate the k-point generating function of the correlated Jacobi ensemble using supersymmetric methods. We use the result for complex matrices for k=1 to derive a closed-form expression for the eigenvalue density. For real matrices we obtain the density in terms of a twofold integral that we evaluate numerically. For both expressions we find agreement when comparing with Monte Carlo simulations. Relations between these quantities for the Jacobi and the Cauchy-Lorentz ensemble are derived.

  12. F-Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation

    PubMed Central

    Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah

    2014-01-01

    F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics. PMID:24672327

  13. F-expansion method and new exact solutions of the Schrödinger-KdV equation.

    PubMed

    Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah

    2014-01-01

    F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics.

  14. Hamilton's missing link.

    PubMed

    van Veelen, Matthijs

    2007-06-07

    Hamilton's famous rule was presented in 1964 in a paper called "The genetical theory of social behaviour (I and II)", Journal of Theoretical Biology 7, 1-16, 17-32. The paper contains a mathematical genetical model from which the rule supposedly follows, but it does not provide a link between the paper's central result, which states that selection dynamics take the population to a state where mean inclusive fitness is maximized, and the rule, which states that selection will lead to maximization of individual inclusive fitness. This note provides a condition under which Hamilton's rule does follow from his central result.

  15. New algorithms for solving third- and fifth-order two point boundary value problems based on nonsymmetric generalized Jacobi Petrov–Galerkin method

    PubMed Central

    Doha, E.H.; Abd-Elhameed, W.M.; Youssri, Y.H.

    2014-01-01

    Two families of certain nonsymmetric generalized Jacobi polynomials with negative integer indexes are employed for solving third- and fifth-order two point boundary value problems governed by homogeneous and nonhomogeneous boundary conditions using a dual Petrov–Galerkin method. The idea behind our method is to use trial functions satisfying the underlying boundary conditions of the differential equations and the test functions satisfying the dual boundary conditions. The resulting linear systems from the application of our method are specially structured and they can be efficiently inverted. The use of generalized Jacobi polynomials simplify the theoretical and numerical analysis of the method and also leads to accurate and efficient numerical algorithms. The presented numerical results indicate that the proposed numerical algorithms are reliable and very efficient. PMID:26425358

  16. Generalized Lagrangian Jacobi Gauss collocation method for solving unsteady isothermal gas through a micro-nano porous medium

    NASA Astrophysics Data System (ADS)

    Parand, Kourosh; Latifi, Sobhan; Delkhosh, Mehdi; Moayeri, Mohammad M.

    2018-01-01

    In the present paper, a new method based on the Generalized Lagrangian Jacobi Gauss (GLJG) collocation method is proposed. The nonlinear Kidder equation, which explains unsteady isothermal gas through a micro-nano porous medium, is a second-order two-point boundary value ordinary differential equation on the unbounded interval [0, ∞). Firstly, using the quasilinearization method, the equation is converted to a sequence of linear ordinary differential equations. Then, by using the GLJG collocation method, the problem is reduced to solving a system of algebraic equations. It must be mentioned that this equation is solved without domain truncation and variable changing. A comparison with some numerical solutions made and the obtained results indicate that the presented solution is highly accurate. The important value of the initial slope, y'(0), is obtained as -1.191790649719421734122828603800159364 for η = 0.5. Comparing to the best result obtained so far, it is accurate up to 36 decimal places.

  17. MOC Efficiency Improvements Using a Jacobi Inscatter Approximation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Stimpson, Shane; Collins, Benjamin; Kochunas, Brendan

    2016-08-31

    In recent weeks, attention has been given to resolving the convergence issues encountered with TCP 0 by trying a Jacobi (J) inscatter approach when group sweeping, where the inscatter source is constructed using the previous iteration flux. This is in contrast to a Gauss-Seidel (GS) approach, which has been the default to-date, where the scattering source uses the most up-to-date flux values. The former is consistent with CASMO, which has no issues with TCP 0 convergence. Testing this out on a variety of problems has demonstrated that the Jacobi approach does indeed provide substantially more stability, though can take moremore » outer iterations to converge. While this is not surprising, there are improvements that can be made to the MOC sweeper to capitalize on the Jacobi approximation and provide substantial speedup. For example, the loop over groups, which has traditionally been the outermost loop in MPACT, can be moved to the interior, avoiding duplicate modular ray trace and coarse ray trace setup (mapping coarse mesh surface indexes), which needs to be performed repeatedly when group is outermost.« less

  18. Stable Numerical Approach for Fractional Delay Differential Equations

    NASA Astrophysics Data System (ADS)

    Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.

    2017-12-01

    In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.

  19. Ratchet motion induced by a correlated stochastic force

    NASA Astrophysics Data System (ADS)

    Cortés, Emilio

    2000-01-01

    We apply a rigorous formalism we have just worked out (Cortés and Espinosa, Physica A 267 (1999) 414) about escape rates and the Hamilton-Jacobi equation, to study the ratchet motion of a Brownian particle and calculate the probability current in a periodic non-symmetric potential subject to correlated fluctuations. We are able to obtain the current behaviour as a function of the correlation time parameter and compare with other results in the literature.

  20. Approximate optimal guidance for the advanced launch system

    NASA Technical Reports Server (NTRS)

    Feeley, T. S.; Speyer, J. L.

    1993-01-01

    A real-time guidance scheme for the problem of maximizing the payload into orbit subject to the equations of motion for a rocket over a spherical, non-rotating earth is presented. An approximate optimal launch guidance law is developed based upon an asymptotic expansion of the Hamilton - Jacobi - Bellman or dynamic programming equation. The expansion is performed in terms of a small parameter, which is used to separate the dynamics of the problem into primary and perturbation dynamics. For the zeroth-order problem the small parameter is set to zero and a closed-form solution to the zeroth-order expansion term of Hamilton - Jacobi - Bellman equation is obtained. Higher-order terms of the expansion include the effects of the neglected perturbation dynamics. These higher-order terms are determined from the solution of first-order linear partial differential equations requiring only the evaluation of quadratures. This technique is preferred as a real-time, on-line guidance scheme to alternative numerical iterative optimization schemes because of the unreliable convergence properties of these iterative guidance schemes and because the quadratures needed for the approximate optimal guidance law can be performed rapidly and by parallel processing. Even if the approximate solution is not nearly optimal, when using this technique the zeroth-order solution always provides a path which satisfies the terminal constraints. Results for two-degree-of-freedom simulations are presented for the simplified problem of flight in the equatorial plane and compared to the guidance scheme generated by the shooting method which is an iterative second-order technique.

  1. Schrödinger equation revisited

    PubMed Central

    Schleich, Wolfgang P.; Greenberger, Daniel M.; Kobe, Donald H.; Scully, Marlan O.

    2013-01-01

    The time-dependent Schrödinger equation is a cornerstone of quantum physics and governs all phenomena of the microscopic world. However, despite its importance, its origin is still not widely appreciated and properly understood. We obtain the Schrödinger equation from a mathematical identity by a slight generalization of the formulation of classical statistical mechanics based on the Hamilton–Jacobi equation. This approach brings out most clearly the fact that the linearity of quantum mechanics is intimately connected to the strong coupling between the amplitude and phase of a quantum wave. PMID:23509260

  2. Quaternion Regularization of the Equations of the Perturbed Spatial Restricted Three-Body Problem: I

    NASA Astrophysics Data System (ADS)

    Chelnokov, Yu. N.

    2017-11-01

    We develop a quaternion method for regularizing the differential equations of the perturbed spatial restricted three-body problem by using the Kustaanheimo-Stiefel variables, which is methodologically closely related to the quaternion method for regularizing the differential equations of perturbed spatial two-body problem, which was proposed by the author of the present paper. A survey of papers related to the regularization of the differential equations of the two- and threebody problems is given. The original Newtonian equations of perturbed spatial restricted three-body problem are considered, and the problem of their regularization is posed; the energy relations and the differential equations describing the variations in the energies of the system in the perturbed spatial restricted three-body problem are given, as well as the first integrals of the differential equations of the unperturbed spatial restricted circular three-body problem (Jacobi integrals); the equations of perturbed spatial restricted three-body problem written in terms of rotating coordinate systems whose angular motion is described by the rotation quaternions (Euler (Rodrigues-Hamilton) parameters) are considered; and the differential equations for angular momenta in the restricted three-body problem are given. Local regular quaternion differential equations of perturbed spatial restricted three-body problem in the Kustaanheimo-Stiefel variables, i.e., equations regular in a neighborhood of the first and second body of finite mass, are obtained. The equations are systems of nonlinear nonstationary eleventhorder differential equations. These equations employ, as additional dependent variables, the energy characteristics of motion of the body under study (a body of a negligibly small mass) and the time whose derivative with respect to a new independent variable is equal to the distance from the body of negligibly small mass to the first or second body of finite mass. The equations obtained in

  3. Robust Maneuvering Envelope Estimation Based on Reachability Analysis in an Optimal Control Formulation

    NASA Technical Reports Server (NTRS)

    Lombaerts, Thomas; Schuet, Stefan R.; Wheeler, Kevin; Acosta, Diana; Kaneshige, John

    2013-01-01

    This paper discusses an algorithm for estimating the safe maneuvering envelope of damaged aircraft. The algorithm performs a robust reachability analysis through an optimal control formulation while making use of time scale separation and taking into account uncertainties in the aerodynamic derivatives. Starting with an optimal control formulation, the optimization problem can be rewritten as a Hamilton- Jacobi-Bellman equation. This equation can be solved by level set methods. This approach has been applied on an aircraft example involving structural airframe damage. Monte Carlo validation tests have confirmed that this approach is successful in estimating the safe maneuvering envelope for damaged aircraft.

  4. On the conservation of the Jacobi integral in the post-Newtonian circular restricted three-body problem

    NASA Astrophysics Data System (ADS)

    Dubeibe, F. L.; Lora-Clavijo, F. D.; González, Guillermo A.

    2017-05-01

    In the present paper, using the first-order approximation of the n-body Lagrangian (derived on the basis of the post-Newtonian gravitational theory of Einstein, Infeld, and Hoffman), we explicitly write down the equations of motion for the planar circular restricted three-body problem in the Solar system. Additionally, with some simplified assumptions, we obtain two formulas for estimating the values of the mass-distance and velocity-speed of light ratios appropriate for a given post-Newtonian approximation. We show that the formulas derived in the present study, lead to good numerical accuracy in the conservation of the Jacobi constant and almost allow for an equivalence between the Lagrangian and Hamiltonian approaches at the same post-Newtonian order. Accordingly, the dynamics of the system is analyzed in terms of the Poincaré sections method and Lyapunov exponents, finding that for specific values of the Jacobi constant the dynamics can be either chaotic or regular. Our results suggest that the chaoticity of the post-Newtonian system is slightly increased in comparison with its Newtonian counterpart.

  5. Dynamic Programming Algorithms for Planning and Robotics in Continuous Domains and the Hamilton-Jacobi Equation

    DTIC Science & Technology

    2008-09-22

    provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently...CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT Same as Report (SAR) 18. NUMBER OF PAGES 72 19a. NAME OF RESPONSIBLE PERSON a . REPORT unclassified b...2008 Ian Mitchell, University of British Columbia 3 Basic Path Planning • Find the optimal path p(s) to a target (or from a source) • Inputs – Cost c

  6. Structure and decays of nuclear three-body systems: The Gamow coupled-channel method in Jacobi coordinates

    NASA Astrophysics Data System (ADS)

    Wang, S. M.; Michel, N.; Nazarewicz, W.; Xu, F. R.

    2017-10-01

    Background: Weakly bound and unbound nuclear states appearing around particle thresholds are prototypical open quantum systems. Theories of such states must take into account configuration mixing effects in the presence of strong coupling to the particle continuum space. Purpose: To describe structure and decays of three-body systems, we developed a Gamow coupled-channel (GCC) approach in Jacobi coordinates by employing the complex-momentum formalism. We benchmarked the complex-energy Gamow shell model (GSM) against the new framework. Methods: The GCC formalism is expressed in Jacobi coordinates, so that the center-of-mass motion is automatically eliminated. To solve the coupled-channel equations, we use hyperspherical harmonics to describe the angular wave functions while the radial wave functions are expanded in the Berggren ensemble, which includes bound, scattering, and Gamow states. Results: We show that the GCC method is both accurate and robust. Its results for energies, decay widths, and nucleon-nucleon angular correlations are in good agreement with the GSM results. Conclusions: We have demonstrated that a three-body GSM formalism explicitly constructed in the cluster-orbital shell model coordinates provides results similar to those with a GCC framework expressed in Jacobi coordinates, provided that a large configuration space is employed. Our calculations for A =6 systems and 26O show that nucleon-nucleon angular correlations are sensitive to the valence-neutron interaction. The new GCC technique has many attractive features when applied to bound and unbound states of three-body systems: it is precise, is efficient, and can be extended by introducing a microscopic model of the core.

  7. orbit-estimation: Fast orbital parameters estimator

    NASA Astrophysics Data System (ADS)

    Mackereth, J. Ted; Bovy, Jo

    2018-04-01

    orbit-estimation tests and evaluates the Stäckel approximation method for estimating orbit parameters in galactic potentials. It relies on the approximation of the Galactic potential as a Stäckel potential, in a prolate confocal coordinate system, under which the vertical and horizontal motions decouple. By solving the Hamilton Jacobi equations at the turning points of the horizontal and vertical motions, it is possible to determine the spatial boundary of the orbit, and hence calculate the desired orbit parameters.

  8. Computing interface motion in compressible gas dynamics

    NASA Technical Reports Server (NTRS)

    Mulder, W.; Osher, S.; Sethan, James A.

    1992-01-01

    An analysis is conducted of the coupling of Osher and Sethian's (1988) 'Hamilton-Jacobi' level set formulation of the equations of motion for propagating interfaces to a system of conservation laws for compressible gas dynamics, giving attention to both the conservative and nonconservative differencing of the level set function. The capabilities of the method are illustrated in view of the results of numerical convergence studies of the compressible Rayleigh-Taylor and Kelvin-Helmholtz instabilities for air-air and air-helium boundaries.

  9. Dynamical behavior and Jacobi stability analysis of wound strings

    NASA Astrophysics Data System (ADS)

    Lake, Matthew J.; Harko, Tiberiu

    2016-06-01

    We numerically solve the equations of motion (EOM) for two models of circular cosmic string loops with windings in a simply connected internal space. Since the windings cannot be topologically stabilized, stability must be achieved (if at all) dynamically. As toy models for realistic compactifications, we consider windings on a small section of mathbb {R}^2, which is valid as an approximation to any simply connected internal manifold if the winding radius is sufficiently small, and windings on an S^2 of constant radius mathcal {R}. We then use Kosambi-Cartan-Chern (KCC) theory to analyze the Jacobi stability of the string equations and determine bounds on the physical parameters that ensure dynamical stability of the windings. We find that, for the same initial conditions, the curvature and topology of the internal space have nontrivial effects on the microscopic behavior of the string in the higher dimensions, but that the macroscopic behavior is remarkably insensitive to the details of the motion in the compact space. This suggests that higher-dimensional signatures may be extremely difficult to detect in the effective (3+1)-dimensional dynamics of strings compactified on an internal space, even if configurations with nontrivial windings persist over long time periods.

  10. Hunting grounds for Jacobi transitions and hyperdeformations

    DOE PAGES

    Herskind, B.; Benzoni, G.; Wilson, J. N.; ...

    2003-04-01

    In recent attempts to search for exotic shapes, hyperdeformation (HD), and Jacobi transitions in Hf, Ba, Xe, Sn and Nd nuclei, ridge structures presumably originating from nuclei of very elongated shapes have been observed in 126Ba, with Gammasphere (GS) and in 126Xe, with Euroball-IV (EB-IV). After the promising results from GS, a second experiment in 126Ba followed at EB-IV, taking advantage of the use of the BGO Inner Ball (IB) for selecting the highest spins. The decay of the Giant Dipole Resonances (GDR) is also studied, and the analysis in progress. The Quasi-continuum transitions in the Jacobi region, show amore » significant decrease in energy for both 126Ba and 126Xe, compared to the Thomas-Fermi- and the LSD model predictions. Similar effects were recently found for other nuclei by Ward et al.« less

  11. Modulation stability analysis of exact multidimensional solutions to the generalized nonlinear Schrödinger equation and the Gross-Pitaevskii equation using a variational approach.

    PubMed

    Petrović, Nikola Z; Aleksić, Najdan B; Belić, Milivoj

    2015-04-20

    We analyze the modulation stability of spatiotemporal solitary and traveling wave solutions to the multidimensional nonlinear Schrödinger equation and the Gross-Pitaevskii equation with variable coefficients that were obtained using Jacobi elliptic functions. For all the solutions we obtain either unconditional stability, or a conditional stability that can be furnished through the use of dispersion management.

  12. Coherent distributions for the rigid rotator

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Grigorescu, Marius

    2016-06-15

    Coherent solutions of the classical Liouville equation for the rigid rotator are presented as positive phase-space distributions localized on the Lagrangian submanifolds of Hamilton-Jacobi theory. These solutions become Wigner-type quasiprobability distributions by a formal discretization of the left-invariant vector fields from their Fourier transform in angular momentum. The results are consistent with the usual quantization of the anisotropic rotator, but the expected value of the Hamiltonian contains a finite “zero point” energy term. It is shown that during the time when a quasiprobability distribution evolves according to the Liouville equation, the related quantum wave function should satisfy the time-dependent Schrödingermore » equation.« less

  13. Efficient Jacobi-Gauss collocation method for solving initial value problems of Bratu type

    NASA Astrophysics Data System (ADS)

    Doha, E. H.; Bhrawy, A. H.; Baleanu, D.; Hafez, R. M.

    2013-09-01

    In this paper, we propose the shifted Jacobi-Gauss collocation spectral method for solving initial value problems of Bratu type, which is widely applicable in fuel ignition of the combustion theory and heat transfer. The spatial approximation is based on shifted Jacobi polynomials J {/n (α,β)}( x) with α, β ∈ (-1, ∞), x ∈ [0, 1] and n the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes. Illustrative examples have been discussed to demonstrate the validity and applicability of the proposed technique. Comparing the numerical results of the proposed method with some well-known results show that the method is efficient and gives excellent numerical results.

  14. Calculating qP-wave traveltimes in 2-D TTI media by high-order fast sweeping methods with a numerical quartic equation solver

    NASA Astrophysics Data System (ADS)

    Han, Song; Zhang, Wei; Zhang, Jie

    2017-09-01

    A fast sweeping method (FSM) determines the first arrival traveltimes of seismic waves by sweeping the velocity model in different directions meanwhile applying a local solver. It is an efficient way to numerically solve Hamilton-Jacobi equations for traveltime calculations. In this study, we develop an improved FSM to calculate the first arrival traveltimes of quasi-P (qP) waves in 2-D tilted transversely isotropic (TTI) media. A local solver utilizes the coupled slowness surface of qP and quasi-SV (qSV) waves to form a quartic equation, and solve it numerically to obtain possible traveltimes of qP-wave. The proposed quartic solver utilizes Fermat's principle to limit the range of the possible solution, then uses the bisection procedure to efficiently determine the real roots. With causality enforced during sweepings, our FSM converges fast in a few iterations, and the exact number depending on the complexity of the velocity model. To improve the accuracy, we employ high-order finite difference schemes and derive the second-order formulae. There is no weak anisotropy assumption, and no approximation is made to the complex slowness surface of qP-wave. In comparison to the traveltimes calculated by a horizontal slowness shooting method, the validity and accuracy of our FSM is demonstrated.

  15. Multimodal electromechanical model of piezoelectric transformers by Hamilton's principle.

    PubMed

    Nadal, Clement; Pigache, Francois

    2009-11-01

    This work deals with a general energetic approach to establish an accurate electromechanical model of a piezoelectric transformer (PT). Hamilton's principle is used to obtain the equations of motion for free vibrations. The modal characteristics (mass, stiffness, primary and secondary electromechanical conversion factors) are also deduced. Then, to illustrate this general electromechanical method, the variational principle is applied to both homogeneous and nonhomogeneous Rosen-type PT models. A comparison of modal parameters, mechanical displacements, and electrical potentials are presented for both models. Finally, the validity of the electrodynamical model of nonhomogeneous Rosen-type PT is confirmed by a numerical comparison based on a finite elements method and an experimental identification.

  16. Painlevé equations, elliptic integrals and elementary functions

    NASA Astrophysics Data System (ADS)

    Żołądek, Henryk; Filipuk, Galina

    2015-02-01

    The six Painlevé equations can be written in the Hamiltonian form, with time dependent Hamilton functions. We present a rather new approach to this result, leading to rational Hamilton functions. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems with two degrees of freedom. We realize the Bäcklund transformations of the Painlevé equations as symplectic birational transformations in C4 and we interpret the cases with classical solutions as the cases of partial integrability of the extended Hamiltonian systems. We prove that the extended Hamiltonian systems do not have any additional algebraic first integral besides the known special cases of the third and fifth Painlevé equations. We also show that the original Painlevé equations admit the first integrals expressed in terms of the elementary functions only in the special cases mentioned above. In the proofs we use equations in variations with respect to a parameter and Liouville's theory of elementary functions.

  17. Redundancy of constraints in the classical and quantum theories of gravitation.

    NASA Technical Reports Server (NTRS)

    Moncrief, V.

    1972-01-01

    It is shown that in Dirac's version of the quantum theory of gravitation, the Hamiltonian constraints are greatly redundant. If the Hamiltonian constraint condition is satisfied at one point on the underlying, closed three-dimensional manifold, then it is automatically satisfied at every point, provided only that the momentum constraints are everywhere satisfied. This permits one to replace the usual infinity of Hamiltonian constraints by a single condition which may be taken in the form of an integral over the manifold. Analogous theorems are given for the classical Einstein Hamilton-Jacobi equations.

  18. Cosmic censorship of rotating Anti-de Sitter black hole

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gwak, Bogeun; Lee, Bum-Hoon, E-mail: rasenis@sogang.ac.kr, E-mail: bhl@sogang.ac.kr

    2016-02-01

    We test the validity of cosmic censorship in the rotating anti-de Sitter black hole. For this purpose, we investigate whether the extremal black hole can be overspun by the particle absorption. The particle absorption will change the mass and angular momentum of the black hole, which is analyzed using the Hamilton-Jacobi equations consistent with the laws of thermodynamics. We have found that the mass of the extremal black hole increases more than the angular momentum. Therefore, the outer horizon of the black hole still exists, and cosmic censorship is valid.

  19. Clock synchronization by accelerated observers - Metric construction for arbitrary congruences of world lines

    NASA Technical Reports Server (NTRS)

    Henriksen, R. N.; Nelson, L. A.

    1985-01-01

    Clock synchronization in an arbitrarily accelerated observer congruence is considered. A general solution is obtained that maintains the isotropy and coordinate independence of the one-way speed of light. Attention is also given to various particular cases including, rotating disk congruence or ring congruence. An explicit, congruence-based spacetime metric is constructed according to Einstein's clock synchronization procedure and the equation for the geodesics of the space-time was derived using Hamilton-Jacobi method. The application of interferometric techniques (absolute phase radio interferometry, VLBI) to the detection of the 'global Sagnac effect' is also discussed.

  20. Mean field games with congestion

    NASA Astrophysics Data System (ADS)

    Achdou, Yves; Porretta, Alessio

    2018-03-01

    We consider a class of systems of time dependent partial differential equations which arise in mean field type models with congestion. The systems couple a backward viscous Hamilton-Jacobi equation and a forward Kolmogorov equation both posed in $(0,T)\\times (\\mathbb{R}^N /\\mathbb{Z}^N)$. Because of congestion and by contrast with simpler cases, the latter system can never be seen as the optimality conditions of an optimal control problem driven by a partial differential equation. The Hamiltonian vanishes as the density tends to $+\\infty$ and may not even be defined in the regions where the density is zero. After giving a suitable definition of weak solutions, we prove the existence and uniqueness results of the latter under rather general assumptions. No restriction is made on the horizon $T$.

  1. Hamilton's rule and the causes of social evolution

    PubMed Central

    Bourke, Andrew F. G.

    2014-01-01

    Hamilton's rule is a central theorem of inclusive fitness (kin selection) theory and predicts that social behaviour evolves under specific combinations of relatedness, benefit and cost. This review provides evidence for Hamilton's rule by presenting novel syntheses of results from two kinds of study in diverse taxa, including cooperatively breeding birds and mammals and eusocial insects. These are, first, studies that empirically parametrize Hamilton's rule in natural populations and, second, comparative phylogenetic analyses of the genetic, life-history and ecological correlates of sociality. Studies parametrizing Hamilton's rule are not rare and demonstrate quantitatively that (i) altruism (net loss of direct fitness) occurs even when sociality is facultative, (ii) in most cases, altruism is under positive selection via indirect fitness benefits that exceed direct fitness costs and (iii) social behaviour commonly generates indirect benefits by enhancing the productivity or survivorship of kin. Comparative phylogenetic analyses show that cooperative breeding and eusociality are promoted by (i) high relatedness and monogamy and, potentially, by (ii) life-history factors facilitating family structure and high benefits of helping and (iii) ecological factors generating low costs of social behaviour. Overall, the focal studies strongly confirm the predictions of Hamilton's rule regarding conditions for social evolution and their causes. PMID:24686934

  2. Hamilton's rule and the causes of social evolution.

    PubMed

    Bourke, Andrew F G

    2014-05-19

    Hamilton's rule is a central theorem of inclusive fitness (kin selection) theory and predicts that social behaviour evolves under specific combinations of relatedness, benefit and cost. This review provides evidence for Hamilton's rule by presenting novel syntheses of results from two kinds of study in diverse taxa, including cooperatively breeding birds and mammals and eusocial insects. These are, first, studies that empirically parametrize Hamilton's rule in natural populations and, second, comparative phylogenetic analyses of the genetic, life-history and ecological correlates of sociality. Studies parametrizing Hamilton's rule are not rare and demonstrate quantitatively that (i) altruism (net loss of direct fitness) occurs even when sociality is facultative, (ii) in most cases, altruism is under positive selection via indirect fitness benefits that exceed direct fitness costs and (iii) social behaviour commonly generates indirect benefits by enhancing the productivity or survivorship of kin. Comparative phylogenetic analyses show that cooperative breeding and eusociality are promoted by (i) high relatedness and monogamy and, potentially, by (ii) life-history factors facilitating family structure and high benefits of helping and (iii) ecological factors generating low costs of social behaviour. Overall, the focal studies strongly confirm the predictions of Hamilton's rule regarding conditions for social evolution and their causes.

  3. Exact traveling-wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional Schrödinger equation with polynomial nonlinearity of arbitrary order.

    PubMed

    Petrović, Nikola Z; Belić, Milivoj; Zhong, Wei-Ping

    2011-02-01

    We obtain exact traveling wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with variable coefficients and polynomial Kerr nonlinearity of an arbitrarily high order. Exact solutions, given in terms of Jacobi elliptic functions, are presented for the special cases of cubic-quintic and septic models. We demonstrate that the widely used method for finding exact solutions in terms of Jacobi elliptic functions is not applicable to the nonlinear Schrödinger equation with saturable nonlinearity. ©2011 American Physical Society

  4. 78 FR 63852 - Airworthiness Directives; Hamilton Standard Division and Hamilton Sundstrand Corporation Propellers

    Federal Register 2010, 2011, 2012, 2013, 2014

    2013-10-25

    ... Blades and Hubs That Do Not Have an Updated ALS For Hamilton Standard Division propeller models 6/5500/F... approved update to the ALS, within one year after the effective date of this AD, perform an MI on the...

  5. RIACS

    NASA Technical Reports Server (NTRS)

    Oliger, Joseph

    1997-01-01

    Topics considered include: high-performance computing; cognitive and perceptual prostheses (computational aids designed to leverage human abilities); autonomous systems. Also included: development of a 3D unstructured grid code based on a finite volume formulation and applied to the Navier-stokes equations; Cartesian grid methods for complex geometry; multigrid methods for solving elliptic problems on unstructured grids; algebraic non-overlapping domain decomposition methods for compressible fluid flow problems on unstructured meshes; numerical methods for the compressible navier-stokes equations with application to aerodynamic flows; research in aerodynamic shape optimization; S-HARP: a parallel dynamic spectral partitioner; numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains; application of high-order shock capturing schemes to direct simulation of turbulence; multicast technology; network testbeds; supercomputer consolidation project.

  6. Hamilton Naki, transplant surgeon.

    PubMed

    Nzerue, Chike M

    2006-03-01

    A biographic sketch of Hamilton Naki is presented here. He was a great self-taught surgeon whose contributions to the world of transplantation were largely ignored due to the apartheid system of South Africa. He assisted Christian Barnard in the first human heart transplant in 1967.

  7. General nonextremal rotating charged Gödel black holes in minimal five-dimensional gauged supergravity.

    PubMed

    Wu, Shuang-Qing

    2008-03-28

    I present the general exact solutions for nonextremal rotating charged black holes in the Gödel universe of five-dimensional minimal supergravity theory. They are uniquely characterized by four nontrivial parameters: namely, the mass m, the charge q, the Kerr equal rotation parameter a, and the Gödel parameter j. I calculate the conserved energy, angular momenta, and charge for the solutions and show that they completely satisfy the first law of black hole thermodynamics. I also study the symmetry and separability of the Hamilton-Jacobi and the massive Klein-Gordon equations in these Einstein-Maxwell-Chern-Simons-Gödel black hole backgrounds.

  8. Numerical computation of diffusion on a surface.

    PubMed

    Schwartz, Peter; Adalsteinsson, David; Colella, Phillip; Arkin, Adam Paul; Onsum, Matthew

    2005-08-09

    We present a numerical method for computing diffusive transport on a surface derived from image data. Our underlying discretization method uses a Cartesian grid embedded boundary method for computing the volume transport in a region consisting of all points a small distance from the surface. We obtain a representation of this region from image data by using a front propagation computation based on level set methods for solving the Hamilton-Jacobi and eikonal equations. We demonstrate that the method is second-order accurate in space and time and is capable of computing solutions on complex surface geometries obtained from image data of cells.

  9. Quantitative genetic versions of Hamilton's rule with empirical applications

    PubMed Central

    McGlothlin, Joel W.; Wolf, Jason B.; Brodie, Edmund D.; Moore, Allen J.

    2014-01-01

    Hamilton's theory of inclusive fitness revolutionized our understanding of the evolution of social interactions. Surprisingly, an incorporation of Hamilton's perspective into the quantitative genetic theory of phenotypic evolution has been slow, despite the popularity of quantitative genetics in evolutionary studies. Here, we discuss several versions of Hamilton's rule for social evolution from a quantitative genetic perspective, emphasizing its utility in empirical applications. Although evolutionary quantitative genetics offers methods to measure each of the critical parameters of Hamilton's rule, empirical work has lagged behind theory. In particular, we lack studies of selection on altruistic traits in the wild. Fitness costs and benefits of altruism can be estimated using a simple extension of phenotypic selection analysis that incorporates the traits of social interactants. We also discuss the importance of considering the genetic influence of the social environment, or indirect genetic effects (IGEs), in the context of Hamilton's rule. Research in social evolution has generated an extensive body of empirical work focusing—with good reason—almost solely on relatedness. We argue that quantifying the roles of social and non-social components of selection and IGEs, in addition to relatedness, is now timely and should provide unique additional insights into social evolution. PMID:24686930

  10. 78 FR 30795 - Airworthiness Directives; Hamilton Standard Division and Hamilton Sundstrand Corporation Propellers

    Federal Register 2010, 2011, 2012, 2013, 2014

    2013-05-23

    ... Airworthiness Limitations Sections (ALSs) of the applicable maintenance manuals to date. Each ALS establishes.... Relevant Service Information We reviewed the Hamilton Sundstrand ALS in Maintenance Manual P5185, Revision... P5189, Revision 8, dated March 26, 2013. The ALS in these maintenance manuals lists the MIs for the...

  11. Inverse Jacobi multiplier as a link between conservative systems and Poisson structures

    NASA Astrophysics Data System (ADS)

    García, Isaac A.; Hernández-Bermejo, Benito

    2017-08-01

    Some aspects of the relationship between conservativeness of a dynamical system (namely the preservation of a finite measure) and the existence of a Poisson structure for that system are analyzed. From the local point of view, due to the flow-box theorem we restrict ourselves to neighborhoods of singularities. In this sense, we characterize Poisson structures around the typical zero-Hopf singularity in dimension 3 under the assumption of having a local analytic first integral with non-vanishing first jet by connecting with the classical Poincaré center problem. From the global point of view, we connect the property of being strictly conservative (the invariant measure must be positive) with the existence of a Poisson structure depending on the phase space dimension. Finally, weak conservativeness in dimension two is introduced by the extension of inverse Jacobi multipliers as weak solutions of its defining partial differential equation and some of its applications are developed. Examples including Lotka-Volterra systems, quadratic isochronous centers, and non-smooth oscillators are provided.

  12. Evolutionary Games with Randomly Changing Payoff Matrices

    NASA Astrophysics Data System (ADS)

    Yakushkina, Tatiana; Saakian, David B.; Bratus, Alexander; Hu, Chin-Kun

    2015-06-01

    Evolutionary games are used in various fields stretching from economics to biology. In most of these games a constant payoff matrix is assumed, although some works also consider dynamic payoff matrices. In this article we assume a possibility of switching the system between two regimes with different sets of payoff matrices. Potentially such a model can qualitatively describe the development of bacterial or cancer cells with a mutator gene present. A finite population evolutionary game is studied. The model describes the simplest version of annealed disorder in the payoff matrix and is exactly solvable at the large population limit. We analyze the dynamics of the model, and derive the equations for both the maximum and the variance of the distribution using the Hamilton-Jacobi equation formalism.

  13. Gravitational instantons from minimal surfaces

    NASA Astrophysics Data System (ADS)

    Aliev, A. N.; Hortaçsu, M.; Kalayci, J.; Nutku, Y.

    1999-02-01

    Physical properties of gravitational instantons which are derivable from minimal surfaces in three-dimensional Euclidean space are examined using the Newman-Penrose formalism for Euclidean signature. The gravitational instanton that corresponds to the helicoid minimal surface is investigated in detail. This is a metric of Bianchi type 0264-9381/16/2/024/img9, or E(2), which admits a hidden symmetry due to the existence of a quadratic Killing tensor. It leads to a complete separation of variables in the Hamilton-Jacobi equation for geodesics, as well as in Laplace's equation for a massless scalar field. The scalar Green function can be obtained in closed form, which enables us to calculate the vacuum fluctuations of a massless scalar field in the background of this instanton.

  14. 9. INTERIOR VIEW OF BREW HOUSE, STEAM ENGINE READS: HAMILTON ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    9. INTERIOR VIEW OF BREW HOUSE, STEAM ENGINE- READS: HAMILTON CORLISS ENGINES, THE HOOVEN, OWENS & RENTSCHLER CO., BUILDERS, HAMILTON, OHIO, U.S.A. - August Schell Brewing Company, Twentieth Street South, New Ulm, Brown County, MN

  15. Hamilton Naki, transplant surgeon.

    PubMed Central

    Nzerue, Chike M.

    2006-01-01

    A biographic sketch of Hamilton Naki is presented here. He was a great self-taught surgeon whose contributions to the world of transplantation were largely ignored due to the apartheid system of South Africa. He assisted Christian Barnard in the first human heart transplant in 1967. Images p448-a PMID:16573312

  16. Systems of Inhomogeneous Linear Equations

    NASA Astrophysics Data System (ADS)

    Scherer, Philipp O. J.

    Many problems in physics and especially computational physics involve systems of linear equations which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the dimension of the system is not too large standard methods like Gaussian elimination or QR decomposition are sufficient. Systems with a tridiagonal matrix are important for cubic spline interpolation and numerical second derivatives. They can be solved very efficiently with a specialized Gaussian elimination method. Practical applications often involve very large dimensions and require iterative methods. Convergence of Jacobi and Gauss-Seidel methods is slow and can be improved by relaxation or over-relaxation. An alternative for large systems is the method of conjugate gradients.

  17. Variational energy principle for compressible, baroclinic flow. 2: Free-energy form of Hamilton's principle

    NASA Technical Reports Server (NTRS)

    Schmid, L. A.

    1977-01-01

    The first and second variations are calculated for the irreducible form of Hamilton's Principle that involves the minimum number of dependent variables necessary to describe the kinetmatics and thermodynamics of inviscid, compressible, baroclinic flow in a specified gravitational field. The form of the second variation shows that, in the neighborhood of a stationary point that corresponds to physically stable flow, the action integral is a complex saddle surface in parameter space. There exists a form of Hamilton's Principle for which a direct solution of a flow problem is possible. This second form is related to the first by a Friedrichs transformation of the thermodynamic variables. This introduces an extra dependent variable, but the first and second variations are shown to have direct physical significance, namely they are equal to the free energy of fluctuations about the equilibrium flow that satisfies the equations of motion. If this equilibrium flow is physically stable, and if a very weak second order integral constraint on the correlation between the fluctuations of otherwise independent variables is satisfied, then the second variation of the action integral for this free energy form of Hamilton's Principle is positive-definite, so the action integral is a minimum, and can serve as the basis for a direct trail and error solution. The second order integral constraint states that the unavailable energy must be maximum at equilibrium, i.e. the fluctuations must be so correlated as to produce a second order decrease in the total unavailable energy.

  18. Zero-g tests of involving Hamilton standard personnel and others

    NASA Technical Reports Server (NTRS)

    1979-01-01

    Zero-g tests of involving Hamilton standard personnel, Don Williams and Larry Magers. View includes Williams and Magers tumbling in zero-g as photographer takes picures. Williams is wearing a headset (30361); Williams floats among Hamilton standard technicians (30362).

  19. Hamilton's Principle for Beginners

    ERIC Educational Resources Information Center

    Brun, J. L.

    2007-01-01

    I find that students have difficulty with Hamilton's principle, at least the first time they come into contact with it, and therefore it is worth designing some examples to help students grasp its complex meaning. This paper supplies the simplest example to consolidate the learning of the quoted principle: that of a free particle moving along a…

  20. 78 FR 49660 - Airworthiness Directives; Hamilton Standard Division and Hamilton Sundstrand Corporation Propellers

    Federal Register 2010, 2011, 2012, 2013, 2014

    2013-08-15

    ... done. (f) MI for Blades and Hubs That Have an Updated Airworthiness Limitations Section (ALS) For..., that have an approved update to the ALS, within 45 days after the effective date of this AD, perform an... and Hubs That Do Not Have an Updated ALS For Hamilton Standard Division propeller models 6/5500/F and...

  1. Numerical analysis for trajectory controllability of a coupled multi-order fractional delay differential system via the shifted Jacobi method

    NASA Astrophysics Data System (ADS)

    Priya, B. Ganesh; Muthukumar, P.

    2018-02-01

    This paper deals with the trajectory controllability for a class of multi-order fractional linear systems subject to a constant delay in state vector. The solution for the coupled fractional delay differential equation is established by the Mittag-Leffler function. The necessary and sufficient condition for the trajectory controllability is formulated and proved by the generalized Gronwall's inequality. The approximate trajectory for the proposed system is obtained through the shifted Jacobi operational matrix method. The numerical simulation of the approximate solution shows the theoretical results. Finally, some remarks and comments on the existing results of constrained controllability for the fractional dynamical system are also presented.

  2. An integrable family of Monge-Ampère equations and their multi-Hamiltonian structure

    NASA Astrophysics Data System (ADS)

    Nutku, Y.; Sarioǧlu, Ö.

    1993-02-01

    We have identified a completely integrable family of Monge-Ampère equations through an examination of their Hamiltonian structure. Starting with a variational formulation of the Monge-Ampère equations we have constructed the first Hamiltonian operator through an application of Dirac's theory of constraints. The completely integrable class of Monge-Ampère equations are then obtained by solving the Jacobi identities for a sufficiently general form of the second Hamiltonian operator that is compatible with the first.

  3. Invariants of the Jacobi-Porstendorfer room model for radon progeny in indoor air.

    PubMed

    Thomas, Josef; Jilek, Karel

    2012-06-01

    The Jacobi-Porstendörfer room model, describing the dynamical behaviour of radon and radon progeny in indoor air, has been successfully used for decades. The inversion of the model-the determination of the five parameters from measured results which provide better information on the room environment than mere ratios of unattached and attached radon progeny-is treated as an algebraic task. The linear interdependence of the used equations strongly limits the algebraic invertibility of experimental results. For a unique solution, the fulfilment of two invariants of the room model for the measured results is required. Non-fulfilment of these model invariants by the measured results leads to a set of non-identical solutions and indicates the violation of the conditions required by the room model or the incorrectness or excessive uncertainties of the measured results. The limited and non-unique algebraic invertibility of the room model is analysed numerically using our own data for the radon progeny.

  4. The effect of the Gauss-Bonnet term on Hawking radiation from arbitrary dimensional black brane

    NASA Astrophysics Data System (ADS)

    Kuang, Xiao-Mei; Saavedra, Joel; Övgün, Ali

    2017-09-01

    We investigate the probabilities of the tunneling and the radiation spectra of massive spin-1 particles from arbitrary dimensional Gauss-Bonnet-Axions (GBA) Anti-de Sitter (AdS) black branes, via using the WKB approximation to the Proca spin-1 field equation. The tunneling probabilities and Hawking temperature of the arbitrary dimensional GBA AdS black brane is calculated via the Hamilton-Jacobi approach. We also compute the Hawking temperature via the Parikh-Wilczek tunneling approach. The results obtained from the two methods are consistent. In our setup, the Gauss-Bonnet (GB) coupling affects the Hawking temperature if and only if the momentum of the axion fields is non-vanishing.

  5. Algorithm For Optimal Control Of Large Structures

    NASA Technical Reports Server (NTRS)

    Salama, Moktar A.; Garba, John A..; Utku, Senol

    1989-01-01

    Cost of computation appears competitive with other methods. Problem to compute optimal control of forced response of structure with n degrees of freedom identified in terms of smaller number, r, of vibrational modes. Article begins with Hamilton-Jacobi formulation of mechanics and use of quadratic cost functional. Complexity reduced by alternative approach in which quadratic cost functional expressed in terms of control variables only. Leads to iterative solution of second-order time-integral matrix Volterra equation of second kind containing optimal control vector. Cost of algorithm, measured in terms of number of computations required, is of order of, or less than, cost of prior algoritms applied to similar problems.

  6. Value function in economic growth model

    NASA Astrophysics Data System (ADS)

    Bagno, Alexander; Tarasyev, Alexandr A.; Tarasyev, Alexander M.

    2017-11-01

    Properties of the value function are examined in an infinite horizon optimal control problem with an unlimited integrand index appearing in the quality functional with a discount factor. Optimal control problems of such type describe solutions in models of economic growth. Necessary and sufficient conditions are derived to ensure that the value function satisfies the infinitesimal stability properties. It is proved that value function coincides with the minimax solution of the Hamilton-Jacobi equation. Description of the growth asymptotic behavior for the value function is provided for the logarithmic, power and exponential quality functionals and an example is given to illustrate construction of the value function in economic growth models.

  7. Stochastic optimal control as non-equilibrium statistical mechanics: calculus of variations over density and current

    NASA Astrophysics Data System (ADS)

    Chernyak, Vladimir Y.; Chertkov, Michael; Bierkens, Joris; Kappen, Hilbert J.

    2014-01-01

    In stochastic optimal control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive), for a system participating in forced and controlled Langevin dynamics. We extend the SOC problem by introducing an additional cost-of-dynamics, characterized by a vector potential. We propose derivation of the generalized gauge-invariant Hamilton-Jacobi-Bellman equation as a variation over density and current, suggest hydrodynamic interpretation and discuss examples, e.g., ergodic control of a particle-within-a-circle, illustrating non-equilibrium space-time complexity.

  8. On a Lagrange-Hamilton formalism describing position and momentum uncertainties

    NASA Technical Reports Server (NTRS)

    Schuch, Dieter

    1993-01-01

    According to Heisenberg's uncertainty relation, in quantum mechanics it is not possible to determine, simultaneously, exact values for the position and the momentum of a material system. Calculating the mean value of the Hamiltonian operator with the aid of exact analytic Gaussian wave packet solutions, these uncertainties cause an energy contribution additional to the classical energy of the system. For the harmonic oscillator, e.g., this nonclassical energy represents the ground state energy. It will be shown that this additional energy contribution can be considered as a Hamiltonian function, if it is written in appropriate variables. With the help of the usual Lagrange-Hamilton formalism known from classical particle mechanics, but now considering this new Hamiltonian function, it is possible to obtain the equations of motion for position and momentum uncertainties.

  9. Reconstruction of color biomedical images by means of quaternion generic Jacobi-Fourier moments in the framework of polar pixels

    PubMed Central

    Camacho-Bello, César; Padilla-Vivanco, Alfonso; Toxqui-Quitl, Carina; Báez-Rojas, José Javier

    2016-01-01

    Abstract. A detailed analysis of the quaternion generic Jacobi-Fourier moments (QGJFMs) for color image description is presented. In order to reach numerical stability, a recursive approach is used during the computation of the generic Jacobi radial polynomials. Moreover, a search criterion is performed to establish the best values for the parameters α and β of the radial Jacobi polynomial families. Additionally, a polar pixel approach is taken into account to increase the numerical accuracy in the calculation of the QGJFMs. To prove the mathematical theory, some color images from optical microscopy and human retina are used. Experiments and results about color image reconstruction are presented. PMID:27014716

  10. Continuous-time mean-variance portfolio selection with value-at-risk and no-shorting constraints

    NASA Astrophysics Data System (ADS)

    Yan, Wei

    2012-01-01

    An investment problem is considered with dynamic mean-variance(M-V) portfolio criterion under discontinuous prices which follow jump-diffusion processes according to the actual prices of stocks and the normality and stability of the financial market. The short-selling of stocks is prohibited in this mathematical model. Then, the corresponding stochastic Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and the solution of the stochastic HJB equation based on the theory of stochastic LQ control and viscosity solution is obtained. The efficient frontier and optimal strategies of the original dynamic M-V portfolio selection problem are also provided. And then, the effects on efficient frontier under the value-at-risk constraint are illustrated. Finally, an example illustrating the discontinuous prices based on M-V portfolio selection is presented.

  11. An Anharmonic Solution to the Equation of Motion for the Simple Pendulum

    ERIC Educational Resources Information Center

    Johannessen, Kim

    2011-01-01

    An anharmonic solution to the differential equation describing the oscillations of a simple pendulum at large angles is discussed. The solution is expressed in terms of functions not involving the Jacobi elliptic functions. In the derivation, a sinusoidal expression, including a linear and a Fourier sine series in the argument, has been applied.…

  12. A generalization of Hamilton's rule--love others how much?

    PubMed

    Alger, Ingela; Weibull, Jörgen W

    2012-04-21

    According to Hamilton's (1964a, b) rule, a costly action will be undertaken if its fitness cost to the actor falls short of the discounted benefit to the recipient, where the discount factor is Wright's index of relatedness between the two. We propose a generalization of this rule, and show that if evolution operates at the level of behavior rules, rather than directly at the level of actions, evolution will select behavior rules that induce a degree of cooperation that may differ from that predicted by Hamilton's rule as applied to actions. In social dilemmas there will be less (more) cooperation than under Hamilton's rule if the actions are strategic substitutes (complements). Our approach is based on natural selection, defined in terms of personal (direct) fitness, and applies to a wide range of pairwise interactions. Copyright © 2011 Elsevier Ltd. All rights reserved.

  13. Travelling wave solutions and conservation laws for the Korteweg-de Vries-Bejamin-Bona-Mahony equation

    NASA Astrophysics Data System (ADS)

    Simbanefayi, Innocent; Khalique, Chaudry Masood

    2018-03-01

    In this work we study the Korteweg-de Vries-Benjamin-Bona-Mahony (KdV-BBM) equation, which describes the two-way propagation of waves. Using Lie symmetry method together with Jacobi elliptic function expansion and Kudryashov methods we construct its travelling wave solutions. Also, we derive conservation laws of the KdV-BBM equation using the variational derivative approach. In this method, we begin by computing second-order multipliers for the KdV-BBM equation followed by a derivation of the respective conservation laws for each multiplier.

  14. 77 FR 52135 - Hamilton Bank, Baltimore, Maryland; Approval of Conversion Application

    Federal Register 2010, 2011, 2012, 2013, 2014

    2012-08-28

    ... DEPARTMENT OF THE TREASURY Office of the Comptroller of the Currency [OCC Charter Number 701904] Hamilton Bank, Baltimore, Maryland; Approval of Conversion Application Notice is hereby given that on August 13, 2012, the Office of the Comptroller of the Currency (OCC) approved the application of Hamilton...

  15. Improvement of transport-corrected scattering stability and performance using a Jacobi inscatter algorithm for 2D-MOC

    DOE PAGES

    Stimpson, Shane; Collins, Benjamin; Kochunas, Brendan

    2017-03-10

    The MPACT code, being developed collaboratively by the University of Michigan and Oak Ridge National Laboratory, is the primary deterministic neutron transport solver being deployed within the Virtual Environment for Reactor Applications (VERA) as part of the Consortium for Advanced Simulation of Light Water Reactors (CASL). In many applications of the MPACT code, transport-corrected scattering has proven to be an obstacle in terms of stability, and considerable effort has been made to try to resolve the convergence issues that arise from it. Most of the convergence problems seem related to the transport-corrected cross sections, particularly when used in the 2Dmore » method of characteristics (MOC) solver, which is the focus of this work. Here in this paper, the stability and performance of the 2-D MOC solver in MPACT is evaluated for two iteration schemes: Gauss-Seidel and Jacobi. With the Gauss-Seidel approach, as the MOC solver loops over groups, it uses the flux solution from the previous group to construct the inscatter source for the next group. Alternatively, the Jacobi approach uses only the fluxes from the previous outer iteration to determine the inscatter source for each group. Consequently for the Jacobi iteration, the loop over groups can be moved from the outermost loop$-$as is the case with the Gauss-Seidel sweeper$-$to the innermost loop, allowing for a substantial increase in efficiency by minimizing the overhead of retrieving segment, region, and surface index information from the ray tracing data. Several test problems are assessed: (1) Babcock & Wilcox 1810 Core I, (2) Dimple S01A-Sq, (3) VERA Progression Problem 5a, and (4) VERA Problem 2a. The Jacobi iteration exhibits better stability than Gauss-Seidel, allowing for converged solutions to be obtained over a much wider range of iteration control parameters. Additionally, the MOC solve time with the Jacobi approach is roughly 2.0-2.5× faster per sweep. While the performance and stability of

  16. Quadratically Convergent Method for Simultaneously Approaching the Roots of Polynomial Solutions of a Class of Differential Equations

    NASA Astrophysics Data System (ADS)

    Recchioni, Maria Cristina

    2001-12-01

    This paper investigates the application of the method introduced by L. Pasquini (1989) for simultaneously approaching the zeros of polynomial solutions to a class of second-order linear homogeneous ordinary differential equations with polynomial coefficients to a particular case in which these polynomial solutions have zeros symmetrically arranged with respect to the origin. The method is based on a family of nonlinear equations which is associated with a given class of differential equations. The roots of the nonlinear equations are related to the roots of the polynomial solutions of differential equations considered. Newton's method is applied to find the roots of these nonlinear equations. In (Pasquini, 1994) the nonsingularity of the roots of these nonlinear equations is studied. In this paper, following the lines in (Pasquini, 1994), the nonsingularity of the roots of these nonlinear equations is studied. More favourable results than the ones in (Pasquini, 1994) are proven in the particular case of polynomial solutions with symmetrical zeros. The method is applied to approximate the roots of Hermite-Sobolev type polynomials and Freud polynomials. A lower bound for the smallest positive root of Hermite-Sobolev type polynomials is given via the nonlinear equation. The quadratic convergence of the method is proven. A comparison with a classical method that uses the Jacobi matrices is carried out. We show that the algorithm derived by the proposed method is sometimes preferable to the classical QR type algorithms for computing the eigenvalues of the Jacobi matrices even if these matrices are real and symmetric.

  17. Local spectral properties of reflectionless Jacobi, CMV, and Schrödinger operators

    NASA Astrophysics Data System (ADS)

    Gesztesy, Fritz; Zinchenko, Maxim

    We prove that Jacobi, CMV, and Schrödinger operators, which are reflectionless on a homogeneous set E (in the sense of Carleson), under the assumption of a Blaschke-type condition on their discrete spectra accumulating at E, have purely absolutely continuous spectrum on E.

  18. A Heuristic Fast Method to Solve the Nonlinear Schroedinger Equation in Fiber Bragg Gratings with Arbitrary Shape Input Pulse

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Emami, F.; Hatami, M.; Keshavarz, A. R.

    2009-08-13

    Using a combination of Runge-Kutta and Jacobi iterative method, we could solve the nonlinear Schroedinger equation describing the pulse propagation in FBGs. By decomposing the electric field to forward and backward components in fiber Bragg grating and utilizing the Fourier series analysis technique, the boundary value problem of a set of coupled equations governing the pulse propagation in FBG changes to an initial condition coupled equations which can be solved by simple Runge-Kutta method.

  19. Stochastic optimal control of ultradiffusion processes with application to dynamic portfolio management

    NASA Astrophysics Data System (ADS)

    Marcozzi, Michael D.

    2008-12-01

    We consider theoretical and approximation aspects of the stochastic optimal control of ultradiffusion processes in the context of a prototype model for the selling price of a European call option. Within a continuous-time framework, the dynamic management of a portfolio of assets is effected through continuous or point control, activation costs, and phase delay. The performance index is derived from the unique weak variational solution to the ultraparabolic Hamilton-Jacobi equation; the value function is the optimal realization of the performance index relative to all feasible portfolios. An approximation procedure based upon a temporal box scheme/finite element method is analyzed; numerical examples are presented in order to demonstrate the viability of the approach.

  20. Motion of charged particle in Reissner-Nordström spacetime: a Jacobi-metric approach

    NASA Astrophysics Data System (ADS)

    Das, Praloy; Sk, Ripon; Ghosh, Subir

    2017-11-01

    The present work discusses motion of neutral and charged particles in Reissner-Nordström spacetime. The constant energy paths are derived in a variational principle framework using the Jacobi metric which is parameterized by conserved particle energy. Of particular interest is the case of particle charge and Reissner-Nordström black hole charge being of same sign, since this leads to a clash of opposing forces—gravitational (attractive) and Coulomb (repulsive). Our paper aims to complement the recent work of Pugliese et al. (Eur Phys J C 77:206. arXiv:1304.2940, 2017; Phys Rev D 88:024042. arXiv:1303.6250, 2013). The energy dependent Gaussian curvature (induced by the Jacobi metric) plays an important role in classifying the trajectories.

  1. [Anna Hamilton (1864-1935), the excellence of nursing.

    PubMed

    Diebolt, Évelyne

    2017-12-01

    A Frenchwoman, Anna Hamilton (1864-1935), daughter of a Franco-English couple, reads with passion the works of Florence Nightingale and takes an interest in nursing. In order to practice it, she first passes the equivalent of a bachelor’s degree in self-education and registers at the Marseille medical school. She wants to prepare a medical thesis on the nursing staff in the hospitals in Europe and is conducting an investigation throughout Europe. She passed her thesis on June 15, 1900 entitled “Considerations on hospital nurses”. This work is immediately published. That same year, she took up a post at the “Maison de santé protestante” in Bordeaux (MSP), founded in 1863. Without managerial staff, she is forced to recruit them abroad. She publishes a professional journal : “La Garde-Malade hospitalière” (1906-1914). Then the war turned the MSP into a military hospital, but the institution continued to receive local paying patients. She was given permission to call the school of nurses : Florence Nightingale School. Anna Hamilton is working with American women to create a medical and social service in Aisne. A graduate, Antoinette Hervey, then opened a medical-social service in Rouen, which would employ up to 30 visiting nurses. In 1916, the MSP received a donation from the domain of Bagatelle. The board of directors wants to sell it, but Anna Hamilton manages to finance a hospital-school thanks to families bereaved by the war and a subscription announced in the “Journal of Nursing”. Other establishments created by former students of the MSP opened : the School-hospital Ambroise Paré in Lille, a nursing home for nurses in Chambon-sur-Lignon in 1927 (the Edith-Seltzer foundation) and a sanatorium in Briançon. After a busy life, Anna Hamilton died of cancer in 1935 and is buried in Bordeaux.

  2. Bridging the Gap Between Stationary Homogeneous Isotropic Turbulence and Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Sohrab, Siavash

    A statistical theory of stationary isotropic turbulence is presented with eddies possessing Gaussian velocity distribution, Maxwell-Boltzmann speed distribution in harmony with perceptions of Heisenberg, and Planck energy distribution in harmony with perceptions of Chandrasekhar and in agreement with experimental observations of Van Atta and Chen. Defining the action S = - mΦ in terms of velocity potential of atomic motion, scale-invariant Schrödinger equation is derivedfrom invariant Bernoulli equation. Thus, the gap between the problems of turbulence and quantum mechanics is closed through connections between Cauchy-Euler-Bernoulli equations of hydrodynamics, Hamilton-Jacobi equation of classical mechanics, and finally Schrödinger equation of quantum mechanics. Transitions of particle (molecular cluster cji) from a small rapidly-oscillating eddy ej (high-energy level-j) to a large slowly-oscillating eddy ei (low energy-level-i) leads to emission of a sub-particle (molecule mji) that carries away the excess energy ɛji = h (νj -νi) in harmony with Bohr theory of atomic spectra. ∖ ∖ NASA Grant No. NAG3-1863.

  3. Comparing direct and iterative equation solvers in a large structural analysis software system

    NASA Technical Reports Server (NTRS)

    Poole, E. L.

    1991-01-01

    Two direct Choleski equation solvers and two iterative preconditioned conjugate gradient (PCG) equation solvers used in a large structural analysis software system are described. The two direct solvers are implementations of the Choleski method for variable-band matrix storage and sparse matrix storage. The two iterative PCG solvers include the Jacobi conjugate gradient method and an incomplete Choleski conjugate gradient method. The performance of the direct and iterative solvers is compared by solving several representative structural analysis problems. Some key factors affecting the performance of the iterative solvers relative to the direct solvers are identified.

  4. Alexander Hamilton: Soldier-Statesmen of the Constitution. A Bicentennial Series No. 16.

    ERIC Educational Resources Information Center

    Army Center of Military History, Washington, DC.

    Alexander Hamilton was among the most intellectually gifted of the Founding Fathers and a brilliant political theorist, but he lacked practical political experience, and his major political contributions occurred only when his specific policies were adopted and carried forward by others with broader vision. This booklet on Hamilton is one in a…

  5. Measuring Social Capital in Hamilton, Ontario

    ERIC Educational Resources Information Center

    Kitchen, Peter; Williams, Allison; Simone, Dylan

    2012-01-01

    Social capital has been studied by academics for more than 20 years and within the past decade there has been an explosion of growth in research linking social capital to health. This paper investigates social capital in Hamilton, Ontario by way of a telephone survey of 1,002 households in three neighbourhood groups representing high, mixed and…

  6. Solution of D dimensional Dirac equation for coulombic potential using NU method and its thermodynamics properties

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Cari, C., E-mail: cari@staff.uns.ac.id; Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Yunianto, M., E-mail: muhtaryunianto@staff.uns.ac.id

    2016-02-08

    The analytical solution of Ddimensional Dirac equation for Coulombic potential is investigated using Nikiforov-Uvarov method. The D dimensional relativistic energy spectra are obtained from relativistic energy eigenvalue equation by using Mat Lab software.The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi and Laguerre Polynomials. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy which will be applied to determine some thermodynamical properties of the system. The thermodynamical properties of the system are expressed in terms of error function and imaginary error function.

  7. New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan's tau function.

    PubMed

    Milne, S C

    1996-12-24

    In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi's (1829) 4 and 8 squares identities to 4n(2) or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan's tau function tau(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the eta-function identities in appendix I of Macdonald's work [Macdonald, I. G. (1972) Invent. Math. 15, 91-143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415-456] identities involving representing a positive integer by sums of 4n(2) or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson's C(l) nonterminating (6)phi(5) summation theorem, and Andrews' basic hypergeometric series proof of Jacobi's 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n(2) or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

  8. Yerkes, Hamilton and the experimental study of the ape mind: from evolutionary psychiatry to eugenic politics.

    PubMed

    Thomas, Marion

    2006-06-01

    Robert Yerkes is a pivotal figure in American psychology and primatology in the first half of the twentieth century. As is well known, Yerkes first studied ape intelligence in 1915, on a visit to the private California laboratory of the psychiatrist Gilbert Hamilton, a former student. Less widely appreciated is how far the work done at the Hamilton lab, in its aims and ambitions as well as its techniques, served as a template for much of Yerkes's research thereafter. This paper uses the Hamilton-Yerkes relationship to re-examine Yerkes's career and, more generally, that of American psychology in the early twentieth century. Three points especially are emphasized: first, the role of Freudian psychoanalysis as a spur to Hamilton's experimental studies of ape intelligence; second, the importance of Hamilton's laboratory, with its semi-wild population of monkeys and ape, as a model for Yerkes's efforts to create a laboratory of his own; and third, the influence on Yerkes of Hamilton's optimism about experimental psychological studies of nonhuman primates as a source of lessons beneficial to a troubled human world.

  9. Output Feedback-Based Boundary Control of Uncertain Coupled Semilinear Parabolic PDE Using Neurodynamic Programming.

    PubMed

    Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

    2018-04-01

    In this paper, neurodynamic programming-based output feedback boundary control of distributed parameter systems governed by uncertain coupled semilinear parabolic partial differential equations (PDEs) under Neumann or Dirichlet boundary control conditions is introduced. First, Hamilton-Jacobi-Bellman (HJB) equation is formulated in the original PDE domain and the optimal control policy is derived using the value functional as the solution of the HJB equation. Subsequently, a novel observer is developed to estimate the system states given the uncertain nonlinearity in PDE dynamics and measured outputs. Consequently, the suboptimal boundary control policy is obtained by forward-in-time estimation of the value functional using a neural network (NN)-based online approximator and estimated state vector obtained from the NN observer. Novel adaptive tuning laws in continuous time are proposed for learning the value functional online to satisfy the HJB equation along system trajectories while ensuring the closed-loop stability. Local uniformly ultimate boundedness of the closed-loop system is verified by using Lyapunov theory. The performance of the proposed controller is verified via simulation on an unstable coupled diffusion reaction process.

  10. Application of Hamilton's Law of Varying Action

    NASA Technical Reports Server (NTRS)

    Bailey, C. D.

    1973-01-01

    The application of Hamilton's Law to the direct solution of nonstationary as well as stationary problems in mechanics of solids is discussed. Solutions are demonstrated for conservative and monconservative, stationary and/or nonstationary particle motion. Mathematical models are developed to establish the relationships of the parameters.

  11. Jacobi Shape Transitions Within the LSD Model and the Skyrme-Etf Approach

    NASA Astrophysics Data System (ADS)

    Bartel, Johann; Pomorski, Krzysztof

    The "Modified Funny-Hills parametrisation" is used together with the Lublin-Strasbourg Drop Model to evaluate the stability of rotating nuclei. The Jacobi transition into triaxial shapes is studied. By a comparison with selfconsistent semiclassical calculations in the framework of the Extended Thomas-Fermi method, the validity of the present approach is demonstrated and possible improvements are indicated.

  12. Applying the Zel'dovich approximation to general relativity

    NASA Astrophysics Data System (ADS)

    Croudace, K. M.; Parry, J.; Salopek, D. S.; Stewart, J. M.

    1994-03-01

    Starting from general relativity, we give a systematic derivation of the Zel'dovich approximation describing the nonlinear evolution of collisionless dust. We begin by evolving dust along world lines, and we demonstrate that the Szekeres line element is an exact but apparently unstable solution of the evolution equations describing pancake collapse. Next, we solve the Einstein field equations by employing Hamilton-Jacobi techniques and a spatial gradient expansion. We give a prescription for evolving a primordial or 'seed' metric up to the formation of pancakes, and demonstrate its validity by rederiving the Szekeres solution approximately at third order and exactly at fifth order in spatial gradients. Finally we show that the range of validity of the expansion can be improved quite significantly if one notes that the 3-metric must have nonnegative eigenvalues. With this improvement the exact Szekeres solution is obtained after only one iteration.

  13. Zero-sum two-player game theoretic formulation of affine nonlinear discrete-time systems using neural networks.

    PubMed

    Mehraeen, Shahab; Dierks, Travis; Jagannathan, S; Crow, Mariesa L

    2013-12-01

    In this paper, the nearly optimal solution for discrete-time (DT) affine nonlinear control systems in the presence of partially unknown internal system dynamics and disturbances is considered. The approach is based on successive approximate solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in optimal control. Successive approximation approach for updating control and disturbance inputs for DT nonlinear affine systems are proposed. Moreover, sufficient conditions for the convergence of the approximate HJI solution to the saddle point are derived, and an iterative approach to approximate the HJI equation using a neural network (NN) is presented. Then, the requirement of full knowledge of the internal dynamics of the nonlinear DT system is relaxed by using a second NN online approximator. The result is a closed-loop optimal NN controller via offline learning. A numerical example is provided illustrating the effectiveness of the approach.

  14. Optimal coordination and control of posture and movements.

    PubMed

    Johansson, Rolf; Fransson, Per-Anders; Magnusson, Måns

    2009-01-01

    This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton-Jacobi equation for optimal control of rigid-body motion are obtained by solving an algebraic matrix equation. The stability is investigated with Lyapunov function theory and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and movement model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses. Validation examples with experimental data are provided.

  15. Integrability of geodesics in near-horizon extremal geometries: Case of Myers-Perry black holes in arbitrary dimensions

    NASA Astrophysics Data System (ADS)

    Demirchian, Hovhannes; Nersessian, Armen; Sadeghian, Saeedeh; Sheikh-Jabbari, M. M.

    2018-05-01

    We investigate dynamics of probe particles moving in the near-horizon limit of extremal Myers-Perry black holes in arbitrary dimensions. Employing ellipsoidal coordinates we show that this problem is integrable and separable, extending the results of the odd dimensional case discussed by Hakobyan et al. [Phys. Lett. B 772, 586 (2017)., 10.1016/j.physletb.2017.07.028]. We find the general solution of the Hamilton-Jacobi equations for these systems and present explicit expressions for the Liouville integrals and discuss Killing tensors and the associated constants of motion. We analyze special cases of the background near-horizon geometry were the system possesses more constants of motion and is hence superintegrable. Finally, we consider a near-horizon extremal vanishing horizon case which happens for Myers-Perry black holes in odd dimensions and show that geodesic equations on this geometry are also separable and work out its integrals of motion.

  16. Event-Triggered Adaptive Dynamic Programming for Continuous-Time Systems With Control Constraints.

    PubMed

    Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo

    2016-08-31

    In this paper, an event-triggered near optimal control structure is developed for nonlinear continuous-time systems with control constraints. Due to the saturating actuators, a nonquadratic cost function is introduced and the Hamilton-Jacobi-Bellman (HJB) equation for constrained nonlinear continuous-time systems is formulated. In order to solve the HJB equation, an actor-critic framework is presented. The critic network is used to approximate the cost function and the action network is used to estimate the optimal control law. In addition, in the proposed method, the control signal is transmitted in an aperiodic manner to reduce the computational and the transmission cost. Both the networks are only updated at the trigger instants decided by the event-triggered condition. Detailed Lyapunov analysis is provided to guarantee that the closed-loop event-triggered system is ultimately bounded. Three case studies are used to demonstrate the effectiveness of the proposed method.

  17. Learning-Based Adaptive Optimal Tracking Control of Strict-Feedback Nonlinear Systems.

    PubMed

    Gao, Weinan; Jiang, Zhong-Ping; Weinan Gao; Zhong-Ping Jiang; Gao, Weinan; Jiang, Zhong-Ping

    2018-06-01

    This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any a priori knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals.

  18. Fermions tunneling from a general static Riemann black hole

    NASA Astrophysics Data System (ADS)

    Chen, Ge-Rui; Huang, Yong-Chang

    2015-05-01

    In this paper we investigate the tunneling of fermions from a general static Riemann black hole by following Kerner and Mann (Class Quantum Gravit 25:095014, 2008a; Phys Lett B 665:277-283, 2008b) methods. By applying the WKB approximation and the Hamilton-Jacobi ansatz to the Dirac equation, we obtain the standard Hawking temperature. Furthermore, Kerner and Mann (Class Quantum Gravit 25:095014, 2008a; Phys Lett B 665:277-283, 2008b) only calculated the tunneling spectrum of the Dirac particles with spin-up, and we extend the methods to investigate the tunneling of Dirac particles with arbitrary spin directions and also obtain the expected Hawking temperature. Our result provides further evidence for the universality of black hole radiation.

  19. Maximal analytic extension and hidden symmetries of the dipole black ring

    NASA Astrophysics Data System (ADS)

    Armas, Jay

    2011-12-01

    We construct analytic extensions across the Killing horizons of non-extremal and extremal dipole black rings in Einstein-Maxwell’s theory using different methods. We show that these extensions are non-globally hyperbolic, have multiple asymptotically flat regions and, in the non-extremal case, are also maximal and timelike complete. Moreover, we find that in both cases, the causal structure of the maximally extended spacetime resembles that of the four-dimensional Reissner-Nordström black hole. Furthermore, motivated by the physical interpretation of one of these extensions, we find a separable solution to the Hamilton-Jacobi equation corresponding to zero energy null geodesics and relate it to the existence of a conformal Killing tensor and a conformal Killing-Yano tensor in a specific dimensionally reduced spacetime.

  20. The GUP effect on Hawking radiation of the 2 + 1 dimensional black hole

    NASA Astrophysics Data System (ADS)

    Gecim, Ganim; Sucu, Yusuf

    2017-10-01

    We investigate the Generalized Uncertainty Principle (GUP) effect on the Hawking radiation of the 2 + 1 dimensional Martinez-Zanelli black hole by using the Hamilton-Jacobi method. In this connection, we discuss the tunneling probabilities and Hawking temperature of the spin-1/2 and spin-0 particles for the black hole. Therefore, we use the modified Klein-Gordon and Dirac equations based on the GUP. Then, we observe that the Hawking temperature of the scalar and Dirac particles depend on not only the black hole properties, but also the properties of the tunneling particle, such as angular momentum, energy and mass. And, in this situation, we see that the tunneling probability and the Hawking radiation of the Dirac particle is different from that of the scalar particle.

  1. Mayer control problem with probabilistic uncertainty on initial positions

    NASA Astrophysics Data System (ADS)

    Marigonda, Antonio; Quincampoix, Marc

    2018-03-01

    In this paper we introduce and study an optimal control problem in the Mayer's form in the space of probability measures on Rn endowed with the Wasserstein distance. Our aim is to study optimality conditions when the knowledge of the initial state and velocity is subject to some uncertainty, which are modeled by a probability measure on Rd and by a vector-valued measure on Rd, respectively. We provide a characterization of the value function of such a problem as unique solution of an Hamilton-Jacobi-Bellman equation in the space of measures in a suitable viscosity sense. Some applications to a pursuit-evasion game with uncertainty in the state space is also discussed, proving the existence of a value for the game.

  2. Synthesis of a controller for stabilizing the motion of a rigid body about a fixed point

    NASA Astrophysics Data System (ADS)

    Zabolotnov, Yu. M.; Lobanov, A. A.

    2017-05-01

    A method for the approximate design of an optimal controller for stabilizing the motion of a rigid body about a fixed point is considered. It is assumed that rigid body motion is nearly the motion in the classical Lagrange case. The method is based on the common use of the Bellman dynamic programming principle and the averagingmethod. The latter is used to solve theHamilton-Jacobi-Bellman equation approximately, which permits synthesizing the controller. The proposed method for controller design can be used in many problems close to the problem of motion of the Lagrange top (the motion of a rigid body in the atmosphere, the motion of a rigid body fastened to a cable in deployment of the orbital cable system, etc.).

  3. Adaptive near-optimal neuro controller for continuous-time nonaffine nonlinear systems with constrained input.

    PubMed

    Esfandiari, Kasra; Abdollahi, Farzaneh; Talebi, Heidar Ali

    2017-09-01

    In this paper, an identifier-critic structure is introduced to find an online near-optimal controller for continuous-time nonaffine nonlinear systems having saturated control signal. By employing two Neural Networks (NNs), the solution of Hamilton-Jacobi-Bellman (HJB) equation associated with the cost function is derived without requiring a priori knowledge about system dynamics. Weights of the identifier and critic NNs are tuned online and simultaneously such that unknown terms are approximated accurately and the control signal is kept between the saturation bounds. The convergence of NNs' weights, identification error, and system states is guaranteed using Lyapunov's direct method. Finally, simulation results are performed on two nonlinear systems to confirm the effectiveness of the proposed control strategy. Copyright © 2017 Elsevier Ltd. All rights reserved.

  4. Neural network robust tracking control with adaptive critic framework for uncertain nonlinear systems.

    PubMed

    Wang, Ding; Liu, Derong; Zhang, Yun; Li, Hongyi

    2018-01-01

    In this paper, we aim to tackle the neural robust tracking control problem for a class of nonlinear systems using the adaptive critic technique. The main contribution is that a neural-network-based robust tracking control scheme is established for nonlinear systems involving matched uncertainties. The augmented system considering the tracking error and the reference trajectory is formulated and then addressed under adaptive critic optimal control formulation, where the initial stabilizing controller is not needed. The approximate control law is derived via solving the Hamilton-Jacobi-Bellman equation related to the nominal augmented system, followed by closed-loop stability analysis. The robust tracking control performance is guaranteed theoretically via Lyapunov approach and also verified through simulation illustration. Copyright © 2017 Elsevier Ltd. All rights reserved.

  5. On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics

    NASA Astrophysics Data System (ADS)

    Motsepa, Tanki; Masood Khalique, Chaudry

    2018-05-01

    In this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.

  6. Extension of the Schrodinger equation

    NASA Astrophysics Data System (ADS)

    Somsikov, Vyacheslav

    2017-03-01

    Extension of the Schrodinger equation is submitted by removing its limitations appearing due to the limitations of the formalism of Hamilton, based on which this equation was obtained. For this purpose the problems of quantum mechanics arising from the limitations of classical mechanics are discussed. These limitations, in particular, preclude the use of the Schrodinger equation to describe the time symmetry violation. The extension of the Schrodinger equation is realized based on the principle of duality symmetry. According to this principle the dynamics of the systems is determined by the symmetry of the system and by the symmetry of the space. The extension of the Schrodinger equation was obtained from the dual expression of energy, represented in operator form. For this purpose the independent micro - and macro-variables that determine respectively the dynamics of quantum particle system relative to its center of mass and the movement of the center of mass in space are used. The solution of the extended Schrodinger equation for the system near equilibrium is submitted. The main advantage of the extended Schrodinger equation is that it is applicable to describe the interaction and evolution of quantum systems in inhomogeneous field of external forces.

  7. Fisher's method of scoring in statistical image reconstruction: comparison of Jacobi and Gauss-Seidel iterative schemes.

    PubMed

    Hudson, H M; Ma, J; Green, P

    1994-01-01

    Many algorithms for medical image reconstruction adopt versions of the expectation-maximization (EM) algorithm. In this approach, parameter estimates are obtained which maximize a complete data likelihood or penalized likelihood, in each iteration. Implicitly (and sometimes explicitly) penalized algorithms require smoothing of the current reconstruction in the image domain as part of their iteration scheme. In this paper, we discuss alternatives to EM which adapt Fisher's method of scoring (FS) and other methods for direct maximization of the incomplete data likelihood. Jacobi and Gauss-Seidel methods for non-linear optimization provide efficient algorithms applying FS in tomography. One approach uses smoothed projection data in its iterations. We investigate the convergence of Jacobi and Gauss-Seidel algorithms with clinical tomographic projection data.

  8. Hamilton County: A Rural School District Profile.

    ERIC Educational Resources Information Center

    Harned, Catherine

    Using state education agency, census, industry employment and occupational information data, this paper provides a detailed picture of a rural school district in Southern Illinois. Mining and agriculture are the major industries in Hamilton County. The major mining employer closed in February 1988, and the drought of 1988 is likely to adversely…

  9. Gradient estimates on the weighted p-Laplace heat equation

    NASA Astrophysics Data System (ADS)

    Wang, Lin Feng

    2018-01-01

    In this paper, by a regularization process we derive new gradient estimates for positive solutions to the weighted p-Laplace heat equation when the m-Bakry-Émery curvature is bounded from below by -K for some constant K ≥ 0. When the potential function is constant, which reduce to the gradient estimate established by Ni and Kotschwar for positive solutions to the p-Laplace heat equation on closed manifolds with nonnegative Ricci curvature if K ↘ 0, and reduce to the Davies, Hamilton and Li-Xu's gradient estimates for positive solutions to the heat equation on closed manifolds with Ricci curvature bounded from below if p = 2.

  10. A Spectral Algorithm for Solving the Relativistic Vlasov-Maxwell Equations

    NASA Technical Reports Server (NTRS)

    Shebalin, John V.

    2001-01-01

    A spectral method algorithm is developed for the numerical solution of the full six-dimensional Vlasov-Maxwell system of equations. Here, the focus is on the electron distribution function, with positive ions providing a constant background. The algorithm consists of a Jacobi polynomial-spherical harmonic formulation in velocity space and a trigonometric formulation in position space. A transform procedure is used to evaluate nonlinear terms. The algorithm is suitable for performing moderate resolution simulations on currently available supercomputers for both scientific and engineering applications.

  11. Optimal Low-Thrust Limited-Power Transfers between Arbitrary Elliptic Coplanar Orbits

    NASA Technical Reports Server (NTRS)

    daSilvaFernandes, Sandro; dasChagasCarvalho, Francisco

    2007-01-01

    In this work, a complete first order analytical solution, which includes the short periodic terms, for the problem of optimal low-thrust limited-power transfers between arbitrary elliptic coplanar orbits in a Newtonian central gravity field is obtained through Hamilton-Jacobi theory and a perturbation method based on Lie series.

  12. The genus Ivalia Jacoby 1887 (Coleoptera: Chrysomelidae: Galerucinae: Alticini) of the mount Kinabalu, Sabah, Malaysia

    USDA-ARS?s Scientific Manuscript database

    The following new species of Ivalia Jacoby 1887 are described from the mount Kinabalu (Sabah, Malaysia): I. besar, I. biasa, I. fulvomaculata, I. haruka, I. marginata, I. minutissima, I. nigrofasciata, I. pseudostriolata, I. rubrorbiculata, I. striolata. Chabria kinabalensis Bryant 1938 is transferr...

  13. Efficient solution for finding Hamilton cycles in undirected graphs.

    PubMed

    Alhalabi, Wadee; Kitanneh, Omar; Alharbi, Amira; Balfakih, Zain; Sarirete, Akila

    2016-01-01

    The Hamilton cycle problem is closely related to a series of famous problems and puzzles (traveling salesman problem, Icosian game) and, due to the fact that it is NP-complete, it was extensively studied with different algorithms to solve it. The most efficient algorithm is not known. In this paper, a necessary condition for an arbitrary un-directed graph to have Hamilton cycle is proposed. Based on this condition, a mathematical solution for this problem is developed and several proofs and an algorithmic approach are introduced. The algorithm is successfully implemented on many Hamiltonian and non-Hamiltonian graphs. This provides a new effective approach to solve a problem that is fundamental in graph theory and can influence the manner in which the existing applications are used and improved.

  14. 'From Man to Bacteria': W.D. Hamilton, the theory of inclusive fitness, and the post-war social order.

    PubMed

    Swenson, Sarah A

    2015-02-01

    W.D. Hamilton's theory of inclusive fitness aimed to define the evolved limits of altruism with mathematical precision. Although it was meant to apply universally, it has been almost irretrievably entwined with the particular case of social insects that featured in his famous 1964 papers. The assumption that social insects were central to Hamilton's early work contradicts material in his rich personal archive. In fact, careful study of Hamilton's notes, letters, diaries, and early essays indicates the extent to which he had humans in mind when he decided altruism was a topic worthy of biological inquiry. For this reason, this article reconsiders the role of extra-scientific factors in Hamilton's early theorizing. In doing so, it offers an alternative perspective as to why Hamilton saw self-sacrifice to be an important subject. Although the traditional narrative prioritizes his distaste for benefit-of-the-species explanations as a motivating factor behind his foundational work, I argue that greater attention ought to be given to Hamilton's hope that science could be used to address social ills. By reconsidering the meaning Hamilton intended inclusive fitness to have, we see that while he was no political ideologue, the socio-political relevance of his theory was nevertheless integral to its development. Copyright © 2015 Elsevier Ltd. All rights reserved.

  15. Neural-network-based online HJB solution for optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems.

    PubMed

    Liu, Derong; Wang, Ding; Wang, Fei-Yue; Li, Hongliang; Yang, Xiong

    2014-12-01

    In this paper, the infinite horizon optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems is investigated using neural-network-based online solution of Hamilton-Jacobi-Bellman (HJB) equation. By establishing an appropriate bounded function and defining a modified cost function, the optimal robust guaranteed cost control problem is transformed into an optimal control problem. It can be observed that the optimal cost function of the nominal system is nothing but the optimal guaranteed cost of the original uncertain system. A critic neural network is constructed to facilitate the solution of the modified HJB equation corresponding to the nominal system. More importantly, an additional stabilizing term is introduced for helping to verify the stability, which reinforces the updating process of the weight vector and reduces the requirement of an initial stabilizing control. The uniform ultimate boundedness of the closed-loop system is analyzed by using the Lyapunov approach as well. Two simulation examples are provided to verify the effectiveness of the present control approach.

  16. Infinite horizon problems on stratifiable state-constraints sets

    NASA Astrophysics Data System (ADS)

    Hermosilla, C.; Zidani, H.

    2015-02-01

    This paper deals with a state-constrained control problem. It is well known that, unless some compatibility condition between constraints and dynamics holds, the Value Function has not enough regularity, or can fail to be the unique constrained viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. Here, we consider the case of a set of constraints having a stratified structure. Under this circumstance, the interior of this set may be empty or disconnected, and the admissible trajectories may have the only option to stay on the boundary without possible approximation in the interior of the constraints. In such situations, the classical pointing qualification hypothesis is not relevant. The discontinuous Value Function is then characterized by means of a system of HJB equations on each stratum that composes the state-constraints. This result is obtained under a local controllability assumption which is required only on the strata where some chattering phenomena could occur.

  17. Bohmian Photonics for Independent Control of the Phase and Amplitude of Waves

    NASA Astrophysics Data System (ADS)

    Yu, Sunkyu; Piao, Xianji; Park, Namkyoo

    2018-05-01

    The de Broglie-Bohm theory is one of the nonstandard interpretations of quantum phenomena that focuses on reintroducing definite positions of particles, in contrast to the indeterminism of the Copenhagen interpretation. In spite of intense debate on its measurement and nonlocality, the de Broglie-Bohm theory based on the reformulation of the Schrödinger equation allows for the description of quantum phenomena as deterministic trajectories embodied in the modified Hamilton-Jacobi mechanics. Here, we apply the Bohmian reformulation to Maxwell's equations to achieve the independent manipulation of optical phase evolution and energy confinement. After establishing the deterministic design method based on the Bohmian approach, we investigate the condition of optical materials enabling scattering-free light with bounded or random phase evolutions. We also demonstrate a unique form of optical confinement and annihilation that preserves the phase information of incident light. Our separate tailoring of wave information extends the notion and range of artificial materials.

  18. Problems of Mathematical Finance by Stochastic Control Methods

    NASA Astrophysics Data System (ADS)

    Stettner, Łukasz

    The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.

  19. Entanglement in Quantum-Classical Hybrid

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    2011-01-01

    It is noted that the phenomenon of entanglement is not a prerogative of quantum systems, but also occurs in other, non-classical systems such as quantum-classical hybrids, and covers the concept of entanglement as a special type of global constraint imposed upon a broad class of dynamical systems. Application of hybrid systems for physics of life, as well as for quantum-inspired computing, has been outlined. In representing the Schroedinger equation in the Madelung form, there is feedback from the Liouville equation to the Hamilton-Jacobi equation in the form of the quantum potential. Preserving the same topology, the innovators replaced the quantum potential with other types of feedback, and investigated the property of these hybrid systems. A function of probability density has been introduced. Non-locality associated with a global geometrical constraint that leads to an entanglement effect was demonstrated. Despite such a quantum like characteristic, the hybrid can be of classical scale and all the measurements can be performed classically. This new emergence of entanglement sheds light on the concept of non-locality in physics.

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

    PubMed

    Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

    2018-04-01

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

  1. Online Solution of Two-Player Zero-Sum Games for Continuous-Time Nonlinear Systems With Completely Unknown Dynamics.

    PubMed

    Fu, Yue; Chai, Tianyou

    2016-12-01

    Regarding two-player zero-sum games of continuous-time nonlinear systems with completely unknown dynamics, this paper presents an online adaptive algorithm for learning the Nash equilibrium solution, i.e., the optimal policy pair. First, for known systems, the simultaneous policy updating algorithm (SPUA) is reviewed. A new analytical method to prove the convergence is presented. Then, based on the SPUA, without using a priori knowledge of any system dynamics, an online algorithm is proposed to simultaneously learn in real time either the minimal nonnegative solution of the Hamilton-Jacobi-Isaacs (HJI) equation or the generalized algebraic Riccati equation for linear systems as a special case, along with the optimal policy pair. The approximate solution to the HJI equation and the admissible policy pair is reexpressed by the approximation theorem. The unknown constants or weights of each are identified simultaneously by resorting to the recursive least square method. The convergence of the online algorithm to the optimal solutions is provided. A practical online algorithm is also developed. Simulation results illustrate the effectiveness of the proposed method.

  2. A multi-domain spectral method for time-fractional differential equations

    NASA Astrophysics Data System (ADS)

    Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

    2015-07-01

    This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

  3. Many Faces, Many Voices: Multicultural Literary Experiences for Youth. The Virginia Hamilton Conference (Kent, Ohio).

    ERIC Educational Resources Information Center

    Manna, Anthony L., Ed.; Brodie, Carolyn S., Ed.

    This volume contains keynote and workshop presentations from several Virginia Hamilton Conferences on multicultural literature for children and young people. The papers and speeches are as follows: (1) "A Toiler, A Teller" (Virginia Hamilton); (2) "The Next America" (Arnold Adoff); (3) "The Magic of Imagining: Transaction…

  4. Logical inference approach to relativistic quantum mechanics: Derivation of the Klein–Gordon equation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Donker, H.C., E-mail: h.donker@science.ru.nl; Katsnelson, M.I.; De Raedt, H.

    2016-09-15

    The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein–Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space–time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds. - Highlights: • Logical inference applied to relativistic, massive, charged, and spinless particle experiments leads to the Klein–Gordon equation. • The relativistic Hamilton–Jacobi is scrutinized by employing a field description formore » the four-velocity. • Logical inference allows analysis of experiments with uncertainty in detection events and experimental conditions.« less

  5. The North American light rail experience : insights for Hamilton.

    DOT National Transportation Integrated Search

    2012-04-01

    This report provides a high level overview of the North American Light Rail Experience with the goal of : providing insights for Hamilton, Ontario. Light rail transit (LRT) is a term that emerged at the : Transportation Research Boards first confe...

  6. A least-squares finite element method for 3D incompressible Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Jiang, Bo-Nan; Lin, T. L.; Hou, Lin-Jun; Povinelli, Louis A.

    1993-01-01

    The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.

  7. 75 FR 24938 - City of Hamilton, Ohio American Municipal Power, Inc.; Notice of Application for Transfer of...

    Federal Register 2010, 2011, 2012, 2013, 2014

    2010-05-06

    ...) and American Municipal Power, Inc. (AMP) filed an application for a partial transfer of license of the... to Hamilton and AMP. Applicants' Contacts: City of Hamilton--Mr. Mark Brandenburger, City Manager...

  8. Optical soliton solutions, periodic wave solutions and complexitons of the cubic Schrödinger equation with a bounded potential

    NASA Astrophysics Data System (ADS)

    Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Zou, Li

    2018-01-01

    In this paper, we consider the cubic Schrödinger equation with a bounded potential, which describes the propagation properties of optical soliton solutions. By employing an ansatz method, we precisely derive the bright and dark soliton solutions of the equation. Moreover, we obtain three classes of analytic periodic wave solutions expressed in terms of the Jacobi's elliptic functions including cn ,sn and dn functions. Finally, by using a tanh function method, its complexitons solutions are derived in a very natural way. It is hoped that our results can enrich the nonlinear dynamical behaviors of the cubic Schrödinger equation with a bounded potential.

  9. Portfolio Optimization with Stochastic Dividends and Stochastic Volatility

    ERIC Educational Resources Information Center

    Varga, Katherine Yvonne

    2015-01-01

    We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…

  10. Can noncommutative effects account for the present speed up of the cosmic expansion?

    NASA Astrophysics Data System (ADS)

    Obregon, Octavio; Quiros, Israel

    2011-08-01

    In this paper we investigate to which extent noncommutativity, an intrinsically quantum property, may influence the Friedmann-Robertson-Walker cosmological dynamics at late times/large scales. To our purpose it will be enough to explore the asymptotic properties of the cosmological model in the phase space. Our recipe to build noncommutativity into our model is based in the approach of Ref. and can be summarized in the following steps: i) the Hamiltonian is derived from the Einstein-Hilbert action (plus a self-interacting scalar field action) for a Friedmann-Robertson-Walker space-time with flat spatial sections, ii) canonical quantization recipe is applied, i.e., the mini-superspace variables are promoted to operators, and the WDW equation is written in terms of these variables, iii) noncommutativity in the mini-superspace is achieved through the replacement of the standard product of functions by the Moyal star product in the WDW equation, and, finally, iv) semiclassical cosmological equations are obtained by means of the WKB approximation applied to the (equivalent) modified Hamilton-Jacobi equation. We demonstrate, indeed, that noncommutative effects of the kind considered here can be those responsible for the present speed up of the cosmic expansion.

  11. Off-policy reinforcement learning for H∞ control design.

    PubMed

    Luo, Biao; Wu, Huai-Ning; Huang, Tingwen

    2015-01-01

    The H∞ control design problem is considered for nonlinear systems with unknown internal system model. It is known that the nonlinear H∞ control problem can be transformed into solving the so-called Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that is generally impossible to be solved analytically. Even worse, model-based approaches cannot be used for approximately solving HJI equation, when the accurate system model is unavailable or costly to obtain in practice. To overcome these difficulties, an off-policy reinforcement leaning (RL) method is introduced to learn the solution of HJI equation from real system data instead of mathematical system model, and its convergence is proved. In the off-policy RL method, the system data can be generated with arbitrary policies rather than the evaluating policy, which is extremely important and promising for practical systems. For implementation purpose, a neural network (NN)-based actor-critic structure is employed and a least-square NN weight update algorithm is derived based on the method of weighted residuals. Finally, the developed NN-based off-policy RL method is tested on a linear F16 aircraft plant, and further applied to a rotational/translational actuator system.

  12. Real-time approximate optimal guidance laws for the advanced launch system

    NASA Technical Reports Server (NTRS)

    Speyer, Jason L.; Feeley, Timothy; Hull, David G.

    1989-01-01

    An approach to optimal ascent guidance for a launch vehicle is developed using an expansion technique. The problem is to maximize the payload put into orbit subject to the equations of motion of a rocket over a rotating spherical earth. It is assumed that the thrust and gravitational forces dominate over the aerodynamic forces. It is shown that these forces can be separated by a small parameter epsilon, where epsilon is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in a series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The zeroth-order problem is that of putting maximum payload into orbit subject to the equations of motion of a rocket in a vacuum over a flat earth. The neglected inertial and aerodynamic terms are included in higher order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only quadrature integrations. These quadrature integrations can be performed rapidly, so that real-time approximate optimization can be used to construct the launch guidance law.

  13. Aeroelastic equations of motion of a Darrieus vertical-axis wind-turbine blade

    NASA Technical Reports Server (NTRS)

    Kaza, K. R. V.; Kvaternik, R. G.

    1979-01-01

    The second-degree nonlinear aeroelastic equations of motion for a slender, flexible, nonuniform, Darrieus vertical-axis wind turbine blade which is undergoing combined flatwise bending, edgewise bending, torsion, and extension are developed using Hamilton's principle. The blade aerodynamic loading is obtained from strip theory based on a quasi-steady approximation of two-dimensional incompressible unsteady airfoil theory. The derivation of the equations has its basis in the geometric nonlinear theory of elasticity and the resulting equations are consistent with the small deformation approximation in which the elongations and shears are negligible compared to unity. These equations are suitable for studying vibrations, static and dynamic aeroelastic instabilities, and dynamic response. Several possible methods of solution of the equations, which have periodic coefficients, are discussed.

  14. Durand Neighbourhood Heritage Inventory: Toward a Digital Citywide Survey Approach to Heritage Planning in Hamilton

    NASA Astrophysics Data System (ADS)

    Angel, V.; Garvey, A.; Sydor, M.

    2017-08-01

    In the face of changing economies and patterns of development, the definition of heritage is diversifying, and the role of inventories in local heritage planning is coming to the fore. The Durand neighbourhood is a layered and complex area located in inner-city Hamilton, Ontario, Canada, and the second subject area in a set of pilot inventory studies to develop a new city-wide inventory strategy for the City of Hamilton,. This paper presents an innovative digital workflow developed to undertake the Durand Built Heritage Inventory project. An online database was developed to be at the centre of all processes, including digital documentation, record management, analysis and variable outputs. Digital tools were employed for survey work in the field and analytical work in the office, resulting in a GIS-based dataset that can be integrated into Hamilton's larger municipal planning system. Together with digital mapping and digitized historical resources, the Durand database has been leveraged to produce both digital and static outputs to shape recommendations for the protection of Hamilton's heritage resources.

  15. Spacetime encodings. III. Second order Killing tensors

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Brink, Jeandrew

    2010-01-15

    This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing tensor. The derivation of the spacetimes presented in this paper borrows from ideas about dynamical systems, and illustrates concepts that can be generalized to higher-order Killing tensors. The relationship between the components of the Killing equations and metric functions are given explicitly. The origin of the four separable coordinate systems found by Carter is explained and classified in terms of the analytic structure associated with the Killing equations. A geometric picture ofmore » what the orbital invariants may represent is built. Requiring that a SAV spacetime admits a second-order Killing tensor is very restrictive, selecting very few candidates from the group of all possible SAV spacetimes. This restriction arises due to the fact that the consistency conditions associated with the Killing equations require that the field variables obey a second-order differential equation, as opposed to a fourth-order differential equation that imposes the weaker condition that the spacetime be SAV. This paper introduces ideas that could lead to the explicit computation of more general orbital invariants in the form of higher-order Killing tensors.« less

  16. Nine formulations of quantum mechanics

    NASA Astrophysics Data System (ADS)

    Styer, Daniel F.; Balkin, Miranda S.; Becker, Kathryn M.; Burns, Matthew R.; Dudley, Christopher E.; Forth, Scott T.; Gaumer, Jeremy S.; Kramer, Mark A.; Oertel, David C.; Park, Leonard H.; Rinkoski, Marie T.; Smith, Clait T.; Wotherspoon, Timothy D.

    2002-03-01

    Nine formulations of nonrelativistic quantum mechanics are reviewed. These are the wavefunction, matrix, path integral, phase space, density matrix, second quantization, variational, pilot wave, and Hamilton-Jacobi formulations. Also mentioned are the many-worlds and transactional interpretations. The various formulations differ dramatically in mathematical and conceptual overview, yet each one makes identical predictions for all experimental results.

  17. Fermionic Tunneling Effect and Hawking Radiation in a Non Commutative FRW Universe

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bouhalouf, H.; Aissaoui, H.; Mebarki, N.

    2010-10-31

    The formalism of a non commutative gauge gravity is applied to an FRW universe and the corresponding modified metric, veirbein and spin connection components are obtained. Moreover, using the Hamilton-Jacobi method and as a pure space-time deformation effect, the NCG Hawking radiation via a fermionic tunneling transition through the dynamical NCG horizon is also studied.

  18. Recursion Operators and Tri-Hamiltonian Structure of the First Heavenly Equation of Plebański

    NASA Astrophysics Data System (ADS)

    Sheftel, Mikhail; Yazıcı, Devrim

    2016-09-01

    We present first heavenly equation of Plebański in a two-component evolutionary form and obtain Lagrangian and Hamiltonian representations of this system. We study all point symmetries of the two-component system and, using the inverse Noether theorem in the Hamiltonian form, obtain all the integrals of motion corresponding to each variational (Noether) symmetry. We derive two linearly independent recursion operators for symmetries of this system related by a discrete symmetry of both the two-component system and its symmetry condition. Acting by these operators on the first Hamiltonian operator J_0 we obtain second and third Hamiltonian operators. However, we were not able to find Hamiltonian densities corresponding to the latter two operators. Therefore, we construct two recursion operators, which are either even or odd, respectively, under the above-mentioned discrete symmetry. Acting with them on J_0, we generate another two Hamiltonian operators J_+ and J_- and find the corresponding Hamiltonian densities, thus obtaining second and third Hamiltonian representations for the first heavenly equation in a two-component form. Using P. Olver's theory of the functional multi-vectors, we check that the linear combination of J_0, J_+ and J_- with arbitrary constant coefficients satisfies Jacobi identities. Since their skew symmetry is obvious, these three operators are compatible Hamiltonian operators and hence we obtain a tri-Hamiltonian representation of the first heavenly equation. Our well-founded conjecture applied here is that P. Olver's method works fine for nonlocal operators and our proof of the Jacobi identities and bi-Hamiltonian structures crucially depends on the validity of this conjecture.

  19. Superposition of elliptic functions as solutions for a large number of nonlinear equations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Khare, Avinash; Saxena, Avadh

    2014-03-15

    For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions cn(x, m) and dn(x, m) with modulus m, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schrödinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schrödinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schrödinger equation, λϕ{sup 4}, the discrete MKdV as well asmore » for several coupled field equations. Further, for a large number of nonlinear equations, we show that whenever a nonlinear equation admits a periodic solution in terms of dn{sup 2}(x, m), it also admits solutions in terms of dn {sup 2}(x,m)±√(m) cn (x,m) dn (x,m), even though cn(x, m)dn(x, m) is not a solution of these nonlinear equations. Finally, we also obtain superposed solutions of various forms for several coupled nonlinear equations.« less

  20. The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices

    NASA Astrophysics Data System (ADS)

    Dehghan, Mehdi; Hajarian, Masoud

    2012-08-01

    A matrix P is called a symmetric orthogonal if P = P T = P -1. A matrix X is said to be a generalised bisymmetric with respect to P if X = X T = PXP. It is obvious that any symmetric matrix is also a generalised bisymmetric matrix with respect to I (identity matrix). By extending the idea of the Jacobi and the Gauss-Seidel iterations, this article proposes two new iterative methods, respectively, for computing the generalised bisymmetric (containing symmetric solution as a special case) and skew-symmetric solutions of the generalised Sylvester matrix equation ? (including Sylvester and Lyapunov matrix equations as special cases) which is encountered in many systems and control applications. When the generalised Sylvester matrix equation has a unique generalised bisymmetric (skew-symmetric) solution, the first (second) iterative method converges to the generalised bisymmetric (skew-symmetric) solution of this matrix equation for any initial generalised bisymmetric (skew-symmetric) matrix. Finally, some numerical results are given to illustrate the effect of the theoretical results.

  1. Perturbations of Jacobi polynomials and piecewise hypergeometric orthogonal systems

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Neretin, Yu A

    2006-12-31

    A family of non-complete orthogonal systems of functions on the ray [0,{infinity}] depending on three real parameters {alpha}, {beta}, {theta} is constructed. The elements of this system are piecewise hypergeometric functions with singularity at x=1. For {theta}=0 these functions vanish on [1,{infinity}) and the system is reduced to the Jacobi polynomials P{sub n}{sup {alpha}}{sup ,{beta}} on the interval [0,1]. In the general case the functions constructed can be regarded as an interpretation of the expressions P{sub n+{theta}}{sup {alpha}}{sup ,{beta}}. They are eigenfunctions of an exotic Sturm-Liouville boundary-value problem for the hypergeometric differential operator. The spectral measure for this problem ismore » found.« less

  2. [Correlations between Beck's suicidal ideation scale, suicidal risk assessment scale RSD and Hamilton's depression rating scale].

    PubMed

    Ducher, J-L; Dalery, J

    2008-04-01

    Most of the people who will attempt suicide, talk about it beforehand. Therefore, recognition of suicidal risk is not absolutely impossible. Beck's suicidal ideation scale and Ducher's suicidal risk assessment scale (RSD) are common tools to help practicians in this way. These scales and the Hamilton's depression scale were included in an international multicentric, phase IV, double-blind study, according to two parallel groups who had been administered a fixed dose of fluvoxamin or fluoxetin for six weeks. This allowed examination of the correlations between these scales and the relations, which could possibly exist between suicidal risk, depression and anxiety. (a) Relationships between the Beck's suicidal ideation scale, the suicidal risk assessment scale RSD and Hamilton's depression before treatment. Before treatment, the analysis was conducted with 108 male and female depressive outpatients, aged 18 or over. Results revealed a significant positive correlation (with a Pearson's correlation coefficient r equal to 0.69 and risk p<0.0001) between Beck's suicidal ideation scale and the suicidal risk assessment scale RSD. These scales correlate less consistently with Hamilton's depression (Beck/Hamilton's depression: r=0.34; p=0.0004-RSD/Hamilton's depression: r=0.35; p=0.0002). We observed that the clinical anxiety scale by Snaith is also strongly correlated to these two suicidal risk assessment scales (Beck/CAS: r=0.48; p<0.0001-RSD/CAS: r=0.35; p=0.0005). Besides, the item "suicide" of Hamilton's depression scale accounts for more than a third of the variability of Beck's suicidal ideation scale and the suicidal risk assessment scale RSD. According to these results, the suicidal risk evaluated by these two scales seems to be significantly correlated with anxiety as much as with depression. On the other hand, the Clinical Global Impression is fairly significantly correlated with Beck's suicidal ideation scale (r=0.22; p=0.02), unlike the suicidal risk assessment

  3. Finite-time H∞ filtering for non-linear stochastic systems

    NASA Astrophysics Data System (ADS)

    Hou, Mingzhe; Deng, Zongquan; Duan, Guangren

    2016-09-01

    This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

  4. Policy Iteration for $H_\\infty $ Optimal Control of Polynomial Nonlinear Systems via Sum of Squares Programming.

    PubMed

    Zhu, Yuanheng; Zhao, Dongbin; Yang, Xiong; Zhang, Qichao

    2018-02-01

    Sum of squares (SOS) polynomials have provided a computationally tractable way to deal with inequality constraints appearing in many control problems. It can also act as an approximator in the framework of adaptive dynamic programming. In this paper, an approximate solution to the optimal control of polynomial nonlinear systems is proposed. Under a given attenuation coefficient, the Hamilton-Jacobi-Isaacs equation is relaxed to an optimization problem with a set of inequalities. After applying the policy iteration technique and constraining inequalities to SOS, the optimization problem is divided into a sequence of feasible semidefinite programming problems. With the converged solution, the attenuation coefficient is further minimized to a lower value. After iterations, approximate solutions to the smallest -gain and the associated optimal controller are obtained. Four examples are employed to verify the effectiveness of the proposed algorithm.

  5. Experimental evaluation of HJB optimal controllers for the attitude dynamics of a multirotor aerial vehicle.

    PubMed

    Prado, Igor Afonso Acampora; Pereira, Mateus de Freitas Virgílio; de Castro, Davi Ferreira; Dos Santos, Davi Antônio; Balthazar, Jose Manoel

    2018-06-01

    The present paper is concerned with the design and experimental evaluation of optimal control laws for the nonlinear attitude dynamics of a multirotor aerial vehicle. Three design methods based on Hamilton-Jacobi-Bellman equation are taken into account. The first one is a linear control with guarantee of stability for nonlinear systems. The second and third are a nonlinear suboptimal control techniques. These techniques are based on an optimal control design approach that takes into account the nonlinearities present in the vehicle dynamics. The stability Proof of the closed-loop system is presented. The performance of the control system designed is evaluated via simulations and also via an experimental scheme using the Quanser 3-DOF Hover. The experiments show the effectiveness of the linear control method over the nonlinear strategy. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

  6. Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Cari, C., E-mail: cari@staff.uns.ac.id; Pratiwi, B. N., E-mail: namakubetanurpratiwi@gmail.com

    2016-02-08

    The analytical solution of D-dimensional Dirac equation for hyperbolic tangent potential is investigated using Nikiforov-Uvarov method. In the case of spin symmetry the D dimensional Dirac equation reduces to the D dimensional Schrodinger equation. The D dimensional relativistic energy spectra are obtained from D dimensional relativistic energy eigen value equation by using Mat Lab software. The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi polynomials. The thermodynamically properties of materials are generated from the non-relativistic energy eigen-values in the classical limit. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy.more » The thermal quantities of the system, partition function and specific heat, are expressed in terms of error function and imaginary error function which are numerically calculated using Mat Lab software.« less

  7. 77 FR 27272 - Environmental Impact Statement: Hamilton and Clermont Counties, OH

    Federal Register 2010, 2011, 2012, 2013, 2014

    2012-05-09

    .... In the interim, new information came to light regarding the archaeological resources present in... highway and light rail improvements in the SR 32 corridor between US 50 and IR 275 in Hamilton and...

  8. Notes on the occurrence of Oligonychus milleri (McGregor) and oligonychus ununguis (Jacobi) (Acari: Tetranychidae) in Brazil

    USDA-ARS?s Scientific Manuscript database

    We verified infestation of Oligonychus milleri (McGregor) on plantations of Pinus caribaea (Pinaceae) and of Oligonychus ununguis (Jacobi) on plantations of Eucalyptus urophylla x Eucalyptus grandis (Myrtaceae) in State of Rondônia, Northern region of Brazil. This represents the first record of O. m...

  9. Science, suffrage, and experimentation: Mary Putnam Jacobi and the controversy over vivisection in late nineteenth-century America.

    PubMed

    Bittel, Carla Jean

    2005-01-01

    This article examines the medical activism of the New York physician Mary Putnam Jacobi (1842-1906), to illustrate the problems of gender and science at the center of the vivisection debate in late nineteenth-century America. In the post-Civil War era, individuals both inside and outside the medical community considered vivisection to be a controversial practice. Physicians divided over the value of live animal experimentation, while reformers and activists campaigned against it. Jacobi stepped into the center of the controversy and tried to use her public defense of experimentation to the advantage of women in the medical profession. Her advocacy of vivisection was part of her broader effort to reform medical education, especially at women's institutions. It was also a political strategy aimed at associating women with scientific practices to advance a women's rights agenda. Her work demonstrates how debates over women in medicine and science in medicine, suffrage, and experimentation overlapped at a critical moment of historical transition.

  10. Hamilton's rule, inclusive fitness maximization, and the goal of individual behaviour in symmetric two-player games.

    PubMed

    Okasha, S; Martens, J

    2016-03-01

    Hamilton's original work on inclusive fitness theory assumed additivity of costs and benefits. Recently, it has been argued that an exact version of Hamilton's rule for the spread of a pro-social allele (rb > c) holds under nonadditive pay-offs, so long as the cost and benefit terms are defined as partial regression coefficients rather than pay-off parameters. This article examines whether one of the key components of Hamilton's original theory can be preserved when the rule is generalized to the nonadditive case in this way, namely that evolved organisms will behave as if trying to maximize their inclusive fitness in social encounters. © 2015 European Society For Evolutionary Biology. Journal of Evolutionary Biology © 2015 European Society For Evolutionary Biology.

  11. A Riccati solution for the ideal MHD plasma response with applications to real-time stability control

    NASA Astrophysics Data System (ADS)

    Glasser, Alexander; Kolemen, Egemen; Glasser, A. H.

    2018-03-01

    Active feedback control of ideal MHD stability in a tokamak requires rapid plasma stability analysis. Toward this end, we reformulate the δW stability method with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the generic tokamak ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD matrix Riccati differential equation. Since Riccati equations are prevalent in the control theory literature, such a shift in perspective brings to bear a range of numerical methods that are well-suited to the robust, fast solution of control problems. We discuss the usefulness of Riccati techniques in solving the stiff ordinary differential equations often encountered in ideal MHD stability analyses—for example, in tokamak edge and stellarator physics. We demonstrate the applicability of such methods to an existing 2D ideal MHD stability code—DCON [A. H. Glasser, Phys. Plasmas 23, 072505 (2016)]—enabling its parallel operation in near real-time, with wall-clock time ≪1 s . Such speed may help enable active feedback ideal MHD stability control, especially in tokamak plasmas whose ideal MHD equilibria evolve with inductive timescale τ≳ 1s—as in ITER.

  12. A real-time approximate optimal guidance law for flight in a plane

    NASA Technical Reports Server (NTRS)

    Feeley, Timothy S.; Speyer, Jason L.

    1990-01-01

    A real-time guidance scheme is presented for the problem of maximizing the payload into orbit subject to the equations of motion of a rocket over a nonrotating spherical earth. The flight is constrained to a path in the equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of the problem can be separated into primary and perturbation effects by a small parameter, epsilon, which is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The neglected perturbation terms are included in the higher-order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only integrations which are quadratures. The quadratures can be performed rapidly with emerging computer capability, so that real-time approximate optimization can be used to construct the launch guidance law. The application of this technique to flight in three-dimensions is made apparent from the solution presented.

  13. Moving the Education Needle: A Conversation with Scott Hamilton

    ERIC Educational Resources Information Center

    Jacobs, Joanne

    2014-01-01

    Scott Hamilton is the Forrest Gump of education reform, although with a lot more IQ points and fewer chocolates. He worked for Bill Bennett in the U.S. Department of Education and for Benno Schmidt at the Edison Project. He authorized charter schools in Massachusetts, co-founded the KIPP network, quadrupled the size of Teach For America (TFA), and…

  14. Stochastic dynamic programming illuminates the link between environment, physiology, and evolution.

    PubMed

    Mangel, Marc

    2015-05-01

    I describe how stochastic dynamic programming (SDP), a method for stochastic optimization that evolved from the work of Hamilton and Jacobi on variational problems, allows us to connect the physiological state of organisms, the environment in which they live, and how evolution by natural selection acts on trade-offs that all organisms face. I first derive the two canonical equations of SDP. These are valuable because although they apply to no system in particular, they share commonalities with many systems (as do frictionless springs). After that, I show how we used SDP in insect behavioral ecology. I describe the puzzles that needed to be solved, the SDP equations we used to solve the puzzles, and the experiments that we used to test the predictions of the models. I then briefly describe two other applications of SDP in biology: first, understanding the developmental pathways followed by steelhead trout in California and second skipped spawning by Norwegian cod. In both cases, modeling and empirical work were closely connected. I close with lessons learned and advice for the young mathematical biologists.

  15. Stabilization of a gravel channel by large streamside obstructions and bedrock bends, Jacoby Creek, northwestern California

    Treesearch

    Thomas E. Lisle

    1996-01-01

    Abstract - Jacoby Creek (bed width =12 m; bankfull discharge = 32.6 m 3 /s) contains stationary gravel bars that have forms and positions controlled by numerous large streamside obstructions (bedrock outcrops, large woody debris, and rooted bank projections) and bedrock bends. Bank-projection width and bar volume measured in 104 channel segments 1 bed-width long are...

  16. Nonlinear Aeroelastic Equations of Motion of Twisted, Nonuniform, Flexible Horizontal-Axis Wind Turbine Blades

    NASA Technical Reports Server (NTRS)

    Kaza, K. R. V.

    1980-01-01

    The second-degree nonlinear equations of motion for a flexible, twisted, nonuniform, horizontal axis wind turbine blade were developed using Hamilton's principle. A mathematical ordering scheme which was consistent with the assumption of a slender beam was used to discard some higher-order elastic and inertial terms in the second-degree nonlinear equations. The blade aerodynamic loading which was employed accounted for both wind shear and tower shadow and was obtained from strip theory based on a quasi-steady approximation of two-dimensional, incompressible, unsteady, airfoil theory. The resulting equations had periodic coefficients and were suitable for determining the aeroelastic stability and response of large horizontal-axis wind turbine blades.

  17. A high-order positivity-preserving single-stage single-step method for the ideal magnetohydrodynamic equations

    NASA Astrophysics Data System (ADS)

    Christlieb, Andrew J.; Feng, Xiao; Seal, David C.; Tang, Qi

    2016-07-01

    We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage (i.e., it has no internal stages to store), single-step (i.e., it has no time history that needs to be stored), maintains a discrete divergence-free condition on the magnetic field, and has the capacity to preserve the positivity of the density and pressure. To accomplish this, we use a Taylor discretization of the Picard integral formulation (PIF) of the finite difference WENO method proposed in Christlieb et al. (2015) [23], where the focus is on a high-order discretization of the fluxes (as opposed to the conserved variables). We use the version where fluxes are expanded to third-order accuracy in time, and for the fluid variables space is discretized using the classical fifth-order finite difference WENO discretization. We use constrained transport in order to obtain divergence-free magnetic fields, which means that we simultaneously evolve the magnetohydrodynamic (that has an evolution equation for the magnetic field) and magnetic potential equations alongside each other, and set the magnetic field to be the (discrete) curl of the magnetic potential after each time step. In this work, we compute these derivatives to fourth-order accuracy. In order to retain a single-stage, single-step method, we develop a novel Lax-Wendroff discretization for the evolution of the magnetic potential, where we start with technology used for Hamilton-Jacobi equations in order to construct a non-oscillatory magnetic field. The end result is an algorithm that is similar to our previous work Christlieb et al. (2014) [8], but this time the time stepping is replaced through a Taylor method with the addition of a positivity-preserving limiter. Finally, positivity preservation is realized by introducing a parameterized flux limiter that considers a linear combination of high and low-order numerical fluxes. The choice of the free

  18. A multigrid method for steady Euler equations on unstructured adaptive grids

    NASA Technical Reports Server (NTRS)

    Riemslagh, Kris; Dick, Erik

    1993-01-01

    A flux-difference splitting type algorithm is formulated for the steady Euler equations on unstructured grids. The polynomial flux-difference splitting technique is used. A vertex-centered finite volume method is employed on a triangular mesh. The multigrid method is in defect-correction form. A relaxation procedure with a first order accurate inner iteration and a second-order correction performed only on the finest grid, is used. A multi-stage Jacobi relaxation method is employed as a smoother. Since the grid is unstructured a Jacobi type is chosen. The multi-staging is necessary to provide sufficient smoothing properties. The domain is discretized using a Delaunay triangular mesh generator. Three grids with more or less uniform distribution of nodes but with different resolution are generated by successive refinement of the coarsest grid. Nodes of coarser grids appear in the finer grids. The multigrid method is started on these grids. As soon as the residual drops below a threshold value, an adaptive refinement is started. The solution on the adaptively refined grid is accelerated by a multigrid procedure. The coarser multigrid grids are generated by successive coarsening through point removement. The adaption cycle is repeated a few times. Results are given for the transonic flow over a NACA-0012 airfoil.

  19. Hamiltonization of Solids of Revolution Through Reduction

    NASA Astrophysics Data System (ADS)

    Balseiro, Paula

    2017-12-01

    In this paper, we study the relation between conserved quantities of nonholonomic systems and the hamiltonization problem employing the geometric methods of Balseiro (Arch Ration Mech Anal 214:453-501, 2014) and Balseiro and Garcia-Naranjo (Arch Ration Mech Anal 205(1):267-310, 2012). We illustrate the theory with classical examples describing the dynamics of solids of revolution rolling without sliding on a plane. In these cases, using the existence of two conserved quantities we obtain, by means of gauge transformations and symmetry reduction, genuine Poisson brackets describing the reduced dynamics.

  20. AdS/CFT and local renormalization group with gauge fields

    NASA Astrophysics Data System (ADS)

    Kikuchi, Ken; Sakai, Tadakatsu

    2016-03-01

    We revisit a study of local renormalization group (RG) with background gauge fields incorporated using the AdS/CFT correspondence. Starting with a (d+1)-dimensional bulk gravity coupled to scalars and gauge fields, we derive a local RG equation from a flow equation by working in the Hamilton-Jacobi formulation of the bulk theory. The Gauss's law constraint associated with gauge symmetry plays an important role. RG flows of the background gauge fields are governed by vector β-functions, and some of their interesting properties are known to follow. We give a systematic rederivation of them on the basis of the flow equation. Fixing an ambiguity of local counterterms in such a manner that is natural from the viewpoint of the flow equation, we determine all the coefficients uniquely appearing in the trace of the stress tensor for d=4. A relation between a choice of schemes and a virial current is discussed. As a consistency check, these are found to satisfy the integrability conditions of local RG transformations. From these results, we are led to a proof of a holographic c-theorem by determining a full family of schemes where a trace anomaly coefficient is related with a holographic c-function.

  1. Solutions of some problems in applied mathematics using MACSYMA

    NASA Technical Reports Server (NTRS)

    Punjabi, Alkesh; Lam, Maria

    1987-01-01

    Various Symbolic Manipulation Programs (SMP) were tested to check the functioning of their commands and suitability under various operating systems. Support systems for SMP were found to be relatively better than the one for MACSYMA. The graphics facilities for MACSYMA do not work as expected under the UNIX operating system. Not all commands for MACSYMA function as described in the manuals. Shape representation is a central issue in computer graphics and computer-aided design. Aside from appearance, there are other application dependent, desirable properties like continuity to certain order, symmetry, axis-independence, and variation-diminishing properties. Several shape representations are studied, which include the Osculatory Method, a Piecewise Cubic Polynomial Method using two different slope estimates, Piecewise Cubic Hermite Form, a method by Harry McLaughlin, and a Piecewise Bezier Method. They are applied to collected physical and chemical data. Relative merits and demerits of these methods are examined. Kinematics of a single link, non-dissipative robot arm is studied using MACSYMA. Lagranian is set-up and Lagrange's equations are derived. From there, Hamiltonian equations of motion are obtained. Equations suggest that bifurcation of solutions can occur, depending upon the value of a single parameter. Using the characteristic function W, the Hamilton-Jacobi equation is derived. It is shown that the H-J equation can be solved in closed form. Analytical solutions to the H-J equation are obtained.

  2. Hawking Radiation from a Spherically Symmetric Static Black Hole

    NASA Astrophysics Data System (ADS)

    Dai, Qian; Liu, Wenbiao

    2007-08-01

    The massive particles’ Hawking radiation from a spherically symmetric static black hole is investigated with Parikh-Wilczek method, Hamilton Jacobi method and Damour Ruffini’s method. When energy conservation is considered, the same result can be concluded that the radiation spectrum is not precisely thermal. The corrected spectrum is consistent to the underlying unitary quantum theory, which can be used to explain the information loss paradox possibly.

  3. On mixed derivatives type high dimensional multi-term fractional partial differential equations approximate solutions

    NASA Astrophysics Data System (ADS)

    Talib, Imran; Belgacem, Fethi Bin Muhammad; Asif, Naseer Ahmad; Khalil, Hammad

    2017-01-01

    In this research article, we derive and analyze an efficient spectral method based on the operational matrices of three dimensional orthogonal Jacobi polynomials to solve numerically the mixed partial derivatives type multi-terms high dimensions generalized class of fractional order partial differential equations. We transform the considered fractional order problem to an easily solvable algebraic equations with the aid of the operational matrices. Being easily solvable, the associated algebraic system leads to finding the solution of the problem. Some test problems are considered to confirm the accuracy and validity of the proposed numerical method. The convergence of the method is ensured by comparing our Matlab software simulations based obtained results with the exact solutions in the literature, yielding negligible errors. Moreover, comparative results discussed in the literature are extended and improved in this study.

  4. High-accuracy power series solutions with arbitrarily large radius of convergence for the fractional nonlinear Schrödinger-type equations

    NASA Astrophysics Data System (ADS)

    Khawaja, U. Al; Al-Refai, M.; Shchedrin, Gavriil; Carr, Lincoln D.

    2018-06-01

    Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These effective descriptions thus appear commonly in physical and mathematical modeling. We present a new series method providing systematic controlled accuracy for solutions of fractional nonlinear differential equations, including the fractional nonlinear Schrödinger equation and the fractional nonlinear diffusion equation. The method relies on spatially iterative use of power series expansions. Our approach permits an arbitrarily large radius of convergence and thus solves the typical divergence problem endemic to power series approaches. In the specific case of the fractional nonlinear Schrödinger equation we find fractional generalizations of cnoidal waves of Jacobi elliptic functions as well as a fractional bright soliton. For the fractional nonlinear diffusion equation we find the combination of fractional and nonlinear effects results in a more strongly localized solution which nevertheless still exhibits power law tails, albeit at a much lower density.

  5. The Montgomery Äsberg and the Hamilton Ratings of Depression

    PubMed Central

    Carmody, Thomas; Rush, A. John; Bernstein, Ira; Warden, Diane; Brannan, Stephen; Burnham, Daniel; Woo, Ada; Trivedi, Madhukar

    2007-01-01

    The 17-item Hamilton Rating Scale for Depression (HRSD17) and the Montgomery Äsberg Depression Rating Scale (MADRS) are two widely used clinicianrated symptom scales. A 6-item version of the HRSD (HRSD6) was created by Bech to address the psychometric limitations of the HRSD17. The psychometric properties of these measures were compared using classical test theory (CTT) and item response theory (IRT) methods. IRT methods were used to equate total scores on any two scales. Data from two distinctly different outpatient studies of nonpsychotic major depression: a 12-month study of highly treatment-resistant patients (n=233) and an 8-week acute phase drug treatment trial (n=985) were used for robustness of results. MADRS and HRSD6 items generally contributed more to the measurement of depression than HRSD17 items as shown by higher item-total correlations and higher IRT slope parameters. The MADRS and HRSD6 were unifactorial while the HRSD17 contained 2 factors. The MADRS showed about twice the precision in estimating depression as either the HRSD17 or HRSD6 for average severity of depression. An HRSD17 of 7 corresponded to an 8 or 9 on the MADRS and 4 on the HRSD6. The MADRS would be superior to the HRSD17 in the conduct of clinical trials. PMID:16769204

  6. The observational constraint on constant-roll inflation

    NASA Astrophysics Data System (ADS)

    Gao, Qing

    2018-07-01

    We discuss the constant-roll inflation with constant ɛ2 and constant \\bar η . By using the method of Bessel function approximation, the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts, and the tensor to scalar ratio are derived up to the first order of ɛ1. The model with constant ɛ2 is ruled out by the observations at the 3σ confidence level, and the model with constant \\bar η is consistent with the observations at the 1σ confidence level. The potential for the model with constant \\bar η is also obtained from the Hamilton-Jacobi equation. Although the observations constrain the constant-roll inflation to be the slow-roll inflation, the n s- r results from the constant-roll inflation are not the same as those from the slow-roll inflation even when \\bar η 0.01.

  7. Optimality of affine control system of several species in competition on a sequential batch reactor

    NASA Astrophysics Data System (ADS)

    Rodríguez, J. C.; Ramírez, H.; Gajardo, P.; Rapaport, A.

    2014-09-01

    In this paper, we analyse the optimality of affine control system of several species in competition for a single substrate on a sequential batch reactor, with the objective being to reach a given (low) level of the substrate. We allow controls to be bounded measurable functions of time plus possible impulses. A suitable modification of the dynamics leads to a slightly different optimal control problem, without impulsive controls, for which we apply different optimality conditions derived from Pontryagin principle and the Hamilton-Jacobi-Bellman equation. We thus characterise the singular trajectories of our problem as the extremal trajectories keeping the substrate at a constant level. We also establish conditions for which an immediate one impulse (IOI) strategy is optimal. Some numerical experiences are then included in order to illustrate our study and show that those conditions are also necessary to ensure the optimality of the IOI strategy.

  8. Reinforcement learning for adaptive optimal control of unknown continuous-time nonlinear systems with input constraints

    NASA Astrophysics Data System (ADS)

    Yang, Xiong; Liu, Derong; Wang, Ding

    2014-03-01

    In this paper, an adaptive reinforcement learning-based solution is developed for the infinite-horizon optimal control problem of constrained-input continuous-time nonlinear systems in the presence of nonlinearities with unknown structures. Two different types of neural networks (NNs) are employed to approximate the Hamilton-Jacobi-Bellman equation. That is, an recurrent NN is constructed to identify the unknown dynamical system, and two feedforward NNs are used as the actor and the critic to approximate the optimal control and the optimal cost, respectively. Based on this framework, the action NN and the critic NN are tuned simultaneously, without the requirement for the knowledge of system drift dynamics. Moreover, by using Lyapunov's direct method, the weights of the action NN and the critic NN are guaranteed to be uniformly ultimately bounded, while keeping the closed-loop system stable. To demonstrate the effectiveness of the present approach, simulation results are illustrated.

  9. Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws

    NASA Technical Reports Server (NTRS)

    Shu, Chi-Wang

    1997-01-01

    In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton- Jacobi equations. ENO and WENO schemes are high order accurate finite difference schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible. ENO and WENO schemes have been quite successful in applications, especially for problems containing both shocks and complicated smooth solution structures, such as compressible turbulence simulations and aeroacoustics. These lecture notes are basically self-contained. It is our hope that with these notes and with the help of the quoted references, the reader can understand the algorithms and code them up for applications.

  10. Hamiltonian modelling of relative motion.

    PubMed

    Kasdin, N Jeremy; Gurfil, Pini

    2004-05-01

    This paper presents a Hamiltonian approach to modelling relative spacecraft motion based on derivation of canonical coordinates for the relative state-space dynamics. The Hamiltonian formulation facilitates the modelling of high-order terms and orbital perturbations while allowing us to obtain closed-form solutions to the relative motion problem. First, the Hamiltonian is partitioned into a linear term and a high-order term. The Hamilton-Jacobi equations are solved for the linear part by separation, and new constants for the relative motions are obtained, they are called epicyclic elements. The influence of higher order terms and perturbations, such as the oblateness of the Earth, are incorporated into the analysis by a variation of parameters procedure. Closed-form solutions for J(2-) and J(4-)invariant orbits and for periodic high-order unperturbed relative motion, in terms of the relative motion elements only, are obtained.

  11. VIEW SOUTH FROM HAMILTON AVENUE BUILDING 25 LEFT; BUILDING 32 ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    VIEW SOUTH FROM HAMILTON AVENUE BUILDING 25 LEFT; BUILDING 32 MACHINE SHOP (1890) LEFT CENTER BUILDING 31 RIGGER'S SHOP (1890) CENTER BUILDING 28 BLACKSMITH SHOP (1885) RIGHT CENTER; BUILDING 27 PATTERN SHOP (1853) RIGHT - John A. Roebling's Sons Company & American Steel & Wire Company, South Broad, Clark, Elmer, Mott & Hudson Streets, Trenton, Mercer County, NJ

  12. Nonlocal Symmetries, Conservation Laws and Interaction Solutions of the Generalised Dispersive Modified Benjamin-Bona-Mahony Equation

    NASA Astrophysics Data System (ADS)

    Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Wang, Xiu-Bin; Zhang, Tian-Tian

    2018-05-01

    We consider the generalised dispersive modified Benjamin-Bona-Mahony equation, which describes an approximation status for long surface wave existed in the non-linear dispersive media. By employing the truncated Painlevé expansion method, we derive its non-local symmetry and Bäcklund transformation. The non-local symmetry is localised by a new variable, which provides the corresponding non-local symmetry group and similarity reductions. Moreover, a direct method can be provided to construct a kind of finite symmetry transformation via the classic Lie point symmetry of the normal prolonged system. Finally, we find that the equation is a consistent Riccati expansion solvable system. With the help of the Jacobi elliptic function, we get its interaction solutions between solitary waves and cnoidal periodic waves.

  13. New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems

    PubMed Central

    Abd-Elhameed, W. M.

    2014-01-01

    This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Chebyshev polynomials are deduced as special cases. Some new reduction formulae for summing some terminating hypergeometric functions of unit argument are also deduced. As an application, and with the aid of the new introduced derivatives formulae, an algorithm for solving special sixth-order boundary value problems are implemented with the aid of applying Galerkin method. A numerical example is presented hoping to ascertain the validity and the applicability of the proposed algorithms. PMID:25386599

  14. Existence and stability of dispersive solutions to the Kadomtsev-Petviashvili equation in the presence of dispersion effect

    NASA Astrophysics Data System (ADS)

    Das, Amiya; Ganguly, Asish

    2017-07-01

    The paper deals with Kadomtsev-Petviashvili (KP) equation in presence of a small dispersion effect. The nature of solutions are examined under the dispersion effect by using Lyapunov function and dynamical system theory. We prove that when dispersion is added to the KP equation, in certain regions, yet there exist bounded traveling wave solutions in the form of solitary waves, periodic and elliptic functions. The general solution of the equation with or without the dispersion effect are obtained in terms of Weirstrass ℘ functions and Jacobi elliptic functions. New form of kink-type solutions are established by exploring a new technique based on factorization method, use of functional transformation and the Abel's first order nonlinear equation. Furthermore, the stability analysis of the dispersive solutions are examined which shows that the traveling wave velocity is a bifurcation parameter which governs between different classes of waves. We use the phase plane analysis and show that at a critical velocity, the solution has a transcritical bifurcation.

  15. Light Rail Transit in Hamilton: Health, Environmental and Economic Impact Analysis

    ERIC Educational Resources Information Center

    Topalovic, P.; Carter, J.; Topalovic, M.; Krantzberg, G.

    2012-01-01

    Hamilton's historical roots as an electric, industrial and transportation-oriented city provide it with a high potential for rapid transit, especially when combined with its growing population, developing economy, redeveloping downtown core and its plans for sustainable growth. This paper explores the health, environmental, social and economic…

  16. Chaos M-ary modulation and demodulation method based on Hamilton oscillator and its application in communication.

    PubMed

    Fu, Yongqing; Li, Xingyuan; Li, Yanan; Yang, Wei; Song, Hailiang

    2013-03-01

    Chaotic communication has aroused general interests in recent years, but its communication effect is not ideal with the restriction of chaos synchronization. In this paper a new chaos M-ary digital modulation and demodulation method is proposed. By using region controllable characteristics of spatiotemporal chaos Hamilton map in phase plane and chaos unique characteristic, which is sensitive to initial value, zone mapping method is proposed. It establishes the map relationship between M-ary digital information and the region of Hamilton map phase plane, thus the M-ary information chaos modulation is realized. In addition, zone partition demodulation method is proposed based on the structure characteristic of Hamilton modulated information, which separates M-ary information from phase trajectory of chaotic Hamilton map, and the theory analysis of zone partition demodulator's boundary range is given. Finally, the communication system based on the two methods is constructed on the personal computer. The simulation shows that in high speed transmission communications and with no chaos synchronization circumstance, the proposed chaotic M-ary modulation and demodulation method has outperformed some conventional M-ary modulation methods, such as quadrature phase shift keying and M-ary pulse amplitude modulation in bit error rate. Besides, it has performance improvement in bandwidth efficiency, transmission efficiency and anti-noise performance, and the system complexity is low and chaos signal is easy to generate.

  17. Data dependence for the amplitude equation of surface waves

    NASA Astrophysics Data System (ADS)

    Secchi, Paolo

    2016-04-01

    We consider the amplitude equation for nonlinear surface wave solutions of hyperbolic conservation laws. This is an asymptotic nonlocal, Hamiltonian evolution equation with quadratic nonlinearity. For example, this equation describes the propagation of nonlinear Rayleigh waves (Hamilton et al. in J Acoust Soc Am 97:891-897, 1995), surface waves on current-vortex sheets in incompressible MHD (Alì and Hunter in Q Appl Math 61(3):451-474, 2003; Alì et al. in Stud Appl Math 108(3):305-321, 2002) and on the incompressible plasma-vacuum interface (Secchi in Q Appl Math 73(4):711-737, 2015). The local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables was shown in Hunter (J Hyperbolic Differ Equ 3(2):247-267, 2006), Secchi (Q Appl Math 73(4):711-737, 2015). In the present paper we prove the continuous dependence in strong norm of solutions on the initial data. This completes the proof of the well-posedness of the problem in the classical sense of Hadamard.

  18. Perceptions of Quality Life in Hamilton's Neighbourhood Hubs: A Qualitative Analysis

    ERIC Educational Resources Information Center

    Eby, Jeanette; Kitchen, Peter; Williams, Allison

    2012-01-01

    This paper examines perceptions of quality of life in Hamilton, Ontario, Canada from the perspective of residents and key community stakeholders. A series of eight focus groups were conducted. Six sessions were held with residents of neighbourhood "hubs", areas characterized by high levels of poverty. The following themes were…

  19. Air Quality in Hamilton: Who Is Concerned? Perceptions from Three Neighbourhoods

    ERIC Educational Resources Information Center

    Simone, Dylan; Eyles, John; Newbold, K. Bruce; Kitchen, Peter; Williams, Allison

    2012-01-01

    This study investigates the factors influencing perceptions of air quality in the industrial city of Hamilton, Canada. The research employs data collected via a telephone survey of 1,002 adult residents in three neighbourhoods. Perceptions in the neighbourhoods were examined by individual socio-demographic factors (age, gender, marital and…

  20. Parallelized implicit propagators for the finite-difference Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Parker, Jonathan; Taylor, K. T.

    1995-08-01

    We describe the application of block Gauss-Seidel and block Jacobi iterative methods to the design of implicit propagators for finite-difference models of the time-dependent Schrödinger equation. The block-wise iterative methods discussed here are mixed direct-iterative methods for solving simultaneous equations, in the sense that direct methods (e.g. LU decomposition) are used to invert certain block sub-matrices, and iterative methods are used to complete the solution. We describe parallel variants of the basic algorithm that are well suited to the medium- to coarse-grained parallelism of work-station clusters, and MIMD supercomputers, and we show that under a wide range of conditions, fine-grained parallelism of the computation can be achieved. Numerical tests are conducted on a typical one-electron atom Hamiltonian. The methods converge robustly to machine precision (15 significant figures), in some cases in as few as 6 or 7 iterations. The rate of convergence is nearly independent of the finite-difference grid-point separations.

  1. Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ho, Choon-Lin, E-mail: hcl@mail.tku.edu.tw

    2011-04-15

    Research Highlights: > Physical examples involving exceptional orthogonal polynomials. > Exceptional polynomials as deformations of classical orthogonal polynomials. > Exceptional polynomials from Darboux-Crum transformation. - Abstract: An interesting discovery in the last two years in the field of mathematical physics has been the exceptional X{sub l} Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have lowest degree l = 1, 2, and ..., and yet they form complete set with respect to some positive-definite measure. While the mathematical properties of these new X{sub l} polynomials deserve further analysis, it ismore » also of interest to see if they play any role in physical systems. In this paper we indicate some physical models in which these new polynomials appear as the main part of the eigenfunctions. The systems we consider include the Dirac equations coupled minimally and non-minimally with some external fields, and the Fokker-Planck equations. The systems presented here have enlarged the number of exactly solvable physical systems known so far.« less

  2. Preconstruction Biogeochemical Analysis of Mercury in Wetlands Bordering the Hamilton Army Airfield (HAAF) Wetlands Restoration Site. Part 3

    DTIC Science & Technology

    2009-12-01

    ER D C/ EL T R- 09 -2 1 Preconstruction Biogeochemical Analysis of Mercury in Wetlands Bordering the Hamilton Army Airfield (HAAF) Wetlands...Preconstruction Biogeochemical Analysis of Mercury in Wetlands Bordering the Hamilton Army Airfield (HAAF) Wetlands Restoration Site Part 3 Elly P. H... mercury methylation and demethylation, and biogeochemical parameters related to the mercury cycle as measured by both conventional and emerging methods

  3. Hamilton and Hardy for the 21st Century

    PubMed Central

    Ogden, Trevor

    2016-01-01

    Hamilton and Hardy’s Industrial Toxicology is now 80 years old, and the new sixth edition links us with a pioneer era. This is an impressive book, but the usefulness of the hardback version as a reference book is unfortunately limited by its poor index. There is now an ebook version, and for the practitioner on the move this has the great advantages of searchability and portability. However, Wiley ebooks can apparently only be downloaded when first purchased, so their lifetime is limited to that of the device. The Kindle edition should avoid this shortcoming.

  4. Octavia Butler and Virginia Hamilton: Black Women Writers and Science Fiction.

    ERIC Educational Resources Information Center

    Hampton, Gregory Jerome; Brooks, Wanda M.

    2003-01-01

    Notes that African American literature has always had science fiction elements in its focus on narratives of the alienated and marginalized "other." Contends that Octavia Butler and Virginia Hamilton are two African American writers of science fiction who examine the connections between the stories of a culture and the genre of science…

  5. A Survey of Environmental Education in Hamilton County Schools (K-12).

    ERIC Educational Resources Information Center

    Garver, Janice B.

    Environmental education (EE) courses and programs offered in grades K-12 in Hamilton County (Ohio) public, private, and parochial schools were surveyed by means of a questionnaire mailed to 67 district level administrators, principals, and teachers. Questionnaires were returned from 5 private, 4 parochial, and 27 public schools, representing a 57…

  6. High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

    NASA Technical Reports Server (NTRS)

    Shu, Chi-Wang

    2000-01-01

    This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the

  7. Form of the manifestly covariant Lagrangian

    NASA Astrophysics Data System (ADS)

    Johns, Oliver Davis

    1985-10-01

    The preferred form for the manifestly covariant Lagrangian function of a single, charged particle in a given electromagnetic field is the subject of some disagreement in the textbooks. Some authors use a ``homogeneous'' Lagrangian and others use a ``modified'' form in which the covariant Hamiltonian function is made to be nonzero. We argue in favor of the ``homogeneous'' form. We show that the covariant Lagrangian theories can be understood only if one is careful to distinguish quantities evaluated on the varied (in the sense of the calculus of variations) world lines from quantities evaluated on the unvaried world lines. By making this distinction, we are able to derive the Hamilton-Jacobi and Klein-Gordon equations from the ``homogeneous'' Lagrangian, even though the covariant Hamiltonian function is identically zero on all world lines. The derivation of the Klein-Gordon equation in particular gives Lagrangian theoretical support to the derivations found in standard quantum texts, and is also shown to be consistent with the Feynman path-integral method. We conclude that the ``homogeneous'' Lagrangian is a completely adequate basis for covariant Lagrangian theory both in classical and quantum mechanics. The article also explores the analogy with the Fermat theorem of optics, and illustrates a simple invariant notation for the Lagrangian and other four-vector equations.

  8. Nonlinear model of a rotating hub-beams structure: Equations of motion

    NASA Astrophysics Data System (ADS)

    Warminski, Jerzy

    2018-01-01

    Dynamics of a rotating structure composed of a rigid hub and flexible beams is presented in the paper. A nonlinear model of a beam takes into account bending, extension and nonlinear curvature. The influence of geometric nonlinearity and nonconstant angular velocity on dynamics of the rotating structure is presented. The exact equations of motion and associated boundary conditions are derived on the basis of the Hamilton's principle. The simplification of the exact nonlinear mathematical model is proposed taking into account the second order approximation. The reduced partial differential equations of motion together with associated boundary conditions can be used to study natural or forced vibrations of a rotating structure considering constant or nonconstant angular speed of a rigid hub and an arbitrary number of flexible blades.

  9. Neural network-based optimal adaptive output feedback control of a helicopter UAV.

    PubMed

    Nodland, David; Zargarzadeh, Hassan; Jagannathan, Sarangapani

    2013-07-01

    Helicopter unmanned aerial vehicles (UAVs) are widely used for both military and civilian operations. Because the helicopter UAVs are underactuated nonlinear mechanical systems, high-performance controller design for them presents a challenge. This paper introduces an optimal controller design via an output feedback for trajectory tracking of a helicopter UAV, using a neural network (NN). The output-feedback control system utilizes the backstepping methodology, employing kinematic and dynamic controllers and an NN observer. The online approximator-based dynamic controller learns the infinite-horizon Hamilton-Jacobi-Bellman equation in continuous time and calculates the corresponding optimal control input by minimizing a cost function, forward-in-time, without using the value and policy iterations. Optimal tracking is accomplished by using a single NN utilized for the cost function approximation. The overall closed-loop system stability is demonstrated using Lyapunov analysis. Finally, simulation results are provided to demonstrate the effectiveness of the proposed control design for trajectory tracking.

  10. Model-Free Adaptive Control for Unknown Nonlinear Zero-Sum Differential Game.

    PubMed

    Zhong, Xiangnan; He, Haibo; Wang, Ding; Ni, Zhen

    2018-05-01

    In this paper, we present a new model-free globalized dual heuristic dynamic programming (GDHP) approach for the discrete-time nonlinear zero-sum game problems. First, the online learning algorithm is proposed based on the GDHP method to solve the Hamilton-Jacobi-Isaacs equation associated with optimal regulation control problem. By setting backward one step of the definition of performance index, the requirement of system dynamics, or an identifier is relaxed in the proposed method. Then, three neural networks are established to approximate the optimal saddle point feedback control law, the disturbance law, and the performance index, respectively. The explicit updating rules for these three neural networks are provided based on the data generated during the online learning along the system trajectories. The stability analysis in terms of the neural network approximation errors is discussed based on the Lyapunov approach. Finally, two simulation examples are provided to show the effectiveness of the proposed method.

  11. Decentralized stabilization for a class of continuous-time nonlinear interconnected systems using online learning optimal control approach.

    PubMed

    Liu, Derong; Wang, Ding; Li, Hongliang

    2014-02-01

    In this paper, using a neural-network-based online learning optimal control approach, a novel decentralized control strategy is developed to stabilize a class of continuous-time nonlinear interconnected large-scale systems. First, optimal controllers of the isolated subsystems are designed with cost functions reflecting the bounds of interconnections. Then, it is proven that the decentralized control strategy of the overall system can be established by adding appropriate feedback gains to the optimal control policies of the isolated subsystems. Next, an online policy iteration algorithm is presented to solve the Hamilton-Jacobi-Bellman equations related to the optimal control problem. Through constructing a set of critic neural networks, the cost functions can be obtained approximately, followed by the control policies. Furthermore, the dynamics of the estimation errors of the critic networks are verified to be uniformly and ultimately bounded. Finally, a simulation example is provided to illustrate the effectiveness of the present decentralized control scheme.

  12. Particle motion around magnetized black holes: Preston-Poisson space-time

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Konoplya, R. A.

    We analyze the motion of massless and massive particles around black holes immersed in an asymptotically uniform magnetic field and surrounded by some mechanical structure, which provides the magnetic field. The space-time is described by the Preston-Poisson metric, which is the generalization of the well-known Ernst metric with a new parameter, tidal force, characterizing the surrounding structure. The Hamilton-Jacobi equations allow the separation of variables in the equatorial plane. The presence of a tidal force from the surroundings considerably changes the parameters of the test particle motion: it increases the radius of circular orbits of particles and increases the bindingmore » energy of massive particles going from a given circular orbit to the innermost stable orbit near the black hole. In addition, it increases the distance of the minimal approach, time delay, and bending angle for a ray of light propagating near the black hole.« less

  13. Hawking radiation of Dirac particles from black strings

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ahmed, Jamil; Saifullah, K., E-mail: jamil_051@yahoo.com, E-mail: saifullah@qau.edu.pk

    2011-08-01

    Hawking radiation has been studied as a phenomenon of quantum tunneling in different black holes. In this paper we extend this semi-classical approach to cylindrically symmetric black holes. Using the Hamilton-Jacobi method and WKB approximation we calculate the tunneling probabilities of incoming and outgoing Dirac particles from the event horizon and find the Hawking temperature of these black holes. We obtain results both for uncharged as well as charged particles.

  14. Protecting Critical Rail Infrastructure

    DTIC Science & Technology

    2006-12-01

    Gulliver.Trb.Org/Publications/Sr/Sr270.Pdf. 38. Allan J. DeBlasio, Terrance J. Regan, Margaret E . Zirker, Katherine S. Fichter, Kristin Lovejoy ...getrpt?GAO-04-598T. 4. Ibid. 5. Thomas H. Kean, Lee H. Hamilton, Richard Ben-Veniste, Fred F. Fielding, Jamie S. Gorelick, Slade Gorton, Bob Kerrey...Committee, Current and Projected National Security Threats to the United States, Vice Admiral Lowell E . Jacoby, United States Navy, Director, Defense

  15. Confronting quasi-exponential inflation with WMAP seven

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Pal, Barun Kumar; Pal, Supratik; Basu, B., E-mail: barunp1985@rediffmail.com, E-mail: pal@th.physik.uni-bonn.de, E-mail: banasri@isical.ac.in

    2012-04-01

    We confront quasi-exponential models of inflation with WMAP seven years dataset using Hamilton Jacobi formalism. With a phenomenological Hubble parameter, representing quasi exponential inflation, we develop the formalism and subject the analysis to confrontation with WMAP seven using the publicly available code CAMB. The observable parameters are found to fair extremely well with WMAP seven. We also obtain a ratio of tensor to scalar amplitudes which may be detectable in PLANCK.

  16. Identification of potential fish carcinogens in sediment from Hamilton Harbour, Ontario, Canada

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Balch, G.C.; Metcalfe, C.D.; Huestis, S.Y.

    1995-01-01

    A carcinogenicity- and mutagenicity-directed fractionation approach was used to identify the carcinogenic compounds in contaminated sediments that are putatively responsible for the high prevalence of tumors in bottom-dwelling fish from Hamilton Harbour, Ontario. Mutagenic activity was detected with Ames tester strains (TA98, TA100) in relatively nonpolar fractions of sediment extract containing PAHs and nitrogen-containing aromatic compounds (NCACs). These fractions were also carcinogenic in an in vivo carcinogenicity bioassay with rainbow trout (Oncorhynchus mykiss). When a more polar extract fraction was tested for mutagenicity and carcinogenicity, weak mutagenic activity was detected with an O-acetyltransferase-enriched Ames tester strain (YG1024), and weak carcinogenicmore » activity was detected in the rainbow trout assay. These data indicate that PAHs in contaminated Hamilton Harbour sediments are potent fish carcinogens, but it is also evident that other organic compounds in the sediment, such as NCACs and nitroarenes, may contribute to carcinogenicity.« less

  17. Notes on the Occurrence of Oligonychus milleri (McGregor) and Oligonychus ununguis (Jacobi) (Acari: Tetranychidae) in Brazil.

    PubMed

    Castro, E B; Zanardi, O C; Garlet, J; Ochoa, R; Feres, R J F

    2018-06-01

    We verified infestation of Oligonychus milleri (McGregor) on plantations of Pinus caribaea (Pinaceae) and of Oligonychus ununguis (Jacobi) on plantations of Eucalyptus urophylla x Eucalyptus grandis (Myrtaceae) in State of Rondônia, Northern region of Brazil. This represents the first record of O. milleri in Brazil. Oligonychus ununguis was recorded previously, on cypress. The damage caused by these two spider mites in the plantations is described herein.

  18. Application of the Group Foliation Method to the Complex Monge-Ampère Equation

    NASA Astrophysics Data System (ADS)

    Nutku, Y.; Sheftel, M. B.

    2001-04-01

    We apply the method of group foliation to the complex Monge-Ampère equation ( CMA 2) to establish a regular framework for finding its non-invariant solutions. We employ an infinite symmetry subgroup of CMA 2 to produce a foliation of the solution space into orbits of solutions with respect to this group and a corresponding splitting of CMA 2 into an automorphic system and a resolvent system. We propose a new approach to group foliation which is based on the commutator algebra of operators of invariant differentiation. This algebra together with its Jacobi identities provides the commutator representation of the resolvent system.

  19. Solving Partial Differential Equations in a data-driven multiprocessor environment

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gaudiot, J.L.; Lin, C.M.; Hosseiniyar, M.

    1988-12-31

    Partial differential equations can be found in a host of engineering and scientific problems. The emergence of new parallel architectures has spurred research in the definition of parallel PDE solvers. Concurrently, highly programmable systems such as data-how architectures have been proposed for the exploitation of large scale parallelism. The implementation of some Partial Differential Equation solvers (such as the Jacobi method) on a tagged token data-flow graph is demonstrated here. Asynchronous methods (chaotic relaxation) are studied and new scheduling approaches (the Token No-Labeling scheme) are introduced in order to support the implementation of the asychronous methods in a data-driven environment.more » New high-level data-flow language program constructs are introduced in order to handle chaotic operations. Finally, the performance of the program graphs is demonstrated by a deterministic simulation of a message passing data-flow multiprocessor. An analysis of the overhead in the data-flow graphs is undertaken to demonstrate the limits of parallel operations in dataflow PDE program graphs.« less

  20. Gauge Fields in Homogeneous and Inhomogeneous Cosmologies

    NASA Astrophysics Data System (ADS)

    Darian, Bahman K.

    Despite its formidable appearance, the study of classical Yang-Mills (YM) fields on homogeneous cosmologies is amenable to a formal treatment. This dissertation is a report on a systematic approach to the general construction of invariant YM fields on homogeneous cosmologies undertaken for the first time in this context. This construction is subsequently followed by the investigation of the behavior of YM field variables for the most simple of self-gravitating YM fields. Particularly interesting was a dynamical system analysis and the discovery of chaotic signature in the axially symmetric Bianchi I-YM cosmology. Homogeneous YM fields are well studied and are known to have chaotic properties. The chaotic behavior of YM field variables in homogeneous cosmologies might eventually lead to an invariant definition of chaos in (general) relativistic cosmological models. By choosing the gauge fields to be Abelian, the construction and the field equations presented so far reduce to that of electromagnetic field in homogeneous cosmologies. A perturbative analysis of gravitationally interacting electromagnetic and scalar fields in inhomogeneous cosmologies is performed via the Hamilton-Jacobi formulation of general relativity. An essential feature of this analysis is the spatial gradient expansion of the generating functional (Hamilton principal function) to solve the Hamiltonian constraint. Perturbations of a spatially flat Friedman-Robertson-Walker cosmology with an exponential potential for the scalar field are presented.

  1. Fast Numerical Solution of the Plasma Response Matrix for Real-time Ideal MHD Control

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Glasser, Alexander; Kolemen, Egemen; Glasser, Alan H.

    To help effectuate near real-time feedback control of ideal MHD instabilities in tokamak geometries, a parallelized version of A.H. Glasser’s DCON (Direct Criterion of Newcomb) code is developed. To motivate the numerical implementation, we first solve DCON’s δW formulation with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD Riccati equation. We then describe our adaptation of DCON with numerical methods natural to solutions of the Riccati equation, parallelizing it to enable its operation in near real-time. We replace DCON’s serial integration of perturbed modes—which satisfy a singular Euler- Lagrange equation—with a domain-decomposed integration of state transition matrices. Output is shown to match results from DCON with high accuracy, and with computation time < 1s. Such computational speed may enable active feedback ideal MHD stability control, especially in plasmas whose ideal MHD equilibria evolve with inductive timescalemore » $$\\tau$$ ≳ 1s—as in ITER. Further potential applications of this theory are discussed.« less

  2. Tunneling method for Hawking radiation in the Nariai case

    NASA Astrophysics Data System (ADS)

    Belgiorno, F.; Cacciatori, S. L.; Dalla Piazza, F.

    2017-08-01

    We revisit the tunneling picture for the Hawking effect in light of the charged Nariai manifold, because this general relativistic solution, which displays two horizons, provides the bonus to allow the knowledge of exact solutions of the field equations. We first perform a revisitation of the tunneling ansatz in the framework of particle creation in external fields à la Nikishov, which corroborates the interpretation of the semiclassical emission rate Γ_{emission} as the conditional probability rate for the creation of a couple of particles from the vacuum. Then, particle creation associated with the Hawking effect on the Nariai manifold is calculated in two ways. On the one hand, we apply the Hamilton-Jacobi formalism for tunneling, in the case of a charged scalar field on the given background. On the other hand, the knowledge of the exact solutions for the Klein-Gordon equations on Nariai manifold, and their analytic properties on the extended manifold, allow us a direct computation of the flux of particles leaving the horizon, and, as a consequence, we obtain a further corroboration of the semiclassical tunneling picture from the side of S-matrix formalism.

  3. Distributed Optimal Consensus Control for Multiagent Systems With Input Delay.

    PubMed

    Zhang, Huaipin; Yue, Dong; Zhao, Wei; Hu, Songlin; Dou, Chunxia; Huaipin Zhang; Dong Yue; Wei Zhao; Songlin Hu; Chunxia Dou; Hu, Songlin; Zhang, Huaipin; Dou, Chunxia; Yue, Dong; Zhao, Wei

    2018-06-01

    This paper addresses the problem of distributed optimal consensus control for a continuous-time heterogeneous linear multiagent system subject to time varying input delays. First, by discretization and model transformation, the continuous-time input-delayed system is converted into a discrete-time delay-free system. Two delicate performance index functions are defined for these two systems. It is shown that the performance index functions are equivalent and the optimal consensus control problem of the input-delayed system can be cast into that of the delay-free system. Second, by virtue of the Hamilton-Jacobi-Bellman (HJB) equations, an optimal control policy for each agent is designed based on the delay-free system and a novel value iteration algorithm is proposed to learn the solutions to the HJB equations online. The proposed adaptive dynamic programming algorithm is implemented on the basis of a critic-action neural network (NN) structure. Third, it is proved that local consensus errors of the two systems and weight estimation errors of the critic-action NNs are uniformly ultimately bounded while the approximated control policies converge to their target values. Finally, two simulation examples are presented to illustrate the effectiveness of the developed method.

  4. Actor-critic-based optimal tracking for partially unknown nonlinear discrete-time systems.

    PubMed

    Kiumarsi, Bahare; Lewis, Frank L

    2015-01-01

    This paper presents a partially model-free adaptive optimal control solution to the deterministic nonlinear discrete-time (DT) tracking control problem in the presence of input constraints. The tracking error dynamics and reference trajectory dynamics are first combined to form an augmented system. Then, a new discounted performance function based on the augmented system is presented for the optimal nonlinear tracking problem. In contrast to the standard solution, which finds the feedforward and feedback terms of the control input separately, the minimization of the proposed discounted performance function gives both feedback and feedforward parts of the control input simultaneously. This enables us to encode the input constraints into the optimization problem using a nonquadratic performance function. The DT tracking Bellman equation and tracking Hamilton-Jacobi-Bellman (HJB) are derived. An actor-critic-based reinforcement learning algorithm is used to learn the solution to the tracking HJB equation online without requiring knowledge of the system drift dynamics. That is, two neural networks (NNs), namely, actor NN and critic NN, are tuned online and simultaneously to generate the optimal bounded control policy. A simulation example is given to show the effectiveness of the proposed method.

  5. Fast Numerical Solution of the Plasma Response Matrix for Real-time Ideal MHD Control

    DOE PAGES

    Glasser, Alexander; Kolemen, Egemen; Glasser, Alan H.

    2018-03-26

    To help effectuate near real-time feedback control of ideal MHD instabilities in tokamak geometries, a parallelized version of A.H. Glasser’s DCON (Direct Criterion of Newcomb) code is developed. To motivate the numerical implementation, we first solve DCON’s δW formulation with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD Riccati equation. We then describe our adaptation of DCON with numerical methods natural to solutions of the Riccati equation, parallelizing it to enable its operation in near real-time. We replace DCON’s serial integration of perturbed modes—which satisfy a singular Euler- Lagrange equation—with a domain-decomposed integration of state transition matrices. Output is shown to match results from DCON with high accuracy, and with computation time < 1s. Such computational speed may enable active feedback ideal MHD stability control, especially in plasmas whose ideal MHD equilibria evolve with inductive timescalemore » $$\\tau$$ ≳ 1s—as in ITER. Further potential applications of this theory are discussed.« less

  6. Level set immersed boundary method for gas-liquid-solid interactions with phase-change

    NASA Astrophysics Data System (ADS)

    Dhruv, Akash; Balaras, Elias; Riaz, Amir; Kim, Jungho

    2017-11-01

    We will discuss an approach to simulate the interaction between two-phase flows with phase changes and stationary/moving structures. In our formulation, the Navier-Stokes and heat advection-diffusion equations are solved on a block-structured grid using adaptive mesh refinement (AMR) along with sharp jump in pressure, velocity and temperature across the interface separating the different phases. The jumps are implemented using a modified Ghost Fluid Method (Lee et al., J. Comput. Physics, 344:381-418, 2017), and the interface is tracked with a level set approach. Phase transition is achieved by calculating mass flux near the interface and extrapolating it to the rest of the domain using a Hamilton-Jacobi equation. Stationary/moving structures are simulated with an immersed boundary formulation based on moving least squares (Vanella & Balaras, J. Comput. Physics, 228:6617-6628, 2009). A variety of canonical problems involving vaporization, film boiling and nucleate boiling is presented to validate the method and demonstrate the its formal accuracy. The robustness of the solver in complex problems, which are crucial in efficient design of heat transfer mechanisms for various applications, will also be demonstrated. Work supported by NASA, Grant NNX16AQ77G.

  7. Hamilton's principle and normal mode coupling in an aspherical planet with a fluid core

    NASA Astrophysics Data System (ADS)

    Al-Attar, David; Crawford, Ophelia; Valentine, Andrew P.; Trampert, Jeannot

    2018-04-01

    We apply Hamilton's principle to obtain the exact equations of motion for an elastic planet that is rotating, self-gravitating, and comprises both fluid and solid regions. This variational problem is complicated by the occurrence of tangential slip at fluid-solid boundaries, but we show how this can be accommodated both directly and using the method of Lagrange multipliers. A novelty of our approach is that the planet's motion is described relative to an arbitrary reference configuration, with this generality offering advantages for numerical calculations. In particular, aspherical topography on the free surface or internal boundaries of the planet's equilibrium configuration can be converted exactly into effective volumetric heterogeneities within a geometrically spherical reference body by applying a suitable particle relabelling transformation. The theory is then specialised to consider the linearised motion of a planet about a steadily rotating equilibrium configuration, with these results having applications to normal mode coupling calculations used within studies of long period seismology, tidal deformation, and related fields. In particular, we explain how our new theory will, for the first time, allow aspherical boundary topography to be incorporated exactly within such coupling calculations.

  8. Values Education and the Board of Education for the City of Hamilton.

    ERIC Educational Resources Information Center

    Kocmarek, Ivan; Barrs, Steve

    1988-01-01

    Describes a values education program developed in the city of Hamilton, Ontario. Advocates removing values education from the realm of the hidden curriculum as found in the traditional school model of knowledge of facts, mastery of technical skills, and awareness of attitudes. Emphasizes the importance of continual interaction between school and…

  9. 76 FR 25534 - Airworthiness Directives; Hamilton Sundstrand Propellers Model 247F Propellers

    Federal Register 2010, 2011, 2012, 2013, 2014

    2011-05-05

    ... 5 p.m., Monday through Friday, except Federal holidays. The AD docket contains this AD, the... through FR2279 inclusive, FR 2398, FR2449 to FR2958 inclusive, FR20010710 to FR20010722 inclusive, and FR20010723RT to FR20020127RT inclusive, installed. Propeller blades reworked to Hamilton Sundstrand Service...

  10. Who Tells "Our" Story: Intersectional Temporalities in "Hamilton: An American Musical"

    ERIC Educational Resources Information Center

    Silva, Andie; Inayatulla, Shereen

    2017-01-01

    This article examines the ways in which "Hamilton: An American Musical" can be read less as a historical account and more as a prediction of a future immigrant, who is called upon to (re)define US nationhood. Keeping with the tempo of the musical as well as the broader issues of time, space and identity it attempts to address, this…

  11. The Hamilton Rating Scale for Depression: The making of a “gold standard” and the unmaking of a chronic illness, 1960–1980

    PubMed Central

    Worboys, Michael

    2013-01-01

    Objectives: To show why and how the Hamilton Rating Scale for Depression became the ‘Gold Standard’ for assessing therapies from the mid-1960s and how it was used to frame depression as a short-term and curable illness rather than a chronic one. Methods: My approach is that of the social construction of knowledge, identifying the interests, institutional contexts and practices that produce knowledge claims and then mapping the social processes of their circulation, validation and acceptance. Results: The circulation and validation of Hamilton Rating Scale for Depression was relatively slow and it became a ‘Gold Standard’ ‘from below’, from an emerging consensus amongst psychiatrists undertaking clinical trials for depression, which from the 1960s were principally with psychopharmaceuticals for short-term illness. Hamilton Rating Scale for Depression, drug trials and the construction of depression as non-chronic were mutually constituted. Discussion: Hamilton Rating Scale for Depression framed depression and its sufferers in new ways, leading psychiatrists to understand illness as a treatable episode, rather than a life course condition. As such, Hamilton Rating Scale for Depression served the interests of psychiatrists and psychiatry in its new era of drug therapy outside the mental hospital. However, Hamilton Rating Scale for Depression was a strange kind of ‘standard’, being quite non-standard in the widely varying ways it was used and the meanings given to its findings. PMID:23172888

  12. Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades

    NASA Technical Reports Server (NTRS)

    Hodges, D. H.; Dowell, E. H.

    1974-01-01

    The equations of motion are developed by two complementary methods, Hamilton's principle and the Newtonian method. The resulting equations are valid to second order for long, straight, slender, homogeneous, isotropic beams undergoing moderate displacements. The ordering scheme is based on the restriction that squares of the bending slopes, the torsion deformation, and the chord/radius and thickness/radius ratios are negligible with respect to unity. All remaining nonlinear terms are retained. The equations are valid for beams with mass centroid axis and area centroid (tension) axis offsets from the elastic axis, nonuniform mass and stiffness section properties, variable pretwist, and a small precone angle. The strain-displacement relations are developed from an exact transformation between the deformed and undeformed coordinate systems. These nonlinear relations form an important contribution to the final equations. Several nonlinear structural and inertial terms in the final equations are identified that can substantially influence the aeroelastic stability and response of hingeless helicopter rotor blades.

  13. A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

    NASA Astrophysics Data System (ADS)

    Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

    2017-09-01

    Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

  14. Hamilton and the square root of minus one

    NASA Astrophysics Data System (ADS)

    Weinberger, Peter

    2014-04-01

    Quaternions, objects consisting of a scalar and a vector, sound like a mysterious concept from the past. In the nineteenth century, the theory of quaternions was praised as one of the most brilliant achievements in mathematical physics. The originator of this theory, Hamilton, surely one of the greatest scientists in that area, spent about 18 years in discussing all kinds of algebraic and geometric properties of quaternions. His research was communicated to the Philosophical Magazine in three series of papers comprising a total of 29 contributions. In this commentary, these three series of papers are revisited concentrating primarily on the algebraic properties of quaternions.

  15. A Robust Locally Preconditioned Semi-Coarsening Multigrid Algorithm for the 2-D Navier-Stokes Equations

    NASA Technical Reports Server (NTRS)

    Cain, Michael D.

    1999-01-01

    The goal of this thesis is to develop an efficient and robust locally preconditioned semi-coarsening multigrid algorithm for the two-dimensional Navier-Stokes equations. This thesis examines the performance of the multigrid algorithm with local preconditioning for an upwind-discretization of the Navier-Stokes equations. A block Jacobi iterative scheme is used because of its high frequency error mode damping ability. At low Mach numbers, the performance of a flux preconditioner is investigated. The flux preconditioner utilizes a new limiting technique based on local information that was developed by Siu. Full-coarsening and-semi-coarsening are examined as well as the multigrid V-cycle and full multigrid. The numerical tests were performed on a NACA 0012 airfoil at a range of Mach numbers. The tests show that semi-coarsening with flux preconditioning is the most efficient and robust combination of coarsening strategy, and iterative scheme - especially at low Mach numbers.

  16. A FAST ITERATIVE METHOD FOR SOLVING THE EIKONAL EQUATION ON TRIANGULATED SURFACES*

    PubMed Central

    Fu, Zhisong; Jeong, Won-Ki; Pan, Yongsheng; Kirby, Robert M.; Whitaker, Ross T.

    2012-01-01

    This paper presents an efficient, fine-grained parallel algorithm for solving the Eikonal equation on triangular meshes. The Eikonal equation, and the broader class of Hamilton–Jacobi equations to which it belongs, have a wide range of applications from geometric optics and seismology to biological modeling and analysis of geometry and images. The ability to solve such equations accurately and efficiently provides new capabilities for exploring and visualizing parameter spaces and for solving inverse problems that rely on such equations in the forward model. Efficient solvers on state-of-the-art, parallel architectures require new algorithms that are not, in many cases, optimal, but are better suited to synchronous updates of the solution. In previous work [W. K. Jeong and R. T. Whitaker, SIAM J. Sci. Comput., 30 (2008), pp. 2512–2534], the authors proposed the fast iterative method (FIM) to efficiently solve the Eikonal equation on regular grids. In this paper we extend the fast iterative method to solve Eikonal equations efficiently on triangulated domains on the CPU and on parallel architectures, including graphics processors. We propose a new local update scheme that provides solutions of first-order accuracy for both architectures. We also propose a novel triangle-based update scheme and its corresponding data structure for efficient irregular data mapping to parallel single-instruction multiple-data (SIMD) processors. We provide detailed descriptions of the implementations on a single CPU, a multicore CPU with shared memory, and SIMD architectures with comparative results against state-of-the-art Eikonal solvers. PMID:22641200

  17. Structure and metamorphism of the Franciscan Complex, Mt. Hamilton area, Northern California

    USGS Publications Warehouse

    Blake, M.C.; Wentworth, C.M.

    1999-01-01

    Truncation of metamorphic isograds and fold axes within coherent terranes of Franciscan metagraywacke by intervening zones of melange indicate that the melange is tectonic and formed after the subduction-related metamorphism and folding. These relations are expressed in two terranes of blueschist-facies rocks of the Franciscan Complex in the Mt. Hamilton area, northern California-the Jurassic Yolla Bolly terrane and the structurally underlying Cretaceous Burnt Hills terrane. Local preservation in both terranes of basal radiolarian chert and oceanic basalt beneath continent-derived metagraywacke and argillite demonstrates thrust repetition within the coherent terranes, although these relations are scarce near Mt. Hamilton. The metagraywackes range from albite-pumpellyite blueschists to those containing well-crystallized jadeitic pyroxene, and a jadeite-in isograd can be defined in parts of the area. Primary bedding defines locally coherent structural orientations and folds within the metagraywacke units. These units are crosscut by thin zones of tectonic melange containing blocks of high-grade blueschist, serpentinite, and other exotic rocks, and a broader, but otherwise identical melange zone marks the discordant boundary between the two terranes.

  18. Towards developing robust algorithms for solving partial differential equations on MIMD machines

    NASA Technical Reports Server (NTRS)

    Saltz, Joel H.; Naik, Vijay K.

    1988-01-01

    Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

  19. Towards developing robust algorithms for solving partial differential equations on MIMD machines

    NASA Technical Reports Server (NTRS)

    Saltz, J. H.; Naik, V. K.

    1985-01-01

    Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

  20. The right-hand side of the Jacobi identity: to be naught or not to be ?

    NASA Astrophysics Data System (ADS)

    Kiselev, Arthemy V.

    2016-01-01

    The geometric approach to iterated variations of local functionals -e.g., of the (master-)action functional - resulted in an extension of the deformation quantisation technique to the set-up of Poisson models of field theory. It also allowed of a rigorous proof for the main inter-relations between the Batalin-Vilkovisky (BV) Laplacian Δ and variational Schouten bracket [,]. The ad hoc use of these relations had been a known analytic difficulty in the BV- formalism for quantisation of gauge systems; now achieved, the proof does actually not require the assumption of graded-commutativity. Explained in our previous work, geometry's self- regularisation is rendered by Gel'fand's calculus of singular linear integral operators supported on the diagonal. We now illustrate that analytic technique by inspecting the validity mechanism for the graded Jacobi identity which the variational Schouten bracket does satisfy (whence Δ2 = 0, i.e., the BV-Laplacian is a differential acting in the algebra of local functionals). By using one tuple of three variational multi-vectors twice, we contrast the new logic of iterated variations - when the right-hand side of Jacobi's identity vanishes altogether - with the old method: interlacing its steps and stops, it could produce some non-zero representative of the trivial class in the top- degree horizontal cohomology. But we then show at once by an elementary counterexample why, in the frames of the old approach that did not rely on Gel'fand's calculus, the BV-Laplacian failed to be a graded derivation of the variational Schouten bracket.

  1. Hawking temperature of rotating charged black strings from tunneling

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ahmed, Jamil; Saifullah, K., E-mail: jamil_051@yahoo.com, E-mail: saifullah@qau.edu.pk

    2011-11-01

    Thermal radiations from spherically symmetric black holes have been studied from the point of view of quantum tunneling. In this paper we extend this approach to study radiation of fermions from charged and rotating black strings. Using WKB approximation and Hamilton-Jacobi method we work out the tunneling probabilities of incoming and outgoing fermions and find the correct Hawking temperature for these objects. We show that in appropriate limits the results reduce to those for the uncharged and non-rotating black strings.

  2. Ballistic Transport for Limit-Periodic Jacobi Matrices with Applications to Quantum Many-Body Problems

    NASA Astrophysics Data System (ADS)

    Fillman, Jake

    2017-03-01

    We study Jacobi matrices that are uniformly approximated by periodic operators. We show that if the rate of approximation is sufficiently rapid, then the associated quantum dynamics are ballistic in a rather strong sense; namely, the (normalized) Heisenberg evolution of the position operator converges strongly to a self-adjoint operator that is injective on the space of absolutely summable sequences. In particular, this means that all transport exponents corresponding to well-localized initial states are equal to one. Our result may be applied to a class of quantum many-body problems. Specifically, we establish a lower bound on the Lieb-Robinson velocity for an isotropic XY spin chain on the integers with limit-periodic couplings.

  3. Nonlinear flap-lag-axial equations of a rotating beam with arbitrary precone angle

    NASA Technical Reports Server (NTRS)

    Kvaternik, R. G.; White, W. F., Jr.; Kaza, K. R. V.

    1978-01-01

    In an attempt both to unify and extend the analytical basis of several aspects of the dynamic behavior of flexible rotating beams, the second-degree nonlinear equations of motion for the coupled flapwise bending, lagwise bending, and axial extension of an untwisted, torsionally rigid, nonuniform, rotating beam having an arbitrary angle of precone with the plane perpendicular to the axis of rotation are derived using Hamilton's principle. The derivation of the equations is based on the geometric nonlinear theory of elasticity and the resulting equations are consistent with the assumption that the strains are negligible compared to unity. No restrictions are imposed on the relative displacements or angular rotations of the cross sections of the beam other than those implied by the assumption of small strains. Illustrative numerical results, obtained by using an integrating matrix as the basis for the method of solution, are presented both for the purpose of validating the present method of solution and indicating the range of applicability of the equations of motion and the method of solution.

  4. The Code Red Project: Engaging Communities in Health System Change in Hamilton, Canada

    ERIC Educational Resources Information Center

    DeLuca, Patrick F.; Buist, Steve; Johnston, Neil

    2012-01-01

    The communication of determinants of health and health outcomes normally executed through academic channels often fail to reach lay audiences. In April of 2010, the results of collaboration between academe and mass media were published in the Hamilton Spectator, one of Canada's 10 largest English-language daily newspapers as a 7-day series. The…

  5. The Election of 1800: Alexander Hamilton and the Death of the Federalist Party.

    ERIC Educational Resources Information Center

    Holbrook-DeFeo, Gary

    1993-01-01

    Describes the significance of the election of 1800 in the development of political parties in the United States. Contends that Alexander Hamilton's view of the United States Constitution was dangerous for the new nation and led to a permanent split in the Federalist Party. Includes a resource bibliography for teachers wishing to incorporate this…

  6. Second order nonlinear equations of motion for spinning highly flexible line-elements. [for spacecraft solar sail

    NASA Technical Reports Server (NTRS)

    Salama, M.; Trubert, M.

    1979-01-01

    A formulation is given for the second order nonlinear equations of motion for spinning line-elements having little or no intrinsic structural stiffness. Such elements have been employed in recent studies of structural concepts for future large space structures such as the Heliogyro solar sailer. The derivation is based on Hamilton's variational principle and includes the effect of initial geometric imperfections (axial, curvature, and twist) on the line-element dynamics. For comparison with previous work, the nonlinear equations are reduced to a linearized form frequently found in the literature. The comparison has revealed several new spin-stiffening terms that have not been previously identified and/or retained. They combine geometric imperfections, rotary inertia, Coriolis, and gyroscopic terms.

  7. Value-oriented citizenship index: New extensions of Kelman and Hamilton's theory to prevent autocracy.

    PubMed

    Morselli, Davide; Passini, Stefano

    2015-11-01

    In Crimes of obedience, Kelman and Hamilton argue that societies can be protected by the degeneration of authority only when citizenship is based on a strong values orientation. This reference to values may be the weakest point in their theory because they do not explicitly define these values. Nevertheless, their empirical findings suggest that the authors are referring to specific democratic principles and universal values (e.g., equality, fairness, harmlessness). In this article, a composite index known as the value-oriented citizenship (VOC) index is introduced and empirically analysed. The results confirm that the VOC index discriminates between people who relate to authority based on values rather than based on their role or on rules in general. The article discusses the utility of the VOC index to develop Kelman and Hamilton's framework further empirically as well as its implications for the analysis of the relationship between individuals and authority. Copyright © 2015 Elsevier Inc. All rights reserved.

  8. Experiments on Frequency Dependence of the Deflection of Light in Yang-Mills Gravity

    NASA Astrophysics Data System (ADS)

    Hao, Yun; Zhu, Yiyi; Hsu, Jong-Ping

    2018-01-01

    In Yang-Mills gravity based on flat space-time, the eikonal equation for a light ray is derived from the modified Maxwell's wave equations in the geometric-optics limit. One obtains a Hamilton-Jacobi type equation, GLµv∂µΨ∂vΨ = 0 with an effective Riemannian metric tensor GLµv. According to Yang-Mills gravity, light rays (and macroscopic objects) move as if they were in an effective curved space-time with a metric tensor. The deflection angle of a light ray by the sun is about 1.53″ for experiments with optical frequencies ≈ 1014Hz. It is roughly 12% smaller than the usual value 1.75″. However, the experimental data in the past 100 years for the deflection of light by the sun in optical frequencies have uncertainties of (10-20)% due to large systematic errors. If one does not take the geometric-optics limit, one has the equation, GLµv[∂µΨ∂vΨcosΨ+ (∂µ∂vΨ)sinΨ] = 0, which suggests that the deflection angle could be frequency-dependent, according to Yang-Mills gravity. Nowadays, one has very accurate data in the radio frequencies ≈ 109Hz with uncertainties less than 0.1%. Thus, one can test this suggestion by using frequencies ≈ 1012 Hz, which could have a small uncertainty 0.1% due to the absence of systematic errors in the very long baseline interferometry.

  9. 77 FR 52058 - Notice of Inventory Completion: Longyear Museum of Anthropology, Colgate University, Hamilton, NY

    Federal Register 2010, 2011, 2012, 2013, 2014

    2012-08-28

    ... Inventory Completion: Longyear Museum of Anthropology, Colgate University, Hamilton, NY AGENCY: National Park Service, Interior. ACTION: Notice. SUMMARY: The Longyear Museum of Anthropology has completed an... cultural affiliation with the human remains should contact the Longyear Museum of Anthropology at the...

  10. The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

    NASA Technical Reports Server (NTRS)

    Estabrook, F. B.; Wahlquist, H. D.

    1975-01-01

    The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

  11. Sense of Place and Health in Hamilton, Ontario: A Case Study.

    PubMed

    Williams, Allison; Kitchen, Peter

    2012-09-01

    The concept of sense of place has received considerable attention by social scientists in recent years. Research has indicated that a person's sense of place is influenced by a number of factors including the built environment, socio-economic status (SES), well-being and health. Relatively few studies have examined sense of place at the neighbourhood level, particularly among communities exhibiting different levels of SES. This article investigates sense of place among three neighbourhood groups in Hamilton, Ontario representing areas of low, mixed and high SES. It analyses data from a 16-point sense of place scale derived from the Hamilton Household Quality of Life Survey carried out in 2010-2011 among 1,002 respondents. The paper found that sense of place was highest among residents of the high SES neighbourhood group as well as among home owners, people residing in single-detached homes, retired residents and those living in their neighbourhood for more than 10 years. From a health perspective, the paper found that a strong association existed between sense of place and self-perceived mental health across the three neighbourhood groups. Furthermore, by way of regression modeling, the paper examined the factors influencing health-related sense of place. Among the sample of respondents, a strong connection was found between housing, particularly home ownership, and high levels of health-related sense of place.

  12. Refraction seismic studies in the Miami River, Whitewater River, and Mill Creek valleys, Hamilton and Butler Counties, Ohio

    USGS Publications Warehouse

    Watkins, Joel S.

    1963-01-01

    Between September 17 and November 9, 1962, the U.S. Geological Survey, in cooperation with Ohio Division of Water, Miami Conservancy District, and c,ty of Cincinnati, Ohio, co.,:ducted a refraction seismic study in Hamilton and Butler Counties, southwest Ohio. The area lies between Hamilton, Ohio, and the Ohio River and includes a preglacial valley now occupied by portions of the Miami River, Whitewater River, and Mill Creek. The valley is partially filled with glacial debris which yields large quantities of good-quality water. The object of the study was to determine the thickness of these glacial deposits and the shape of the preglacial valley.

  13. Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.

    PubMed

    Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong

    2015-11-01

    The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.

  14. Response to ``Comment on `Bohmian mechanics with complex action: A new trajectory-based formulation of quantum mechanics' '' [J. Chem. Phys. 127, 197101 (2007)

    NASA Astrophysics Data System (ADS)

    Goldfarb, Yair; Degani, Ilan; Tannor, David J.

    2007-11-01

    In their comment, Sanz and Miret-Artés (SMA) describe previous trajectory-based formalisms based on the quantum Hamilton-Jacobi (QHJ) formalism. In this reply, we highlight our unique contributions: the identification of the smallness of the quantum force in the complex QHJ and its solution using complex trajectories. SMA also raise the question of how the term locality should be used in quantum mechanics. We suggest that at least certain aspects of nonlocality can depend on the method used to solve the problem.

  15. Approximately adaptive neural cooperative control for nonlinear multiagent systems with performance guarantee

    NASA Astrophysics Data System (ADS)

    Wang, Jing; Yang, Tianyu; Staskevich, Gennady; Abbe, Brian

    2017-04-01

    This paper studies the cooperative control problem for a class of multiagent dynamical systems with partially unknown nonlinear system dynamics. In particular, the control objective is to solve the state consensus problem for multiagent systems based on the minimisation of certain cost functions for individual agents. Under the assumption that there exist admissible cooperative controls for such class of multiagent systems, the formulated problem is solved through finding the optimal cooperative control using the approximate dynamic programming and reinforcement learning approach. With the aid of neural network parameterisation and online adaptive learning, our method renders a practically implementable approximately adaptive neural cooperative control for multiagent systems. Specifically, based on the Bellman's principle of optimality, the Hamilton-Jacobi-Bellman (HJB) equation for multiagent systems is first derived. We then propose an approximately adaptive policy iteration algorithm for multiagent cooperative control based on neural network approximation of the value functions. The convergence of the proposed algorithm is rigorously proved using the contraction mapping method. The simulation results are included to validate the effectiveness of the proposed algorithm.

  16. Finite-horizon differential games for missile-target interception system using adaptive dynamic programming with input constraints

    NASA Astrophysics Data System (ADS)

    Sun, Jingliang; Liu, Chunsheng

    2018-01-01

    In this paper, the problem of intercepting a manoeuvring target within a fixed final time is posed in a non-linear constrained zero-sum differential game framework. The Nash equilibrium solution is found by solving the finite-horizon constrained differential game problem via adaptive dynamic programming technique. Besides, a suitable non-quadratic functional is utilised to encode the control constraints into a differential game problem. The single critic network with constant weights and time-varying activation functions is constructed to approximate the solution of associated time-varying Hamilton-Jacobi-Isaacs equation online. To properly satisfy the terminal constraint, an additional error term is incorporated in a novel weight-updating law such that the terminal constraint error is also minimised over time. By utilising Lyapunov's direct method, the closed-loop differential game system and the estimation weight error of the critic network are proved to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is demonstrated by using a simple non-linear system and a non-linear missile-target interception system, assuming first-order dynamics for the interceptor and target.

  17. Adaptive critic designs for optimal control of uncertain nonlinear systems with unmatched interconnections.

    PubMed

    Yang, Xiong; He, Haibo

    2018-05-26

    In this paper, we develop a novel optimal control strategy for a class of uncertain nonlinear systems with unmatched interconnections. To begin with, we present a stabilizing feedback controller for the interconnected nonlinear systems by modifying an array of optimal control laws of auxiliary subsystems. We also prove that this feedback controller ensures a specified cost function to achieve optimality. Then, under the framework of adaptive critic designs, we use critic networks to solve the Hamilton-Jacobi-Bellman equations associated with auxiliary subsystem optimal control laws. The critic network weights are tuned through the gradient descent method combined with an additional stabilizing term. By using the newly established weight tuning rules, we no longer need the initial admissible control condition. In addition, we demonstrate that all signals in the closed-loop auxiliary subsystems are stable in the sense of uniform ultimate boundedness by using classic Lyapunov techniques. Finally, we provide an interconnected nonlinear plant to validate the present control scheme. Copyright © 2018 Elsevier Ltd. All rights reserved.

  18. Spacetime encodings. II. Pictures of integrability

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Brink, Jeandrew

    I visually explore the features of geodesic orbits in arbitrary stationary axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst potential. Some of the geometric features of integrable and chaotic orbits are highlighted. The geodesic problem for these SAV spacetimes is rewritten as a 2 degree of freedom problem and the connection between current ideas in dynamical systems and the study of two manifolds sought. The relationship between the Hamilton-Jacobi equations, canonical transformations, constants of motion, and Killing tensors are commented on. Wherever possible I illustrate the concepts by means of examples from general relativity. This investigation ismore » designed to build the readers' intuition about how integrability arises, and to summarize some of the known facts about 2 degree of freedom systems. Evidence is given, in the form of an orbit-crossing structure, that geodesics in SAV spacetimes might admit a fourth constant of motion that is quartic in momentum (by contrast with Kerr spacetime, where Carter's fourth constant is quadratic)« less

  19. Can one ADM quantize relativistic bosonicstrings and membranes?

    NASA Astrophysics Data System (ADS)

    Moncrief, Vincent

    2006-04-01

    The standard methods for quantizing relativistic strings diverge significantly from the Dirac-Wheeler-DeWitt program for quantization of generally covariant systems and one wonders whether the latter could be successfully implemented as an alternative to the former. As a first step in this direction, we consider the possibility of quantizing strings (and also relativistic membranes) via a partially gauge-fixed ADM (Arnowitt, Deser and Misner) formulation of the reduced field equations for these systems. By exploiting some (Euclidean signature) Hamilton-Jacobi techniques that Mike Ryan and I had developed previously for the quantization of Bianchi IX cosmological models, I show how to construct Diff( S 1)-invariant (or Diff(Σ)-invariant in the case of membranes) ground state wave functionals for the cases of co-dimension one strings and membranes embedded in Minkowski spacetime. I also show that the reduced Hamiltonian density operators for these systems weakly commute when applied to physical (i.e. Diff( S 1) or Diff(Σ)-invariant) states. While many open questions remain, these preliminary results seem to encourage further research along the same lines.

  20. Negative correlation between nuptial throat colour and blood parasite load in male European green lizards supports the Hamilton-Zuk hypothesis

    NASA Astrophysics Data System (ADS)

    Molnár, Orsolya; Bajer, Katalin; Mészáros, Boglárka; Török, János; Herczeg, Gábor

    2013-06-01

    During female mate choice, conspicuous male sexual signals are used to infer male quality and choose the best sire for the offspring. The theory of parasite-mediated sexual selection (Hamilton-Zuk hypothesis) presumes that parasite infection can influence the elaboration of sexual signals: resistant individuals can invest more energy into signal expression and thus advertise their individual quality through signal intensity. By preferring these males, females can provide resistance genes for their offspring. Previous research showed that nuptial throat colour of male European green lizard, Lacerta viridis, plays a role in both inter- and intrasexual selections as a condition-dependent multiple signalling system. The aim of this study was to test the predictions of the Hamilton-Zuk hypothesis on male European green lizards. By blood sampling 30 adult males during the reproductive season, we found members of the Haemogregarinidae family in all but one individual (prevalence = 96 %). The infection intensity showed strong negative correlation with the throat and belly colour brightness in line with the predictions of the Hamilton-Zuk hypothesis. In addition, we found other correlations between infection intensity and other fitness-related traits, suggesting that parasite load has a remarkable effect on individual fitness. This study shows that throat patch colour of the European green lizards not only is a multiple signalling system but also possibly acts as an honest sexual signal of health state in accordance with the Hamilton-Zuk hypothesis.

  1. Modeling collective behavior of dislocations in crystalline materials

    NASA Astrophysics Data System (ADS)

    Varadhan, Satya N.

    Elastic interaction of dislocations leads to collective behavior and determines plastic response at the mesoscale. Notable characteristics of mesoscale plasticity include the formation of dislocation patterns, propagative instability phenomena due to strain aging such as the Luders and Portevin-Le Chatelier effects, and size-dependence of low stress. This work presents a unified approach to modeling collective behavior based on mesoscale field dislocation mechanics and crystal plasticity, using constitutive models with physical basis. Successful application is made to: compression of a bicrystal, where "smaller is stronger"---the flow stress increases as the specimen size is reduced; torsional creep of ice single crystals, where the plastic strain rate increases with time under constant applied torque; strain aging in a single crystal alloy, where the transition from homogeneous deformation to intermittent bands to continuous band is captured as the applied deformation rate is increased. A part of this work deals with the kinematics of dislocation density evolution. An explicit Galerkin/least-squares formulation is introduced for the quasilinear evolution equation, which leads to a symmetric and well-conditioned system of equations with constant coefficients, making it attractive for large-scale problems. It is shown that the evolution equation simplifies to the Hamilton-Jacobi equations governing geometric optics and level set methods in the following physical contexts: annihilation of dislocations, expansion of a polygonal dislocation loop and operation of a Frank-Read source. The weak solutions to these equations are not unique, and the numerical method is able to capture solutions corresponding to shock as well as expansion fans.

  2. An Optimization Principle for Deriving Nonequilibrium Statistical Models of Hamiltonian Dynamics

    NASA Astrophysics Data System (ADS)

    Turkington, Bruce

    2013-08-01

    A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. Given a vector of resolved variables, selected to describe the macroscopic state of the system, a family of quasi-equilibrium probability densities on phase space corresponding to the resolved variables is employed as a statistical model, and the evolution of the mean resolved vector is estimated by optimizing over paths of these densities. Specifically, a cost function is constructed to quantify the lack-of-fit to the microscopic dynamics of any feasible path of densities from the statistical model; it is an ensemble-averaged, weighted, squared-norm of the residual that results from submitting the path of densities to the Liouville equation. The path that minimizes the time integral of the cost function determines the best-fit evolution of the mean resolved vector. The closed reduced equations satisfied by the optimal path are derived by Hamilton-Jacobi theory. When expressed in terms of the macroscopic variables, these equations have the generic structure of governing equations for nonequilibrium thermodynamics. In particular, the value function for the optimization principle coincides with the dissipation potential that defines the relation between thermodynamic forces and fluxes. The adjustable closure parameters in the best-fit reduced equations depend explicitly on the arbitrary weights that enter into the lack-of-fit cost function. Two particular model reductions are outlined to illustrate the general method. In each example the set of weights in the optimization principle contracts into a single effective closure parameter.

  3. 'Morals can not be drawn from facts but guidance may be': the early life of W.D. Hamilton's theory of inclusive fitness.

    PubMed

    Swenson, Sarah A

    2015-12-01

    W.D. Hamilton's theory of inclusive fitness saw the evolution of altruism from the point of view of the gene. It was at heart a theory of limits, redefining altruistic behaviours as ultimately selfish. This theory inspired two controversial texts published almost in tandem, E.O. Wilson's Sociobiology: The New Synthesis (1975) and Richard Dawkins's The Selfish Gene (1976). When Wilson and Dawkins were attacked for their evolutionary interpretations of human societies, they claimed a distinction between reporting what is and declaring what ought to be. Can the history of sociobiological theories be so easily separated from its sociopolitical context? This paper draws upon unpublished materials from the 1960s and early 1970s and documents some of the ways in which Hamilton saw his research as contributing to contemporary concerns. It pays special attention to the 1969 Man and Beast Smithsonian Institution symposium in order to explore the extent to which Hamilton intended his theory to be merely descriptive versus prescriptive. From this, we may see that Hamilton was deeply concerned about the political chaos he perceived in the world around him, and hoped to arrive at a level of self-understanding through science that could inform a new social order.

  4. Respiratory medicine at McMaster University, Hamilton, Ontario: 1968 to 2013

    PubMed Central

    Jones, Norman L; O’Byrne, Paul M

    2014-01-01

    The medical school at McMaster University (Hamilton, Ontario) was conceived in 1965 and admitted the first class in 1969. John Evans became the founding Dean and he invited Moran Campbell to be the first Chairman of the Department of Medicine. Moran Campbell, already a world figure in respiratory medicine and physiology, arrived at McMaster in September 1968, and he invited Norman Jones to be Coordinator of the Respiratory Programme. At that time, Hamilton had a population of 300,000, with two full-time respirologists, Robert Cornett at the Hamilton General Hospital and Michael Newhouse at St Joseph’s Hospital. From the clinical perspective, the aim of the Respiratory Programme was to develop a network approach to clinical problems among the five hospitals in the Hamilton region, with St Joseph’s Hospital serving as a regional referral centre, and each hospital developing its own focus: intensive care and burns units at the Hamilton General Hospital; cancer at the Henderson (later Juravinski) Hospital; tuberculosis and rehabilitation at the Chedoke Hospital; pediatrics and neonatal intensive care at the McMaster University Medical Centre; and community care at the Joseph Brant Hospital in Burlington (Ontario). The network provided an ideal base for a specialty residency program. There was also the need to establish viable research. These objectives were achieved through collaboration, support of hospital administration, and recruitment of clinicians and faculty, mainly from our own trainees and research fellows. By the mid-1970s the respiratory group numbered more than 25; outpatient clinic visits and research had grown beyond our initial expectations. The international impact of the group became reflected in the clinical and basic research endeavours. ASTHMA: Freddy Hargreave and Jerry Dolovich established methods to measure airway responsiveness to histamine and methacholine. Allergen inhalation was shown to increase airway responsiveness for several weeks

  5. Optical soliton solutions for the higher-order dispersive cubic-quintic nonlinear Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru

    2017-12-01

    In this paper, we analyze new optical soliton solutions to the higher-order dispersive cubic-quintic nonlinear Schrödinger equation (NLSE) using three integration schemes. The schemes used in this paper are modified tanh-coth (MTC), extended Jacobi elliptic function expansion (EJEF), and two variable (G‧ / G , 1 / G) -expansion methods. We obtain new solutions that to the best of our knowledge do not exist previously. The obtained solutions includes bright, dark, combined bright-dark, singular as well as periodic waves solitons. The obtained solutions may be used to explain and understand the physical nature of the wave spreads in the most dispersive optical medium. Some interesting figures for the physical interpretation of the obtained solutions are also presented.

  6. Chain mapping approach of Hamiltonian for FMO complex using associated, generalized and exceptional Jacobi polynomials

    NASA Astrophysics Data System (ADS)

    Mahdian, M.; Arjmandi, M. B.; Marahem, F.

    2016-06-01

    The excitation energy transfer (EET) in photosynthesis complex has been widely investigated in recent years. However, one of the main problems is simulation of this complex under realistic condition. In this paper by using the associated, generalized and exceptional Jacobi polynomials, firstly, we introduce the spectral density of Fenna-Matthews-Olson (FMO) complex. Afterward, we obtain a map that transforms the Hamiltonian of FMO complex as an open quantum system to a one-dimensional chain of oscillatory modes with only nearest neighbor interaction in which the system is coupled only to first mode of chain. The frequency and coupling strength of each mode can be analytically obtained from recurrence coefficient of mentioned orthogonal polynomials.

  7. The simulation of shock- and impact-driven flows with Mie-Gruneisen equations of state

    NASA Astrophysics Data System (ADS)

    Ward, Geoffrey M.

    after shock interaction is also examined. The formation of incipient weak shock waves in the heavy fluid driven by waves emanating from the perturbed transmitted shock is observed when an expansion wave is reflected. Next, the ghost fluid method [83] is explored for application to impact-driven flows with Mie-Gruneisen equations of state in a vacuum. Free surfaces are defined utilizing a level-set approach. The level-set is reinitialized to the signed distance function periodically by solution to a Hamilton-Jacobi differential equation in artificial time. Flux reconstruction along each Cartesian direction of the domain is performed by subdividing in a way that allows for robust treatment of grid-scale sized voids. Ghost cells in voided regions near the material-vacuum interface are determined from surface-normal Riemann problem solution. The method is then applied to several impact problems of interest. First, a one-dimensional impact problem is examined in Mie-Gruneisen aluminum with simple point erosion used to model separation by spallation under high tension. A similar three-dimensional axisymmetric simulation of two rods impacting is then performed without a model for spallation. Further results for three-dimensional axisymmetric simulation of a sphere hitting a plate are then presented. Finally, a brief investigation of the assumptions utilized in modeling solids as isotropic fluids is undertaken. An Eulerian solver approach to handling elastic and elastic-plastic solids is utilized for comparison to the simple fluid model assumption. First, in one dimension an impact problem is examined for elastic, elastic-plastic, and fluid equations of state for aluminum. The results demonstrate that in one dimension the fluid models the plastic shock structure of the flow well. Further investigation is made using a three-dimensional axisymmetric simulation of an impact problem involving a copper cylinder surrounded by aluminum. An aluminum slab impact drives a faster shock in

  8. Recognizing the Presidents: Was Alexander Hamilton President?

    PubMed

    Roediger, Henry L; DeSoto, K Andrew

    2016-05-01

    Studies over the past 40 years have shown that Americans can recall about half the U.S. presidents. Do people know the presidents even though they are unable to access them for recall? We investigated this question using the powerful cues of a recognition test. Specifically, we tested the ability of 326 online subjects to recognize U.S. presidents when presented with their full names among various types of lures. The hit rate for presidential recognition was .88, well above the proportion produced in free recall but far from perfect. Presidents Franklin Pierce and Chester Arthur were recognized less than 60% of the time. Interestingly, four nonpresidents were falsely recognized at relatively high rates, and Alexander Hamilton was more frequently identified as president than were several actual presidents. Even on a recognition test, knowledge of American presidents is imperfect and prone to error. The false alarm data support the theory that false fame can arise from contextual familiarity. © The Author(s) 2016.

  9. A New Control Paradigm for Stochastic Differential Equations

    NASA Astrophysics Data System (ADS)

    Schmid, Matthias J. A.

    This study presents a novel comprehensive approach to the control of dynamic systems under uncertainty governed by stochastic differential equations (SDEs). Large Deviations (LD) techniques are employed to arrive at a control law for a large class of nonlinear systems minimizing sample path deviations. Thereby, a paradigm shift is suggested from point-in-time to sample path statistics on function spaces. A suitable formal control framework which leverages embedded Freidlin-Wentzell theory is proposed and described in detail. This includes the precise definition of the control objective and comprises an accurate discussion of the adaptation of the Freidlin-Wentzell theorem to the particular situation. The new control design is enabled by the transformation of an ill-posed control objective into a well-conditioned sequential optimization problem. A direct numerical solution process is presented using quadratic programming, but the emphasis is on the development of a closed-form expression reflecting the asymptotic deviation probability of a particular nominal path. This is identified as the key factor in the success of the new paradigm. An approach employing the second variation and the differential curvature of the effective action is suggested for small deviation channels leading to the Jacobi field of the rate function and the subsequently introduced Jacobi field performance measure. This closed-form solution is utilized in combination with the supplied parametrization of the objective space. For the first time, this allows for an LD based control design applicable to a large class of nonlinear systems. Thus, Minimum Large Deviations (MLD) control is effectively established in a comprehensive structured framework. The construction of the new paradigm is completed by an optimality proof for the Jacobi field performance measure, an interpretive discussion, and a suggestion for efficient implementation. The potential of the new approach is exhibited by its extension

  10. Aircraft loss-of-control prevention and recovery: A hybrid control strategy

    NASA Astrophysics Data System (ADS)

    Dongmo, Jean-Etienne Temgoua

    The Complexity of modern commercial and military aircrafts has necessitated better protection and recovery systems. With the tremendous advances in computer technology, control theory and better mathematical models, a number of issues (Prevention, Reconfiguration, Recovery, Operation near critical points, ... etc) moderately addressed in the past have regained interest in the aeronautical industry. Flight envelope is essential in all flying aerospace vehicles. Typically, flying the vehicle means remaining within the flight envelope at all times. Operation outside the normal flight regime is usually subject to failure of components (Actuators, Engines, Deflection Surfaces) , pilots's mistakes, maneuverability near critical points and environmental conditions (crosswinds...) and in general characterized as Loss-Of-Control (LOC) because the aircraft no longer responds to pilot's inputs as expected. For the purpose of this work, (LOC) in aircraft is defined as the departure from the safe set (controlled flight) recognized as the maximum controllable (reachable) set in the initial flight envelope. The LOC can be reached either through failure, unintended maneuvers, evolution near irregular points and disturbances. A coordinated strategy is investigated and designed to ensure that the aircraft can maneuver safely in their constraint domain and can also recover from abnormal regime. The procedure involves the computation of the largest controllable (reachable) set (Safe set) contained in the initial prescribed envelope. The problem is posed as a reachability problem using Hamilton-Jacobi Partial Differential Equation (HJ-PDE) where a cost function is set to he minimized along trajectory departing from the given set. Prevention is then obtained by computing the controller which would allow the flight vehicle to remain in the maximum controlled set in a multi-objective set up. Then the recovery procedure is illustrated with a two-point boundary value problem. Once

  11. Covariant approach of perturbations in Lovelock type brane gravity

    NASA Astrophysics Data System (ADS)

    Bagatella-Flores, Norma; Campuzano, Cuauhtemoc; Cruz, Miguel; Rojas, Efraín

    2016-12-01

    We develop a covariant scheme to describe the dynamics of small perturbations on Lovelock type extended objects propagating in a flat Minkowski spacetime. The higher-dimensional analogue of the Jacobi equation in this theory becomes a wave type equation for a scalar field Φ . Whithin this framework, we analyse the stability of membranes with a de Sitter geometry where we find that the Jacobi equation specializes to a Klein-Gordon (KG) equation for Φ possessing a tachyonic mass. This shows that, to some extent, these types of extended objects share the symmetries of the Dirac-Nambu-Goto (DNG) action which is by no means coincidental because the DNG model is the simplest included in this type of gravity.

  12. Optimized growth and reorientation of anisotropic material based on evolution equations

    NASA Astrophysics Data System (ADS)

    Jantos, Dustin R.; Junker, Philipp; Hackl, Klaus

    2018-07-01

    Modern high-performance materials have inherent anisotropic elastic properties. The local material orientation can thus be considered to be an additional design variable for the topology optimization of structures containing such materials. In our previous work, we introduced a variational growth approach to topology optimization for isotropic, linear-elastic materials. We solved the optimization problem purely by application of Hamilton's principle. In this way, we were able to determine an evolution equation for the spatial distribution of density mass, which can be evaluated in an iterative process within a solitary finite element environment. We now add the local material orientation described by a set of three Euler angles as additional design variables into the three-dimensional model. This leads to three additional evolution equations that can be separately evaluated for each (material) point. Thus, no additional field unknown within the finite element approach is needed, and the evolution of the spatial distribution of density mass and the evolution of the Euler angles can be evaluated simultaneously.

  13. Surface modification of ZnO nanorods with Hamilton receptors.

    PubMed

    Zeininger, Lukas; Klaumünzer, Martin; Peukert, Wolfgang; Hirsch, Andreas

    2015-04-13

    A new prototype of a Hamilton receptor suitable for the functionalization of inorganic nanoparticles was synthesized and characterized. The hydrogen bonding receptor was coupled to a catechol moiety, which served as anchor group for the functionalization of metal oxides, in particular zinc oxide. Synthesized zinc oxide nanorods [ZnO] were used for surface functionalization. The wet-chemical functionalization procedure towards monolayer-grafted particles [ZnO-HR] is described and a detailed characterization study is presented. In addition, the detection of specific cyanurate molecules is demonstrated. The hybrid structures [ZnO-HR-CA] were stable towards agglomeration and exhibited enhanced dispersability in apolar solvents. This observation, in combination with several spectroscopic experiments gave evidence of the highly directional supramolecular recognition at the surface of nanoparticles.

  14. 78 FR 22873 - Hamilton Street Hydro, LLC; Notice of Preliminary Permit Application Accepted for Filing and...

    Federal Register 2010, 2011, 2012, 2013, 2014

    2013-04-17

    ... Hydro, LLC; Notice of Preliminary Permit Application Accepted for Filing and Soliciting Comments, Motions To Intervene, and Competing Applications On February 19, 2013, Hamilton Street Hydro, LLC, filed an application for a preliminary permit, pursuant to section 4(f) of the Federal Power Act (FPA...

  15. 78 FR 22872 - Hamilton Street Hydro, LLC; Notice of Preliminary Permit Application Accepted for Filing and...

    Federal Register 2010, 2011, 2012, 2013, 2014

    2013-04-17

    ... Hydro, LLC; Notice of Preliminary Permit Application Accepted for Filing and Soliciting Comments, Motions To Intervene, and Competing Applications On February 19, 2013, Hamilton Street Hydro, LLC, filed an application for a preliminary permit, pursuant to section 4(f) of the Federal Power Act (FPA...

  16. Mobile Air Monitoring: Measuring Change in Air Quality in the City of Hamilton, 2005-2010

    ERIC Educational Resources Information Center

    Adams, Matthew D.; DeLuca, Patrick F.; Corr, Denis; Kanaroglou, Pavlos S.

    2012-01-01

    This paper examines the change in air pollutant concentrations between 2005 and 2010 occurring in the City of Hamilton, Ontario, Canada. After analysis of stationary air pollutant concentration data, we analyze mobile air pollutant concentration data. Air pollutants included in the analysis are CO, PM[subscript 2.5], SO[subscript 2], NO,…

  17. 78 FR 28838 - Hamilton Street Hydro, LLC; Notice of Preliminary Permit Application Accepted for Filing and...

    Federal Register 2010, 2011, 2012, 2013, 2014

    2013-05-16

    ... Hydro, LLC; Notice of Preliminary Permit Application Accepted for Filing and Soliciting Comments, Motions To Intervene, and Competing Applications On March 26, 2013, Hamilton Street Hydro, LLC, filed an application for a preliminary permit, pursuant to section 4(f) of the Federal Power Act (FPA), proposing to...

  18. Asymptotics for moist deep convection I: refined scalings and self-sustaining updrafts

    NASA Astrophysics Data System (ADS)

    Hittmeir, Sabine; Klein, Rupert

    2018-04-01

    Moist processes are among the most important drivers of atmospheric dynamics, and scale analysis and asymptotics are cornerstones of theoretical meteorology. Accounting for moist processes in systematic scale analyses therefore seems of considerable importance for the field. Klein and Majda (Theor Comput Fluid Dyn 20:525-551, 2006) proposed a scaling regime for the incorporation of moist bulk microphysics closures in multiscale asymptotic analyses of tropical deep convection. This regime is refined here to allow for mixtures of ideal gases and to establish consistency with a more general multiple scales modeling framework for atmospheric flows. Deep narrow updrafts, the so-called hot towers, constitute principal building blocks of larger scale storm systems. They are analyzed here in a sample application of the new scaling regime. A single quasi-one-dimensional upright columnar cloud is considered on the vertical advective (or tower life cycle) time scale. The refined asymptotic scaling regime is essential for this example as it reveals a new mechanism for the self-sustainance of such updrafts. Even for strongly positive convectively available potential energy, a vertical balance of buoyancy forces is found in the presence of precipitation. This balance induces a diagnostic equation for the vertical velocity, and it is responsible for the generation of self-sustained balanced updrafts. The time-dependent updraft structure is encoded in a Hamilton-Jacobi equation for the precipitation mixing ratio. Numerical solutions of this equation suggest that the self-sustained updrafts may strongly enhance hot tower life cycles.

  19. A nonlinear relaxation/quasi-Newton algorithm for the compressible Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Edwards, Jack R.; Mcrae, D. S.

    1992-01-01

    A highly efficient implicit method for the computation of steady, two-dimensional compressible Navier-Stokes flowfields is presented. The discretization of the governing equations is hybrid in nature, with flux-vector splitting utilized in the streamwise direction and central differences with flux-limited artificial dissipation used for the transverse fluxes. Line Jacobi relaxation is used to provide a suitable initial guess for a new nonlinear iteration strategy based on line Gauss-Seidel sweeps. The applicability of quasi-Newton methods as convergence accelerators for this and other line relaxation algorithms is discussed, and efficient implementations of such techniques are presented. Convergence histories and comparisons with experimental data are presented for supersonic flow over a flat plate and for several high-speed compression corner interactions. Results indicate a marked improvement in computational efficiency over more conventional upwind relaxation strategies, particularly for flowfields containing large pockets of streamwise subsonic flow.

  20. Morphological and molecular review of Jacob's Mountain Stream Keelback Opisthotropis jacobi Angel Bourret, 1933 (Squamata: Natricidae) with description of a sibling species from northern Vietnam.

    PubMed

    Ziegler, Thomas; David, Patrick; Ziegler, Tim N; Pham, Cuong T; Nguyen, Truong Q; Le, Minh D

    2018-01-21

    New morphological data including hemipenis morphology is provided for Opisthotropis jacobi, a poorly known Mountain Stream Keelback from Vietnam and China, based on three newly collected individuals from Sa Pa (Lao Cai Province) and Tam Dao (Vinh Phuc Province) in northern Vietnam. In addition, morphological data from Vietnam is summarized based on the original description (Angel Bourret 1933), on the overview book by Bourret (1936) and on a number of smaller, little-known contributions by the latter author along with re-examination of specimens deposited in the herpetological collection of the Muséum national d'Histoire naturelle, Paris. We also sequenced a fragment of the mitochondrial cytochrome b from the newly collected specimens of the Jacob's Mountain Stream Keelback and performed molecular analyses of new and existing data of the genus. A recently discovered Opisthotropis population from Tay Yen Tu Nature Reserve in Bac Giang Province, northern Vietnam, which at the first glance resembled O. jacobi morphologically, is shown to diverge both genetically and morphologically from the existing species and is herein described as a new species. Opisthotropis voquyi sp. nov. is characterized by the combination of the following characters: internasal not in contact with loreal; one preocular; usually two postoculars; one anterior temporal; one posterior temporal; 7 or 8, rarely 9 supralabials; 25 maxillary teeth; subcaudals 74-86; 15 dorsal scale rows at neck, at midbody and before vent; body scales smooth or only with few faint keels; and dorsal scales being greyish, greyish-brown or brown in preservative, posteriorly more or less edged with pale greyish-brown. Phylogenetically, the new species is supported as a sister taxon to O. jacobi, but the two taxa are approximately 10% divergent based on cytochrome b data.

  1. Inertial Manifold and Large Deviations Approach to Reduced PDE Dynamics

    NASA Astrophysics Data System (ADS)

    Cardin, Franco; Favretti, Marco; Lovison, Alberto

    2017-09-01

    In this paper a certain type of reaction-diffusion equation—similar to the Allen-Cahn equation—is the starting point for setting up a genuine thermodynamic reduction i.e. involving a finite number of parameters or collective variables of the initial system. We firstly operate a finite Lyapunov-Schmidt reduction of the cited reaction-diffusion equation when reformulated as a variational problem. In this way we gain a finite-dimensional ODE description of the initial system which preserves the gradient structure of the original one and that is exact for the static case and only approximate for the dynamic case. Our main concern is how to deal with this approximate reduced description of the initial PDE. To start with, we note that our approximate reduced ODE is similar to the approximate inertial manifold introduced by Temam and coworkers for Navier-Stokes equations. As a second approach, we take into account the uncertainty (loss of information) introduced with the above mentioned approximate reduction by considering the stochastic version of the ODE. We study this reduced stochastic system using classical tools from large deviations, viscosity solutions and weak KAM Hamilton-Jacobi theory. In the last part we suggest a possible use of a result of our approach in the comprehensive treatment non equilibrium thermodynamics given by Macroscopic Fluctuation Theory.

  2. Moyal dynamics and trajectories

    NASA Astrophysics Data System (ADS)

    Braunss, G.

    2010-01-01

    We give first an approximation of the operator δh: f → δhf := h*planckf - f*planckh in terms of planck2n, n >= 0, where h\\equiv h(p,q), (p,q)\\in {\\mathbb R}^{2 n} , is a Hamilton function and *planck denotes the star product. The operator, which is the generator of time translations in a *planck-algebra, can be considered as a canonical extension of the Liouville operator Lh: f → Lhf := {h, f}Poisson. Using this operator we investigate the dynamics and trajectories of some examples with a scheme that extends the Hamilton-Jacobi method for classical dynamics to Moyal dynamics. The examples we have chosen are Hamiltonians with a one-dimensional quartic potential and two-dimensional radially symmetric nonrelativistic and relativistic Coulomb potentials, and the Hamiltonian for a Schwarzschild metric. We further state a conjecture concerning an extension of the Bohr-Sommerfeld formula for the calculation of the exact eigenvalues for systems with classically periodic trajectories.

  3. End of Life Disposal for Three Libration Point Missions through Manipulation of the Jacobi Constant and Zero Velocity Curves

    NASA Technical Reports Server (NTRS)

    Peterson, Jeremy D.; Brown, Jonathan M.

    2015-01-01

    The aim of this investigation is to determine the feasibility of mission disposal by inserting the spacecraft into a heliocentric orbit along the unstable manifold and then manipulating the Jacobi constant to prevent the spacecraft from returning to the Earth-Moon system. This investigation focuses around L1 orbits representative of ACE, WIND, and SOHO. It will model the impulsive delta-V necessary to close the zero velocity curves after escape through the L1 gateway in the circular restricted three body model and also include full ephemeris force models and higher fidelity finite maneuver models for the three spacecraft.

  4. Comment on “Maxwell's equations and electromagnetic Lagrangian density in fractional form” [J. Math. Phys. 53, 033505 (2012)

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Rabei, Eqab M.; Al-Jamel, A.; Widyan, H.

    In a recent paper, Jaradat et al. [J. Math. Phys. 53, 033505 (2012)] have presented the fractional form of the electromagnetic Lagrangian density within the Riemann-Liouville fractional derivative. They claimed that the Agrawal procedure [O. P. Agrawal, J. Math. Anal. Appl. 272, 368 (2002)] is used to obtain Maxwell's equations in the fractional form, and the Hamilton's equations of motion together with the conserved quantities obtained from fractional Noether's theorem are reported. In this comment, we draw the attention that there are some serious steps of the procedure used in their work are not applicable even though their final resultsmore » are correct. Their work should have been done based on a formulation as reported by Baleanu and Muslih [Phys. Scr. 72, 119 (2005)].« less

  5. Pair production of scalar dyons in Kerr-Newman black holes

    NASA Astrophysics Data System (ADS)

    Chen, Chiang-Mei; Kim, Sang Pyo; Sun, Jia-Rui; Tang, Fu-Yi

    2018-06-01

    We study the spontaneous pair production of scalar dyons in the near extremal dyonic Kerr-Newman (KN) black hole, which contains a warped AdS3 structure in the near horizon region. The leading term contribution of the pair production rate and the absorption cross section ratio are also calculated using the Hamilton-Jacobi approach and the thermal interpretation is given. In addition, the holographic dual conformal field theories (CFTs) descriptions of the pair production rate and absorption cross section ratios are analyzed both in the J-, Q- and P-pictures respectively based on the threefold dyonic KN/CFTs dualities.

  6. Adiabiatic invariants of the Kepler problem: an elementary treatment

    NASA Astrophysics Data System (ADS)

    Borghi, Riccardo

    2013-09-01

    An elementary introduction to the adiabatic invariants of the Kepler problem is proposed. Unlike the other didactical expositions already present in the literature, which are based on the Hamilton-Jacobi theory of mechanics, our derivation is suitable to be grasped even by first-year undergraduates. A central role in the present analysis is played by an elementary proof of the virial theorem for the Kepler problem which is based on the chain rule for derivatives. As a byproduct of our analysis, an interpretation of Keplerian orbit eccentricities in terms of the time average of the position vector direction is also provided.

  7. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kerner, Ryan; Mann, R.B.

    We investigate quantum tunnelling methods for calculating black hole temperature, specifically the null-geodesic method of Parikh and Wilczek and the Hamilton-Jacobi Ansatz method of Angheben et al. We consider application of these methods to a broad class of spacetimes with event horizons, including Rindler and nonstatic spacetimes such as Kerr-Newman and Taub-NUT. We obtain a general form for the temperature of Taub-NUT-AdS black holes that is commensurate with other methods. We examine the limitations of these methods for extremal black holes, taking the extremal Reissner-Nordstrom spacetime as a case in point.

  8. Measuring Depression at the End of Life: Is the Hamilton Depression Rating Scale a Valid Instrument?

    ERIC Educational Resources Information Center

    Olden, Megan; Rosenfeld, Barry; Pessin, Hayley; Breitbart, William

    2009-01-01

    Depression at the end of life is a common mental health issue with serious implications for quality of life and decision making. This study investigated the reliability and validity of one of the most frequently used measures of depression, the Hamilton Depression Rating Scale (HAM-D) in 422 patients with terminal cancer admitted to a palliative…

  9. Comparison of Implicit Schemes for the Incompressible Navier-Stokes Equations

    NASA Technical Reports Server (NTRS)

    Rogers, Stuart E.

    1995-01-01

    For a computational flow simulation tool to be useful in a design environment, it must be very robust and efficient. To develop such a tool for incompressible flow applications, a number of different implicit schemes are compared for several two-dimensional flow problems in the current study. The schemes include Point-Jacobi relaxation, Gauss-Seidel line relaxation, incomplete lower-upper decomposition, and the generalized minimum residual method preconditioned with each of the three other schemes. The efficiency of the schemes is measured in terms of the computing time required to obtain a steady-state solution for the laminar flow over a backward-facing step, the flow over a NACA 4412 airfoil, and the flow over a three-element airfoil using overset grids. The flow solver used in the study is the INS2D code that solves the incompressible Navier-Stokes equations using the method of artificial compressibility and upwind differencing of the convective terms. The results show that the generalized minimum residual method preconditioned with the incomplete lower-upper factorization outperforms all other methods by at least a factor of 2.

  10. Finite-horizon control-constrained nonlinear optimal control using single network adaptive critics.

    PubMed

    Heydari, Ali; Balakrishnan, Sivasubramanya N

    2013-01-01

    To synthesize fixed-final-time control-constrained optimal controllers for discrete-time nonlinear control-affine systems, a single neural network (NN)-based controller called the Finite-horizon Single Network Adaptive Critic is developed in this paper. Inputs to the NN are the current system states and the time-to-go, and the network outputs are the costates that are used to compute optimal feedback control. Control constraints are handled through a nonquadratic cost function. Convergence proofs of: 1) the reinforcement learning-based training method to the optimal solution; 2) the training error; and 3) the network weights are provided. The resulting controller is shown to solve the associated time-varying Hamilton-Jacobi-Bellman equation and provide the fixed-final-time optimal solution. Performance of the new synthesis technique is demonstrated through different examples including an attitude control problem wherein a rigid spacecraft performs a finite-time attitude maneuver subject to control bounds. The new formulation has great potential for implementation since it consists of only one NN with single set of weights and it provides comprehensive feedback solutions online, though it is trained offline.

  11. Black holes, hidden symmetries, and complete integrability

    NASA Astrophysics Data System (ADS)

    Frolov, Valeri P.; Krtouš, Pavel; Kubizňák, David

    2017-11-01

    The study of higher-dimensional black holes is a subject which has recently attracted vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of higher-dimensional black holes with the spherical horizon topology and described by the Kerr-NUT-(A)dS metrics are very similar to the properties of the well known four-dimensional Kerr metric. This remarkable result stems from the existence of a single object called the principal tensor. In our review we discuss explicit and hidden symmetries of higher-dimensional Kerr-NUT-(A)dS black hole spacetimes. We start with discussion of the Killing and Killing-Yano objects representing explicit and hidden symmetries. We demonstrate that the principal tensor can be used as a "seed object" which generates all these symmetries. It determines the form of the geometry, as well as guarantees its remarkable properties, such as special algebraic type of the spacetime, complete integrability of geodesic motion, and separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations. The review also contains a discussion of different applications of the developed formalism and its possible generalizations.

  12. Modeling and Computation of Transboundary Industrial Pollution with Emission Permits Trading by Stochastic Differential Game

    PubMed Central

    2015-01-01

    Transboundary industrial pollution requires international actions to control its formation and effects. In this paper, we present a stochastic differential game to model the transboundary industrial pollution problems with emission permits trading. More generally, the process of emission permits price is assumed to be stochastic and to follow a geometric Brownian motion (GBM). We make use of stochastic optimal control theory to derive the system of Hamilton-Jacobi-Bellman (HJB) equations satisfied by the value functions for the cooperative and the noncooperative games, respectively, and then propose a so-called fitted finite volume method to solve it. The efficiency and the usefulness of this method are illustrated by the numerical experiments. The two regions’ cooperative and noncooperative optimal emission paths, which maximize the regions’ discounted streams of the net revenues, together with the value functions, are obtained. Additionally, we can also obtain the threshold conditions for the two regions to decide whether they cooperate or not in different cases. The effects of parameters in the established model on the results have been also examined. All the results demonstrate that the stochastic emission permits prices can motivate the players to make more flexible strategic decisions in the games. PMID:26402322

  13. Modeling and Computation of Transboundary Industrial Pollution with Emission Permits Trading by Stochastic Differential Game.

    PubMed

    Chang, Shuhua; Wang, Xinyu; Wang, Zheng

    2015-01-01

    Transboundary industrial pollution requires international actions to control its formation and effects. In this paper, we present a stochastic differential game to model the transboundary industrial pollution problems with emission permits trading. More generally, the process of emission permits price is assumed to be stochastic and to follow a geometric Brownian motion (GBM). We make use of stochastic optimal control theory to derive the system of Hamilton-Jacobi-Bellman (HJB) equations satisfied by the value functions for the cooperative and the noncooperative games, respectively, and then propose a so-called fitted finite volume method to solve it. The efficiency and the usefulness of this method are illustrated by the numerical experiments. The two regions' cooperative and noncooperative optimal emission paths, which maximize the regions' discounted streams of the net revenues, together with the value functions, are obtained. Additionally, we can also obtain the threshold conditions for the two regions to decide whether they cooperate or not in different cases. The effects of parameters in the established model on the results have been also examined. All the results demonstrate that the stochastic emission permits prices can motivate the players to make more flexible strategic decisions in the games.

  14. Event-Triggered Distributed Control of Nonlinear Interconnected Systems Using Online Reinforcement Learning With Exploration.

    PubMed

    Narayanan, Vignesh; Jagannathan, Sarangapani

    2017-09-07

    In this paper, a distributed control scheme for an interconnected system composed of uncertain input affine nonlinear subsystems with event triggered state feedback is presented by using a novel hybrid learning scheme-based approximate dynamic programming with online exploration. First, an approximate solution to the Hamilton-Jacobi-Bellman equation is generated with event sampled neural network (NN) approximation and subsequently, a near optimal control policy for each subsystem is derived. Artificial NNs are utilized as function approximators to develop a suite of identifiers and learn the dynamics of each subsystem. The NN weight tuning rules for the identifier and event-triggering condition are derived using Lyapunov stability theory. Taking into account, the effects of NN approximation of system dynamics and boot-strapping, a novel NN weight update is presented to approximate the optimal value function. Finally, a novel strategy to incorporate exploration in online control framework, using identifiers, is introduced to reduce the overall cost at the expense of additional computations during the initial online learning phase. System states and the NN weight estimation errors are regulated and local uniformly ultimately bounded results are achieved. The analytical results are substantiated using simulation studies.

  15. Iterative Adaptive Dynamic Programming for Solving Unknown Nonlinear Zero-Sum Game Based on Online Data.

    PubMed

    Zhu, Yuanheng; Zhao, Dongbin; Li, Xiangjun

    2017-03-01

    H ∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces errors that are detrimental to the control performance. To overcome this problem, an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous-time, unknown nonlinear ZSG with only online data. A model-free approach to the Hamilton-Jacobi-Isaacs equation is developed based on the policy iteration method. Control and disturbance policies and value are approximated by neural networks (NNs) under the critic-actor-disturber structure. The NN weights are solved by the least-squares method. According to the theoretical analysis, our algorithm is equivalent to a Gauss-Newton method solving an optimization problem, and it converges uniformly to the optimal solution. The online data can also be used repeatedly, which is highly efficient. Simulation results demonstrate its feasibility to solve the unknown nonlinear ZSG. When compared with other algorithms, it saves a significant amount of online measurement time.

  16. Model-Free Optimal Tracking Control via Critic-Only Q-Learning.

    PubMed

    Luo, Biao; Liu, Derong; Huang, Tingwen; Wang, Ding

    2016-10-01

    Model-free control is an important and promising topic in control fields, which has attracted extensive attention in the past few years. In this paper, we aim to solve the model-free optimal tracking control problem of nonaffine nonlinear discrete-time systems. A critic-only Q-learning (CoQL) method is developed, which learns the optimal tracking control from real system data, and thus avoids solving the tracking Hamilton-Jacobi-Bellman equation. First, the Q-learning algorithm is proposed based on the augmented system, and its convergence is established. Using only one neural network for approximating the Q-function, the CoQL method is developed to implement the Q-learning algorithm. Furthermore, the convergence of the CoQL method is proved with the consideration of neural network approximation error. With the convergent Q-function obtained from the CoQL method, the adaptive optimal tracking control is designed based on the gradient descent scheme. Finally, the effectiveness of the developed CoQL method is demonstrated through simulation studies. The developed CoQL method learns with off-policy data and implements with a critic-only structure, thus it is easy to realize and overcome the inadequate exploration problem.

  17. Black holes, hidden symmetries, and complete integrability.

    PubMed

    Frolov, Valeri P; Krtouš, Pavel; Kubizňák, David

    2017-01-01

    The study of higher-dimensional black holes is a subject which has recently attracted vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of higher-dimensional black holes with the spherical horizon topology and described by the Kerr-NUT-(A)dS metrics are very similar to the properties of the well known four-dimensional Kerr metric. This remarkable result stems from the existence of a single object called the principal tensor. In our review we discuss explicit and hidden symmetries of higher-dimensional Kerr-NUT-(A)dS black hole spacetimes. We start with discussion of the Killing and Killing-Yano objects representing explicit and hidden symmetries. We demonstrate that the principal tensor can be used as a "seed object" which generates all these symmetries. It determines the form of the geometry, as well as guarantees its remarkable properties, such as special algebraic type of the spacetime, complete integrability of geodesic motion, and separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations. The review also contains a discussion of different applications of the developed formalism and its possible generalizations.

  18. Wavefronts, actions and caustics determined by the probability density of an Airy beam

    NASA Astrophysics Data System (ADS)

    Espíndola-Ramos, Ernesto; Silva-Ortigoza, Gilberto; Sosa-Sánchez, Citlalli Teresa; Julián-Macías, Israel; de Jesús Cabrera-Rosas, Omar; Ortega-Vidals, Paula; Alejandro Juárez-Reyes, Salvador; González-Juárez, Adriana; Silva-Ortigoza, Ramón

    2018-07-01

    The main contribution of the present work is to use the probability density of an Airy beam to identify its maxima with the family of caustics associated with the wavefronts determined by the level curves of a one-parameter family of solutions to the Hamilton–Jacobi equation with a given potential. To this end, we give a classical mechanics characterization of a solution of the one-dimensional Schrödinger equation in free space determined by a complete integral of the Hamilton–Jacobi and Laplace equations in free space. That is, with this type of solution, we associate a two-parameter family of wavefronts in the spacetime, which are the level curves of a one-parameter family of solutions to the Hamilton–Jacobi equation with a determined potential, and a one-parameter family of caustics. The general results are applied to an Airy beam to show that the maxima of its probability density provide a discrete set of: caustics, wavefronts and potentials. The results presented here are a natural generalization of those obtained by Berry and Balazs in 1979 for an Airy beam. Finally, we remark that, in a natural manner, each maxima of the probability density of an Airy beam determines a Hamiltonian system.

  19. Tensor products of U{sub q}{sup Prime }sl-caret(2)-modules and the big q{sup 2}-Jacobi function transform

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gade, R. M.

    2013-01-15

    Four tensor products of evaluation modules of the quantum affine algebra U{sub q}{sup Prime }sl-caret(2) obtained from the negative and positive series, the complementary and the strange series representations are investigated. Linear operators R(z) satisfying the intertwining property on finite linear combinations of the canonical basis elements of the tensor products are described in terms of two sets of infinite sums {l_brace}{tau}{sup (r,t)}{r_brace}{sub r,t Element-Of Z{sub {>=}{sub 0}}} and {l_brace}{tau}{sup (r,t)}{r_brace}{sub r,t Element-Of Z{sub {>=}{sub 0}}} involving big q{sup 2}-Jacobi functions or related nonterminating basic hypergeometric series. Inhomogeneous recurrence relations can be derived for both sets. Evaluations of the simplestmore » sums provide the corresponding initial conditions. For the first set of sums the relations entail a big q{sup 2}-Jacobi function transform pair. An integral decomposition is obtained for the sum {tau}{sup (r,t)}. A partial description of the relation between the decompositions of the tensor products with respect to U{sub q}sl(2) or with respect to its complement in U{sub q}{sup Prime }sl-caret(2) can be formulated in terms of Askey-Wilson function transforms. For a particular combination of two tensor products, the occurrence of proper U{sub q}{sup Prime }sl-caret(2)-submodules is discussed.« less

  20. Topographical scattering of gravity waves

    NASA Astrophysics Data System (ADS)

    Miles, J. W.; Chamberlain, P. G.

    1998-04-01

    A systematic hierarchy of partial differential equations for linear gravity waves in water of variable depth is developed through the expansion of the average Lagrangian in powers of [mid R:][nabla del, Hamilton operator][mid R:] (h=depth, [nabla del, Hamilton operator]h=slope). The first and second members of this hierarchy, the Helmholtz and conventional mild-slope equations, are second order. The third member is fourth order but may be approximated by Chamberlain & Porter's (1995) ‘modified mild-slope’ equation, which is second order and comprises terms in [nabla del, Hamilton operator]2h and ([nabla del, Hamilton operator]h)2 that are absent from the mild-slope equation. Approximate solutions of the mild-slope and modified mild-slope equations for topographical scattering are determined through an iterative sequence, starting from a geometrical-optics approximation (which neglects reflection), then a quasi-geometrical-optics approximation, and on to higher-order results. The resulting reflection coefficient for a ramp of uniform slope is compared with the results of numerical integrations of each of the mild-slope equation (Booij 1983), the modified mild-slope equation (Porter & Staziker 1995), and the full linear equations (Booij 1983). Also considered is a sequence of sinusoidal sandbars, for which Bragg resonance may yield rather strong reflection and for which the modified mild-slope approximation is in close agreement with Mei's (1985) asymptotic approximation.

  1. Geometrical analysis of the LiCN vibrational dynamics: a stability geometrical indicator.

    PubMed

    Vergel, A; Benito, R M; Losada, J C; Borondo, F

    2014-02-01

    The vibrational dynamics of the LiNC/LiCN molecular system is examined making use of the Riemannian geometry. Stability and chaoticity are analyzed, in this context, by means of the Jacobi-Levi-Civita equations, derived from the Jacobi metric, and its solutions. A dynamical indicator, called stability geometrical indicator, is introduced in order to ascertain the dynamical characteristics of stability and chaos in the molecule under study.

  2. Source apportionment of PAH in Hamilton Harbour suspended sediments: comparison of two factor analysis methods.

    PubMed

    Sofowote, Uwayemi M; McCarry, Brian E; Marvin, Christopher H

    2008-08-15

    A total of 26 suspended sediment samples collected over a 5-year period in Hamilton Harbour, Ontario, Canada and surrounding creeks were analyzed for a suite of polycyclic aromatic hydrocarbons and sulfur heterocycles. Hamilton Harbour sediments contain relatively high levels of polycyclic aromatic compounds and heavy metals due to emissions from industrial and mobile sources. Two receptor modeling methods using factor analyses were compared to determine the profiles and relative contributions of pollution sources to the harbor; these methods are principal component analyses (PCA) with multiple linear regression analysis (MLR) and positive matrix factorization (PMF). Both methods identified four factors and gave excellent correlation coefficients between predicted and measured levels of 25 aromatic compounds; both methods predicted similar contributions from coal tar/coal combustion sources to the harbor (19 and 26%, respectively). One PCA factor was identified as contributions from vehicular emissions (61%); PMF was able to differentiate vehicular emissions into two factors, one attributed to gasoline emissions sources (28%) and the other to diesel emissions sources (24%). Overall, PMF afforded better source identification than PCA with MLR. This work constitutes one of the few examples of the application of PMF to the source apportionment of sediments; the addition of sulfur heterocycles to the analyte list greatly aided in the source identification process.

  3. Theory of the control of structures by low authority controllers

    NASA Technical Reports Server (NTRS)

    Aubrun, J. N.

    1978-01-01

    The novel idea presented is based on the observation that if a structure is controlled by distributed systems of sensors and actuators with limited authority, i.e., if the controller is allowed to modify only moderately the natural modes and frequencies of the structure, then it should be possible to apply root perturbation techniques to predict analytically the behavior of the total system. Attention is given to the root perturbation formula first derived by Jacobi for infinitesimal perturbations which neglect the induced eigenvector perturbation, a more general form of Jacobi's formula, first-order structural equations and modal state vectors, state-space equations for damper-augmented structures, and modal damping prediction formulas.

  4. Improving long time behavior of Poisson bracket mapping equation: A non-Hamiltonian approach

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kim, Hyun Woo; Rhee, Young Min, E-mail: ymrhee@postech.ac.kr

    2014-05-14

    Understanding nonadiabatic dynamics in complex systems is a challenging subject. A series of semiclassical approaches have been proposed to tackle the problem in various settings. The Poisson bracket mapping equation (PBME) utilizes a partial Wigner transform and a mapping representation for its formulation, and has been developed to describe nonadiabatic processes in an efficient manner. Operationally, it is expressed as a set of Hamilton's equations of motion, similar to more conventional classical molecular dynamics. However, this original Hamiltonian PBME sometimes suffers from a large deviation in accuracy especially in the long time limit. Here, we propose a non-Hamiltonian variant ofmore » PBME to improve its behavior especially in that limit. As a benchmark, we simulate spin-boson and photosynthetic model systems and find that it consistently outperforms the original PBME and its Ehrenfest style variant. We explain the source of this improvement by decomposing the components of the mapping Hamiltonian and by assessing the energy flow between the system and the bath. We discuss strengths and weaknesses of our scheme with a viewpoint of offering future prospects.« less

  5. Dynamically Consistent Shallow-Atmosphere Equations with a Complete Coriolis force

    NASA Astrophysics Data System (ADS)

    Tort, Marine; Dubos, Thomas; Bouchut, François; Zeitlin, Vladimir

    2014-05-01

    Dynamically Consistent Shallow-Atmosphere Equations with a Complete Coriolis force Marine Tort1, Thomas Dubos1, François Bouchut2 & Vladimir Zeitlin1,3 1 Laboratoire of Dynamical Meteorology, Univ. P. and M. Curie, Ecole Normale Supérieure, and Ecole Polytechnique, FRANCE 2 Université Paris-Est, Laboratoire d'Analyse et de Mathématiques Appliquées, FRANCE 3 Institut Universitaire de France Atmospheric and oceanic motion are usually modeled within the shallow-fluid approximation, which simplifies the 3D spherical geometry. For dynamical consistency, i.e. to ensure conservation laws for potential vorticity, energy and angular momentum, the horizontal component of the Coriolis force is neglected. Here new equation sets combining consistently a simplified shallow-fluid geometry with a complete Coriolis force is presented. The derivation invokes Hamilton's principle of least action with an approximate Lagrangian capturing the small increase with height of the solid-body entrainment velocity due to planetary rotation. A three-dimensional compressible model and a one-layer shallow-water model are obtained. The latter extends previous work done on the f-plane and β-plane. Preliminary numerical results confirm the accuracy of the 3D model within the range of parameters for which the equations are relevant. These new models could be useful to incorporate a full Coriolis force into existing numerical models and to disentangle the effects of the shallow-atmosphere approximation from those of the traditional approximation. Related papers: Tort M., Dubos T., Bouchut F. and Zeitlin V. Consistent shallow-water equations on the rotating sphere with complete Coriolis force and topography. J. Fluid Mech. (under revisions) Tort M. and Dubos T. Dynamically consistent shallow-atmosphere equations with a complete Coriolis force. Q.J.R. Meteorol. Soc. (DOI: 10.1002/qj.2274)

  6. Welcome to My House: African American and European American Students' Responses to Virginia Hamilton's "House of Dies Drear."

    ERIC Educational Resources Information Center

    Spears-Bunton, Linda A.

    1990-01-01

    Addresses the relationship between reader response and culture. Presents portraits of a teacher and her Black students and White students as they studied a series of African American literary texts, including Virginia Hamilton's "House of Dies Drear" (1968). The reading of this text marked a turning point for the teacher and students.…

  7. Fort Hamilton High School Project SPEED: Special Education to Eliminate Dropouts. O.E.E. Evaluation Report, 1982-1983.

    ERIC Educational Resources Information Center

    Nicolaidis, Mary; Sica, Michael

    The major goal of Project SPEED (at Fort Hamilton High School, Brooklyn, New York) was dropout prevention. In its first year of operation, 1982-83, the project provided English as a Second Language (ESL) instruction, bilingual instruction in basic skills required for graduation, and guidance services to approximately 300 limited English proficient…

  8. Non-gaussian signatures of general inflationary trajectories

    NASA Astrophysics Data System (ADS)

    Horner, Jonathan S.; Contaldi, Carlo R.

    2014-09-01

    We carry out a numerical calculation of the bispectrum in generalised trajectories of canonical, single-field inflation. The trajectories are generated in the Hamilton-Jacobi (HJ) formalism based on Hubble Slow Roll (HSR) parameters. The calculation allows generally shape and scale dependent bispectra, or dimensionless fNL, in the out-of-slow-roll regime. The distributions of fNL for various shapes and HSR proposals are shown as an example of how this procedure can be used within the context of Monte Carlo exploration of inflationary trajectories. We also show how allowing out-of-slow-roll behaviour can lead to a bispectrum that is relatively large for equilateral shapes.

  9. Serre duality, Abel's theorem, and Jacobi inversion for supercurves over a thick superpoint

    NASA Astrophysics Data System (ADS)

    Rothstein, Mitchell J.; Rabin, Jeffrey M.

    2015-04-01

    The principal aim of this paper is to extend Abel's theorem to the setting of complex supermanifolds of dimension 1 | q over a finite-dimensional local supercommutative C-algebra. The theorem is proved by establishing a compatibility of Serre duality for the supercurve with Poincaré duality on the reduced curve. We include an elementary algebraic proof of the requisite form of Serre duality, closely based on the account of the reduced case given by Serre in Algebraic groups and class fields, combined with an invariance result for the topology on the dual of the space of répartitions. Our Abel map, taking Cartier divisors of degree zero to the dual of the space of sections of the Berezinian sheaf, modulo periods, is defined via Penkov's characterization of the Berezinian sheaf as the cohomology of the de Rham complex of the sheaf D of differential operators. We discuss the Jacobi inversion problem for the Abel map and give an example demonstrating that if n is an integer sufficiently large that the generic divisor of degree n is linearly equivalent to an effective divisor, this need not be the case for all divisors of degree n.

  10. Healing in places of decline: (re)imagining everyday landscapes in Hamilton, Ontario.

    PubMed

    Wakefield, Sarah; McMullan, Colin

    2005-12-01

    Ongoing interest in therapeutic landscapes has contributed noticeably to the development of a "post-medical geography of health" (Kearns, R.A., Professional Geographer 45 (1993) 139). Drawing on a variety of sources, including in-depth interviews and newspaper coverage from Hamilton, Canada, this paper explores the processes by which ordinary places are characterised as healthy or unhealthy, and investigates how health-affirming and health-denying places exist together in everyday life. We argue that it is possible for places to simultaneously hurt and heal, and that the therapeutic effect of place is largely contingent on individuals' physical and social locations. Further, we attempt to illustrate how these meanings are negotiated at a variety of different geographic scales.

  11. Fort Hamilton High School. Project ELITES: Education for Life Through Extended Services. O.E.E. Evaluation Report, 1981-1982.

    ERIC Educational Resources Information Center

    Torres, Judith A.; And Others

    Project ELITES provides bilingual education to 307 Spanish-speaking, Arabic-speaking, and Greek-speaking students at Fort Hamilton High School, Brooklyn, New York. Project ELITES's philosophy is to mainstream students after two years of participation. The program's individualized approach is obtained through a 3-tiered instructional format:…

  12. Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation

    NASA Astrophysics Data System (ADS)

    Litaker, Eric T.

    1994-12-01

    The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed.

  13. A case study: the initiative to improve RN scheduling at Hamilton Health Sciences.

    PubMed

    Wallace, Laurel-Anne; Pierson, Sharon

    2008-01-01

    In 2003, Hamilton Health Sciences embarked on an initiative to improve and standardize nursing schedules and scheduling practices. The scheduling project was one of several initiatives undertaken by a corporate-wide Nursing Resource Group established to enhance the work environment and patient care and to ensure appropriate utilization of nursing resources across the organization's five hospitals. This article focuses on major activities undertaken in the scheduling initiative. The step-by-step approach described, plus examples of the scheduling resources developed and samples of extended-tour schedules, will all provide insight, potential strategies and practical help for nursing administrators, human resources (HR) personnel and others interested in improving nurse scheduling.

  14. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Vankerschaver, Joris; Liao, Cuicui; Leok, Melvin

    The main goal of this paper is to derive an alternative characterization of the multisymplectic form formula for classical field theories using the geometry of the space of boundary values. We review the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton–Jacobi equation for field theories, and we show that by taking variational derivatives of this functional, we obtain an isotropic submanifold of the space of Cauchy data, described by the so-called multisymplectic form formula. As an examplemore » of the latter, we show that Lorentz's reciprocity principle in electromagnetism is a particular instance of the multisymplectic form formula. We also define a Hamiltonian analogue of Jacobi's solution, and we show that this functional is a Type-II generating functional. We finish the paper by defining a similar framework of generating functions for discrete field theories, and we show that for the linear wave equation, we recover the multisymplectic conservation law of Bridges.« less

  15. The identity of Hamilton's Ticto Barb, Pethia ticto (Teleostei: Cyprinidae).

    PubMed

    Katwate, Unmesh; Raghavan, Rajeev; Dahanukar, Neelesh

    2015-06-04

    While describing the fishes of Ganges, Hamilton described Cyprinus ticto (now allocated to Pethia) from south-eastern parts of Bengal. The unavailability of type material and insufficient diagnostic characters in the original description resulted in ambiguities in the identity of this species. In this paper, we clarify the identity of P. ticto through an integrative-taxonomic approach. Pethia ticto can be distinguished from all other known species of the genus by a combination of characters that includes an abbreviated lateral line with 6-12 pored scales; 23-26 scales in lateral-scale row; 9 predorsal scales; ½4/1/3½-4 scales in transverse series; and a pigmentation pattern that includes a small black humeral spot covering the third and fourth lateral-line scales, a prominent spot on the caudal peduncle on the 16th-19th scales of the lateral-line scale row, and two rows of black spots scattered on the dorsal fin.

  16. Effect of reaction-step-size noise on the switching dynamics of stochastic populations

    NASA Astrophysics Data System (ADS)

    Be'er, Shay; Heller-Algazi, Metar; Assaf, Michael

    2016-05-01

    In genetic circuits, when the messenger RNA lifetime is short compared to the cell cycle, proteins are produced in geometrically distributed bursts, which greatly affects the cellular switching dynamics between different metastable phenotypic states. Motivated by this scenario, we study a general problem of switching or escape in stochastic populations, where influx of particles occurs in groups or bursts, sampled from an arbitrary distribution. The fact that the step size of the influx reaction is a priori unknown and, in general, may fluctuate in time with a given correlation time and statistics, introduces an additional nondemographic reaction-step-size noise into the system. Employing the probability-generating function technique in conjunction with Hamiltonian formulation, we are able to map the problem in the leading order onto solving a stationary Hamilton-Jacobi equation. We show that compared to the "usual case" of single-step influx, bursty influx exponentially decreases the population's mean escape time from its long-lived metastable state. In particular, close to bifurcation we find a simple analytical expression for the mean escape time which solely depends on the mean and variance of the burst-size distribution. Our results are demonstrated on several realistic distributions and compare well with numerical Monte Carlo simulations.

  17. Refining inflation using non-canonical scalars

    NASA Astrophysics Data System (ADS)

    Unnikrishnan, Sanil; Sahni, Varun; Toporensky, Aleksey

    2012-08-01

    This paper revisits the Inflationary scenario within the framework of scalar field models possessing a non-canonical kinetic term. We obtain closed form solutions for all essential quantities associated with chaotic inflation including slow roll parameters, scalar and tensor power spectra, spectral indices, the tensor-to-scalar ratio, etc. We also examine the Hamilton-Jacobi equation and demonstrate the existence of an inflationary attractor. Our results highlight the fact that non-canonical scalars can significantly improve the viability of inflationary models. They accomplish this by decreasing the tensor-to-scalar ratio while simultaneously increasing the value of the scalar spectral index, thereby redeeming models which are incompatible with the cosmic microwave background (CMB) in their canonical version. For instance, the non-canonical version of the chaotic inflationary potential, V(phi) ~ λphi4, is found to agree with observations for values of λ as large as unity! The exponential potential can also provide a reasonable fit to CMB observations. A central result of this paper is that steep potentials (such as Vproptophi-n) usually associated with dark energy, can drive inflation in the non-canonical setting. Interestingly, non-canonical scalars violate the consistency relation r = -8nT, which emerges as a smoking gun test for this class of models.

  18. Free time minimizers for the three-body problem

    NASA Astrophysics Data System (ADS)

    Moeckel, Richard; Montgomery, Richard; Sánchez Morgado, Héctor

    2018-03-01

    Free time minimizers of the action (called "semi-static" solutions by Mañe in International congress on dynamical systems in Montevideo (a tribute to Ricardo Mañé), vol 362, pp 120-131, 1996) play a central role in the theory of weak KAM solutions to the Hamilton-Jacobi equation (Fathi in Weak KAM Theorem in Lagrangian Dynamics Preliminary Version Number 10, 2017). We prove that any solution to Newton's three-body problem which is asymptotic to Lagrange's parabolic homothetic solution is eventually a free time minimizer. Conversely, we prove that every free time minimizer tends to Lagrange's solution, provided the mass ratios lie in a certain large open set of mass ratios. We were inspired by the work of Da Luz and Maderna (Math Proc Camb Philos Soc 156:209-227, 1980) which showed that every free time minimizer for the N-body problem is parabolic and therefore must be asymptotic to the set of central configurations. We exclude being asymptotic to Euler's central configurations by a second variation argument. Central configurations correspond to rest points for the McGehee blown-up dynamics. The large open set of mass ratios are those for which the linearized dynamics at each Euler rest point has a complex eigenvalue.

  19. The Model for Final Stage of Gravitational Collapse Massless Scalar Field

    NASA Astrophysics Data System (ADS)

    Gladush, V. D.; Mironin, D. V.

    It is known that in General relativity, for some spherically symmetric initial conditions, the massless scalar field (SF) experience the gravitational collapse (Choptuik, 1989), and arise a black hole (BH). According Bekenstein, a BH has no "hair scalar", so the SF is completely under the horizon. Thus, the study of the final stage for the gravitational collapse of a SF is reduced to the construction of a solution of Einstein's equations describing the evolution of a SF inside the BH. In this work, we build the Lagrangian for scalar and gravitationalfields in the spherically symmetric case, when the metric coefficients and SF depends only on the time. In this case, it is convenient to use the methods of classical mechanics. Since the metric allows an arbitrary transformation of time, then the corresponding field variable (g00) is included in the Lagrangian without time derivative. It is a non-dynamic variable, and is included in the Lagrangian as a Lagrange multiplier. A variation of the action on this variable gives the constraint. It turns out that Hamiltonian is proportional to the constraint, and so it is zero. The corresponding Hamilton-Jacobi equation easily integrated. Hence, we find the relation between the SF and the metric. To restore of time dependence we using an equation dL / dq' = dS / dq After using a gauge condition, it allows us to find solution. Thus, we find the evolution of the SF inside the BH, which describes the final stage of the gravitational collapse of a SF. It turns out that the mass BH associated with a scalar charge G of the corresponding SF inside the BH ratio M = G/(2√ κ).

  20. Unconventional Hamilton-type variational principle in phase space and symplectic algorithm

    NASA Astrophysics Data System (ADS)

    Luo, En; Huang, Weijiang; Zhang, Hexin

    2003-06-01

    By a novel approach proposed by Luo, the unconventional Hamilton-type variational principle in phase space for elastodynamics of multidegree-of-freedom system is established in this paper. It not only can fully characterize the initial-value problem of this dynamic, but also has a natural symplectic structure. Based on this variational principle, a symplectic algorithm which is called a symplectic time-subdomain method is proposed. A non-difference scheme is constructed by applying Lagrange interpolation polynomial to the time subdomain. Furthermore, it is also proved that the presented symplectic algorithm is an unconditionally stable one. From the results of the two numerical examples of different types, it can be seen that the accuracy and the computational efficiency of the new method excel obviously those of widely used Wilson-θ and Newmark-β methods. Therefore, this new algorithm is a highly efficient one with better computational performance.

  1. Full-dimensional vibrational calculations of five-atom molecules using a combination of Radau and Jacobi coordinates: Applications to methane and fluoromethane

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Zhao, Zhiqiang; Chen, Jun; University of Chinese Academy of Sciences, Beijing 100049

    Full quantum mechanical calculations of vibrational energies of methane and fluoromethane are carried out using a polyspherical description combining Radau and Jacobi coordinates. The Hamiltonian is built in a potential-optimized discrete variable representation, and vibrational energies are solved using an iterative eigensolver. This new approach can be applied to a large variety of molecules. In particular, we show that it is able to accurately and efficiently compute eigenstates for four different molecules : CH{sub 4}, CHD{sub 3}, CH{sub 2}D{sub 2}, and CH{sub 3}F. Very good agreement is obtained with the results reported previously in the literature with different approaches andmore » with experimental data.« less

  2. A Piecewise Deterministic Markov Toy Model for Traffic/Maintenance and Associated Hamilton–Jacobi Integrodifferential Systems on Networks

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Goreac, Dan, E-mail: Dan.Goreac@u-pem.fr; Kobylanski, Magdalena, E-mail: Magdalena.Kobylanski@u-pem.fr; Martinez, Miguel, E-mail: Miguel.Martinez@u-pem.fr

    2016-10-15

    We study optimal control problems in infinite horizon whxen the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (corresponding to a toy traffic model). We adapt the results in Soner (SIAM J Control Optim 24(6):1110–1122, 1986) to prove the regularity of the value function and the dynamic programming principle. Extending the networks and Krylov’s “shaking the coefficients” method, we prove that the value function can be seen as the solution to a linearized optimization problem set on a convenient set of probability measures. The approach relies entirely on viscosity arguments. As a by-product,more » the dual formulation guarantees that the value function is the pointwise supremum over regular subsolutions of the associated Hamilton–Jacobi integrodifferential system. This ensures that the value function satisfies Perron’s preconization for the (unique) candidate to viscosity solution.« less

  3. Direct oral anticoagulants for treatment of HIT: update of Hamilton experience and literature review.

    PubMed

    Warkentin, Theodore E; Pai, Menaka; Linkins, Lori-Ann

    2017-08-31

    Direct oral anticoagulants (DOACs) are attractive options for treatment of heparin-induced thrombocytopenia (HIT). We report our continuing experience in Hamilton, ON, Canada, since January 1, 2015 (when we completed our prospective study of rivaroxaban for HIT), using rivaroxaban for serologically confirmed HIT (4Ts score ≥4 points; positive platelet factor 4 [PF4]/heparin immunoassay, positive serotonin-release assay). We also performed a literature review of HIT treatment using DOACs (rivaroxaban, apixaban, dabigatran, edoxaban). We focused on patients who received DOAC therapy for acute HIT as either primary therapy (group A) or secondary therapy (group B; initial treatment using a non-DOAC/non-heparin anticoagulant with transition to a DOAC during HIT-associated thrombocytopenia). Our primary end point was occurrence of objectively documented thrombosis during DOAC therapy for acute HIT. We found that recovery without new, progressive, or recurrent thrombosis occurred in all 10 Hamilton patients with acute HIT treated with rivaroxaban. Data from the literature review plus these new data identified a thrombosis rate of 1 of 46 patients (2.2%; 95% CI, 0.4%-11.3%) in patients treated with rivaroxaban during acute HIT (group A, n = 25; group B, n = 21); major hemorrhage was seen in 0 of 46 patients. Similar outcomes in smaller numbers of patients were observed with apixaban (n = 12) and dabigatran (n = 11). DOACs offer simplified management of selected patients, as illustrated by a case of persisting (autoimmune) HIT (>2-month platelet recovery with inversely parallel waning of serum-induced heparin-independent serotonin release) with successful outpatient rivaroxaban management of HIT-associated thrombosis. Evidence supporting efficacy and safety of DOACs for acute HIT is increasing, with the most experience reported for rivaroxaban. © 2017 by The American Society of Hematology.

  4. Analytical bound-state solutions of the Schrödinger equation for the Manning-Rosen plus Hulthén potential within SUSY quantum mechanics

    NASA Astrophysics Data System (ADS)

    Ahmadov, A. I.; Naeem, Maria; Qocayeva, M. V.; Tarverdiyeva, V. A.

    2018-01-01

    In this paper, the bound-state solution of the modified radial Schrödinger equation is obtained for the Manning-Rosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any l≠0 angular momentum case via the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary l states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.

  5. [«I stole with my eyes»: Hamilton Naki, a pioneer in heart transplantation].

    PubMed

    López-Valdés, Julio César

    On December 2, 1967, when Denise Darvall was hit by a car, a surgery that made medical history was unfold: Hamilton Naki, a black man, expertly removed her heart and gave it to Christian Barnard, who was preparing the receptor, Louis Washkansky, in an adjacent operating room. Naki's contribution was an outlaw act, a criminal offense under the laws of apartheid due to the difference of races; the law forbade him to cut white meat or touch white blood. Naki was perhaps the second most important man in the team that day. There were few photographs where he and Barnard appeared together, but because of the nature of society was Barnard who won the world's attention.

  6. Topology-independent shape modeling scheme

    NASA Astrophysics Data System (ADS)

    Malladi, Ravikanth; Sethian, James A.; Vemuri, Baba C.

    1993-06-01

    Developing shape models is an important aspect of computer vision research. Geometric and differential properties of the surface can be computed from shape models. They also aid the tasks of object representation and recognition. In this paper we present an innovative new approach for shape modeling which, while retaining important features of the existing methods, overcomes most of their limitations. Our technique can be applied to model arbitrarily complex shapes, shapes with protrusions, and to situations where no a priori assumption about the object's topology can be made. A single instance of our model, when presented with an image having more than one object of interest, has the ability to split freely to represent each object. Our method is based on the level set ideas developed by Osher & Sethian to follow propagating solid/liquid interfaces with curvature-dependent speeds. The interface is a closed, nonintersecting, hypersurface flowing along its gradient field with constant speed or a speed that depends on the curvature. We move the interface by solving a `Hamilton-Jacobi' type equation written for a function in which the interface is a particular level set. A speed function synthesized from the image is used to stop the interface in the vicinity of the object boundaries. The resulting equations of motion are solved by numerical techniques borrowed from the technology of hyperbolic conservation laws. An added advantage of this scheme is that it can easily be extended to any number of space dimensions. The efficacy of the scheme is demonstrated with numerical experiments on synthesized images and noisy medical images.

  7. Analytical Solutions of the Schrödinger Equation for the Manning-Rosen plus Hulthén Potential Within SUSY Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Ahmadov, A. I.; Naeem, Maria; Qocayeva, M. V.; Tarverdiyeva, V. A.

    2018-02-01

    In this paper, the bound state solution of the modified radial Schrödinger equation is obtained for the Manning-Rosen plus Hulthén potential by implementing the novel improved scheme to surmount the centrifugal term. The energy eigenvalues and corresponding radial wave functions are defined for any l ≠ 0 angular momentum case via the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSYQM) methods. By using these two different methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary l states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.

  8. Cooperativity and tunable excited state deactivation: modular self-assembly of depsipeptide dendrons on a Hamilton receptor modified porphyrin platform.

    PubMed

    Gnichwitz, Jan-Frederik; Wielopolski, Mateusz; Hartnagel, Kristine; Hartnagel, Uwe; Guldi, Dirk M; Hirsch, Andreas

    2008-07-02

    A series of novel supramolecular architectures were built around a tin tetraphenyl porphyrin platform 6--functionalized by a 2-fold 1-ethyl-3-3-(3-dimethylaminopropyl)carbodiimide (EDC) promoted condensation reaction--and chiral depsipeptide dendrons of different generations 1-4. Here, implementation of a Hamilton receptor provided the necessary means to keep the constituents together via strong hydrogen bonding. Characterization of all architectures has been performed, including 4 which is the fourth generation, on the basis of NMR and photophysical methods. In particular, several titration experiments were conducted suggesting positive cooperativity, an assessment that is based on association constants that tend to be higher for the second binding step than for the first step. Importantly, molecular modeling calculations reveal a significant deaggregation of the intermolecular network of 6 during the course of the first binding step. As a consequence, an improved accessibility of the second Hamilton receptor unit in 6 emerges and, in turn, facilitates the higher association constants. The features of the equilibrium, that is, the dynamic exchange of depsipeptide dendrons 1-4 with fullerene 5, was tested in photophysical reference experiments. These steady-state and time-resolved measurements showed the tunable excited-state deactivations of these complexes upon photoexcitation.

  9. Outbreak of salmonellosis associated with consumption of pulled pork at a church festival - Hamilton County, Ohio, 2010.

    PubMed

    2014-01-03

    On June 18, 2010, Hamilton County Public Health (HCPH), a local health department in Ohio, began receiving reports of gastrointestinal illness from persons who attended a church festival held during June 11-13 in a suburban community of Hamilton County. HCPH investigated and confirmed the existence of a foodborne outbreak associated with consumption of pulled pork prepared in a private home and sold at the church festival. Sixty-four attendees with gastroenteritis were identified. Salmonella enterica serotype Typhimurium (Salmonella Typhimurium) was found in stool specimens from three patients; no other pathogen was found. Because the outbreak was identified after the church festival had concluded, the environmental investigation was limited to interviews of food handlers. The primary public health interventions consisted of 1) active surveillance for additional cases of salmonellosis associated with the festival, 2) consultation with the festival organizers and food vendors to ensure the pork product was not resold or consumed elsewhere, 3) education of the festival organizers and food vendors about relevant public health regulations and food safety practices, 4) traceback of the implicated product to the retailer in Indiana, and 5) notification of the Indiana State Department of Health. The results of the investigation call attention to the public health implications of unregulated food service at events such as church festivals, which generally are exempt from public health inspection and licensure in Ohio. Food sold in such environments might place populations at risk for foodborne illness.

  10. Validation of the 17-item Hamilton Depression Rating Scale definition of response for adults with major depressive disorder using equipercentile linking to Clinical Global Impression scale ratings: analysis of Pharmacogenomic Research Network Antidepressant Medication Pharmacogenomic Study (PGRN-AMPS) data.

    PubMed

    Bobo, William V; Angleró, Gabriela C; Jenkins, Gregory; Hall-Flavin, Daniel K; Weinshilboum, Richard; Biernacka, Joanna M

    2016-05-01

    The study aimed to define thresholds of clinically significant change in 17-item Hamilton Depression Rating Scale (HDRS-17) scores using the Clinical Global Impression-Improvement (CGI-I) Scale as a gold standard. We conducted a secondary analysis of individual patient data from the Pharmacogenomic Research Network Antidepressant Medication Pharmacogenomic Study, an 8-week, single-arm clinical trial of citalopram or escitalopram treatment of adults with major depression. We used equipercentile linking to identify levels of absolute and percent change in HDRS-17 scores that equated with scores on the CGI-I at 4 and 8 weeks. Additional analyses equated changes in the HDRS-7 and Bech-6 scale scores with CGI-I scores. A CGI-I score of 2 (much improved) corresponded to an absolute decrease (improvement) in HDRS-17 total score of 11 points and a percent decrease of 50-57%, from baseline values. Similar results were observed for percent change in HDRS-7 and Bech-6 scores. Larger absolute (but not percent) decreases in HDRS-17 scores equated with CGI-I scores of 2 in persons with higher baseline depression severity. Our results support the consensus definition of response based on HDRS-17 scores (>50% decrease from baseline). A similar definition of response may apply to the HDRS-7 and Bech-6. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

  11. DDT poisoning of big brown bats, Eptesicus fuscus, in Hamilton, Montana.

    PubMed

    Buchweitz, John P; Carson, Keri; Rebolloso, Sarah; Lehner, Andreas

    2018-06-01

    Dichlorodiphenyltrichloroethane (DDT) is an insecticidal organochlorine pesticide with; known potential for neurotoxic effects in wildlife. The United States Environmental Protection Agency (US EPA) registration for this pesticide has been cancelled and there are currently no federally active products that contain this ingredient in the U.S. We present a case of a colony of big brown bats (E. Fuscus) found dead in the attic roost of an administrative building; in the city of Hamilton, Montana from unknown cause. DDT and its metabolites; dichlorodiphenyldichloroethylene (DDE) and dichlorodiphenyldichloroethane (DDD) were detected in bat tissues by gas chromatography/mass spectrometry (GC-MS) and quantified by gas chromatography tandem quadrupole mass spectrometry (GC-MS/MS). Concentrations of 4081 ppm DDT and 890 ppm DDE wet weight were found in the brain of one bat and are the highest reported concentrations in such a mortality event to date. This case emphasizes the importance of testing wildlife mortalities against a comprehensive panel of toxicologic agents including persistent organic pollutants in the absence of other more common disease threats. Copyright © 2018 Elsevier Ltd. All rights reserved.

  12. Hamilton Jeffers and the Double Star Catalogues

    NASA Astrophysics Data System (ADS)

    Tenn, Joseph S.

    2013-01-01

    Astronomers have long tracked double stars in efforts to find those that are gravitationally-bound binaries and then to determine their orbits. Court reporter and amateur astronomer Shelburne Wesley Burnham (1838-1921) published a massive double star catalogue containing more than 13,000 systems in 1906. The next keeper of the double stars was Lick Observatory astronomer Robert Grant Aitken (1864-1951), who produced a much larger catalogue in 1932. Aitken maintained and expanded Burnham’s records of observations on handwritten file cards, eventually turning them over to Lick Observatory astrometrist Hamilton Moore Jeffers (1893-1976). Jeffers further expanded the collection and put all the observations on punched cards. With the aid of Frances M. "Rete" Greeby (1921-2002), he made two catalogues: an Index Catalogue with basic data about each star, and a complete catalogue of observations, with one observation per punched card. He enlisted Willem van den Bos of Johannesburg to add southern stars, and they published the Index Catalogue of Visual Double Stars, 1961.0. As Jeffers approached retirement he became greatly concerned about the disposition of the catalogues. He wanted to be replaced by another "double star man," but Lick Director Albert E. Whitford (1905-2002) had the new 120-inch reflector, the world’s second largest telescope, and he wanted to pursue modern astrophysics instead. Jeffers was vociferously opposed to turning over the card files to another institution, and especially against their coming under the control of Kaj Strand of the U.S. Naval Observatory. In the end the USNO got the files and has maintained the records ever since, first under Charles Worley (1935-1997), and, since 1997, under Brian Mason. Now called the Washington Double Star Catalog (WDS), it is completely online and currently contains more than 1,000,000 measures of more than 100,000 pairs.

  13. Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

    NASA Technical Reports Server (NTRS)

    Slack, David C.; Whitaker, D. L.; Walters, Robert W.

    1994-01-01

    Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

  14. Bifurcations and stability of standing waves in the nonlinear Schrödinger equation on the tadpole graph

    NASA Astrophysics Data System (ADS)

    Noja, Diego; Pelinovsky, Dmitry; Shaikhova, Gaukhar

    2015-07-01

    We develop a detailed analysis of edge bifurcations of standing waves in the nonlinear Schrödinger (NLS) equation on a tadpole graph (a ring attached to a semi-infinite line subject to the Kirchhoff boundary conditions at the junction). It is shown in the recent work [7] by using explicit Jacobi elliptic functions that the cubic NLS equation on a tadpole graph admits a rich structure of standing waves. Among these, there are different branches of localized waves bifurcating from the edge of the essential spectrum of an associated Schrödinger operator. We show by using a modified Lyapunov-Schmidt reduction method that the bifurcation of localized standing waves occurs for every positive power nonlinearity. We distinguish a primary branch of never vanishing standing waves bifurcating from the trivial solution and an infinite sequence of higher branches with oscillating behavior in the ring. The higher branches bifurcate from the branches of degenerate standing waves with vanishing tail outside the ring. Moreover, we analyze stability of bifurcating standing waves. Namely, we show that the primary branch is composed by orbitally stable standing waves for subcritical power nonlinearities, while all nontrivial higher branches are linearly unstable near the bifurcation point. The stability character of the degenerate branches remains inconclusive at the analytical level, whereas heuristic arguments based on analysis of embedded eigenvalues of negative Krein signatures support the conjecture of their linear instability at least near the bifurcation point. Numerical results for the cubic NLS equation show that this conjecture is valid and that the degenerate branches become spectrally stable far away from the bifurcation point.

  15. Fluid Structure Interaction Techniques For Extrusion And Mixing Processes

    NASA Astrophysics Data System (ADS)

    Valette, Rudy; Vergnes, Bruno; Coupez, Thierry

    2007-05-01

    This work focuses on the development of numerical techniques devoted to the simulation of mixing processes of complex fluids such as twin-screw extrusion or batch mixing. In mixing process simulation, the absence of symmetry of the moving boundaries (the screws or the rotors) implies that their rigid body motion has to be taken into account by using a special treatment We therefore use a mesh immersion technique (MIT), which consists in using a P1+/P1-based (MINI-element) mixed finite element method for solving the velocity-pressure problem and then solving the problem in the whole barrel cavity by imposing a rigid motion (rotation) to nodes found located inside the so called immersed domain, each sub-domain (screw, rotor) being represented by a surface CAD mesh (or its mathematical equation in simple cases). The independent meshes are immersed into a unique background computational mesh by computing the distance function to their boundaries. Intersections of meshes are accounted for, allowing to compute a fill factor usable as for the VOF methodology. This technique, combined with the use of parallel computing, allows to compute the time-dependent flow of generalized Newtonian fluids including yield stress fluids in a complex system such as a twin screw extruder, including moving free surfaces, which are treated by a "level set" and Hamilton-Jacobi method.

  16. Domain Immersion Technique And Free Surface Computations Applied To Extrusion And Mixing Processes

    NASA Astrophysics Data System (ADS)

    Valette, Rudy; Vergnes, Bruno; Basset, Olivier; Coupez, Thierry

    2007-04-01

    This work focuses on the development of numerical techniques devoted to the simulation of mixing processes of complex fluids such as twin-screw extrusion or batch mixing. In mixing process simulation, the absence of symmetry of the moving boundaries (the screws or the rotors) implies that their rigid body motion has to be taken into account by using a special treatment. We therefore use a mesh immersion technique (MIT), which consists in using a P1+/P1-based (MINI-element) mixed finite element method for solving the velocity-pressure problem and then solving the problem in the whole barrel cavity by imposing a rigid motion (rotation) to nodes found located inside the so called immersed domain, each subdomain (screw, rotor) being represented by a surface CAD mesh (or its mathematical equation in simple cases). The independent meshes are immersed into a unique backgound computational mesh by computing the distance function to their boundaries. Intersections of meshes are accounted for, allowing to compute a fill factor usable as for the VOF methodology. This technique, combined with the use of parallel computing, allows to compute the time-dependent flow of generalized Newtonian fluids including yield stress fluids in a complex system such as a twin screw extruder, including moving free surfaces, which are treated by a "level set" and Hamilton-Jacobi method.

  17. Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Damour, Thibault; Jaranowski, Piotr; Schaefer, Gerhard

    2008-07-15

    Using a recent, novel Hamiltonian formulation of the gravitational interaction of spinning binaries, we extend the effective one body (EOB) description of the dynamics of two spinning black holes to next-to-leading order (NLO) in the spin-orbit interaction. The spin-dependent EOB Hamiltonian is constructed from four main ingredients: (i) a transformation between the 'effective' Hamiltonian and the 'real' one; (ii) a generalized effective Hamilton-Jacobi equation involving higher powers of the momenta; (iii) a Kerr-type effective metric (with Pade-resummed coefficients) which depends on the choice of some basic 'effective spin vector' S{sub eff}, and which is deformed by comparable-mass effects; and (iv)more » an additional effective spin-orbit interaction term involving another spin vector {sigma}. As a first application of the new, NLO spin-dependent EOB Hamiltonian, we compute the binding energy of circular orbits (for parallel spins) as a function of the orbital frequency, and of the spin parameters. We also study the characteristics of the last stable circular orbit: binding energy, orbital frequency, and the corresponding dimensionless spin parameter a{sub LSO}{identical_to}cJ{sub LSO}/(G(H{sub LSO}/c{sup 2}){sup 2}). We find that the inclusion of NLO spin-orbit terms has a significant 'moderating' effect on the dynamical characteristics of the circular orbits for large and parallel spins.« less

  18. Prevalence of the Lyme Disease Spirochete, Borrelia burgdorferi, in Blacklegged Ticks, Ixodes scapularis at Hamilton-Wentworth, Ontario

    PubMed Central

    Scott, John D.; Anderson, John F.; Durden, Lance A.; Smith, Morgan L.; Manord, Jodi M.; Clark, Kerry L.

    2016-01-01

    Lyme disease has emerged as a major health concern in Canada, where the etiological agent, Borrelia burgdorferi sensu lato (s.l.), a spirochetal bacterium, is typically spread by the bite of certain ticks. This study explores the presence of B. burgdorferi s.l. in blacklegged ticks, Ixodes scapularis, collected at Dundas, Ontario (a locality within the region of Hamilton-Wentworth). Using passive surveillance, veterinarians and pet groomers were asked to collect blacklegged ticks from dogs and cats with no history of travel. Additionally, I. scapularis specimens were submitted from local residents and collected by flagging. Overall, 12 (41%) of 29 blacklegged ticks were infected with B. burgdorferi s.l. Using polymerase chain reaction (PCR) and DNA sequencing, two borrelial amplicons were characterized as B. burgdorferi sensu stricto (s.s.), a genospecies pathogenic to humans and certain domestic animals. Notably, three different vertebrate hosts each had two engorged I. scapularis females removed on the same day and, likewise, one cat had three repeat occurrences of this tick species. These multiple infestations suggest that a population of I. scapularis may be established in this area. The local public health unit has been underreporting the presence of B. burgdorferi s.l.-infected I. scapularis in the area encompassing Dundas. Our findings raise concerns about the need to erect tick warning signs in parkland areas. Veterinarians, medical professionals, public health officials, and the general public must be vigilant that Lyme disease-carrying blacklegged ticks pose a public health risk in the Dundas area and the surrounding Hamilton-Wentworth region. PMID:27226771

  19. Prevalence of the Lyme Disease Spirochete, Borrelia burgdorferi, in Blacklegged Ticks, Ixodes scapularis at Hamilton-Wentworth, Ontario.

    PubMed

    Scott, John D; Anderson, John F; Durden, Lance A; Smith, Morgan L; Manord, Jodi M; Clark, Kerry L

    2016-01-01

    Lyme disease has emerged as a major health concern in Canada, where the etiological agent, Borrelia burgdorferi sensu lato (s.l.), a spirochetal bacterium, is typically spread by the bite of certain ticks. This study explores the presence of B. burgdorferi s.l. in blacklegged ticks, Ixodes scapularis, collected at Dundas, Ontario (a locality within the region of Hamilton-Wentworth). Using passive surveillance, veterinarians and pet groomers were asked to collect blacklegged ticks from dogs and cats with no history of travel. Additionally, I. scapularis specimens were submitted from local residents and collected by flagging. Overall, 12 (41%) of 29 blacklegged ticks were infected with B. burgdorferi s.l. Using polymerase chain reaction (PCR) and DNA sequencing, two borrelial amplicons were characterized as B. burgdorferi sensu stricto (s.s.), a genospecies pathogenic to humans and certain domestic animals. Notably, three different vertebrate hosts each had two engorged I. scapularis females removed on the same day and, likewise, one cat had three repeat occurrences of this tick species. These multiple infestations suggest that a population of I. scapularis may be established in this area. The local public health unit has been underreporting the presence of B. burgdorferi s.l.-infected I. scapularis in the area encompassing Dundas. Our findings raise concerns about the need to erect tick warning signs in parkland areas. Veterinarians, medical professionals, public health officials, and the general public must be vigilant that Lyme disease-carrying blacklegged ticks pose a public health risk in the Dundas area and the surrounding Hamilton-Wentworth region.

  20. Exploring the Action Landscape via Trial World-Lines

    ERIC Educational Resources Information Center

    Joglekar, Yogesh N.; Tham, Weng Kian

    2011-01-01

    The Hamilton action principle, also known as the principle of least action, and Lagrange equations are an integral part of intermediate and advanced undergraduate mechanics. Although the Hamilton principle is oft stated as "the action for any nearby trial world-line is greater than the action for the classical world-line," the landscape of action…

  1. On Schrödinger's equation, Hertz's mechanics and Van Vleck's determinant

    NASA Astrophysics Data System (ADS)

    Lopes Coelho, R.; Stachel, John

    2013-07-01

    There has been much research on Schrödinger's route to what we now call Schrödinger's equation. Various authors disagree as to the exact nature of the influence of each of the physicists he cites—and of some that he does not. This paper, intended for graduate students of and researchers in quantum theory, clarifies Schrödinger's original aims in formulating a wave equation for matter, discusses how far he fulfilled his original aspirations and in what respects he fell short of his goal. An analysis of Schrödinger's foundational paper enables us to distinguish between a formal and an epistemological part, and consider the input of the physicists cited on the basis of the part in which each reference occurs. It turns out, for instance, that Hamilton's optical-mechanical analogy belongs entirely to the epistemological part. Indeed, no element of this analogy plays any role in the formal part of Schrödinger's argument. Instead of basing his theory on this analogy, as is often done nowadays in the physics literature and even in the history of science, we maintain that the aim of Schrödinger's project was to represent wave phenomena by a ‘wave’ in configuration- or q-space, paralleling Hertz's treatment in his Mechanics (1894). The influence of this book on Schrödinger's foundational paper is demonstrated by an analysis of his unpublished paper: Hertz's Mechanics and Einstein's Theory of Gravitation. This approach enables us to dispense with the optical-mechanical analogy in tracing the route to Schrödinger's equation. We also discuss the curious role of the Van Vleck determinant as the ‘missing link’ in taking the classical limit of Schrödinger's wavefunction. A concluding section discusses the relation of some of Schrödinger's earlier and later work to the development of quantum field theory.

  2. Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu; Department of Physics, Indiana University Northwest, 3400 Broadway, Gary IN 46408; Roy, Pinaki, E-mail: pinaki@isical.ac.in

    We construct energy-dependent potentials for which the Schrödinger equations admit solutions in terms of exceptional orthogonal polynomials. Our method of construction is based on certain point transformations, applied to the equations of exceptional Hermite, Jacobi and Laguerre polynomials. We present several examples of boundary-value problems with energy-dependent potentials that admit a discrete spectrum and the corresponding normalizable solutions in closed form.

  3. Eigensystem analysis of classical relaxation techniques with applications to multigrid analysis

    NASA Technical Reports Server (NTRS)

    Lomax, Harvard; Maksymiuk, Catherine

    1987-01-01

    Classical relaxation techniques are related to numerical methods for solution of ordinary differential equations. Eigensystems for Point-Jacobi, Gauss-Seidel, and SOR methods are presented. Solution techniques such as eigenvector annihilation, eigensystem mixing, and multigrid methods are examined with regard to the eigenstructure.

  4. Geometric approach to nuclear pasta phases

    NASA Astrophysics Data System (ADS)

    Kubis, Sebastian; Wójcik, Włodzimierz

    2016-12-01

    By use of the variational methods and differential geometry in the framework of the liquid drop model we formulate appropriate equilibrium equations for pasta phases with imposed periodicity. The extension of the Young-Laplace equation in the case of charged fluid is obtained. The β equilibrium and virial theorem are also generalized. All equations are shown in gauge invariant form. For the first time, the pasta shape stability analysis is carried out. The proper stability condition in the form of the generalized Jacobi equation is derived. The presented formalism is tested on some particular cases.

  5. Robust Multigrid Smoothers for Three Dimensional Elliptic Equations with Strong Anisotropies

    NASA Technical Reports Server (NTRS)

    Llorente, Ignacio M.; Melson, N. Duane

    1998-01-01

    We discuss the behavior of several plane relaxation methods as multigrid smoothers for the solution of a discrete anisotropic elliptic model problem on cell-centered grids. The methods compared are plane Jacobi with damping, plane Jacobi with partial damping, plane Gauss-Seidel, plane zebra Gauss-Seidel, and line Gauss-Seidel. Based on numerical experiments and local mode analysis, we compare the smoothing factor of the different methods in the presence of strong anisotropies. A four-color Gauss-Seidel method is found to have the best numerical and architectural properties of the methods considered in the present work. Although alternating direction plane relaxation schemes are simpler and more robust than other approaches, they are not currently used in industrial and production codes because they require the solution of a two-dimensional problem for each plane in each direction. We verify the theoretical predictions of Thole and Trottenberg that an exact solution of each plane is not necessary and that a single two-dimensional multigrid cycle gives the same result as an exact solution, in much less execution time. Parallelization of the two-dimensional multigrid cycles, the kernel of the three-dimensional implicit solver, is also discussed. Alternating-plane smoothers are found to be highly efficient multigrid smoothers for anisotropic elliptic problems.

  6. Automated extraction for the analysis of 11-nor-delta9-tetrahydrocannabinol-9-carboxylic acid (THCCOOH) in urine using a six-head probe Hamilton Microlab 2200 system and gas chromatography-mass spectrometry.

    PubMed

    Whitter, P D; Cary, P L; Leaton, J I; Johnson, J E

    1999-01-01

    An automated extraction scheme for the analysis of 11 -nor-delta9-tetrahydrocannabinol-9-carboxylic acid using the Hamilton Microlab 2200, which was modified for gravity-flow solid-phase extraction, has been evaluated. The Hamilton was fitted with a six-head probe, a modular valve positioner, and a peristaltic pump. The automated method significantly increased sample throughput, improved assay consistency, and reduced the time spent performing the extraction. Extraction recovery for the automated method was > 90%. The limit of detection, limit of quantitation, and upper limit of linearity were equivalent to the manual method: 1.5, 3.0, and 300 ng/mL, respectively. Precision at the 15-ng/mL cut-off was as follows: mean = 14.4, standard deviation = 0.5, coefficient of variation = 3.5%. Comparison of 38 patient samples, extracted by the manual and automated extraction methods, demonstrated the following correlation statistics: r = .991, slope 1.029, and y-intercept -2.895. Carryover was < 0.3% at 1000 ng/mL. Aliquoting/extraction time for the automated method (48 urine samples) was 50 min, and the manual procedure required approximately 2.5 h. The automated aliquoting/extraction method on the Hamilton Microlab 2200 and its use in forensic applications are reviewed.

  7. A Solution Space for a System of Null-State Partial Differential Equations: Part 2

    NASA Astrophysics Data System (ADS)

    Flores, Steven M.; Kleban, Peter

    2015-01-01

    This article is the second of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE). The system comprises 2 N null-state equations and three conformal Ward identities which govern CFT correlation functions of 2 N one-leg boundary operators. In the first article (Flores and Kleban, Commun Math Phys, arXiv:1212.2301, 2012), we use methods of analysis and linear algebra to prove that dim , with C N the Nth Catalan number. The analysis of that article is complete except for the proof of a lemma that it invokes. The purpose of this article is to provide that proof. The lemma states that if every interval among ( x 2, x 3), ( x 3, x 4),…,( x 2 N-1, x 2 N ) is a two-leg interval of (defined in Flores and Kleban, Commun Math Phys, arXiv:1212.2301, 2012), then F vanishes. Proving this lemma by contradiction, we show that the existence of such a nonzero function implies the existence of a non-vanishing CFT two-point function involving primary operators with different conformal weights, an impossibility. This proof (which is rigorous in spite of our occasional reference to CFT) involves two different types of estimates, those that give the asymptotic behavior of F as the length of one interval vanishes, and those that give this behavior as the lengths of two intervals vanish simultaneously. We derive these estimates by using Green functions to rewrite certain null-state PDEs as integral equations, combining other null-state PDEs to obtain Schauder interior estimates, and then repeatedly integrating the integral equations with these estimates until we obtain optimal bounds. Estimates in which two interval lengths vanish simultaneously divide into two cases: two adjacent intervals and two non-adjacent intervals. The analysis of the latter case is similar to that for one vanishing

  8. Momentum Maps and Stochastic Clebsch Action Principles

    NASA Astrophysics Data System (ADS)

    Cruzeiro, Ana Bela; Holm, Darryl D.; Ratiu, Tudor S.

    2018-01-01

    We derive stochastic differential equations whose solutions follow the flow of a stochastic nonlinear Lie algebra operation on a configuration manifold. For this purpose, we develop a stochastic Clebsch action principle, in which the noise couples to the phase space variables through a momentum map. This special coupling simplifies the structure of the resulting stochastic Hamilton equations for the momentum map. In particular, these stochastic Hamilton equations collectivize for Hamiltonians that depend only on the momentum map variable. The Stratonovich equations are derived from the Clebsch variational principle and then converted into Itô form. In comparing the Stratonovich and Itô forms of the stochastic dynamical equations governing the components of the momentum map, we find that the Itô contraction term turns out to be a double Poisson bracket. Finally, we present the stochastic Hamiltonian formulation of the collectivized momentum map dynamics and derive the corresponding Kolmogorov forward and backward equations.

  9. Analytical Dynamics and Nonrigid Spacecraft Simulation

    NASA Technical Reports Server (NTRS)

    Likins, P. W.

    1974-01-01

    Application to the simulation of idealized spacecraft are considered both for multiple-rigid-body models and for models consisting of combination of rigid bodies and elastic bodies, with the elastic bodies being defined either as continua, as finite-element systems, or as a collection of given modal data. Several specific examples are developed in detail by alternative methods of analytical mechanics, and results are compared to a Newton-Euler formulation. The following methods are developed from d'Alembert's principle in vector form: (1) Lagrange's form of d'Alembert's principle for independent generalized coordinates; (2) Lagrange's form of d'Alembert's principle for simply constrained systems; (3) Kane's quasi-coordinate formulation of D'Alembert's principle; (4) Lagrange's equations for independent generalized coordinates; (5) Lagrange's equations for simply constrained systems; (6) Lagrangian quasi-coordinate equations (or the Boltzmann-Hamel equations); (7) Hamilton's equations for simply constrained systems; and (8) Hamilton's equations for independent generalized coordinates.

  10. Development of Canonical Transformations from Hamilton's Principle.

    ERIC Educational Resources Information Center

    Quade, C. Richard

    1979-01-01

    The theory of canonical transformations and its development are discussed with regard to its application to Hutton's principle. Included are the derivation of the equations of motion and a lack of symmetry in the formulaion with respect to Lagrangian and the fundamental commutator relations of quantum mechanics. (Author/SA)

  11. Web-based training and interrater reliability testing for scoring the Hamilton Depression Rating Scale.

    PubMed

    Rosen, Jules; Mulsant, Benoit H; Marino, Patricia; Groening, Christopher; Young, Robert C; Fox, Debra

    2008-10-30

    Despite the importance of establishing shared scoring conventions and assessing interrater reliability in clinical trials in psychiatry, these elements are often overlooked. Obstacles to rater training and reliability testing include logistic difficulties in providing live training sessions, or mailing videotapes of patients to multiple sites and collecting the data for analysis. To address some of these obstacles, a web-based interactive video system was developed. It uses actors of diverse ages, gender and race to train raters how to score the Hamilton Depression Rating Scale and to assess interrater reliability. This system was tested with a group of experienced and novice raters within a single site. It was subsequently used to train raters of a federally funded multi-center clinical trial on scoring conventions and to test their interrater reliability. The advantages and limitations of using interactive video technology to improve the quality of clinical trials are discussed.

  12. Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation

    NASA Technical Reports Server (NTRS)

    Helenbrook, B. T.; Atkins, H. L.

    2006-01-01

    We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.

  13. Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations

    NASA Astrophysics Data System (ADS)

    Moghaderi, Hamid; Dehghan, Mehdi; Donatelli, Marco; Mazza, Mariarosa

    2017-12-01

    Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a two-dimensional space-FDE problem discretized by means of a second order finite difference scheme obtained as combination of the Crank-Nicolson scheme and the so-called weighted and shifted Grünwald formula. By fully exploiting the Toeplitz-like structure of the resulting linear system, we provide a detailed spectral analysis of the coefficient matrix at each time step, both in the case of constant and variable diffusion coefficients. Such a spectral analysis has a very crucial role, since it can be used for designing fast and robust iterative solvers. In particular, we employ the obtained spectral information to define a Galerkin multigrid method based on the classical linear interpolation as grid transfer operator and damped-Jacobi as smoother, and to prove the linear convergence rate of the corresponding two-grid method. The theoretical analysis suggests that the proposed grid transfer operator is strong enough for working also with the V-cycle method and the geometric multigrid. On this basis, we introduce two computationally favourable variants of the proposed multigrid method and we use them as preconditioners for Krylov methods. Several numerical results confirm that the resulting preconditioning strategies still keep a linear convergence rate.

  14. Hermann-Bernoulli-Laplace-Hamilton-Runge-Lenz Vector.

    ERIC Educational Resources Information Center

    Subramanian, P. R.; And Others

    1991-01-01

    A way for students to refresh and use their knowledge in both mathematics and physics is presented. By the study of the properties of the "Runge-Lenz" vector the subjects of algebra, analytical geometry, calculus, classical mechanics, differential equations, matrices, quantum mechanics, trigonometry, and vector analysis can be reviewed. (KR)

  15. Career, collections, reports and publications of Dr Francis Buchanan (later Hamilton), 1762-1829: natural history studies in Nepal, Burma (Myanmar), Bangladesh and India. Part 1.

    PubMed

    Watson, Mark F; Noltie, Henry J

    2016-10-01

    During his 20-year career as a surgeon-naturalist with the British East India Company, Francis Buchanan (later Hamilton, known in botany as Buchanan-Hamilton and in ichthyology as Hamilton-Buchanan) undertook pioneering survey explorations in several diverse regions of the Indian subcontinent. A naturalist at heart, his collections of plants and animals are often the first from such regions, notably Nepal, Burma (Myanmar) and Bangladesh. Buchanan had wide-ranging interests beyond natural history, using his talent for observation and meticulous recording to amass a huge body of information on the lands and peoples he encountered. However, much of this information remains unpublished in his survey reports, journals and other manuscripts, and so his role in the building of knowledge for these areas has been under-appreciated. Although a keen and able botanist, it is ironic that his multitudinous botanical discoveries are particularly poorly known, with the vast majority of his material on this subject languishing unpublished in archival collections. These include his original records and working notes which show the methods he used when dealing with 'information overload' and arranging his syntheses ready for publication. Notable is his experimentation with Jussieu's Natural System for classifying his Nepalese plants, and his recognition of biogeographic links of the Nepalese flora with Europe and Japan - both ahead of his fellow countrymen in Britain and India. The life of Francis Buchanan awaits the attention of a biographer who can do justice to his many interests, activities and influences. This is the first of two papers covering his life, providing an empirical baseline for future research and correcting misinformation that abounds in the literature. These papers outline Buchanan's professional career, concentrating on his activities in the exploration of natural history, and placing them in the wider context of botanical research in India.

  16. On Leighton's comparison theorem

    NASA Astrophysics Data System (ADS)

    Ghatasheh, Ahmed; Weikard, Rudi

    2017-06-01

    We give a simple proof of a fairly flexible comparison theorem for equations of the type -(p (u‧ + su)) ‧ + rp (u‧ + su) + qu = 0 on a finite interval where 1 / p, r, s, and q are real and integrable. Flexibility is provided by two functions which may be chosen freely (within limits) according to the situation at hand. We illustrate this by presenting some examples and special cases which include Schrödinger equations with distributional potentials as well as Jacobi difference equations.

  17. Symptoms of anxiety in depression: assessment of item performance of the Hamilton Anxiety Rating Scale in patients with depression.

    PubMed

    Vaccarino, Anthony L; Evans, Kenneth R; Sills, Terrence L; Kalali, Amir H

    2008-01-01

    Although diagnostically dissociable, anxiety is strongly co-morbid with depression. To examine further the clinical symptoms of anxiety in major depressive disorder (MDD), a non-parametric item response analysis on "blinded" data from four pharmaceutical company clinical trials was performed on the Hamilton Anxiety Rating Scale (HAMA) across levels of depressive severity. The severity of depressive symptoms was assessed using the 17-item Hamilton Depression Rating Scale (HAMD). HAMA and HAMD measures were supplied for each patient on each of two post-screen visits (n=1,668 observations). Option characteristic curves were generated for all 14 HAMA items to determine the probability of scoring a particular option on the HAMA in relation to the total HAMD score. Additional analyses were conducted using Pearson's product-moment correlations. Results showed that anxiety-related symptomatology generally increased as a function of overall depressive severity, though there were clear differences between individual anxiety symptoms in their relationship with depressive severity. In particular, anxious mood, tension, insomnia, difficulties in concentration and memory, and depressed mood were found to discriminate over the full range of HAMD scores, increasing continuously with increases in depressive severity. By contrast, many somatic-related symptoms, including muscular, sensory, cardiovascular, respiratory, gastro-intestinal, and genito-urinary were manifested primarily at higher levels of depression and did not discriminate well at lower HAMD scores. These results demonstrate anxiety as a core feature of depression, and the relationship between anxiety-related symptoms and depression should be considered in the assessment of depression and evaluation of treatment strategies and outcome.

  18. Inverse problems, non-roundness and flat pieces of the effective burning velocity from an inviscid quadratic Hamilton-Jacobi model

    NASA Astrophysics Data System (ADS)

    Jing, Wenjia; Tran, Hung V.; Yu, Yifeng

    2017-05-01

    The main goal of this paper is to understand finer properties of the effective burning velocity from a combustion model introduced by Majda and Souganidis (1994 Nonlinearity 7 1-30). Motivated by results in Bangert (1994 Calculus Variations PDE 2 49-63) and applications in turbulent combustion, we show that when the dimension is two and the flow of the ambient fluid is either weak or very strong, the level set of the effective burning velocity has flat pieces. Due to the lack of an applicable Hopf-type rigidity result, we need to identify the exact location of at least one flat piece. Implications on the effective flame front and other related inverse type problems are also discussed.

  19. Ordinal Process Dissociation and the Measurement of Automatic and Controlled Processes

    ERIC Educational Resources Information Center

    Hirshman, Elliot

    2004-01-01

    The process-dissociation equations (L. Jacoby, 1991) have been applied to results from inclusion and exclusion tasks to derive quantitative estimates of the influence of controlled and automatic processes on memory. This research has provoked controversies (e.g., T. Curran & D. Hintzman, 1995) regarding the validity of specific assumptions…

  20. A variational approach to multi-phase motion of gas, liquid and solid based on the level set method

    NASA Astrophysics Data System (ADS)

    Yokoi, Kensuke

    2009-07-01

    We propose a simple and robust numerical algorithm to deal with multi-phase motion of gas, liquid and solid based on the level set method [S. Osher, J.A. Sethian, Front propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulation, J. Comput. Phys. 79 (1988) 12; M. Sussman, P. Smereka, S. Osher, A level set approach for capturing solution to incompressible two-phase flow, J. Comput. Phys. 114 (1994) 146; J.A. Sethian, Level Set Methods and Fast Marching Methods, Cambridge University Press, 1999; S. Osher, R. Fedkiw, Level Set Methods and Dynamics Implicit Surface, Applied Mathematical Sciences, vol. 153, Springer, 2003]. In Eulerian framework, to simulate interaction between a moving solid object and an interfacial flow, we need to define at least two functions (level set functions) to distinguish three materials. In such simulations, in general two functions overlap and/or disagree due to numerical errors such as numerical diffusion. In this paper, we resolved the problem using the idea of the active contour model [M. Kass, A. Witkin, D. Terzopoulos, Snakes: active contour models, International Journal of Computer Vision 1 (1988) 321; V. Caselles, R. Kimmel, G. Sapiro, Geodesic active contours, International Journal of Computer Vision 22 (1997) 61; G. Sapiro, Geometric Partial Differential Equations and Image Analysis, Cambridge University Press, 2001; R. Kimmel, Numerical Geometry of Images: Theory, Algorithms, and Applications, Springer-Verlag, 2003] introduced in the field of image processing.

  1. H(infinity)/H(2)/Kalman filtering of linear dynamical systems via variational techniques with applications to target tracking

    NASA Astrophysics Data System (ADS)

    Rawicz, Paul Lawrence

    In this thesis, the similarities between the structure of the H infinity, H2, and Kalman filters are examined. The filters used in this examination have been derived through duality to the full information controller. In addition, a direct variation of parameters derivation of the Hinfinity filter is presented for both continuous and discrete time (staler case). Direct and controller dual derivations using differential games exist in the literature and also employ variational techniques. Using a variational, rather than a differential games, viewpoint has resulted in a simple relationship between the Riccati equations that arise from the derivation and the results of the Bounded Real Lemma. This same relation has previously been found in the literature and used to relate the Riccati inequality for linear systems to the Hamilton Jacobi inequality for nonlinear systems when implementing the Hinfinity controller. The Hinfinity, H2, and Kalman filters are applied to the two-state target tracking problem. In continuous time, closed form analytic expressions for the trackers and their performance are determined. To evaluate the trackers using a neutral, realistic, criterion, the probability of target escape is developed. That is, the probability that the target position error will be such that the target is outside the radar beam width resulting in a loss of measurement. In discrete time, a numerical example, using the probability of target escape, is presented to illustrate the differences in tracker performance.

  2. Conserved Quantities in General Relativity: From the Quasi-Local Level to Spatial Infinity

    NASA Astrophysics Data System (ADS)

    Chen, Po-Ning; Wang, Mu-Tao; Yau, Shing-Tung

    2015-08-01

    We define quasi-local conserved quantities in general relativity by using the optimal isometric embedding in Wang and Yau (Commun Math Phys 288(3):919-942, 2009) to transplant Killing fields in the Minkowski spacetime back to the 2-surface of interest in a physical spacetime. To each optimal isometric embedding, a dual element of the Lie algebra of the Lorentz group is assigned. Quasi-local angular momentum and quasi-local center of mass correspond to pairing this element with rotation Killing fields and boost Killing fields, respectively. They obey classical transformation laws under the action of the Poincaré group. We further justify these definitions by considering their limits as the total angular momentum and the total center of mass of an isolated system. These expressions were derived from the Hamilton-Jacobi analysis of the gravitational action and thus satisfy conservation laws. As a result, we obtained an invariant total angular momentum theorem in the Kerr spacetime. For a vacuum asymptotically flat initial data set of order 1, it is shown that the limits are always finite without any extra assumptions. We also study these total conserved quantities on a family of asymptotically flat initial data sets evolving by the vacuum Einstein evolution equation. It is shown that the total angular momentum is conserved under the evolution. For the total center of mass, the classical dynamical formula relating the center of mass, energy, and linear momentum is recovered, in the nonlinear context of initial data sets evolving by the vacuum Einstein evolution equation. The definition of quasi-local angular momentum provides an answer to the second problem in classical general relativity on Penrose's list (Proc R Soc Lond Ser A 381(1780):53-63, 1982).

  3. Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

    NASA Technical Reports Server (NTRS)

    Shu, Chi-Wang

    2004-01-01

    -Stokes equations, and Hamilton-Jacobi-like equations.

  4. Clinical and tree hollow populations of human pathogenic yeast in Hamilton, Ontario, Canada are different.

    PubMed

    Carvalho, Chris; Yang, Jiaqi; Vogan, Aaron; Maganti, Harinad; Yamamura, Deborah; Xu, Jianping

    2014-05-01

    Yeast are among the most frequent pathogens in humans. The dominant yeast causing human infections belong to the genus Candida and Candida albicans is the most frequently isolated species. However, several non-C. albicans species are becoming increasingly common in patients worldwide. The relationships between yeast in humans and the natural environments remain poorly understood. Furthermore, it is often difficult to identify or exclude the origins of disease-causing yeast from specific environmental reservoirs. In this study, we compared the yeast isolates from tree hollows and from clinics in Hamilton, Ontario, Canada. Our surveys and analyses showed significant differences in yeast species composition, in their temporal dynamics, and in yeast genotypes between isolates from tree hollows and hospitals. Our results are inconsistent with the hypothesis that yeast from trees constitute a significant source of pathogenic yeast in humans in this region. Similarly, the yeast in humans and clinics do not appear to contribute to yeast in tree hollows. © 2013 Blackwell Verlag GmbH.

  5. Validating the Hamilton Anatomy of Risk Management-Forensic Version and the Aggressive Incidents Scale.

    PubMed

    Cook, Alana N; Moulden, Heather M; Mamak, Mini; Lalani, Shams; Messina, Katrina; Chaimowitz, Gary

    2018-06-01

    The Hamilton Anatomy of Risk Management-Forensic Version (HARM-FV) is a structured professional judgement tool of violence risk developed for use in forensic inpatient psychiatric settings. The HARM-FV is used with the Aggressive Incidents Scale (AIS), which provides a standardized method of recording aggressive incidents. We report the findings of the concurrent validity of the HARM-FV and the AIS with widely used measures of violence risk and aggressive acts, the Historical, Clinical, Risk Management-20, Version 3 (HCR-20 V3 ) and a modified version of the Overt Aggression Scale. We also present findings on the predictive validity of the HARM-FV in the short term (1-month follow-up periods) for varying severities of aggressive acts. The results indicated strong support for the concurrent validity of the HARM-FV and AIS and promising support for the predictive accuracy of the tool for inpatient aggression. This article provides support for the continued clinical use of the HARM-FV within an inpatient forensic setting and highlights areas for further research.

  6. Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

    NASA Astrophysics Data System (ADS)

    Peshkov, Ilya; Pavelka, Michal; Romenski, Evgeniy; Grmela, Miroslav

    2018-01-01

    Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov-type formulation brings the mathematical rigor (the local well posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).

  7. Husbandry stress exacerbates mycobacterial infections in adult zebrafish, Danio rerio (Hamilton)

    USGS Publications Warehouse

    Ramsay, J.M.; Watral, Virginia G.; Schreck, C.B.; Kent, M.L.

    2009-01-01

    Mycobacteria are significant pathogens of laboratory zebrafish, Danio rerio (Hamilton). Stress is often implicated in clinical disease and morbidity associated with mycobacterial infections but has yet to be examined with zebrafish. The aim of this study was to examine the effects of husbandry stressors on zebrafish infected with mycobacteria. Adult zebrafish were exposed to Mycobacterium marinum or Mycobacterium chelonae, two species that have been associated with disease in zebrafish. Infected fish and controls were then subjected to chronic crowding and handling stressors and examined over an 8-week period. Whole-body cortisol was significantly elevated in stressed fish compared to non-stressed fish. Fish infected with M. marinum ATCC 927 and subjected to husbandry stressors had 14% cumulative mortality while no mortality occurred among infected fish not subjected to husbandry stressors. Stressed fish, infected with M. chelonae H1E2 from zebrafish, were 15-fold more likely to be infected than non-stressed fish at week 8 post-injection. Sub-acute, diffuse infections were more common among stressed fish infected with M. marinum or M. chelonae than non-stressed fish. This is the first study to demonstrate an effect of stress and elevated cortisol on the morbidity, prevalence, clinical disease and histological presentation associated with mycobacterial infections in zebrafish. Minimizing husbandry stress may be effective at reducing the severity of outbreaks of clinical mycobacteriosis in zebrafish facilities. ?? 2009 Blackwell Publishing Ltd.

  8. Superspace and global stability in general relativity

    NASA Astrophysics Data System (ADS)

    Gurzadyan, A. V.; Kocharyan, A. A.

    A framework is developed enabling the global analysis of the stability of cosmological models using the local geometric characteristics of the infinite-dimensional superspace, i.e. using the generalized Jacobi equation reformulated for pseudo-Riemannian manifolds. We give a direct formalism for dynamical analysis in the superspace, the requisite equation pertinent for stability analysis of the universe by means of generalized covariant and Fermi derivative is derived. Then, the relevant definitions and formulae are retrieved for cosmological models with a scalar field.

  9. Kinetic energy equations for the average-passage equation system

    NASA Technical Reports Server (NTRS)

    Johnson, Richard W.; Adamczyk, John J.

    1989-01-01

    Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.

  10. Highly elevated levels of perfluorooctane sulfonate and other perfluorinated acids found in biota and surface water downstream of an international airport, Hamilton, Ontario, Canada.

    PubMed

    de Solla, S R; De Silva, A O; Letcher, R J

    2012-02-01

    Per- and poly-fluorinated compounds (PFCs), which include perfluorinated carboxylates (PFCAs) and sulfonates (PFSAs) and various precursors, are used in a wide variety of industrial, commercial and domestic products. This includes aqueous film forming foam (AFFF), which is used by military and commercial airports as fire suppressants. In a preliminary assessment prior to this study, very high concentrations (>1 ppm wet weight) of the PFSA, perfluorooctane sulfonate (PFOS), were discovered in the plasma of snapping turtles (Chelydra serpentina) collected in 2008 from Lake Niapenco in southern Ontario, Canada. We presently report on a suite of C(6) to C(15) PFCAs, C(4), C(6), C(8) and C(10) PFSAs, several PFC precursors (e.g. perfluorooctane sulfonamide, PFOSA), and a cyclic perfluorinated acid used in aircraft hydraulic fluid, perfluoroethylcyclohexane sulfonate (PFECHS) in surface water from the Welland River and Lake Niapenco, downstream of the John C. Munro International Airport, Hamilton, Ontario, Canada. Amphipods, shrimp, and water were sampled from the Welland River and Lake Niapenco, as well as local references. The same suite of PFCs in turtle plasma from Lake Niapenco was compared to those from other southern Ontario sites. PFOS dominated the sum PFCs in all substrates (e.g., >99% in plasma of turtles downstream the Hamilton Airport, and 72.1 to 94.1% at all other sites). PFOS averaged 2223(±247.1SE) ng/g in turtle plasma from Lake Niapenco, and ranged from 9.0 to 171.4 elsewhere. Mean PFOS in amphipods and in water were 518.1(±83.8)ng/g and 130.3(±43.6) ng/L downstream of the airport, and 19.1(±2.7) ng/g and 6.8(±0.5) ng/L at reference sites, respectively. Concentrations of selected PFCs declined with distance downstream from the airport. Although there was no known spill event or publicly reported use of AFFF associated with a fire event at the Hamilton airport, the airport is a likely major source of PFC contamination in the Welland River. Crown

  11. Hawking radiation due to photon and gravitino tunneling

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Majhi, Bibhas Ranjan, E-mail: bibhas@bose.res.i; Samanta, Saurav, E-mail: srvsmnt@gmail.co

    2010-11-15

    Applying the Hamilton-Jacobi method we investigate the tunneling of photon across the event horizon of a static spherically symmetric black hole. The necessity of the gauge condition on the photon field, to derive the semiclassical Hawking temperature, is explicitly shown. Also, the tunneling of photon and gravitino beyond this semiclassical approximation are presented separately. Quantum corrections of the action for both cases are found to be proportional to the semiclassical contribution. Modifications to the Hawking temperature and Bekenstein-Hawking area law are thereby obtained. Using this corrected temperature and Hawking's periodicity argument, the modified metric for the Schwarzschild black hole ismore » given. This corrected version of the metric, up to h order is equivalent to the metric obtained by including one loop back reaction effect. Finally, the coefficient of the leading order correction of entropy is shown to be related to the trace anomaly.« less

  12. A Comprehensive Analytical Solution of the Nonlinear Pendulum

    ERIC Educational Resources Information Center

    Ochs, Karlheinz

    2011-01-01

    In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions…

  13. Communication and relationship skills for rapid response teams at hamilton health sciences.

    PubMed

    Cziraki, Karen; Lucas, Janie; Rogers, Toni; Page, Laura; Zimmerman, Rosanne; Hauer, Lois Ann; Daniels, Charlotte; Gregoroff, Susan

    2008-01-01

    Rapid response teams (RRT) are an important safety strategy in the prevention of deaths in patients who are progressively failing outside of the intensive care unit. The goal is to intervene before a critical event occurs. Effective teamwork and communication skills are frequently cited as critical success factors in the implementation of these teams. However, there is very little literature that clearly provides an education strategy for the development of these skills. Training in simulation labs offers an opportunity to assess and build on current team skills; however, this approach does not address how to meet the gaps in team communication and relationship skill management. At Hamilton Health Sciences (HHS) a two-day program was developed in collaboration with the RRT Team Leads, Organizational Effectiveness and Patient Safety Leaders. Participants reflected on their conflict management styles and considered how their personality traits may contribute to team function. Communication and relationship theories were reviewed and applied in simulated sessions in the relative safety of off-site team sessions. The overwhelming positive response to this training has been demonstrated in the incredible success of these teams from the perspective of the satisfaction surveys of the care units that call the team, and in the multi-phased team evaluation of their application to practice. These sessions offer a useful approach to the development of the soft skills required for successful RRT implementation.

  14. Periodic three-body orbits with vanishing angular momentum in the Jacobi-Poincaré ‘strong’ potential

    NASA Astrophysics Data System (ADS)

    Dmitrašinović, V.; Petrović, Luka V.; Šuvakov, Milovan

    2017-10-01

    Moore (1993 Phys. Rev. Lett. 70 3675) and Montgomery (2005 Ergod. Theor. Dynam. Syst. 25 921-947) have argued that planar periodic orbits of three bodies moving in the Jacobi-Poincaré, or the ‘strong’ pairwise potential \\sumi>j\\frac{-1}{rij^2} , can have all possible topologies. Here we search systematically for such orbits with vanishing angular momentum and find 24 topologically distinct orbits, 22 of which are new, in a small section of the allowed phase space, with a tendency to overcrowd, due to overlapping initial conditions. The topologies of these 24 orbits belong to three algebraic sequences defined as functions of integer n=0, 1, 2, \\ldots . Each sequence extends to n \\to ∞ , but the separation of initial conditions for orbits with n ≥slant 10 becomes practically impossible with a numerical precision of 16 decimal places. Nevertheless, even with a precision of 16 decimals, it is clear that in each sequence both the orbit’s initial angle φn and its period T n approach finite values in the asymptotic limit (n \\to ∞ ). Two of three sequences are overlapping in the sense that their initial angles ϕ occupy the same segment on the circle and their asymptotic values φ∞ are (very) close to each other. The actions of these orbits rise linearly with the index n that describes the orbit’s topology, which is in agreement with the Newtonian case. We show that this behaviour is consistent with the assumption of analyticity of the action as a function of period.

  15. Guidance law development for aeroassisted transfer vehicles using matched asymptotic expansions

    NASA Technical Reports Server (NTRS)

    Calise, Anthony J.; Melamed, Nahum

    1993-01-01

    This report addresses and clarifies a number of issues related to the Matched Asymptotic Expansion (MAE) analysis of skip trajectories, or any class of problems that give rise to inner layers that are not associated directly with satisfying boundary conditions. The procedure for matching inner and outer solutions, and using the composite solution to satisfy boundary conditions is developed and rigorously followed to obtain a set of algebraic equations for the problem of inclination change with minimum energy loss. A detailed evaluation of the zeroth order guidance algorithm for aeroassisted orbit transfer is performed. It is shown that by exploiting the structure of the MAE solution procedure, the original problem, which requires the solution of a set of 20 implicit algebraic equations, can be reduced to a problem of 6 implicit equations in 6 unknowns. A solution that is near optimal, requires a minimum of computation, and thus can be implemented in real time and on-board the vehicle, has been obtained. Guidance law implementation entails treating the current state as a new initial state and repetitively solving the zeroth order MAE problem to obtain the feedback controls. Finally, a general procedure is developed for constructing a MAE solution up to first order, of the Hamilton-Jacobi-Bellman equation based on the method of characteristics. The development is valid for a class of perturbation problems whose solution exhibits two-time-scale behavior. A regular expansion for problems of this type is shown to be inappropriate since it is not valid over a narrow range of the independent variable. That is, it is not uniformly valid. Of particular interest here is the manner in which matching and boundary conditions are enforced when the expansion is carried out to first order. Two cases are distinguished-one where the left boundary condition coincides with, or lies to the right of, the singular region, and another one where the left boundary condition lies to the left

  16. Ground-water flow directions and estimation of aquifer hydraulic properties in the lower Great Miami River Buried Valley aquifer system, Hamilton Area, Ohio

    USGS Publications Warehouse

    Sheets, Rodney A.; Bossenbroek, Karen E.

    2005-01-01

    The Great Miami River Buried Valley Aquifer System is one of the most productive sources of potable water in the Midwest, yielding as much as 3,000 gallons per minute to wells. Many water-supply wells tapping this aquifer system are purposely placed near rivers to take advantage of induced infiltration from the rivers. The City of Hamilton's North Well Field consists of 10 wells near the Great Miami River, all completed in the lower Great Miami River Buried Valley Aquifer System. A well-drilling program and a multiple-well aquifer test were done to investigate ground-water flow directions and to estimate aquifer hydraulic properties in the lower part of the Great Miami River Buried Valley Aquifer System. Descriptions of lithology from 10 well borings indicate varying amounts and thickness of clay or till, and therefore, varying levels of potential aquifer confinement. Borings also indicate that the aquifer properties can change dramatically over relatively short distances. Grain-size analyses indicate an average bulk hydraulic conductivity value of aquifer materials of 240 feet per day; the geometric mean of hydraulic conductivity values of aquifer material was 89 feet per day. Median grain sizes of aquifer material and clay units were 1.3 millimeters and 0.1 millimeters, respectively. Water levels in the Hamilton North Well Field are affected by stream stage in the Great Miami River and barometric pressure. Bank storage in response to stream stage is evident. Results from a multiple-well aquifer test at the well field indicate, as do the lithologic descriptions, that the aquifer is semiconfined in some areas and unconfined in others. Transmissivity and storage coefficient of the semiconfined part of the aquifer were 50,000 feet squared per day and 5x10-4, respectively. The average hydraulic conductivity (450 feet per day) based on the aquifer test is reasonable for glacial outwash but is higher than calculated from grain-size analyses, implying a scale effect

  17. p-Euler equations and p-Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Li, Lei; Liu, Jian-Guo

    2018-04-01

    We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

  18. Factor analysis of the Hamilton Depression Rating Scale in Parkinson's disease.

    PubMed

    Broen, M P G; Moonen, A J H; Kuijf, M L; Dujardin, K; Marsh, L; Richard, I H; Starkstein, S E; Martinez-Martin, P; Leentjens, A F G

    2015-02-01

    Several studies have validated the Hamilton Depression Rating Scale (HAMD) in patients with Parkinson's disease (PD), and reported adequate reliability and construct validity. However, the factorial validity of the HAMD has not yet been investigated. The aim of our analysis was to explore the factor structure of the HAMD in a large sample of PD patients. A principal component analysis of the 17-item HAMD was performed on data of 341 PD patients, available from a previous cross sectional study on anxiety. An eigenvalue ≥1 was used to determine the number of factors. Factor loadings ≥0.4 in combination with oblique rotations were used to identify which variables made up the factors. Kaiser-Meyer-Olkin measure (KMO), Cronbach's alpha, Bartlett's test, communality, percentage of non-redundant residuals and the component correlation matrix were computed to assess factor validity. KMO verified the sample's adequacy for factor analysis and Cronbach's alpha indicated a good internal consistency of the total scale. Six factors had eigenvalues ≥1 and together explained 59.19% of the variance. The number of items per factor varied from 1 to 6. Inter-item correlations within each component were low. There was a high percentage of non-redundant residuals and low communality. This analysis demonstrates that the factorial validity of the HAMD in PD is unsatisfactory. This implies that the scale is not appropriate for studying specific symptom domains of depression based on factorial structure in a PD population. Copyright © 2014 Elsevier Ltd. All rights reserved.

  19. Measuring anxiety in depressed patients: A comparison of the Hamilton anxiety rating scale and the DSM-5 Anxious Distress Specifier Interview.

    PubMed

    Zimmerman, Mark; Martin, Jacob; Clark, Heather; McGonigal, Patrick; Harris, Lauren; Holst, Carolina Guzman

    2017-10-01

    DSM-5 included criteria for an anxious distress specifier for major depressive disorder (MDD). In the present report from the Rhode Island Methods to Improve Diagnostic Assessment and Services (MIDAS) project we examined whether a measure of the specifier, the DSM-5 Anxious Distress Specifier Interview (DADSI), was as valid as the Hamilton Anxiety Scale (HAMA) as a measure of the severity of anxiety in depressed patients. Two hundred three psychiatric patients with MDD were interviewed by trained diagnostic raters who administered the Structured Clinical Interview for DSM-IV (SCID) supplemented with questions to rate the DADSI, HAMA, and Hamilton Depression Rating Scale (HAMD). The patients completed self-report measures of depression, anxiety, and irritability. Sensitivity to change was examined in 30 patients. The DADSI and HAMA were significantly correlated (r = 0.60, p < 0.001). Both the DADSI and HAMA were more highly correlated with measures of anxiety than with measures of the other symptom domains. The HAMD was significantly more highly correlated with the HAMA than with the DADSI. For each anxiety disorder, patients with the disorder scored significantly higher on both the DADSI and HAMA than did patients with no current anxiety disorder. A large effect size of treatment was found for both measures (DADSI: d = 1.48; HAMA: d = 1.37). Both the DADSI and HAMA were valid measures of anxiety severity in depressed patients, though the HAMA was more highly confounded with measures of depression than the DADSI. The DADSI is briefer than the HAMA, and may be more feasible to use in clinical practice. Copyright © 2017 Elsevier Ltd. All rights reserved.

  20. Symptom Frequency Characteristics of the Hamilton Depression Rating Scale of Major Depressive Disorder in Epilepsy.

    PubMed

    Wiglusz, Mariusz S; Landowski, Jerzy; Michalak, Lidia; Cubała, Wiesław J

    2015-09-01

    Depressive disorders are common among patients with epilepsy (PWE). The aim of this study was to explore symptom frequencies of 17-item Hamilton Depression Rating Scale (HDRS-17) and recognize the clinical characteristics of Major Depressive Disorder in PWE. A sample of 40 adults outpatients with epilepsy and depression was diagnosed using SCID-I for DSM-IV-TR and HDRS-17. The total HDRS-17 score was analysed followed by the exploratory analysis based on the hierarchical model. The frequencies of HDRS-17 items varied widely in this study. Insomnia related items and general somatic symptoms items as well as insomnia and somatic factors exhibited constant and higher frequency. Feeling guilty, suicide, psychomotor retardation and depressed mood showed relatively lower frequencies. Other symptoms had variable frequencies across the study population. Depressive disorders are common among PWE. In the study group insomnia and somatic symptoms displayed highest values which could represent atypical clinical features of mood disorders in PWE. There is a need for more studies with a use of standardized approach to the problem.

  1. Full dimensional (15-dimensional) quantum-dynamical simulation of the protonated water-dimer III: Mixed Jacobi-valence parametrization and benchmark results for the zero point energy, vibrationally excited states, and infrared spectrum.

    PubMed

    Vendrell, Oriol; Brill, Michael; Gatti, Fabien; Lauvergnat, David; Meyer, Hans-Dieter

    2009-06-21

    Quantum dynamical calculations are reported for the zero point energy, several low-lying vibrational states, and the infrared spectrum of the H(5)O(2)(+) cation. The calculations are performed by the multiconfiguration time-dependent Hartree (MCTDH) method. A new vector parametrization based on a mixed Jacobi-valence description of the system is presented. With this parametrization the potential energy surface coupling is reduced with respect to a full Jacobi description, providing a better convergence of the n-mode representation of the potential. However, new coupling terms appear in the kinetic energy operator. These terms are derived and discussed. A mode-combination scheme based on six combined coordinates is used, and the representation of the 15-dimensional potential in terms of a six-combined mode cluster expansion including up to some 7-dimensional grids is discussed. A statistical analysis of the accuracy of the n-mode representation of the potential at all orders is performed. Benchmark, fully converged results are reported for the zero point energy, which lie within the statistical uncertainty of the reference diffusion Monte Carlo result for this system. Some low-lying vibrationally excited eigenstates are computed by block improved relaxation, illustrating the applicability of the approach to large systems. Benchmark calculations of the linear infrared spectrum are provided, and convergence with increasing size of the time-dependent basis and as a function of the order of the n-mode representation is studied. The calculations presented here make use of recent developments in the parallel version of the MCTDH code, which are briefly discussed. We also show that the infrared spectrum can be computed, to a very good approximation, within D(2d) symmetry, instead of the G(16) symmetry used before, in which the complete rotation of one water molecule with respect to the other is allowed, thus simplifying the dynamical problem.

  2. Hammett equation and generalized Pauling's electronegativity equation.

    PubMed

    Liu, Lei; Fu, Yao; Liu, Rui; Li, Rui-Qiong; Guo, Qing-Xiang

    2004-01-01

    Substituent interaction energy (SIE) was defined as the energy change of the isodesmic reaction X-spacer-Y + H-spacer-H --> X-spacer-H + H-spacer-Y. It was found that this SIE followed a simple equation, SIE(X,Y) = -ksigma(X)sigma(Y), where k was a constant dependent on the system and sigma was a certain scale of electronic substituent constant. It was demonstrated that the equation was applicable to disubstituted bicyclo[2.2.2]octanes, benzenes, ethylenes, butadienes, and hexatrienes. It was also demonstrated that Hammett's equation was a derivative form of the above equation. Furthermore, it was found that when spacer = nil the above equation was mathematically the same as Pauling's electronegativity equation. Thus it was shown that Hammett's equation was a derivative form of the generalized Pauling's electronegativity equation and that a generalized Pauling's electronegativity equation could be utilized for diverse X-spacer-Y systems. In addition, the total electronic substituent effects were successfully separated into field/inductive and resonance effects in the equation SIE(X,Y) = -k(1)F(X)F(Y) - k(2)R(X)R(Y) - k(3)(F(X)R(Y) + R(X)F(Y)). The existence of the cross term (i.e., F(X)R(Y) and R(X)F(Y)) suggested that the field/inductive effect was not orthogonal to the resonance effect because the field/inductive effect from one substituent interacted with the resonance effect from the other. Further studies on multi-substituted systems suggested that the electronic substituent effects should be pairwise and additive. Hence, the SIE in a multi-substituted system could be described using the equation SIE(X1, X2, ..., Xn) = Sigma(n-1)(i=1)Sigma(n)(j=i+1)k(ij)sigma(X)isigma(X)j.

  3. Semiclassics for matrix Hamiltonians: The Gutzwiller trace formula with applications to graphene-type systems

    NASA Astrophysics Data System (ADS)

    Vogl, M.; Pankratov, O.; Shallcross, S.

    2017-07-01

    We present a tractable and physically transparent semiclassical theory of matrix-valued Hamiltonians, i.e., those that describe quantum systems with internal degrees of freedoms, based on a generalization of the Gutzwiller trace formula for a n ×n dimensional Hamiltonian H (p ̂,q ̂) . The classical dynamics is governed by n Hamilton-Jacobi (HJ) equations that act in a phase space endowed with a classical Berry curvature encoding anholonomy in the parallel transport of the eigenvectors of H (p ,q ) ; these vectors describe the internal structure of the semiclassical particles. At the O (ℏ1) level and for nondegenerate HJ systems, this curvature results in an additional semiclassical phase composed of (i) a Berry phase and (ii) a dynamical phase resulting from the classical particles "moving through the Berry curvature". We show that the dynamical part of this semiclassical phase will, generally, be zero only for the case in which the Berry phase is topological (i.e., depends only on the winding number). We illustrate the method by calculating the Landau spectrum for monolayer graphene, the four-band model of AB bilayer graphene, and for a more complicated matrix Hamiltonian describing the silicene band structure. Finally, we apply our method to an inhomogeneous system consisting of a strain engineered one-dimensional moiré in bilayer graphene, finding localized states near the Dirac point that arise from electron trapping in a semiclassical moiré potential. The semiclassical density of states of these localized states we show to be in perfect agreement with an exact quantum mechanical calculation of the density of states.

  4. A policy iteration approach to online optimal control of continuous-time constrained-input systems.

    PubMed

    Modares, Hamidreza; Naghibi Sistani, Mohammad-Bagher; Lewis, Frank L

    2013-09-01

    This paper is an effort towards developing an online learning algorithm to find the optimal control solution for continuous-time (CT) systems subject to input constraints. The proposed method is based on the policy iteration (PI) technique which has recently evolved as a major technique for solving optimal control problems. Although a number of online PI algorithms have been developed for CT systems, none of them take into account the input constraints caused by actuator saturation. In practice, however, ignoring these constraints leads to performance degradation or even system instability. In this paper, to deal with the input constraints, a suitable nonquadratic functional is employed to encode the constraints into the optimization formulation. Then, the proposed PI algorithm is implemented on an actor-critic structure to solve the Hamilton-Jacobi-Bellman (HJB) equation associated with this nonquadratic cost functional in an online fashion. That is, two coupled neural network (NN) approximators, namely an actor and a critic are tuned online and simultaneously for approximating the associated HJB solution and computing the optimal control policy. The critic is used to evaluate the cost associated with the current policy, while the actor is used to find an improved policy based on information provided by the critic. Convergence to a close approximation of the HJB solution as well as stability of the proposed feedback control law are shown. Simulation results of the proposed method on a nonlinear CT system illustrate the effectiveness of the proposed approach. Copyright © 2013 ISA. All rights reserved.

  5. On the adiabatic representation of Meyer-Miller electronic-nuclear dynamics

    NASA Astrophysics Data System (ADS)

    Cotton, Stephen J.; Liang, Ruibin; Miller, William H.

    2017-08-01

    The Meyer-Miller (MM) classical vibronic (electronic + nuclear) Hamiltonian for electronically non-adiabatic dynamics—as used, for example, with the recently developed symmetrical quasiclassical (SQC) windowing model—can be written in either a diabatic or an adiabatic representation of the electronic degrees of freedom, the two being a canonical transformation of each other, thus giving the same dynamics. Although most recent applications of this SQC/MM approach have been carried out in the diabatic representation—because most of the benchmark model problems that have exact quantum results available for comparison are typically defined in a diabatic representation—it will typically be much more convenient to work in the adiabatic representation, e.g., when using Born-Oppenheimer potential energy surfaces (PESs) and derivative couplings that come from electronic structure calculations. The canonical equations of motion (EOMs) (i.e., Hamilton's equations) that come from the adiabatic MM Hamiltonian, however, in addition to the common first-derivative couplings, also involve second-derivative non-adiabatic coupling terms (as does the quantum Schrödinger equation), and the latter are considerably more difficult to calculate. This paper thus revisits the adiabatic version of the MM Hamiltonian and describes a modification of the classical adiabatic EOMs that are entirely equivalent to Hamilton's equations but that do not involve the second-derivative couplings. The second-derivative coupling terms have not been neglected; they simply do not appear in these modified adiabatic EOMs. This means that SQC/MM calculations can be carried out in the adiabatic representation, without approximation, needing only the PESs and the first-derivative coupling elements. The results of example SQC/MM calculations are presented, which illustrate this point, and also the fact that simply neglecting the second-derivative couplings in Hamilton's equations (and presumably also in

  6. Modelling vortex-induced fluid-structure interaction.

    PubMed

    Benaroya, Haym; Gabbai, Rene D

    2008-04-13

    The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid-structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy equation describing the fluid-structure interaction. It is demonstrated here that flow-oscillator models are a subclass of the general, physical-based framework. A flow-oscillator model is a reduced-order mechanical model, generally comprising two mechanical oscillators, one modelling the structural oscillation and the other a nonlinear oscillator representing the fluid behaviour coupled to the structural motion.Reduced-order analytical model development continues to be carried out using a Hamilton's principle-based variational approach. This provides flexibility in the long run for generalizing the modelling paradigm to complex, three-dimensional problems with multiple degrees of freedom, although such extension is very difficult. As both experimental and analytical capabilities advance, the critical research path to developing and implementing fluid-structure interaction models entails-formulating generalized equations of motion, as a superset of the flow-oscillator models; and-developing experimentally derived, semi-analytical functions to describe key terms in the governing equations of motion. The developed variational approach yields a system of governing equations. This will allow modelling of multiple d.f. systems. The extensions derived generalize the Hamilton's variational formulation for such problems. The Navier-Stokes equations are derived and coupled to the structural oscillator. This general model has been shown to be a superset of the flow-oscillator model. Based on different assumptions, one can derive a variety of flow-oscillator models.

  7. Risk and efficacy of human-enabled interspecific hybridization for climate-change adaptation: Response to Hamilton and Miller (2016)

    USGS Publications Warehouse

    Kovach, Ryan P.; Luikart, Gordon; Lowe, Winsor H.; Boyer, Matthew C.; Muhlfeld, Clint C.

    2016-01-01

    Hamilton and Miller (2016) provide an interesting and provocative discussion of how hybridization and introgression can promote evolutionary potential in the face of climate change. They argue that hybridization—mating between individuals from genetically distinct populations—can alleviate inbreeding depression and promote adaptive introgression and evolutionary rescue. We agree that deliberate intraspecific hybridization (mating between individuals of the same species) is an underused management tool for increasing fitness in inbred populations (i.e., genetic rescue; Frankham 2015; Whiteley et al. 2015). The potential risks and benefits of assisted gene flow have been discussed in the literature, and an emerging consensus suggests that mating between populations isolated for approximately 50–100 generations can benefit fitness, often with a minor risk of outbreeding depression (Frankham et al. 2011; Aitken & Whitlock 2013; Allendorf et al. 2013).

  8. Hamilton's Principle and Approximate Solutions to Problems in Classical Mechanics

    ERIC Educational Resources Information Center

    Schlitt, D. W.

    1977-01-01

    Shows how to use the Ritz method for obtaining approximate solutions to problems expressed in variational form directly from the variational equation. Application of this method to classical mechanics is given. (MLH)

  9. Non-Linear Acoustic Concealed Weapons Detector

    DTIC Science & Technology

    2006-05-01

    signature analysis 8 the interactions of the beams with concealed objects. The Khokhlov- Zabolotskaya-Kuznetsov ( KZK ) equation is the most widely used...Hamilton developed a finite difference method based on the KZK equation to model pulsed acoustic emissions from axial symmetric sources. Using a...College of William & Mary, we have developed a simulation code using the KZK equation to model non-linear acoustic beams and visualize beam patterns

  10. Hydrology of the Cave Springs area near Chattanooga, Hamilton County, Tennessee

    USGS Publications Warehouse

    Bradfield, Arthur D.

    1992-01-01

    The hydrology of Cave Springs, the second largest spring in East Tennessee,was investigated from July 1987 to September 1989. Wells near the spring supply about 5 million gallons per day of potable water to people in Hamilton County near Chattanooga. Discharge from the spring averaged about 13.5 cubic feet per second (8.72 million gallons per day) during the study period. Withdrawals by the Hixson Utility District from wells upgradient from the outflow averaged 8.6 cubic feet per second (5.54 million gallons per day). Aquifer tests using wells intersecting a large solution cavity supplying water to the spring showed a drawdown of less than 3 feet with a discharge of 9,000 gallons per minute or 20 cubic feet per second. Temperature and specific conductance of ground water near the spring outflow were monitored hourly. Temperatures ranged from 13.5 to 18.2 degrees celsius, and fluctuated seasonally in response to climate. Specific-conductance values ranged from 122 to 405 microsiemens per centimeter at 25 degrees Celsius, but were generally between 163 to 185 microsiemensper centimeter. The drainage area of the basin recharging the spring system was estimated to be 1O squaremiles. A potentiometric map of the recharge basin was developed from water levels measured at domestic and test wells in August 1989. Aquifer tests at five test wells in the study area indicated that specific-capacity values for these wells ranged from 4.1 to 261 gallons per minute per foot of drawdown. Water-quality characteristics of ground water in the area were used in conjunction with potentiometric-surface maps to delineate the approximate area contributing recharge to Cave Springs.

  11. Quadratic time dependent Hamiltonians and separation of variables

    NASA Astrophysics Data System (ADS)

    Anzaldo-Meneses, A.

    2017-06-01

    Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.

  12. Computing generalized Langevin equations and generalized Fokker-Planck equations.

    PubMed

    Darve, Eric; Solomon, Jose; Kia, Amirali

    2009-07-07

    The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

  13. Hamilton's Equations with Euler Parameters for Rigid Body Dynamics Modeling. Chapter 3

    NASA Technical Reports Server (NTRS)

    Shivarama, Ravishankar; Fahrenthold, Eric P.

    2004-01-01

    A combination of Euler parameter kinematics and Hamiltonian mechanics provides a rigid body dynamics model well suited for use in strongly nonlinear problems involving arbitrarily large rotations. The model is unconstrained, free of singularities, includes a general potential energy function and a minimum set of momentum variables, and takes an explicit state space form convenient for numerical implementation. The general formulation may be specialized to address particular applications, as illustrated in several three dimensional example problems.

  14. Calcareous nannofossil and ammonite integrated biostratigraphy across the Jurassic - Cretaceous boundary strata of the Kopanitsa composite section (West Srednogorie Unit, southwest Bulgaria)

    NASA Astrophysics Data System (ADS)

    Stoykova, Kristalina; Idakieva, Vyara; Ivanov, Marin; Reháková, Daniela

    2018-04-01

    Calcareous nannofossil, calpionellid and ammonite occurrences have been directly constrained across the Jurassic-Cretaceous boundary interval in the section of Kopanitsa, SW Bulgaria. This section reveals a continuous and expanded sedimentary record through the Upper Tithonian and Lower Berriasian, besides an excellent calcareous nannofossil and ammonite record. The topmost part of the NJT 16b and the base of NJT 17a nannofossil Subzones correspond to the ammonite Microcanthum / Transitorius Subzone. The major part of the NJT 17a Subzone equates to the Durangites spp. ammonite Zone, whereas the NJT 17b Subzone correlates to the lower part of the B. jacobi ammonite Zone. The NKT nannofossil Zone approximately corresponds to the upper part of the B. jacobi Zone and the NK-1 nannofossil Zone correlates at least to the lowest part of the T. occitanica Zone. The FOs of Nannoconus globulus minor, N. wintereri, N. kamptneri minor, N. steinmannii minor, N. kamptneri kamptneri and N. steinmannii steinmannii are confirmed as reliable bio-horizons for correlations in the Mediterranean Tethys area. The first occurrence of Nannoconus wintereri is regarded as an almost concomitant event with the first occurrence of Berriasella jacobi. We suggest it could be the most useful nannofossil proxy for approximating the base of the B. jacobi Zone. Rare, but relatively well preserved calpionellids and calcareous dinoflagellates together with microfacies analysis were used additionally for stratigraphical and palaeoenvironmental interpretations. The investigated sediments are typical for the steep slope of a steepened ramp, with accumulation of hemipelagic and gravitational deposits.

  15. Hawking radiation of spin-1 particles from a three-dimensional rotating hairy black hole

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sakalli, I.; Ovgun, A., E-mail: ali.ovgun@emu.edu.tr

    We study the Hawking radiation of spin-1 particles (so-called vector particles) from a three-dimensional rotating black hole with scalar hair using a Hamilton–Jacobi ansatz. Using the Proca equation in the WKB approximation, we obtain the tunneling spectrum of vector particles. We recover the standard Hawking temperature corresponding to the emission of these particles from a rotating black hole with scalar hair.

  16. Automated symbolic calculations in nonequilibrium thermodynamics

    NASA Astrophysics Data System (ADS)

    Kröger, Martin; Hütter, Markus

    2010-12-01

    We cast the Jacobi identity for continuous fields into a local form which eliminates the need to perform any partial integration to the expense of performing variational derivatives. This allows us to test the Jacobi identity definitely and efficiently and to provide equations between different components defining a potential Poisson bracket. We provide a simple Mathematica TM notebook which allows to perform this task conveniently, and which offers some additional functionalities of use within the framework of nonequilibrium thermodynamics: reversible equations of change for fields, and the conservation of entropy during the reversible dynamics. Program summaryProgram title: Poissonbracket.nb Catalogue identifier: AEGW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 227 952 No. of bytes in distributed program, including test data, etc.: 268 918 Distribution format: tar.gz Programming language: Mathematica TM 7.0 Computer: Any computer running Mathematica TM 6.0 and later versions Operating system: Linux, MacOS, Windows RAM: 100 Mb Classification: 4.2, 5, 23 Nature of problem: Testing the Jacobi identity can be a very complex task depending on the structure of the Poisson bracket. The Mathematica TM notebook provided here solves this problem using a novel symbolic approach based on inherent properties of the variational derivative, highly suitable for the present tasks. As a by product, calculations performed with the Poisson bracket assume a compact form. Solution method: The problem is first cast into a form which eliminates the need to perform partial integration for arbitrary functionals at the expense of performing variational derivatives. The corresponding equations are conveniently obtained using

  17. Generalization of Jacobi's Decomposition Theorem to the Rotation and Translation of a Solid in a Fluid.

    NASA Astrophysics Data System (ADS)

    Chiang, Rong-Chang

    Jacobi found that the rotation of a symmetrical heavy top about a fixed point is composed of the two torque -free rotations of two triaxial bodies about their centers of mass. His discovery rests on the fact that the orthogonal matrix which represents the rotation of a symmetrical heavy top is decomposed into a product of two orthogonal matrices, each of which represents the torque-free rotations of two triaxial bodies. This theorem is generalized to the Kirchhoff's case of the rotation and translation of a symmetrical solid in a fluid. This theorem requires the explicit computation, by means of theta functions, of the nine direction cosines between the rotating body axes and the fixed space axes. The addition theorem of theta functions makes it possible to decompose the rotational matrix into a product of similar matrices. This basic idea of utilizing the addition theorem is simple but the carry-through of the computation is quite involved and the full proof turns out to be a lengthy process of computing rather long and complex expressions. For the translational motion we give a new treatment. The position of the center of mass as a function of the time is found by a direct evaluation of the elliptic integral by means of a new theta interpretation of Legendre's reduction formula of the elliptic integral. For the complete solution of the problem we have added further the study of the physical aspects of the motion. Based on a complete examination of the all possible manifolds of the steady helical cases it is possible to obtain a full qualitative description of the motion. Many numerical examples and graphs are given to illustrate the rotation and translation of the solid in a fluid.

  18. Basic lubrication equations

    NASA Technical Reports Server (NTRS)

    Hamrock, B. J.; Dowson, D.

    1981-01-01

    Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.

  19. The Relationship between Symptom Relief and Psychosocial Functional Improvement during Acute Electroconvulsive Therapy for Patients with Major Depressive Disorder.

    PubMed

    Lin, Ching-Hua; Yang, Wei-Cheng

    2017-07-01

    We aimed to compare the degree of symptom relief to psychosocial functional (abbreviated as "functional") improvement and explore the relationships between symptom relief and functional improvement during acute electroconvulsive therapy for patients with major depressive disorder. Major depressive disorder inpatients (n=130) requiring electroconvulsive therapy were recruited. Electroconvulsive therapy was generally performed for a maximum of 12 treatments. Symptom severity, using the 17-item Hamilton Depression Rating Scale, and psychosocial functioning (abbreviated as "functioning"), using the Modified Work and Social Adjustment Scale, were assessed before electroconvulsive therapy, after every 3 electroconvulsive therapy treatments, and after the final electroconvulsive therapy. Both 17-item Hamilton Depression Rating Scale and Modified Work and Social Adjustment Scale scores were converted to T-score units to compare the degrees of changes between depressive symptoms and functioning after electroconvulsive therapy. Structural equation modeling was used to test the relationships between 17-item Hamilton Depression Rating Scale and Modified Work and Social Adjustment Scale during acute electroconvulsive therapy. One hundred sixteen patients who completed at least the first 3 electroconvulsive therapy treatments entered the analysis. Reduction of 17-item Hamilton Depression Rating Scale T-scores was significantly greater than that of Modified Work and Social Adjustment Scale T-scores at assessments 2, 3, 4, and 5. The model analyzed by structural equation modeling satisfied all indices of goodness-of-fit (chi-square = 32.882, P =.107, TLI = 0.92, CFI = 0.984, RMSEA = 0.057). The 17-item Hamilton Depression Rating Scale change did not predict subsequent Modified Work and Social Adjustment Scale change. Functioning improved less than depressive symptoms during acute electroconvulsive therapy. Symptom reduction did not predict subsequent functional improvement

  20. Finite-band solutions of the coupled dispersionless hierarchy

    NASA Astrophysics Data System (ADS)

    Li, Zhu

    2016-08-01

    The coupled dispersionless hierarchy is derived with the help of the zero curvature equation. Based on the Lax matrix, we introduce an algebraic curve {{ K }}n of arithmetic genus n, from which we establish the corresponding meromorphic function ϕ, the Baker-Akhiezer function {\\varphi }1, and Dubrovin-type equations. The straightening out of all the flows is given under the Abel-Jacobi coordinates. Using the asymptotic properties of ϕ and {\\varphi }1, we obtain the explicit theta function representations of the meromorphic function ϕ, the Baker-Akhiezer function {\\varphi }1 and of solutions for the whole hierarchy.